ChemWiki - User contributions [en]

Rep:Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158

2013-11-22T16:52:21Z

Pk1811:

<div style="font-size: 40px"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px"><center>Introductory week 1 work</center></div>
 
<div style="font-size: 30px"><center>[[Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185|To mini project]]</center></div>
 
= Part 1: Basic optimisations and the effect of metals and ligands on bond lengths =
A variety of basic calculations and experimentation have been conducted on BH3 and a number of similar molecules, namely BBr3 and GaBr3. As part of this, energies have been calculated at a variety of optimisation levels. The overall aim is to explore the various facilities available as part of the Gaussian and GaussView suite, in addition to investigating the effect that ligands and metals have on the bond lengths of ML3 structures.

To begin, the molecules of choice need to be optimised to energy minima so that the bond lengths resemble the molecule's reality.

== Optimisation of BH3 ==
BH3 was plotted in GaussView and the structure altered to have bonds 1.54, 1.55, and 1.56Å, so breaking the symmetry of the molecule. An optimisation was then conducted as follows:
* '''Method''': B3LYP
* '''Basis set''': 3-21G
* '''Calculation type''': FOPT

The optimisation completed in 55.0 seconds. Analysis of the log file yielded the following information:
<pre>
File Name PK_BH3_OPT
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 3-21G
Charge 0
Spin Singlet
E(RB3LYP) -26.46226429 a.u.
RMS Gradient Norm 0.00008851 a.u.
Imaginary Freq
Dipole Moment 0.0003 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 55.0 seconds.
</pre>

[[Media:PK_BH3_OPT.LOG|Download log file]]

The molecule was confirmed to converge.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1944 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1947 -DE/DX = -0.0002 !
! R3 R(1,4) 1.1948 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9983 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.986 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0157 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

Strangely, despite apparent convergence, the derivative for the displacements had not reached zero. It was decided not to attempt to rectify this as an additional optimisation would be run shortly after, and any concern from lack of convergence can be had at that point.

The non-D3h point group was somewhat surprising considering the apparent symmetry in the molecule. To verify, all the bond lengths and angles were inspected and reported as follows:
* '''B-H bond lengths (Å)''': 1.9445 (H2 B1), 1.9467 (H3 B1), 1.9480 (H4 B1)
* '''H-B-H bond angles (°)''': 119.986 (H2 B1 H4), 120.016 (H4 B1 H3), 119.998 (H2 B1 H3)

There is quite a significant amount of variance between the bond lengths and angles, explaining the lack of D3h group expected. The molecule is symmetric up to 3dp in the bond lengths and 1° in the angles. A superior optimisation is so required.

A second optimisation was run on the optimised structure. The parameters used are as follows;
* '''Method''': B3LYP
* '''Basis set''': 6-31G(d,p)
* '''Calculation type''': FOPT

The charge was set to 0 and the multiplicity as singlet - this was no change to what was originally specified, but was double checked at this point.

[[Media:PK_BH3_OPT_631GDP.LOG|Download log file]]

Once again, convergence was confirmed.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.068331D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0007 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9938 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0055 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

This time, all gradients have reached zero, hence despite the concern had earlier about the non-zero gradients, there is no issue with convergence when investigating the final conformation of the molecule.

The data obtained from the log file is as follows:
<pre>
File Name PK_BH3_OPT_631GDP
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532361 a.u.
RMS Gradient Norm 0.00000706 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 16.0 seconds.
</pre>

Disappointingly the point group was still found to be CS. Again, all the bond lengths and angles were reported and are as follows:
* '''B-H bond lengths (Å)''': 1.19232 (H2 B1), 1.19231 (H3 B1), 1.19231 (H4 B1)
* '''H-B-H bond angles (°)''': 119.994 (H2 B1 H4), 120.005 (H4 B1 H3), 120.001 (H2 B1 H4)

This time, the bond angles and lengths are much more in agreement, but not yet identical as was expected. Bond lengths are in agreement up to 5dp, but bond angles again 1°. It is unusual to see a dipole moment in a molecule as symmetric as this, however the minor imbalance in the molecule reported above likely leads to a minor dipole moment. CRC notes the experimental bond length as 1.1900Å<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref> which is quite close to what has been computed - the basis set provides an excellent approximation for this molecule. The difference between the computed and experimental bond lengths in the first optimisation is much larger (0.8Å), so vindicating the decision to perform a second optimisation.

== Optimisation of GaBr3 ==
GaBr3 was plotted in GaussView and the symmetry fixed to D3h within 0.00001 tolerance. Optimisation was conducted on the HPC to the LanL2DZ basis set (providing Los Alamos ECP pseudo-potentials on all atoms in the system).
* '''Method''': B3LYP
* '''Basis set''': LanL2DZ
* '''Calculation type''': FOPT
Details from the log file are reported below:

<pre>
File Name PK_GABR3_OPT_LANL2DZ
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set LANL2DZ
Charge 0
Spin Singlet
E(RB3LYP) -41.70082783 a.u.
RMS Gradient Norm 0.00000016 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group D3H
Job cpu time: 0 days 0 hours 0 minutes 13.9 seconds.
</pre>

This calculation can be viewed on Dspace: {{DOI|10042/26081}}.

Convergence was again verified:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282684D-12
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3502 -DE/DX = 0.0 !
! R2 R(1,3) 2.3502 -DE/DX = 0.0 !
! R3 R(1,4) 2.3502 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>
All gradients have reached zero, so the molecule has fully converged.

Bond lengths were 2.35018Å for all bonds, and all angles were exactly 120°. Analysis of the CRC Handbook states<ref name="crc"></ref> an experimental bond length of 2.249Å, 0.1Å is not an insignificant difference, but is reasonable considering the rather basic basis set used.

== Optimisation of BBr3 ==
As a further investigation into pseudo-potentials, a molecule of BBr3 was optimised, with full control on the basis sets used on each atom. Boron was subject to 6-31G(d,p), and the bromine atoms LanL2DZ. Calculation was run on the HPC with an overall DFT B3LYP function. The results can be seen online: {{DOI|10042/26079}} Summary data is as follows, according to the log file:

<pre>
File Name PK_BBR3_OPT_GEN
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set Gen
Charge 0
Spin Singlet
E(RB3LYP) -64.43644897 a.u.
RMS Gradient Norm 0.00001048 a.u.
Imaginary Freq
Dipole Moment 0.0003 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 20.0 seconds.
</pre>

Convergence was once again checked and found to indeed converge, with all parameters reaching a stationary point:
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000115 0.001800 YES
RMS Displacement 0.000063 0.001200 YES
Predicted change in Energy=-2.469464D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9339 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0004 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9975 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0021 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

Once again, there is a lack of symmetry in the optimised molecule, this time the molecule was not configured to have a forced D3h symmetry. This can be seen from the parameters below:
* '''Bond lengths (Å)''': 1.93393 (B1 Br2), 1.93397 (B1 Br3), 1.93401 (B1 Br4)
* '''Bond angles (°)''': 119.997 (Br4 B1 Br2), 120.000 (Br2 B1 Br3), 120.002 (Br3 B1 Br4)

The rather large dipole (compared to the 0 it should be) is likely a result of the slightly elongated B1-Br4 bond, making a net dipole in the molecule. As Br is more electronegative than H, this effect is more pronounced here than it is in BH3. The CRC handbook notes<ref name="crc"></ref> the bond length being 1.893Å, which does not exhibit a huge range from what is calculated here, showing this was a good choice of basis set. Further investigation could be made into alternative basis sets to see if a closer value is obtained.

== Summary ==
In conclusion, all the molecules mentioned previously have been optimised, and the bond lengths have been reported below and compared.

{| class="wikitable" border="1"
|+ Comparison of bond lengths for molecules in this part of the report
! Molecule !! colspan=3 | Bond lengths (M-L) Å
|-
! BH3
| 1.19232 || 1.19231 || 1.19231
|-
! GaBr3
| 2.35018 || 2.35018 || 2.35018
|-
! BBr3
| 1.93393 || 1.93397 || 1.93401
|}

An initial observation is the lack of equality in bond lengths for the two boron molecules. This is not an effect of the boron, but rather the nature of the calculation used. The gallium molecule was configured to force the stereochemistry as D3h, and hence Gaussian ensured that bond lengths are identical to create this symmetry. Thus no conclusions can be drawn from this difference.

It is possible to draw some conclusions from the difference in magnitude between the three molecules. The gallium molecule has a significantly larger bond length than either of the boron molecules - it is thought that this is due to the larger atomic radius of gallium compared to boron (one is in group 4, the other is in group 2), which, by necessity of ensuring the nuclei do not clash with each other, leads to a increased bond length. This leads to the approximate 0.4Å increase in bond length seen. The increase in bond length is not huge, as the increase in nuclear radius is quite small - hence it still remains quite close to the BBr3. If the same calculation was run on TlBr3, which is further down the group, a much larger bond length would be expected compared to BBr3.

Comparing BH3 and BBr3, we can see how a change in ligand affects the bond length. In this case, the main differences between the two ligands are in terms of the size of the nuclei and their electronegativities. While the increase in atomic radius would increase the bond length (as per the change in metal centre), the rather charge in electronegativity causes quite a large change in the bond length. This is because the electronegative atom will polarise the bond as it draws a larger share of the electron density. As a result, electron density is pulled away from the bond to the bromine atom, and when the electron density in a bond is reduced, the bond is weakened and therefore lengthened. This leads to the very large (0.7Å) increase in bond length observed.

This information also makes it possible to examine the nature of a bond. Two questions related to the work done here have been posed and answered below.

=== In some structures, GaussView does not draw bonds where we expect. Does this mean there is no bond? Why? ===
It is reported that GaussView only draws a bond depending on whether the two atoms are close enough for the bond to exist (in addition to the inevitable criteria over whether a bond can exist in a given location - for example if a transition metal has filled its coordination sphere). Hence, even if there is no bond shown, it does not necessarily mean no bond exists.

The existence of a bond depends on a number of criteria, one of which is the length, but other factors must be considered such as whether there is sufficient orbital overlap or whether the antibonding interactions at a given distance outweigh any bonding interactions. Hence, the simple distance criteria that GaussView uses is not sufficient to be absolutely sure if a bond is there or not. To fully ensure if a bond exists, it would be necessary to perform a number of additional calculations, such as investigation of the electron density contour maps and analysis of the molecular orbitals. Only these plots can show whether a bond exists or not, and hence GaussView's approximation is not sufficient proof that a bond does not exist.

=== What is a bond? ===
The IUPAC Gold Book defines a chemical bond as<ref name="goldbook-bond">A. D. McNaught and A. Wilkinson, in ''Compendium of Chemical Terminology'', Blackwell Scientific Publications, Oxford, 2nd ed., 2012, p. CT07009</ref>:
<blockquote>When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups.</blockquote>

Models have been built on top of this to describe specific kinds of bonding, the most common of which are:
* Covalent bond, in terms of a bond where each atom in the bond donates one electron, to form a two-electron bond.
* Ionic bond, a bond where negatively charged anions are electrostatically attracted to positively charged cations, leading to a stabilised arrangement compared to the ions being separate.
* Metallic bond, where positive cations of a metal are in a sea of delocalised electrons.

In the latter two cases, electrostatics are involved, and it is this combination of positive and negative charges combined which lead to a very stable and attractive combination, which massively lowers the energy of the system.

For a covalent bond, modern thinking (which also applies to a variety of inorganic compounds too) makes use of molecular orbitals, a combination of bonding and antibonding orbitals being created when atomic orbitals combine. Generally, according to the Klopman-Salem equation<ref name="klopman">G. Klopman, ''J. Am. Chem. Soc.'', 1968, '''90''', 223–234</ref><ref name="salem">L. Salem, ''J. Am. Chem. Soc.'' 1968, '''90''', 543 & 553</ref>, the bonding orbitals created are of a lower energy than the atomic orbitals they were created from. As a result of this, as these bonding orbitals are filled, the molecule is stabilised, and hence the IUPAC definition of a bond is adhered to.

There are many different ways in which this stabilisation can be created, and the methods discussed here are only a few of them (there may still be other kind of stabilising interactions as yet undiscovered). Hence, it is reasonable to argue that any interaction which causes a stabilising effect in a molecule can be deemed a chemical bond, which the terms 'single' and 'double bond' being associated with interactions of a certain magnitude.

= Part 2: Frequencies, vibrations, orbitals and energies =
On the optimised structures reported previously, a number of advanced calculations have been performed. Initially, frequency analysis has been conducted to ensure that the energies calculated are minima. Once this has been confirmed, more advanced calculations have been performed to help find out more about the nature of these compounds.

== Frequency and vibrational analysis of BH3 ==
Through use of a 6-31G(d,p) frequency analysis of the optimised BH3 structure, it is possible to identify whether a minima has been attained. Initially, the results have been compared to what was obtained from the optimisation, and the frequency results summary from the [[media:Pk-bh3-freq.log|log file]] is found below:

<pre>
File Name PK_BH3_FREQ_631GDP
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532361 a.u.
RMS Gradient Norm 0.00000702 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 18.0 seconds.
</pre>

Other than a minor change in the gradient, the results are the same as was reported previously. Convergence was again confirmed:
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000089 0.001800 YES
RMS Displacement 0.000045 0.001200 YES
Predicted change in Energy=-1.487544D-09
Optimization completed.
-- Stationary point found.
</pre>

Low frequencies were reported as
<pre>
Low frequencies --- -25.0305 -12.9079 0.0006 0.0007 0.0009 15.0420
</pre>

which are outside the range of -15 to +15 cm-1. Hence, the molecule was reoptimised with <code>scf=conver=9 int=ultrafine</code> keywords and a tight convergence to yield the following data in the [[media:Pk_bh3_opt_tight.log|log file]]:

<pre>
File Name PK_BH3_OPT_TIGHT_631GDP
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532360 a.u.
RMS Gradient Norm 0.00000594 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 13.0 seconds.
</pre>

Convergence was obtained on the optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000015 YES
RMS Force 0.000007 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000034 0.000040 YES
Predicted change in Energy=-7.783630D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0008 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9938 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0054 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The frequency calculation was then subsequently run, using the same keywords (but no tight setting). The [[media:Pk-bh3-freq-tight.log|log file]] reported the following data:

<pre>
File Name PK_BH3_FREQ_TIGHT_631GDP
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532360 a.u.
RMS Gradient Norm 0.00000594 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

This time there was convergence:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000086 0.001800 YES
RMS Displacement 0.000043 0.001200 YES
Predicted change in Energy=-1.187652D-09
Optimization completed.
-- Stationary point found.
</pre>

Regrettably the low frequencies were still out of range:

<pre>
Low frequencies --- -19.8568 -17.0127 -9.6394 0.0004 0.0005 0.0007
Low frequencies --- 1162.9117 1213.0852 1213.1686
</pre>

At this point the optimisation was conducted again with the same keywords and forcing a D3h symmetry. The [[media:Pk-bh3-opt-forced.log|log file]] showed:

<pre>
File Name PK_BH3_OPT_FORCED_631GDP
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532364 a.u.
RMS Gradient Norm 0.00000571 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group D3H
Job cpu time: 0 days 0 hours 0 minutes 13.0 seconds.
</pre>

with convergence:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000015 YES
RMS Force 0.000007 0.000010 YES
Maximum Displacement 0.000045 0.000060 YES
RMS Displacement 0.000030 0.000040 YES
Predicted change in Energy=-7.760436D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The frequency calculation was then run again, with the [[media:Pk-bh3-freq-forced.log|log file]] yielding:

<pre>
File Name PK_BH3_FREQ_FORCED_631GDP
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532364
RMS Gradient Norm 0.00000572
Imaginary Freq 0
Dipole Moment 0.0000
Point Group D3H
Job cpu time: 0 days 0 hours 0 minutes 18.0 seconds.
</pre>

with convergence:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000022 0.001200 YES
Predicted change in Energy=-7.723726D-10
Optimization completed.
-- Stationary point found.
</pre>

This time, the low frequencies were found to be within the allowed range.

<pre>
Low frequencies --- -14.8515 -14.8476 -11.2630 0.0012 0.0162 0.3377
Low frequencies --- 1162.9477 1213.1209 1213.1211
</pre>

Vibrations seen were of the symmetry labels A2", E', E', A1', E', E' which matches what the character tables for D3h suggests.

=== Visual representation of vibrational peaks ===
The vibrational peaks can be seen in GaussView and are shown below:

[[Image:Pk-bh3-Ir.svg]]

{| class="wikitable" border="1"
|+ Vibrations for BH3
! Mode !! Frequency (cm-1) || Intensity || Image || Symmetry (D3h point group)
|-
| 1 || 1162.95 || 92.5709
|[[Image:Pk-bh3-1.gif|200px]]
Symmetric wag of all protons.
| A"2 (according to log)
|-
| 2 || 1213.12 || 14.0537
|[[Image:Pk-bh3-2.gif|200px]]
Rock of H-B-H group with associated scissoring of third H.
| E' (according to log)
|-
| 3 || 1213.12 || 14.0532
|[[Image:Pk-bh3-3.gif|200px]]
H-B-H scissoring.
| E' (according to log)
|-
| 4 || 2582.68 || 0.0000
|[[Image:Pk-bh3-4.gif|200px]]
Symmetric stretch of all B-H bonds out in the same direction as the bond.
| A'1 (totally symmetric)
|-
| 5 || 2715.82 || 126.3288
|[[Image:Pk-bh3-5.gif|200px]]
Antisymmetric stretch of H-B-H group
| E' (according to log)
|-
| 6 || 2715.82 || 126.3227
|[[Image:Pk-bh3-6.gif|200px]]
Antisymmetric stretch of all protons.
| E' (according to log)
|}

Of note, there are only three peaks in the IR spectrum, despite there being 6 modes. One of these modes has an intensity of 0, and so it will not show up in the IR spectrum. This intensity is zero as the vibration is totally symmetric, which means there is no change in dipole moment and hence is not IR active. This still leaves 2 peaks missing. The peaks with an E' symmetry are defined as such as they are degenerate, and there are 2 pairs of 2 peaks with the same wavenumber. Hence, both peaks will appear superimposed upon eachother (due to their degeneracy), and the intensities will be added together. The result is that only one peak shows for the two modes for the same wavenumber. All missing peaks are therefore accounted for.

== Vibrational analysis for GaBr3 ==
Frequency analysis from the optimised structure of GaBr3 was conducted on the HPC and the results are available on Dspace: {{DOI|10042/26119}}.

The summary of the results is as follows.

<pre>
File Name PK_GABR3_FREQ_LANL2DZ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set LANL2DZ
Charge 0
Spin Singlet
E(RB3LYP) -41.70082783 a.u.
RMS Gradient Norm 0.00000011 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group D3H
Job cpu time: 0 days 0 hours 0 minutes 12.3 seconds.
</pre>

Convergence was confirmed
<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-6.142862D-13
Optimization completed.
-- Stationary point found.
</pre>

and all vibrations were found to be in the -15 to 15 cm-1 range:
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>

The lowest normal mode is 76.3744cm-1 which corresponds to a combined rocking and scissoring vibration, and is shown in animated form below. This almost has the same energy as the next lowest frequency and is assumed to be degenerate within the boundaries of approximation in the calculation.

[[Image:Pk-ir-gabr3.svg]]

{| class="wikitable"
|+ Vibrations for GaBr3
|-
! Mode
! Frequency (cm-1)
! Intensity
! Image
! Symmetry (D3h point group)
|-
| 1
| 76.37
| 76.38
| [[Image:Pk-gabr3-mode-1.gif|200px]]

Rocking of two bromine atoms, leading to a scissoring effect of third.
| E' (according to log)
|-
| 2
| 76.38
| 3.3447
| [[Image:Pk-gabr3-mode-2.gif|200px]]

Scissoring of two bromine atoms (Br-Ga-Br).
| E' (according to log)
|-
| 3
| 99.70
| 9.2161
| [[Image:Pk-gabr3-mode-3.gif|200px]]

Wag of all bromine atoms.
| A"2 (according to log)
|-
| 4
| 197.34
| 0.0000
| [[Image:Pk-gabr3-mode-4.gif|200px]]

Symmetric stretch of all Ga-Br bonds out in the same direction as the bond.
| A'1 (totally symmetric)
|-
| 5
| 316.18
| 57.0704
| [[Image:Pk-gabr3-mode-5.gif|200px]]

Antisymmetric stretch of Br-Ga-Br group
| E' (according to log)
|-
| 6
| 316.19
| 57.0746
| [[Image:Pk-gabr3-mode-6.gif|200px]]

Antisymmetric stretch of all bromine atoms.
| E' (according to log)
|}

Once again there are fewer peaks than modes - this is for the same reason as observed with BH3. The intensity of 0 for the 4th mode is also due to the same reason why the mode with no intensity for BH3 has no intensity.

=== Comparison to BH3 ===

{| class="wikitable"
|+ Comparisons between BH3 and GaBr3 (modes have been matched by symmetry label and similarity in appearance)
|-
! Mode
! GaBr3 Frequency (cm-1)
! GaBr3 Intensity
! GaBr3 Image
! BH3 Image
! BH3 Frequency (cm-1)
! BH3 Intensity
|-
| 1
| 76.37
| 76.38
| [[Image:Pk-gabr3-mode-1.gif|200px]]
| [[Image:Pk-bh3-2.gif|200px]]
| 1213.12
| 14.0537
|-
| 2
| 76.38
| 3.3447
| [[Image:Pk-gabr3-mode-2.gif|200px]]
| [[Image:Pk-bh3-3.gif|200px]]
| 1213.12
| 14.0532
|-
| 3
| 99.70
| 9.2161
| [[Image:Pk-gabr3-mode-3.gif|200px]]
| [[Image:Pk-bh3-1.gif|200px]]
| 1162.95
| 92.5709
|-
| 4
| 197.34
| 0.0000
| [[Image:Pk-gabr3-mode-4.gif|200px]]
| [[Image:Pk-bh3-4.gif|200px]]
| 2582.68
| 0.0000
|-
| 5
| 316.18
| 57.0704
| [[Image:Pk-gabr3-mode-5.gif|200px]]
| [[Image:Pk-bh3-5.gif|200px]]
| 2715.82
| 126.3288
|-
| 6
| 316.19
| 57.0746
| [[Image:Pk-gabr3-mode-6.gif|200px]]
| [[Image:Pk-bh3-6.gif|200px]]
| 2715.82
| 126.3227
|}

Whilst all the modes which appear in BH3 also appear in GaBr3 there are a number of significant differences:
# The modes are reordered
# The energies are much reduced for GaBr3

Initially, the intensity and wavenumber of the vibrations for GaBr3 is much smaller than BH3 - this is due to the inverse correlation between nuclei mass and the IR frequency - this is because atoms with a lower mass are easier to move around, and hence need a less energetic photon to be excited. This is likely related to the variance in intensity too. This is reflected in the IR spectra, which show a similar distribution in peaks, but the intensities for the BH3 spectra is much bigger.

Secondly, the reordering of modes is due to the same reason - the more atoms which are moved in a mode, the greater the amount of energy is needed to cause a vibration. Thus the A"2 mode has changed position as a significant increase in the amount of energy needed for this mode to oscillate is needed, more than the energy needed to make the two E' modes below it in terms of energy oscillate (as the Ga atoms in these modes do not move as much).

Otherwise the spectra are quite similar, there is an identical number of peaks with a similar distribution, and all the types of vibration seen in BH3 are also seen in GaBr3 - including identical symmetry labels. Also in both cases, there is a large gap between the A"2 and E' modes, and the other two modes. The higher energy modes in both cases are stretching modes and it may be because in doing so the electron density over the molecule is disrupted (and can potentially lead to bond breakage at long displacements as there is no electron density over the bond), which requires significantly more energy than moving the atom but keeping its displacement fixed.

=== Discussion ===

==== Why must you use the same method and basis set for both the optimisation and frequency analysis calculations? ====
The method and basis set give the conditions for the calculation used in either the optimisation or frequency analysis, more specifically the approximations used in solving the Schrodinger equation. The effect of this is that the energy you obtain during the optimisation of a molecule is specific to that method and basis set, as the energy depends on the approximations used. GaussView represents this by showing the energy in terms of the basis set and method.

Thus, when you calculate the frequency analysis, you must use the same method and basis set, as we must analyse the molecule and its energy in the same conditions that it exists in - an analogy would be to optimise in chloroform solvent and then do a frequency analysis in water - the system is different. As the approximations would be different if the models and basis sets differ, the frequency analysis would give bogus results - it would be doing a frequency analysis for a specific case on a molecule not of that case. This is especially important as at the level you optimised the molecule to, the energy the molecule reaches will be a minima, but when you then perform the frequency analysis, if you use a different method and basis set, the energy may no longer correspond to a minima, and thus the frequency analysis is meaningless.

==== What is the purpose of carrying out a frequency analysis? ====
A frequency analysis is important as it shows whether you have reached an energy minima or maxima. When the gradient is zero, it can either be at the peak or trough of a curve, as at these points the gradient is flat and <math>\frac{dy}{dx} = 0</math>. We need to know whether we are at a maximum or minimum as, in the nature of an optimisation, we are looking to find the most accurate representation of a molecule's actual state of existance, and molecules always try to minimise their energy.

In contrast, if we are at a maxima, we are at a transition state (as these are always of the highest energy). Whilst there may be times we are interested in a transition state, we are not here, and thus we must verify we are at a minimum. The frequency analysis finds the second derivative of the gradient, which is positive if we are at a minimum, or negative if we are at a maximum. Thus, by performing a frequency analysis, we can see if any of the vibrations are negative, and if none are we can be sure we are at an energy minimum. It is important to ensure we are at a minimum before we discuss results or perform further calculations.

==== What do the "Low frequencies" represent? ====
The low frequencies refer to the degrees of vibrational freedom within a molecule. For a molecule with 3 (or more) atoms, this is <math>3N-6</math>, which explains why the 4 atom molecules considered previously have 6 low frequencies. Each low frequency refers to one of the vibrational modes for the molecule, which is not necessary IR (or Raman) active, but the molecule would still exhibit this kind of vibration and hence vibrates at that frequency. This is separate to rotational and translational modes of freedom.

== Molecular orbital analysis for BH3 ==
Using the optimised and confirmed minima structure obtained earlier, the molecular orbitals for BH3 have been calculated, which also allows for calculation of NBOs.

An energy calculation was run on the HPC using the <code>pop=full,nbo</code> keyword and the results are available on Dspace: {{DOI|10042/26167}}.

The summary is as follows:

<pre>
File Name PK_BH3_EGY_631GDP
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532361 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 7.4 seconds.
</pre>

All data appears to be identical to the original energy calculation.

MOs 1-8 were calculated in GaussView and plotted on the MO diagram of BH3 shown below:

[[Image:Pk-bh3-mo.png|700px]]

== Molecular orbital and NBO analysis for ammonia ==
Ammonia was optimised and then a frequency calculation run as per the previous method, the choice of keywords and symmetry forcing (but to C3v) was needed in order to get the low frequencies within the acceptable range.

For the optimisation, the final data according to the [[media:Pk-nh3-opt.log|log file]] is:

<pre>
File Name PK_NH3_OPT_631GDP
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -56.55776873 a.u.
RMS Gradient Norm 0.00000323 a.u.
Imaginary Freq
Dipole Moment 1.8465 Debye
Point Group C3V
Job cpu time: 0 days 0 hours 0 minutes 27.0 seconds.
</pre>

and convergence confirmed:
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000015 YES
RMS Force 0.000004 0.000010 YES
Maximum Displacement 0.000012 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-9.846374D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

Low frequencies from the frequency calculation (which differs in energy terms by 0.00000001) [[media:Pk-nh3-freq.log|log file]] are:

<pre>
Low frequencies --- -0.0138 -0.0030 0.0013 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

which show a minima has been obtained. There were no negative frequencies.

'''Summary table:'''

<pre>
File Name PK_NH3_FREQ_631GDP
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -56.55776872 a.u.
RMS Gradient Norm 0.00000322 a.u.
Imaginary Freq 0
Dipole Moment 1.8465 Debye
Point Group C3
Job cpu time: 0 days 0 hours 0 minutes 15.0 seconds.
</pre>

with convergence:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131338D-10
Optimization completed.
-- Stationary point found.
</pre>

Of concern, the symmetry has become C3, however there has been little change in energy, hence little change in structure, so this is assumed to be a bug in GaussView.

Now being satisfied that a minima has been reached, a MO and NBO calculation was conducted as was done on the BH3 ([[media:Pk-nh3-egy.log|log file]]). The NBO was then plotted from -1.125 to 1.125 and is shown below.

[[Image:Pk-nh3-nbo.PNG]]

'''Energy calculation summary table:'''
<pre>
Ammonia egy
File Name PK_NH3_EGY_631GDP
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -56.55776873 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 1.8465 Debye
Point Group C3V
Job cpu time: 0 days 0 hours 0 minutes 10.0 seconds.
</pre>

As expected, the electronegative nitrogen has a great degree of negative charge - as shown by the red character. The exact charges are -1.125 on the nitrogen and 0.375 on all the protons. The power of NBO for observing the charge density of a molecule is thus seen.

== Energy calculations for NH3BH3 ==
Now optimised energies for NH3 and BH3 have been found, it is now possible to calculate the energy for NH3BH3, find the difference between all three components, and therefore find the energy of association. From this point on it is assumed that the keywords used previously during optimisation are always used. Initially an optimisation was conducted at the same level as before and the [[media:Pk-nh3bh3-opt.log|log file]] reported:

<pre>
File Name PK_NH3BH3_OPT
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -83.22468909 a.u.
RMS Gradient Norm 0.00000047 a.u.
Imaginary Freq
Dipole Moment 5.5646 Debye
Point Group C3V
Job cpu time: 0 days 0 hours 1 minutes 14.0 seconds.
</pre>

and convergence checked:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000007 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.706880D-11
Optimization completed.
-- Stationary point found.
</pre>

A frequency analysis was then conducted. The [[media:Pk-nh3bh3-freq.log|log file]] reported a final energy of -83.22468909, which is identical to what was found in the optimisation, and no frequencies were negative. Low frequencies were in the acceptable range:

<pre>
Low frequencies --- -4.8361 -1.6211 -1.2960 0.0335 0.0539 0.2001
Low frequencies --- 263.3086 632.9964 638.4686
</pre>

Other summary data is as follows:

<pre>
File Name PK_NH3BH3_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -83.22468909 a.u.
RMS Gradient Norm 0.00000052 a.u.
Imaginary Freq 0
Dipole Moment 5.5646 Debye
Point Group C3V
Job cpu time: 0 days 0 hours 0 minutes 48.0 seconds.
</pre>

and convergence:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.893142D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Calculation of association energy ===
Now that all three components are optimised to the correct level, and are all found as minima, it is possible to find the association energy.

The energies of all 3 components are (in AU):

* E(BH3)=-26.61532361
* E(NH3)=-56.55776873 -83.1730923
* E(NH3BH3)= -83.22468909
* Association energy: -0.0515967

One atomic unit is equal to one Hartree, and the conversion is equal to 1 Hartree = 2625.49962 kJ mol-1<ref name="codata">CODATA 2010</ref>, which gives a final association or dissociation energy of -135.47 kJ mol-1. This is approximately 40 kJ mol-1 below the enthalpy of formation as reported previously<ref name="assoc"> Yu. Kh. Shaulov, G. O. Shmyreva, V. S. Tubyanskaya, ''Zhurnal Fizicheskoi Khimii'', 1966, '''40''', 122</ref>. Considering there are a number of factors not considered in this calculation (for example interactions between the components during the formation or dissocation), the calculation gives a reasonable approximation to the nature of the association process.

= References =
<references />

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T16:50:58Z

Pk1811:

<div style="font-size: 40px;"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px;"><center>Ionic liquids: Designer solvents</center></div>
 
<div style="font-size: 30px;"><center>[[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|Back to week 1 work]]</center></div>
 
= Introduction =
The aim of this project is to explore the physical nature of ionic liquids, which have application in designing solvents through customisation of the nature of the cation and anion<ref name="abs">M. Freemantle. ''Chem. Eng. News'', 1998, '''76''', 32–37</ref>. In this work, a variety of cations have been investigated to identify what trends are present in the variation in central atom and its ligands.

= Structures of methyl-ligand complexes =
== Optimisations ==
A number of cations have been optimised using Gaussian 09 D.01, namely [N(CH3)4]+, [P(CH3)4]+ and [F(CH3)3]+. All these complexes have been optimised to a DFT B3LYP 6-31G(d,p) level with the <code>int=ultrafine scf=conver=9</code> keywords and tight convergence - this is as a consequence of behaviour seen in previous work<ref name="labintro">P. Kent, unpublished work ([[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|lab intro]])</ref> where low frequencies did not exist within a tight range unless these keywords were specified. All calculations were run on the supplied laptop due to a significant queue of jobs on the HPC (except for [S(CH3)3]+ as it took a very long time), and the log files are available here:

* [N(CH3)4]+: [[media:Pk_log_nch34_opt.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_opt.log]]
* [S(CH3)3]+: The first attempt did not converge: {{DOI|10042/26201}}. A partially optimised structure was resubmitted as a second attempt: {{DOI|10042/26205}}. This also did not converge so a final optimisation was run on this partially optimised structure with the <code>nosymm</code> keyword. This converged: {{DOI|10042/26214}}.

Once done, convergence was verified via inspection of the log file.

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name nch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000090 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 1 minutes 27.0 seconds.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name pch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701126 a.u.
RMS Gradient Norm 0.00000675 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 24 minutes 21.0 seconds.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_opt3
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000101 a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 52.2 seconds.
</pre>

=== Convergence outputs ===

''' [N(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000014 0.000060 YES
RMS Displacement 0.000005 0.000040 YES
Predicted change in Energy=-1.010077D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000015 YES
RMS Force 0.000005 0.000010 YES
Maximum Displacement 0.000026 0.000060 YES
RMS Displacement 0.000009 0.000040 YES
Predicted change in Energy=-1.723206D-06
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''

Initial failed optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000015 NO
RMS Force 0.000006 0.000010 YES
Maximum Displacement 0.002915 0.000060 NO
RMS Displacement 0.000869 0.000040 NO
Predicted change in Energy=-5.685776D-09
Optimization stopped.
-- Number of steps exceeded, NStep= 61
-- Flag reset to prevent archiving.
</pre>

During this failed optimisation, it appears the molecule just spent a large amount of time rotating around the C3 axis through the sulphur.

The final optimisation yielded:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000049 0.000060 YES
RMS Displacement 0.000018 0.000040 YES
Predicted change in Energy=-6.520157D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==
Following this, frequency analysis was conducted with the same keywords and calculation level to ensure a minima has been found. This is ensured by checking there are no negative vibrations in the molecule. Calculations were again run on the laptop, and the log files, summaries, and frequencies are listed below. Actual animations of the modes have not been exported, however a Jmol of the log file is available and the modes can be seen by right clicking and choosing '''model -> the mode you want to see'''. This time, a range of
-30 to +30 cm-1 has been accepted for the low frequencies as molecules investigated are quite complex, and a relatively simple basis set has been used. Optimising to 6-311G(d,p) would likely bring the frequencies within the range used previously however this would be at the expense of much longer computation times.

* [N(CH3)4]+: [[media:Pk_log_nch34_freq.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_freq.log]]
* [S(CH3)3]+: {{DOI|10042/26273}}

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name NCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000085 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 3 minutes 17.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000009 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.014288D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name PCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701149 a.u.
RMS Gradient Norm 0.00000668 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 12 minutes 11.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001774 0.001800 YES
RMS Displacement 0.000659 0.001200 YES
Predicted change in Energy=-3.008780D-08
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000104 a.u.
Imaginary Freq 0
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 9 minutes 6.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000093 0.001800 YES
RMS Displacement 0.000033 0.001200 YES
Predicted change in Energy=-7.179584D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Vibration modes ===

''' [N(CH3)4]+ '''
<pre>
Low frequencies --- 0.0007 0.0011 0.0013 21.5288 21.5288 21.5288
Low frequencies --- 188.5488 292.6546 292.6546
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [P(CH3)4]+ '''
<pre>
Low frequencies --- -15.1139 -0.0002 0.0012 0.0012 5.8940 14.7736
Low frequencies --- 156.2222 191.5376 191.9513
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_pch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [S(CH3)3]+ '''
<pre>
Low frequencies --- -8.5871 0.0029 0.0049 0.0051 5.7111 9.1755
Low frequencies --- 162.4159 200.3446 200.5391
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_sch33_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== Conclusions on molecular structure ==
Investigation of structures is focused on the central atom as this is the only point at which variance should occur. The length of the M-C bonds and the angle between C-M-C on each complex is reported below:

{| class="wikitable" border="1"
! Complex !! M-C Length (Å) !! Angle (°) !! M-C length (lit<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref>) (Å)
|-
| [P(CH3)4]+ || 1.82 || 109.5 || 1.84
|-
| [N(CH3)4]+ || 1.51 || 109.5 || 1.46
|-
| [S(CH3)3]+ || 1.82 || 102.7 || 1.79
|}

''Literature bond lengths are found by adding the covalent radii for the atoms.''

Two key trends are:
* As you go down a group, the bond length decreases
* As you go across a group (so losing a ligand), the bond angle is reduced)

The first trend is straightforward to explain, as bond lengths increase down the group. This is in tandem with the increase in atomic radius down the group as orbitals in a greater shell begin to be filled. Thus, as you move from period 2 (N) to period 3 (P), the length of the bond increases and is in turn the overall size of each ion. There is slight variance in the length of a C-H bond in each complex, however no pattern is immediately discernible (it increases in the order S > P > N) - it is thought this is just some random error in the calculation.

Whilst there is an increase in bond length, there is no change in orientation of the bonds, thus the symmetry of TD is maintained in both the phosphorous and nitrogen molecules. As a result of this, the bond angle is the same for these two complexes. No other arrangement of the ligands is sterically possible, so ensuring that this symmetry label cannot be changed, and therefore the bond angle also cannot change. The bond angle is different for sulphur, as a result of the change of symmetry to C3v, it is not known if the change in central atom contributes to this change - further investigation would be required.

Of note, the bond length does not appear to change going across the period. There is actually a small increase of 0.01Å if the bond length is reported accurate to 0.001Å, however it is not known if this is just an inherent error in the calculation or not. In any event, it is expected that there is a slight decrease in the bond length as you move towards the right of a period, as the increased nuclear charge better shields the electrons and thus shortens the bond length, but this is not observed here. This may be a result of this complex containing one less ligand, with the arrangement instead taken (along with the lone pair) resulting in some interactions (steric or electronic repulsion) which causes the carbon and core atoms to move apart from each other. This theory is supported by the large deviation from bond length for the sulphur complex, indicating some feature about the arrangement it has taken is causing the bond length to be artificially lengthened.

Otherwise no strange observations are seen with the structures, with all methyl groups taking the expected tetrahedral structure, and either tetrahedral or C3v structures for the central atom as expected by the number of ligands which are present.

= Molecular orbitals and NBO charges of methyl-ligand complexes =
All three complexes discussed previously have been subject to a full NBO and MO analysis via an energy calculation with the <code>pop=(full,nbo)</code> keyword, retaining any previously used keywords as appropriate. Calculations were performed on the laptop due to load on the HPC, except for the sulphur complex as the calculation took too long on the laptop.

Log files are available as follows:

* '''[N(CH3)4]+''': [[media:Pk_log_nch34_egy.log]]
* '''[P(CH3)4]+''': [[media:Pk_log_pch34_egy.log]]
* '''[S(CH3)3]+''': {{DOI|10042/26274}}
== Calculation output ==

''' [N(CH3)4]+ '''

<pre>
File Name NCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

''' [P(CH3)4]+ '''

<pre>
File Name PCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701105 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 20.0 seconds.
</pre>

''' [S(CH3)3]+ '''

<pre>File Name sch33_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 0 minutes 57.7 seconds.
</pre>

== Sample MOs for [N(CH3)4]+ ==
A variety of 5 molecular orbitals have been calculated and shown below. Only occupied non-core MOs from the totally bonding to totally antibonding are shown.

{| class="wikitable" border="1"
|+ Totally bonding towards the top
! MO number !! Energy (hartree) !! Picture !! Degeneracy !! Notes
|-
| 6 || -1.19645 || [[Image:Pk-n-mo0.png|200px]] || Singly degenerate || This MO exhibits a great degree of strong bonding interactions across the entire molecule up to the protons, the orbitals of which do not appear to be part of this MO. This is seen by the huge red surface containing almost the entirety of the molecule. As a result of the huge amount of delocalisation seen in the MO, there is a lot of through space interactions between adjacent carbon groups, as seen by how the MO forms a 'cage' around the entire molecule - the empty space between two carbon atoms is part of this red object. As there are no other molecular orbitals other than this huge one, there is no concept of a node in this MO diagram.
|-
| 10 || -0.80745 || [[Image:Pk-n-mo1.png|200px]] || Singly degenerate || This is the first MO in this series of 5 to contain a slight degree of antibonding character, as seen by the fact each ligand is in its own (+) phase orbital, whereas the central atom is in a (-) phase one. This leads to a minor degree of antibonding character, and also a node in the centre of the M-C bond where the two MOs end. Through space interactions are present in each ligand MO, with all the protons and the central carbon existing within the boundaries of the MO, and hence there are through-space interactions between the protons. MOs of the same phase interact weakly with each other due to the large distance between each green orbital (seen in the picture), however the interaction between the (+) and (-) orbitals is quite strong as the nodal area is very small in size - the orbitals are nearly touching. The level of delocalisation is reduced, with delocalisation only occurring across each ligand group - the ligands themselves are not delocalised onto one unit.
|-
| 14 || -0.62248 || [[Image:Pk-n-mo2.png|200px]] || Doubly degenerate || For this MO, nodes exist on every carbon atom, as each MO covers two halves of a carbon atom, two protons, and nothing else. This does lead to delocalisation across the protons and carbon atoms, however this also does result in strong antibonding interactions at each carbon as the (+) and (-) MOs become quite close. Some protons, and the central atom are not covered at all by this MO, however from what is delocalised, there is a significant amount of through space interactions between protons on differing methyl ligands - this is of note as the ligand protons are quite a distance away. There may be some weak bonding interactions between orbitals of the same phase, however they are quite a distance away (separated by the central atom) so this is expected to be quite weak.
|-
| 17 || -0.58035 || [[Image:Pk-n-mo3.png|200px]] || Triply degenerate || This one again has a node on each carbon, however it differs in that each orbital only covers a single proton and half a carbon. This results in there being no through-space interactions in this molecule. Additionally, there are many strong antibonding interactions as all the orbitals are quite close together, with the a (+) orbital being surrounded by a (-) orbital on every side. If there are any bonding interactions, these are going to be very weak.
|-
| 21 || -0.57934 || [[Image:Pk-n-mo4.png|200px]] || Triply degenerate || This MO is similar to the previous, but differs in that each orbital now consists of two protons, so there are no protons which aren't enclosed in an orbital. Again, there are nodes in each carbon, but also a node in the central atom, with orbitals now also covering the central atom. This results in there being strong antibonding interactions over almost the entire molecule, with (+) interacting with (-) almost over the entire surface of every orbital. Through-space interactions are now back with there being two protons in each orbital, making it possible for these to interact, and there is also the potential for protons and central atom to interact as well. This orbital is only slightly higher energy than the previous one, and this is solely because of the increased degree of antibonding interactions present.
|}

== NBO charge distributions ==

NBO charge distributions were calculated from the checkpoint file for a range of -1.750 to 1.750 as this ensured the range of charges for all 3 complexes could be accommodated on the same scale. The charges are as follows:

{| class="wikitable" border="1"
! Complex !! Central atom charge (e) !! Carbon charge (e) !! Proton charge (e)
|-
| [P(NH3)4]+ || 1.667 || -1.060 || 0.298
|-
| [N(NH3)4]+ || -0.295 || -0.846 || 0.297
|-
| [S(NH3)3]+ || 0.917 || -0.483 || 0.269
|}

<gallery>
File:Pk-nbo-n.png|Nitrogen complex
File:Pk-nbo-p.png|Phosphorous complex
File:Pk-nbo-s.png|Sulphur complex
</gallery>

There appears to be a slight trend of the central atom's charge with electronegativity, with the charge much lower as it becomes more electronegative (and hence drawing a greater share of electrons to it). This in turn makes the carbon more positive as electron density is removed from it. The protons remain rather positively charged and do not appear to be greatly affected by the centre, but this is likely because they are too far away for the inductive effect to occur.

Interestingly, nitrogen is more eletronegative than sulphur, yet sulphur has a greater negative charge. The reduced degree of polarisation in the bond for the nitrogen complex also suggests why the bond length for the nitrogen complex is shorter compared to the sulphur. The reason for this increased amount of negative charge is due to the lone pair present on sulphur (hence the configuration it takes according to the Jmol clip above), and so there is simply more negative charge present on the sulphur.

Thus, for the general complex [NR4]+, the positive charge located on the nitrogen in the picture is indeed located on the nitrogen, however it is somewhat delocalised over the protons too. As the nitrogen contains the greatest degree of positive charge, though, the + sign is conventionally placed here as it gives the indication as to where most of the charge is.

Analysis of the log files show the exact NBO contributions to the bond:

'''[P(NH3)3]+'''
<pre>
1. (1.98031) BD ( 1) P 1 - C 2
( 40.43%) 0.6358* P 1 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.4030 0.0006 0.0000 -0.4429
0.0006 0.0000 0.6188 -0.0009 0.0385
-0.0538 -0.0591 -0.0036 0.0254
( 59.57%) 0.7718* C 2 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.4044
-0.0074 0.4444 -0.0081 -0.6209 0.0114
0.0121 -0.0169 -0.0186 -0.0011 0.0080
</pre>

This shows almost equal contribution from each atom to the bond, with each atom assuming a sp3 arrangement as is expected by the TD symmetry. Carbon is sp3 as expected due to its saturation. As the carbon is slightly more negatively charged according to the charge distributions, the marginal increase in contribution from the carbon vs the phosphorous agrees with the charge distribution seen.

'''[N(NH3)3]+'''
<pre>
4. (1.98452) BD ( 1) C 1 - N 13
( 33.65%) 0.5801* C 1 s( 20.77%)p 3.81( 79.06%)d 0.01( 0.16%)
0.0003 0.4552 -0.0237 0.0026 -0.5129
-0.0218 -0.5129 -0.0218 -0.5129 -0.0218
0.0234 0.0234 0.0234 0.0000 0.0000
( 66.35%) 0.8146* N 13 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 0.5000 -0.0007 0.0000 0.4999
-0.0001 0.4999 -0.0001 0.4999 -0.0001
0.0103 0.0103 0.0103 0.0000 0.0000
</pre>

A similar argument can be made here. The large contribution from the nitrogen is surprising, but considering the smaller bond length for this complex based on the central atom, an increased contribution from the nitrogen is not unreasonable. However this does disagree somewhat with the charge distribution which shows there is a much larger electron density on the carbon. It is thus thought that since it is possible to reach orbitals closer to the core on nitrogen rather than phosphorous, it makes nitrogen able to donate a greater share of electrons, and so polarises the bond towards it as a result of its electronegativity.

'''[S(NH3)3]+'''
<pre>
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
-0.0003 -0.4437 -0.0140 0.0033 0.7546
-0.0059 0.3161 -0.0025 0.3634 0.0098
-0.0189 -0.0222 -0.0093 -0.0186 0.0096
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 -0.0001 -0.4117 0.0075 -0.0012
0.0000 -0.7489 0.0330 0.0000 -0.3137
0.0138 0.0000 -0.4037 -0.0260 -0.0353
-0.0572 -0.0240 -0.0347 0.0051
</pre>

Finally, for the sulphur, the bond is an almost equal contribution from each atom in the bond. The charges of the S and C atoms according to the charge distribution are both similar and negative, suggesting little polarisation in this bond, and so the balance seen here is to be expected.

= Ligand influences on nitrogen centre complexes =
To investigate how changes to the ligands affects the cation, two variants on the nitrogen complex analysed previously have been used. One has one of the protons on a methyl ligand replaced with CH2OH, the other has the proton replaced with CH2CN. Each complex is then optimised and subject to a frequency analysis so as to allow for investigation of its structure. A MO and NBO calculation is then subsequently run to analyse how the change in ligand affects the ions electronic behaviour.

== Optimisations ==
Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26206}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26207}}

=== Summary output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
File Name nch33ch2oh_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000102 a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 1 hours 22 minutes 37.5 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
File Name nch33ch2cn_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000045 a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 50 minutes 39.5 seconds.
</pre>

=== Convergence output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000034 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-5.591936D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000011 0.000040 YES
Predicted change in Energy=-2.269581D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==

Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26290}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26291}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000106 a.u.
Imaginary Freq 0
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 26 minutes 10.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000102 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-5.078379D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000059 a.u.
Imaginary Freq 0
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 29 minutes 19.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-6.144746D-12
Optimization completed.
-- Stationary point found.
</pre>

=== Vibrational modes ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2oh_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

'''[N(CH3)3(CH2CN)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2cn_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== MO and NBO calculations ==
<code>pop=(nbo,full)</code> energy calculations were then performed on the complexes to generate MOs and NBO charge diagrams, just as has been done previously. All calculations were performed on the HPC and log files are available as follows:

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26294}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26295}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 59.3 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 25.0 seconds.
</pre>

=== NBO charge distributions ===
The main difference between these ligands is that CN is an EWG, and OH is an EDG, the latter due to the lone pairs which make it possible to enolise. Therefore comparison of the charge density of the structure can show how these ligands affect the overall structure of the molecule. The NBO charge distributions from -0.750 to 0.750 are shown below.

<gallery>
File:Pk-nbo-cn.png|CN ligand complex
File:Pk-nbo-oh.png|OH ligand complex
</gallery>

''n.b. the charge for the atom in the centre of the CN complex is -0.289''

It is seen that, in both cases, the nitrogen makes up the majority of the C-N bond to the C with the substituent:

'''OH case:'''
<pre>
4. (1.98195) BD ( 1) N 1 - C 14
( 67.28%) 0.8202* N 1 s( 23.48%)p 3.26( 76.49%)d 0.00( 0.03%)
0.0000 -0.4845 -0.0026 -0.0002 0.7401
-0.0032 0.3146 -0.0015 0.3438 -0.0026
-0.0092 -0.0105 -0.0043 -0.0088 0.0045
( 32.72%) 0.5720* C 14 s( 20.28%)p 3.92( 79.55%)d 0.01( 0.18%)
-0.0003 -0.4501 0.0135 0.0006 -0.7171
-0.0206 -0.3677 -0.0077 -0.3815 -0.0037
-0.0247 -0.0249 -0.0101 -0.0185 0.0102
</pre>

'''CN case:'''
<pre>
4. (1.97747) BD ( 1) N 1 - C 14
( 64.52%) 0.8033* N 1 s( 24.08%)p 3.15( 75.89%)d 0.00( 0.04%)
0.0000 0.4907 -0.0010 0.0003 0.6601
-0.0021 0.5684 0.0038 0.0000 0.0000
0.0166 0.0000 0.0000 0.0024 -0.0097
( 35.48%) 0.5956* C 14 s( 20.81%)p 3.80( 79.05%)d 0.01( 0.14%)
0.0000 0.4557 -0.0205 0.0000 -0.6428
-0.0249 -0.6135 -0.0174 0.0000 0.0000
0.0320 0.0000 0.0000 -0.0011 -0.0197
</pre>

==== Ligand influence on charge distribution ====

There is quite a significant change in electron density for the OH complex with the carbon between the OH group and the centre becoming much more positive. This is surprising considering the OH is a donating group, however this is simply explained. As the carbon is between two electronegative groups, a lot of electron density is withdrawn from it, and hence it becomes very positive. However, the centre has become more negatively charged (-0.322 vs -0.295). Hence, the donated electrons are moving straight from the oxygen to the centre, while the carbon between's electrons are also donated to both the oxygen and nitrogen as part of the electronegative pull these atoms have on the carbon.

Regarding the CN complex, the electron withdrawal is clearly seen on the carbon the CN ligand is bonded to, as this has become less negatively charged (-0.289 vs -0.295), showing that once again, electron withdrawal is occuring at a distance that causes electrons to travel from the nitrogen through the carbon.

In conclusion, it is seen that the electron inductive effects of the ligands has a direct influence on the central atom, as these effects travel through the carbon to directly pull or push electrons from the central atom. This is likely due to the large contribution of charge from the nitrogen in the CN bond to the relevant C, so meaning any inductive effects on the C are very likely to influence the N due to the polarisation of the bond towards the N seen.

=== Sample MOs ===
The HOMO and LUMO for these two complexes are reported below:

{| class="wikitable" border="1"
! !! [N(CH3)3(CH2OH)]+ !!
[N(CH3)3(CH2CN)]+
|-
| HOMO || [[Image:Pk-homo-oh.png|200px]] || [[Image:Pk-homo-cn.png|200px]]
|-
| LUMO || [[Image:Pk-lumo-oh.png|200px]] || [[Image:Pk-lumo-cn.png|200px]]
|-
| HOMO Energy (hartree) || -0.48763 || -0.50047
|-
| LUMO Energy (hartree) || -0.12459 || -0.18183
|}

=== Discussion of MOs ===

The most notable change is that there is an increased amount of delocalisation present in the alcohol-containing complex's LUMO vs the cyanide containing one. Whilst it was thought that this is a result of the electron donation, further investigation showed that this is one orbital created by through-space interactions of every proton in the complex. The present of the alcohol group adds protons to fill a space in the molecule where would there otherwise be no protons (see the cyanide complex). This means that the distance between any two protons is small enough for an interaction to occur, and as there are protons around the entirety of the molecule, one orbital surrounds the entire molecule. The original theory was discarded after it was noted that the nitrogen centre has its own orbital of the opposite phase in the centre of the complex, which leads to a very large number of strong antibonding interactions as it comes close to the delocalised proton orbital. Despite the increased degree of through-space interactions, this LUMO is higher in energy than the CN one, simply because of the increased number of antibonding interactions.

The CN complex LUMO does not have such a large delocalisation, and as a result some methyl protons occupy their own orbital of the opposite polarity.

A similar story is seen for the HOMO, which is lower in energy for the CN molecule. The overall volume of orbitals is smaller for the CN molecule, as the CN group is symmetric and simple (pi-bond like) in nature, leading to a very simple arrangement of orbitals at this point. In contrast, for the OH complex, a very complex d-orbital MO is seen over the alcohol group, which then results in some interactions over the nitrogen.

One possible result of this is that it is easier to perform electrophillic attacks on the OH complex at the nitrogen, as the presence of an orbital over the nitrogen would allow for a positively charged group to come in and perform some reaction. These reactions may include ligand substitution or oxidative addition. This kind of attack would not be possible on the CN complex HOMO as no orbital exists on the central nitrogen, and hence cannot be attacked. The only reactions possible on this HOMO would therefore be substitutions on the CN group, which is not as interesting as ligand substitution or oxidative addition on the center of the complex.

Likewise, the OH complex is likely to be more susceptable to attack by nucleophiles. This is however not due to the large delocalised MO (which is present on the CN complex too), as this only covers protons and does not allow any reactions to occur on a ligand or on the nitrogen. However on the OH group, there is an orbital which contains both the nitrogen centre and the OH ligand, making it incredibly likely that nucleophillic attack will lead to substitution of the CH2OH group. This is necessary as this large orbital covering the entire molecule is likely to hinder attack of the nitrogen centre - as any attack of the nitrogen center must be on an orbital of the nitrogen centre. This cannot occur on the CN group as the orbital over the nitrogen is completely shielded by other orbitals.

Finally, the HOMO-LUMO gap has changed from 0.31864 e (for the CN complex) to 0.36304 e. This makes it harder for an electron to be promoted from the HOMO to the LUMO in the OH complex. Therefore, any photochemical reactivity which is seen would occur in the CN complex but not the OH one. Considering there is a wealth of reported<ref name="photo">F. Crescitelli, B. Karvaly, ''Photochemistry and Photobiology'', 1989, '''50''', 785–791</ref> photoreactivity for CN systems, it is very likely that photochemistry will occur with the cyanide-containing complex.

= Conclusions =
Ionic solvents are formed of a liquid solution of cations and ions, the nature of which massively alter thes behaviour of the solvent. This nature has been shown to be changed by altering the central atom, structure, and ligands of various positive complexes, as has been seen. This report examined how the electronegativity and periodicity of the central atom, and the electron donating ability of a ligand affects the chemistry of the ion in terms of changing the structure, charge density, and molecular orbitals. Some possible pathways of reactivity of the ions have been proposed, which gives some indication as to how a change of the ion's nature massively changes its solvation properties, as solvation can occur through the coordination of the solute to the solvent ion.

Future work can include investigation into how the different ions coordinate to different substrates added to the calculation, and molecular orbital and NBO calculations can give some idea into whether the theories proposed as to where the ion may be reactive are correct.

= References =
<references />

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T16:45:52Z

Pk1811: /* Discussion of MOs */

<div style="font-size: 40px;"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px;"><center>Ionic liquids: Designer solvents</center></div>
 
<div style="font-size: 30px;"><center>[[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|Back to week 1 work]]</center></div>
 
= Introduction =
The aim of this project is to explore the physical nature of ionic liquids, which have application in designing solvents through customisation of the nature of the cation and anion<ref name="abs">M. Freemantle. ''Chem. Eng. News'', 1998, '''76''', 32–37</ref>. In this work, a variety of cations have been investigated to identify what trends are present in the variation in central atom and its ligands.

= Structures of methyl-ligand complexes =
== Optimisations ==
A number of cations have been optimised using Gaussian 09 D.01, namely [N(CH3)4]+, [P(CH3)4]+ and [F(CH3)3]+. All these complexes have been optimised to a DFT B3LYP 6-31G(d,p) level with the <code>int=ultrafine scf=conver=9</code> keywords and tight convergence - this is as a consequence of behaviour seen in previous work<ref name="labintro">P. Kent, unpublished work ([[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|lab intro]])</ref> where low frequencies did not exist within a tight range unless these keywords were specified. All calculations were run on the supplied laptop due to a significant queue of jobs on the HPC (except for [S(CH3)3]+ as it took a very long time), and the log files are available here:

* [N(CH3)4]+: [[media:Pk_log_nch34_opt.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_opt.log]]
* [S(CH3)3]+: The first attempt did not converge: {{DOI|10042/26201}}. A partially optimised structure was resubmitted as a second attempt: {{DOI|10042/26205}}. This also did not converge so a final optimisation was run on this partially optimised structure with the <code>nosymm</code> keyword. This converged: {{DOI|10042/26214}}.

Once done, convergence was verified via inspection of the log file.

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name nch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000090 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 1 minutes 27.0 seconds.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name pch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701126 a.u.
RMS Gradient Norm 0.00000675 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 24 minutes 21.0 seconds.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_opt3
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000101 a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 52.2 seconds.
</pre>

=== Convergence outputs ===

''' [N(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000014 0.000060 YES
RMS Displacement 0.000005 0.000040 YES
Predicted change in Energy=-1.010077D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000015 YES
RMS Force 0.000005 0.000010 YES
Maximum Displacement 0.000026 0.000060 YES
RMS Displacement 0.000009 0.000040 YES
Predicted change in Energy=-1.723206D-06
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''

Initial failed optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000015 NO
RMS Force 0.000006 0.000010 YES
Maximum Displacement 0.002915 0.000060 NO
RMS Displacement 0.000869 0.000040 NO
Predicted change in Energy=-5.685776D-09
Optimization stopped.
-- Number of steps exceeded, NStep= 61
-- Flag reset to prevent archiving.
</pre>

During this failed optimisation, it appears the molecule just spent a large amount of time rotating around the C3 axis through the sulphur.

The final optimisation yielded:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000049 0.000060 YES
RMS Displacement 0.000018 0.000040 YES
Predicted change in Energy=-6.520157D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==
Following this, frequency analysis was conducted with the same keywords and calculation level to ensure a minima has been found. This is ensured by checking there are no negative vibrations in the molecule. Calculations were again run on the laptop, and the log files, summaries, and frequencies are listed below. Actual animations of the modes have not been exported, however a Jmol of the log file is available and the modes can be seen by right clicking and choosing '''model -> the mode you want to see'''. This time, a range of
-30 to +30 cm-1 has been accepted for the low frequencies as molecules investigated are quite complex, and a relatively simple basis set has been used. Optimising to 6-311G(d,p) would likely bring the frequencies within the range used previously however this would be at the expense of much longer computation times.

* [N(CH3)4]+: [[media:Pk_log_nch34_freq.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_freq.log]]
* [S(CH3)3]+: {{DOI|10042/26273}}

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name NCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000085 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 3 minutes 17.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000009 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.014288D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name PCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701149 a.u.
RMS Gradient Norm 0.00000668 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 12 minutes 11.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001774 0.001800 YES
RMS Displacement 0.000659 0.001200 YES
Predicted change in Energy=-3.008780D-08
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000104 a.u.
Imaginary Freq 0
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 9 minutes 6.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000093 0.001800 YES
RMS Displacement 0.000033 0.001200 YES
Predicted change in Energy=-7.179584D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Vibration modes ===

''' [N(CH3)4]+ '''
<pre>
Low frequencies --- 0.0007 0.0011 0.0013 21.5288 21.5288 21.5288
Low frequencies --- 188.5488 292.6546 292.6546
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [P(CH3)4]+ '''
<pre>
Low frequencies --- -15.1139 -0.0002 0.0012 0.0012 5.8940 14.7736
Low frequencies --- 156.2222 191.5376 191.9513
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_pch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [S(CH3)3]+ '''
<pre>
Low frequencies --- -8.5871 0.0029 0.0049 0.0051 5.7111 9.1755
Low frequencies --- 162.4159 200.3446 200.5391
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_sch33_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== Conclusions on molecular structure ==
Investigation of structures is focused on the central atom as this is the only point at which variance should occur. The length of the M-C bonds and the angle between C-M-C on each complex is reported below:

{| class="wikitable" border="1"
! Complex !! M-C Length (Å) !! Angle (°) !! M-C length (lit<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref>) (Å)
|-
| [P(CH3)4]+ || 1.82 || 109.5 || 1.84
|-
| [N(CH3)4]+ || 1.51 || 109.5 || 1.46
|-
| [S(CH3)3]+ || 1.82 || 102.7 || 1.79
|}

''Literature bond lengths are found by adding the covalent radii for the atoms.''

Two key trends are:
* As you go down a group, the bond length decreases
* As you go across a group (so losing a ligand), the bond angle is reduced)

The first trend is straightforward to explain, as bond lengths increase down the group. This is in tandem with the increase in atomic radius down the group as orbitals in a greater shell begin to be filled. Thus, as you move from period 2 (N) to period 3 (P), the length of the bond increases and is in turn the overall size of each ion. There is slight variance in the length of a C-H bond in each complex, however no pattern is immediately discernible (it increases in the order S > P > N) - it is thought this is just some random error in the calculation.

Whilst there is an increase in bond length, there is no change in orientation of the bonds, thus the symmetry of TD is maintained in both the phosphorous and nitrogen molecules. As a result of this, the bond angle is the same for these two complexes. No other arrangement of the ligands is sterically possible, so ensuring that this symmetry label cannot be changed, and therefore the bond angle also cannot change. The bond angle is different for sulphur, as a result of the change of symmetry to C3v, it is not known if the change in metal centre contributes to this change - further investigation would be required.

Of note, the bond length does not appear to change going across the period. There is actually a small increase of 0.01Å if the bond length is reported accurate to 0.001Å, however it is not known if this is just an inherent error in the calculation or not. In any event, it is expected that there is a slight decrease in the bond length as you move towards the right of a period, as the increased nuclear charge better shields the electrons and thus shortens the bond length, but this is not observed here. This may be a result of this complex containing one less ligand, with the arrangement instead taken (along with the lone pair) resulting in some interactions (steric or electronic repulsion) which causes the carbon and metal atoms to move apart from each other. This theory is supported by the large deviation from bond length for the sulphur complex, indicating some feature about the arrangement it has taken is causing the bond length to be artificially lengthened.

Otherwise no strange observations are seen with the structures, with all methyl groups taking the expected tetrahedral structure, and either tetrahedral or C3v structures for the central atom as expected by the number of ligands which are present.

= Molecular orbitals and NBO charges of methyl-ligand complexes =
All three complexes discussed previously have been subject to a full NBO and MO analysis via an energy calculation with the <code>pop=(full,nbo)</code> keyword, retaining any previously used keywords as appropriate. Calculations were performed on the laptop due to load on the HPC, except for the sulphur complex as the calculation took too long on the laptop.

Log files are available as follows:

* '''[N(CH3)4]+''': [[media:Pk_log_nch34_egy.log]]
* '''[P(CH3)4]+''': [[media:Pk_log_pch34_egy.log]]
* '''[S(CH3)3]+''': {{DOI|10042/26274}}
== Calculation output ==

''' [N(CH3)4]+ '''

<pre>
File Name NCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

''' [P(CH3)4]+ '''

<pre>
File Name PCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701105 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 20.0 seconds.
</pre>

''' [S(CH3)3]+ '''

<pre>File Name sch33_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 0 minutes 57.7 seconds.
</pre>

== Sample MOs for [N(CH3)4]+ ==
A variety of 5 molecular orbitals have been calculated and shown below. Only occupied non-core MOs from the totally bonding to totally antibonding are shown.

{| class="wikitable" border="1"
|+ Totally bonding towards the top
! MO number !! Energy (hartree) !! Picture !! Degeneracy !! Notes
|-
| 6 || -1.19645 || [[Image:Pk-n-mo0.png|200px]] || Singly degenerate || This MO exhibits a great degree of strong bonding interactions across the entire molecule up to the protons, the orbitals of which do not appear to be part of this MO. This is seen by the huge red surface containing almost the entirety of the molecule. As a result of the huge amount of delocalisation seen in the MO, there is a lot of through space interactions between adjacent carbon groups, as seen by how the MO forms a 'cage' around the entire molecule - the empty space between two carbon atoms is part of this red object. As there are no other molecular orbitals other than this huge one, there is no concept of a node in this MO diagram.
|-
| 10 || -0.80745 || [[Image:Pk-n-mo1.png|200px]] || Singly degenerate || This is the first MO in this series of 5 to contain a slight degree of antibonding character, as seen by the fact each ligand is in its own (+) phase orbital, whereas the central metal is in a (-) phase one. This leads to a minor degree of antibonding character, and also a node in the centre of the M-C bond where the two MOs end. Through space interactions are present in each ligand MO, with all the protons and the central carbon existing within the boundaries of the MO, and hence there are through-space interactions between the protons. MOs of the same phase interact weakly with each other due to the large distance between each green orbital (seen in the picture), however the interaction between the (+) and (-) orbitals is quite strong as the nodal area is very small in size - the orbitals are nearly touching. The level of delocalisation is reduced, with delocalisation only occurring across each ligand group - the ligands themselves are not delocalised onto one unit.
|-
| 14 || -0.62248 || [[Image:Pk-n-mo2.png|200px]] || Doubly degenerate || For this MO, nodes exist on every carbon atom, as each MO covers two halves of a carbon atom, two protons, and nothing else. This does lead to delocalisationa cross the protons and carbon atoms, however this also does result in strong antibonding interactions at each carbon as the (+) and (-) MOs become quite close. Some protons, and the metal centre are not covered at all by this MO, however from what is delocalised, there is a significant amount of through space interactions between protons on differing methyl ligands - this is of note as the ligand protons are quite a distance away. There may be some weak bonding interactions between orbitals of the same phase, however they are quite a distance away (separated by the metal centre) so this is expected to be quite weak.
|-
| 17 || -0.58035 || [[Image:Pk-n-mo3.png|200px]] || Triply degenerate || This one again has a node on each carbon, however it differs in that each orbital only covers a single proton and half a carbon. This results in there being no through-space interactions in this molecule. Additionally, there are many strong antibonding interactions as all the orbitals are quite close together, with the a (+) orbital being surrounded by a (-) orbital on every side. If there are any bonding interactions, these are going to be very weak.
|-
| 21 || -0.57934 || [[Image:Pk-n-mo4.png|200px]] || Triply degenerate || This MO is similar to the previous, but differs in that each orbital now consists of two protons, so there are no protons which aren't enclosed in an orbital. Again, there are nodes in each carbon, but also a node in the metal center, with orbitals now also covering the metal center. This results in there being strong antibonding interactions over almost the entire molecule, with (+) interacting with (-) almost over the entire surface of every orbital. Through-space interactions are now back with there being two protons in each orbital, making it possible for these to interact, and there is also the potential for protons and metal center to interact as well. This orbital is only slightly higher energy than the previous one, and this is solely because of the increased degree of antibonding interactions present.
|}

== NBO charge distributions ==

NBO charge distributions were calculated from the checkpoint file for a range of -1.750 to 1.750 as this ensured the range of charges for all 3 complexes could be accommodated on the same scale. The charges are as follows:

{| class="wikitable" border="1"
! Complex !! Metal charge (e) !! Carbon charge (e) !! Proton charge (e)
|-
| [P(NH3)4]+ || 1.667 || -1.060 || 0.298
|-
| [N(NH3)4]+ || -0.295 || -0.846 || 0.297
|-
| [S(NH3)3]+ || 0.917 || -0.483 || 0.269
|}

<gallery>
File:Pk-nbo-n.png|Nitrogen complex
File:Pk-nbo-p.png|Phosphorous complex
File:Pk-nbo-s.png|Sulphur complex
</gallery>

There appears to be a slight trend of the metal centre charge with electronegativity, with the charge much lower as it becomes more electronegative (and hence drawing a greater share of electrons to it). This in turn makes the carbon more positive as electron density is removed from it. The protons remain rather positively charged and do not appear to be greatly affected by the metal centre, but this is likely because they are too far away for the inductive effect to occur.

Interestingly, nitrogen is more eletronegative than sulphur, yet sulphur has a greater negative charge. The reduced degree of polarisation in the bond for the nitrogen complex also suggests why the bond length for the nitrogen complex is shorter compared to the sulphur. The reason for this increased amount of negative charge is due to the lone pair present on sulphur (hence the configuration it takes according to the Jmol clip above), and so there is simply more negative charge present on the sulphur.

Thus, for the general complex [NR4]+, the positive charge located on the nitrogen in the picture is indeed located on the nitrogen, however it is somewhat delocalised over the protons too. As the nitrogen contains the greatest degree of positive charge, though, the + sign is conventionally placed here as it gives the indication as to where most of the charge is.

Analysis of the log files show the exact NBO contributions to the bond:

'''[P(NH3)3]+'''
<pre>
1. (1.98031) BD ( 1) P 1 - C 2
( 40.43%) 0.6358* P 1 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.4030 0.0006 0.0000 -0.4429
0.0006 0.0000 0.6188 -0.0009 0.0385
-0.0538 -0.0591 -0.0036 0.0254
( 59.57%) 0.7718* C 2 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.4044
-0.0074 0.4444 -0.0081 -0.6209 0.0114
0.0121 -0.0169 -0.0186 -0.0011 0.0080
</pre>

This shows almost equal contribution from each atom to the bond, with each atom assuming a sp3 arrangement as is expected by the TD symmetry. Carbon is sp3 as expected due to its saturation. As the carbon is slightly more negatively charged according to the charge distributions, the marginal increase in contribution from the carbon vs the phosphorous agrees with the charge distribution seen.

'''[N(NH3)3]+'''
<pre>
4. (1.98452) BD ( 1) C 1 - N 13
( 33.65%) 0.5801* C 1 s( 20.77%)p 3.81( 79.06%)d 0.01( 0.16%)
0.0003 0.4552 -0.0237 0.0026 -0.5129
-0.0218 -0.5129 -0.0218 -0.5129 -0.0218
0.0234 0.0234 0.0234 0.0000 0.0000
( 66.35%) 0.8146* N 13 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 0.5000 -0.0007 0.0000 0.4999
-0.0001 0.4999 -0.0001 0.4999 -0.0001
0.0103 0.0103 0.0103 0.0000 0.0000
</pre>

A similar argument can be made here. The large contribution from the nitrogen is surprising, but considering the smaller bond length for this complex based on the metal, an increased contribution from the nitrogen is not unreasonable. However this does disagree somewhat with the charge distribution which shows there is a much larger electron density on the carbon. It is thus thought that since it is possible to reach orbitals closer to the core on nitrogen rather than phosphorous, it makes nitrogen able to donate a greater share of electrons, and so polarises the bond towards it as a result of its electronegativity.

'''[S(NH3)3]+'''
<pre>
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
-0.0003 -0.4437 -0.0140 0.0033 0.7546
-0.0059 0.3161 -0.0025 0.3634 0.0098
-0.0189 -0.0222 -0.0093 -0.0186 0.0096
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 -0.0001 -0.4117 0.0075 -0.0012
0.0000 -0.7489 0.0330 0.0000 -0.3137
0.0138 0.0000 -0.4037 -0.0260 -0.0353
-0.0572 -0.0240 -0.0347 0.0051
</pre>

Finally, for the sulphur, the bond is an almost equal contribution from each atom in the bond. The charges of the S and C atoms according to the charge distribution are both similar and negative, suggesting little polarisation in this bond, and so the balance seen here is to be expected.

= Ligand influences on nitrogen metal centre complexes =
To investigate how changes to the ligands affects the cation, two variants on the nitrogen complex analysed previously have been used. One has one of the protons on a methyl ligand replaced with CH2OH, the other has the proton replaced with CH2CN. Each complex is then optimised and subject to a frequency analysis so as to allow for investigation of its structure. A MO and NBO calculation is then subsequently run to analyse how the change in ligand affects the ions electronic behaviour.

== Optimisations ==
Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26206}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26207}}

=== Summary output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
File Name nch33ch2oh_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000102 a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 1 hours 22 minutes 37.5 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
File Name nch33ch2cn_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000045 a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 50 minutes 39.5 seconds.
</pre>

=== Convergence output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000034 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-5.591936D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000011 0.000040 YES
Predicted change in Energy=-2.269581D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==

Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26290}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26291}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000106 a.u.
Imaginary Freq 0
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 26 minutes 10.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000102 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-5.078379D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000059 a.u.
Imaginary Freq 0
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 29 minutes 19.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-6.144746D-12
Optimization completed.
-- Stationary point found.
</pre>

=== Vibrational modes ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2oh_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

'''[N(CH3)3(CH2CN)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2cn_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== MO and NBO calculations ==
<code>pop=(nbo,full)</code> energy calculations were then performed on the complexes to generate MOs and NBO charge diagrams, just as has been done previously. All calculations were performed on the HPC and log files are available as follows:

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26294}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26295}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 59.3 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 25.0 seconds.
</pre>

=== NBO charge distributions ===
The main difference between these ligands is that CN is an EWG, and OH is an EDG, the latter due to the lone pairs which make it possible to enolise. Therefore comparison of the charge density of the structure can show how these ligands affect the overall structure of the molecule. The NBO charge distributions from -0.750 to 0.750 are shown below.

<gallery>
File:Pk-nbo-cn.png|CN ligand complex
File:Pk-nbo-oh.png|OH ligand complex
</gallery>

''n.b. the charge for the metal centre in the CN complex is -0.289''

It is seen that, in both cases, the nitrogen makes up the majority of the C-N bond to the C with the substituent:

'''OH case:'''
<pre>
4. (1.98195) BD ( 1) N 1 - C 14
( 67.28%) 0.8202* N 1 s( 23.48%)p 3.26( 76.49%)d 0.00( 0.03%)
0.0000 -0.4845 -0.0026 -0.0002 0.7401
-0.0032 0.3146 -0.0015 0.3438 -0.0026
-0.0092 -0.0105 -0.0043 -0.0088 0.0045
( 32.72%) 0.5720* C 14 s( 20.28%)p 3.92( 79.55%)d 0.01( 0.18%)
-0.0003 -0.4501 0.0135 0.0006 -0.7171
-0.0206 -0.3677 -0.0077 -0.3815 -0.0037
-0.0247 -0.0249 -0.0101 -0.0185 0.0102
</pre>

'''CN case:'''
<pre>
4. (1.97747) BD ( 1) N 1 - C 14
( 64.52%) 0.8033* N 1 s( 24.08%)p 3.15( 75.89%)d 0.00( 0.04%)
0.0000 0.4907 -0.0010 0.0003 0.6601
-0.0021 0.5684 0.0038 0.0000 0.0000
0.0166 0.0000 0.0000 0.0024 -0.0097
( 35.48%) 0.5956* C 14 s( 20.81%)p 3.80( 79.05%)d 0.01( 0.14%)
0.0000 0.4557 -0.0205 0.0000 -0.6428
-0.0249 -0.6135 -0.0174 0.0000 0.0000
0.0320 0.0000 0.0000 -0.0011 -0.0197
</pre>

==== Ligand influence on charge distribution ====

There is quite a significant change in electron density for the OH complex with the carbon between the OH group and the metal centre becoming much more positive. This is surprising considering the OH is a donating group, however this is simply explained. As the carbon is between two electronegative groups, a lot of electron density is withdrawn from it, and hence it becomes very positive. However, the metal centre has become more negatively charged (-0.322 vs -0.295). Hence, the donated electrons are moving straight from the oxygen to the metal centre, while the carbon between's electrons are also donated to both the oxygen and nitrogen as part of the electronegative pull these atoms have on the carbon.

Regarding the CN complex, the electron withdrawal is clearly seen on the carbon the CN ligand is bonded to, as this has become less negatively charged (-0.289 vs -0.295), showing that once again, electron withdrawal is occuring at a distance that causes electrons to travel from the nitrogen through the carbon.

In conclusion, it is seen that the electron inductive effects of the ligands has a direct influence on the the metal centre, as these effects travel through the carbon to directly pull or push electrons from the metal. This is likely due to the large contribution of charge from the nitrogen in the CN bond to the relevant C, so meaning any inductive effects on the C are very likely to influence the N due to the polarisation of the bond towards the N seen.

=== Sample MOs ===
The HOMO and LUMO for these two complexes are reported below:

{| class="wikitable" border="1"
! !! [N(CH3)3(CH2OH)]+ !!
[N(CH3)3(CH2CN)]+
|-
| HOMO || [[Image:Pk-homo-oh.png|200px]] || [[Image:Pk-homo-cn.png|200px]]
|-
| LUMO || [[Image:Pk-lumo-oh.png|200px]] || [[Image:Pk-lumo-cn.png|200px]]
|-
| HOMO Energy (hartree) || -0.48763 || -0.50047
|-
| LUMO Energy (hartree) || -0.12459 || -0.18183
|}

=== Discussion of MOs ===

The most notable change is that there is an increased amount of delocalisation present in the alcohol-containing complex's LUMO vs the cyanide containing one. Whilst it was thought that this is a result of the electron donation, further investigation showed that this is one orbital created by through-space interactions of every proton in the complex. The present of the alcohol group adds protons to fill a space in the molecule where would there otherwise be no protons (see the cyanide complex). This means that the distance between any two protons is small enough for an interaction to occur, and as there are protons around the entirety of the molecule, one orbital surrounds the entire molecule. The original theory was discarded after it was noted that the metal centre has its own orbital of the opposite phase in the centre of the complex, which leads to a very large number of strong antibonding interactions as it comes close to the delocalised proton orbital. Despite the increased degree of through-space interactions, this LUMO is higher in energy than the CN one, simply because of the increased number of antibonding interactions.

The CN complex LUMO does not have such a large delocalisation, and as a result some methyl protons occupy their own orbital of the opposite polarity.

A similar story is seen for the HOMO, which is lower in energy for the CN molecule. The overall volume of orbitals is smaller for the CN molecule, as the CN group is symmetric and simple (pi-bond like) in nature, leading to a very simple arrangement of orbitals at this point. In contrast, for the OH complex, a very complex d-orbital MO is seen over the alcohol group, which then results in some interactions over the nitrogen.

One possible result of this is that it is easier to perform electrophillic attacks on the OH complex at the nitrogen, as the presence of an orbital over the nitrogen would allow for a positively charged group to come in and perform some reaction. These reactions may include ligand substitution or oxidative addition. This kind of attack would not be possible on the CN complex HOMO as no orbital exists on the central nitrogen, and hence cannot be attacked. The only reactions possible on this HOMO would therefore be substitutions on the CN group, which is not as interesting as ligand substitution or oxidative addition on the center of the complex.

Likewise, the OH complex is likely to be more susceptable to attack by nucleophiles. This is however not due to the large delocalised MO (which is present on the CN complex too), as this only covers protons and does not allow any reactions to occur on a ligand or on the metal. However on the OH group, there is an orbital which contains both the nitrogen centre and the OH ligand, making it incredibly likely that nucleophillic attack will lead to substitution of the CH2OH group. This is necessary as this large orbital covering the entire molecule is likely to hinder attack of the metal centre - as any attack of the metal center must be on an orbital of the nitrogen centre. This cannot occur on the CN group as the orbital over the nitrogen is completely shielded by other orbitals.

Finally, the HOMO-LUMO gap has changed from 0.31864 e (for the CN complex) to 0.36304 e. This makes it harder for an electron to be promoted from the HOMO to the LUMO in the OH complex. Therefore, any photochemical reactivity which is seen would occur in the CN complex but not the OH one. Considering there is a wealth of reported<ref name="photo">F. Crescitelli, B. Karvaly, ''Photochemistry and Photobiology'', 1989, '''50''', 785–791</ref> photoreactivity for CN systems, it is very likely that photochemistry will occur with the cyanide-containing complex.

= Conclusions =
Ionic solvents are formed of a liquid solution of cations and ions, the nature of which massively alter thes behaviour of the solvent. This nature has been shown to be changed by altering the metal, structure, and ligands of various positive complexes, as has been seen. This report examined how the electronegativity and periodicity of the metal, and the electron donating ability of a ligand affects the chemistry of the ion in terms of changing the structure, charge density, and molecular orbitals. Some possible pathways of reactivity of the ions have been proposed, which gives some indication as to how a change of the ion's nature massively changes its solvation properties, as solvation can occur through the coordination of the solute to the solvent ion.

Future work can include investigation into how the different ions coordinate to different substrates added to the calculation, and molecular orbital and NBO calculations can give some idea into whether the theories proposed as to where the ion may be reactive are correct.

= References =
<references />

Rep:Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158

2013-11-22T16:37:08Z

Pk1811:

<div style="font-size: 40px"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px"><center>Introductory week 1 work</center></div>
 
<div style="font-size: 30px"><center>[[Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185|To mini project]]</center></div>
 
= Part 1: Basic optimisations and the effect of metals and ligands on bond lengths =
A variety of basic calculations and experimentation have been conducted on BH3 and a number of similar molecules, namely BBr3 and GaBr3. As part of this, energies have been calculated at a variety of optimisation levels. The overall aim is to explore the various facilities available as part of the Gaussian and GaussView suite, in addition to investigating the effect that ligands and metals have on the bond lengths of ML3 structures.

To begin, the molecules of choice need to be optimised to energy minima so that the bond lengths resemble the molecule's reality.

== Optimisation of BH3 ==
BH3 was plotted in GaussView and the structure altered to have bonds 1.54, 1.55, and 1.56Å, so breaking the symmetry of the molecule. An optimisation was then conducted as follows:
* '''Method''': B3LYP
* '''Basis set''': 3-21G
* '''Calculation type''': FOPT

The optimisation completed in 55.0 seconds. Analysis of the log file yielded the following information:
<pre>
File Name PK_BH3_OPT
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 3-21G
Charge 0
Spin Singlet
E(RB3LYP) -26.46226429 a.u.
RMS Gradient Norm 0.00008851 a.u.
Imaginary Freq
Dipole Moment 0.0003 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 55.0 seconds.
</pre>

[[Media:PK_BH3_OPT.LOG|Download log file]]

The molecule was confirmed to converge.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1944 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1947 -DE/DX = -0.0002 !
! R3 R(1,4) 1.1948 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9983 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.986 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0157 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

Strangely, despite apparent convergence, the derivative for the displacements had not reached zero. It was decided not to attempt to rectify this as an additional optimisation would be run shortly after, and any concern from lack of convergence can be had at that point.

The non-D3h point group was somewhat surprising considering the apparent symmetry in the molecule. To verify, all the bond lengths and angles were inspected and reported as follows:
* '''B-H bond lengths (Å)''': 1.9445 (H2 B1), 1.9467 (H3 B1), 1.9480 (H4 B1)
* '''H-B-H bond angles (°)''': 119.986 (H2 B1 H4), 120.016 (H4 B1 H3), 119.998 (H2 B1 H3)

There is quite a significant amount of variance between the bond lengths and angles, explaining the lack of D3h group expected. The molecule is symmetric up to 3dp in the bond lengths and 1° in the angles. A superior optimisation is so required.

A second optimisation was run on the optimised structure. The parameters used are as follows;
* '''Method''': B3LYP
* '''Basis set''': 6-31G(d,p)
* '''Calculation type''': FOPT

The charge was set to 0 and the multiplicity as singlet - this was no change to what was originally specified, but was double checked at this point.

[[Media:PK_BH3_OPT_631GDP.LOG|Download log file]]

Once again, convergence was confirmed.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.068331D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0007 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9938 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0055 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

This time, all gradients have reached zero, hence despite the concern had earlier about the non-zero gradients, there is no issue with convergence when investigating the final conformation of the molecule.

The data obtained from the log file is as follows:
<pre>
File Name PK_BH3_OPT_631GDP
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532361 a.u.
RMS Gradient Norm 0.00000706 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 16.0 seconds.
</pre>

Disappointingly the point group was still found to be CS. Again, all the bond lengths and angles were reported and are as follows:
* '''B-H bond lengths (Å)''': 1.19232 (H2 B1), 1.19231 (H3 B1), 1.19231 (H4 B1)
* '''H-B-H bond angles (°)''': 119.994 (H2 B1 H4), 120.005 (H4 B1 H3), 120.001 (H2 B1 H4)

This time, the bond angles and lengths are much more in agreement, but not yet identical as was expected. Bond lengths are in agreement up to 5dp, but bond angles again 1°. It is unusual to see a dipole moment in a molecule as symmetric as this, however the minor imbalance in the molecule reported above likely leads to a minor dipole moment. CRC notes the experimental bond length as 1.1900Å<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref> which is quite close to what has been computed - the basis set provides an excellent approximation for this molecule. The difference between the computed and experimental bond lengths in the first optimisation is much larger (0.8Å), so vindicating the decision to perform a second optimisation.

== Optimisation of GaBr3 ==
GaBr3 was plotted in GaussView and the symmetry fixed to D3h within 0.00001 tolerance. Optimisation was conducted on the HPC to the LanL2DZ basis set (providing Los Alamos ECP pseudo-potentials on all atoms in the system).
* '''Method''': B3LYP
* '''Basis set''': LanL2DZ
* '''Calculation type''': FOPT
Details from the log file are reported below:

<pre>
File Name PK_GABR3_OPT_LANL2DZ
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set LANL2DZ
Charge 0
Spin Singlet
E(RB3LYP) -41.70082783 a.u.
RMS Gradient Norm 0.00000016 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group D3H
Job cpu time: 0 days 0 hours 0 minutes 13.9 seconds.
</pre>

This calculation can be viewed on Dspace: {{DOI|10042/26081}}.

Convergence was again verified:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282684D-12
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3502 -DE/DX = 0.0 !
! R2 R(1,3) 2.3502 -DE/DX = 0.0 !
! R3 R(1,4) 2.3502 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>
All gradients have reached zero, so the molecule has fully converged.

Bond lengths were 2.35018Å for all bonds, and all angles were exactly 120°. Analysis of the CRC Handbook states<ref name="crc"></ref> an experimental bond length of 2.249Å, 0.1Å is not an insignificant difference, but is reasonable considering the rather basic basis set used.

== Optimisation of BBr3 ==
As a further investigation into pseudo-potentials, a molecule of BBr3 was optimised, with full control on the basis sets used on each atom. Boron was subject to 6-31G(d,p), and the bromine atoms LanL2DZ. Calculation was run on the HPC with an overall DFT B3LYP function. The results can be seen online: {{DOI|10042/26079}} Summary data is as follows, according to the log file:

<pre>
File Name PK_BBR3_OPT_GEN
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set Gen
Charge 0
Spin Singlet
E(RB3LYP) -64.43644897 a.u.
RMS Gradient Norm 0.00001048 a.u.
Imaginary Freq
Dipole Moment 0.0003 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 20.0 seconds.
</pre>

Convergence was once again checked and found to indeed converge, with all parameters reaching a stationary point:
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000115 0.001800 YES
RMS Displacement 0.000063 0.001200 YES
Predicted change in Energy=-2.469464D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9339 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0004 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9975 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0021 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

Once again, there is a lack of symmetry in the optimised molecule, this time the molecule was not configured to have a forced D3h symmetry. This can be seen from the parameters below:
* '''Bond lengths (Å)''': 1.93393 (B1 Br2), 1.93397 (B1 Br3), 1.93401 (B1 Br4)
* '''Bond angles (°)''': 119.997 (Br4 B1 Br2), 120.000 (Br2 B1 Br3), 120.002 (Br3 B1 Br4)

The rather large dipole (compared to the 0 it should be) is likely a result of the slightly elongated B1-Br4 bond, making a net dipole in the molecule. As Br is more electronegative than H, this effect is more pronounced here than it is in BH3. The CRC handbook notes<ref name="crc"></ref> the bond length being 1.893Å, which does not exhibit a huge range from what is calculated here, showing this was a good choice of basis set. Further investigation could be made into alternative basis sets to see if a closer value is obtained.

== Summary ==
In conclusion, all the molecules mentioned previously have been optimised, and the bond lengths have been reported below and compared.

{| class="wikitable" border="1"
|+ Comparison of bond lengths for molecules in this part of the report
! Molecule !! colspan=3 | Bond lengths (M-L) Å
|-
! BH3
| 1.19232 || 1.19231 || 1.19231
|-
! GaBr3
| 2.35018 || 2.35018 || 2.35018
|-
! BBr3
| 1.93393 || 1.93397 || 1.93401
|}

An initial observation is the lack of equality in bond lengths for the two boron molecules. This is not an effect of the boron, but rather the nature of the calculation used. The gallium molecule was configured to force the stereochemistry as D3h, and hence Gaussian ensured that bond lengths are identical to create this symmetry. Thus no conclusions can be drawn from this difference.

It is possible to draw some conclusions from the difference in magnitude between the three molecules. The gallium molecule has a significantly larger bond length than either of the boron molecules - it is thought that this is due to the larger atomic radius of gallium compared to boron (one is in group 4, the other is in group 2), which, by necessity of ensuring the nuclei do not clash with each other, leads to a increased bond length. This leads to the approximate 0.4Å increase in bond length seen. The increase in bond length is not huge, as the increase in nuclear radius is quite small - hence it still remains quite close to the BBr3. If the same calculation was run on TlBr3, which is further down the group, a much larger bond length would be expected compared to BBr3.

Comparing BH3 and BBr3, we can see how a change in ligand affects the bond length. In this case, the main differences between the two ligands are in terms of the size of the nuclei and their electronegativities. While the increase in atomic radius would increase the bond length (as per the change in metal centre), the rather charge in electronegativity causes quite a large change in the bond length. This is because the electronegative atom will polarise the bond as it draws a larger share of the electron density. As a result, electron density is pulled away from the bond to the bromine atom, and when the electron density in a bond is reduced, the bond is weakened and therefore lengthened. This leads to the very large (0.7Å) increase in bond length observed.

This information also makes it possible to examine the nature of a bond. Two questions related to the work done here have been posed and answered below.

=== In some structures, GaussView does not draw bonds where we expect. Does this mean there is no bond? Why? ===
It is reported that GaussView only draws a bond depending on whether the two atoms are close enough for the bond to exist (in addition to the inevitable criteria over whether a bond can exist in a given location - for example if a transition metal has filled its coordination sphere). Hence, even if there is no bond shown, it does not necessarily mean no bond exists.

The existence of a bond depends on a number of criteria, one of which is the length, but other factors must be considered such as whether there is sufficient orbital overlap or whether the antibonding interactions at a given distance outweigh any bonding interactions. Hence, the simple distance criteria that GaussView uses is not sufficient to be absolutely sure if a bond is there or not. To fully ensure if a bond exists, it would be necessary to perform a number of additional calculations, such as investigation of the electron density contour maps and analysis of the molecular orbitals. Only these plots can show whether a bond exists or not, and hence GaussView's approximation is not sufficient proof that a bond does not exist.

=== What is a bond? ===
The IUPAC Gold Book defines a chemical bond as<ref name="goldbook-bond">A. D. McNaught and A. Wilkinson, in ''Compendium of Chemical Terminology'', Blackwell Scientific Publications, Oxford, 2nd ed., 2012, p. CT07009</ref>:
<blockquote>When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups.</blockquote>

Models have been built on top of this to describe specific kinds of bonding, the most common of which are:
* Covalent bond, in terms of a bond where each atom in the bond donates one electron, to form a two-electron bond.
* Ionic bond, a bond where negatively charged anions are electrostatically attracted to positively charged cations, leading to a stabilised arrangement compared to the ions being separate.
* Metallic bond, where positive cations of a metal are in a sea of delocalised electrons.

In the latter two cases, electrostatics are involved, and it is this combination of positive and negative charges combined which lead to a very stable and attractive combination, which massively lowers the energy of the system.

For a covalent bond, modern thinking (which also applies to a variety of inorganic compounds too) makes use of molecular orbitals, a combination of bonding and antibonding orbitals being created when atomic orbitals combine. Generally, according to the Klopman-Salem equation<ref name="klopman">G. Klopman, ''J. Am. Chem. Soc.'', 1968, '''90''', 223–234</ref><ref name="salem">L. Salem, ''J. Am. Chem. Soc.'' 1968, '''90''', 543 & 553</ref>, the bonding orbitals created are of a lower energy than the atomic orbitals they were created from. As a result of this, as these bonding orbitals are filled, the molecule is stabilised, and hence the IUPAC definition of a bond is adhered to.

There are many different ways in which this stabilisation can be created, and the methods discussed here are only a few of them (there may still be other kind of stabilising interactions as yet undiscovered). Hence, it is reasonable to argue that any interaction which causes a stabilising effect in a molecule can be deemed a chemical bond, which the terms 'single' and 'double bond' being associated with interactions of a certain magnitude.

= Part 2: Frequencies, vibrations, orbitals and energies =
On the optimised structures reported previously, a number of advanced calculations have been performed. Initially, frequency analysis has been conducted to ensure that the energies calculated are minima. Once this has been confirmed, more advanced calculations have been performed to help find out more about the nature of these compounds.

== Frequency and vibrational analysis of BH3 ==
Through use of a 6-31G(d,p) frequency analysis of the optimised BH3 structure, it is possible to identify whether a minima has been attained. Initially, the results have been compared to what was obtained from the optimisation, and the frequency results summary from the [[media:Pk-bh3-freq.log|log file]] is found below:

<pre>
File Name PK_BH3_FREQ_631GDP
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532361 a.u.
RMS Gradient Norm 0.00000702 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 18.0 seconds.
</pre>

Other than a minor change in the gradient, the results are the same as was reported previously. Convergence was again confirmed:
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000089 0.001800 YES
RMS Displacement 0.000045 0.001200 YES
Predicted change in Energy=-1.487544D-09
Optimization completed.
-- Stationary point found.
</pre>

Low frequencies were reported as
<pre>
Low frequencies --- -25.0305 -12.9079 0.0006 0.0007 0.0009 15.0420
</pre>

which are outside the range of -15 to +15 cm-1. Hence, the molecule was reoptimised with scf=conver=9 int=ultrafine keywords and a tight convergence to yield the following data in the [[media:Pk_bh3_opt_tight.log|log file]]:

<pre>
File Name PK_BH3_OPT_TIGHT_631GDP
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532360 a.u.
RMS Gradient Norm 0.00000594 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 13.0 seconds.
</pre>

Convergence was obtained on the optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000015 YES
RMS Force 0.000007 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000034 0.000040 YES
Predicted change in Energy=-7.783630D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0008 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9938 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0054 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The frequency calculation was then subsequently run, using the same keywords (but no tight setting). The [[media:Pk-bh3-freq-tight.log|log file]] reported the following data:

<pre>
File Name PK_BH3_FREQ_TIGHT_631GDP
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532360 a.u.
RMS Gradient Norm 0.00000594 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

This time there was convergence:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000086 0.001800 YES
RMS Displacement 0.000043 0.001200 YES
Predicted change in Energy=-1.187652D-09
Optimization completed.
-- Stationary point found.
</pre>

Regrettably the low frequencies were still out of range:

<pre>
Low frequencies --- -19.8568 -17.0127 -9.6394 0.0004 0.0005 0.0007
Low frequencies --- 1162.9117 1213.0852 1213.1686
</pre>

At this point the optimisation was conducted again with the same keywords and forcing a D3h symmetry. The [[media:Pk-bh3-opt-forced.log|log file]] showed:

<pre>
File Name PK_BH3_OPT_FORCED_631GDP
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532364 a.u.
RMS Gradient Norm 0.00000571 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group D3H
Job cpu time: 0 days 0 hours 0 minutes 13.0 seconds.
</pre>

with convergence:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000015 YES
RMS Force 0.000007 0.000010 YES
Maximum Displacement 0.000045 0.000060 YES
RMS Displacement 0.000030 0.000040 YES
Predicted change in Energy=-7.760436D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The frequency calculation was then run again, with the [[media:Pk-bh3-freq-forced.log|log file]] yielding:

<pre>
File Name PK_BH3_FREQ_FORCED_631GDP
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532364
RMS Gradient Norm 0.00000572
Imaginary Freq 0
Dipole Moment 0.0000
Point Group D3H
Job cpu time: 0 days 0 hours 0 minutes 18.0 seconds.
</pre>

with convergence:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000022 0.001200 YES
Predicted change in Energy=-7.723726D-10
Optimization completed.
-- Stationary point found.
</pre>

This time, the low frequencies were found to be within the allowed range.

<pre>
Low frequencies --- -14.8515 -14.8476 -11.2630 0.0012 0.0162 0.3377
Low frequencies --- 1162.9477 1213.1209 1213.1211
</pre>

Vibrations seen were of the symmetry labels A2", E', E', A1', E', E' which matches what the character tables for D3h suggests.

=== Visual representation of vibrational peaks ===
The vibrational peaks can be seen in GaussView and are shown below:

[[Image:Pk-bh3-Ir.svg]]

{| class="wikitable" border="1"
|+ Vibrations for BH3
! Mode !! Frequency (cm-1) || Intensity || Image || Symmetry (D3h point group)
|-
| 1 || 1162.95 || 92.5709
|[[Image:Pk-bh3-1.gif|200px]]
Symmetric wag of all protons.
| A"2 (according to log)
|-
| 2 || 1213.12 || 14.0537
|[[Image:Pk-bh3-2.gif|200px]]
Rock of H-B-H group with associated scissoring of third H.
| E' (according to log)
|-
| 3 || 1213.12 || 14.0532
|[[Image:Pk-bh3-3.gif|200px]]
H-B-H scissoring.
| E' (according to log)
|-
| 4 || 2582.68 || 0.0000
|[[Image:Pk-bh3-4.gif|200px]]
Symmetric stretch of all B-H bonds out in the same direction as the bond.
| A'1 (totally symmetric)
|-
| 5 || 2715.82 || 126.3288
|[[Image:Pk-bh3-5.gif|200px]]
Antisymmetric stretch of H-B-H group
| E' (according to log)
|-
| 6 || 2715.82 || 126.3227
|[[Image:Pk-bh3-6.gif|200px]]
Antisymmetric stretch of all protons.
| E' (according to log)
|}

Of note, there are only three peaks in the IR spectrum, despite there being 6 modes. One of these modes has an intensity of 0, and so it will not show up in the IR spectrum. This intensity is zero as the vibration is totally symmetric, which means there is no change in dipole moment and hence is not IR active. This still leaves 2 peaks missing. The peaks with an E' symmetry are defined as such as they are degenerate, and there are 2 pairs of 2 peaks with the same wavenumber. Hence, both peaks will appear superimposed upon eachother (due to their degeneracy), and the intensities will be added together. The result is that only one peak shows for the two modes for the same wavenumber. All missing peaks are therefore accounted for.

== Vibrational analysis for GaBr3 ==
Frequency analysis from the optimised structure of GaBr3 was conducted on the HPC and the results are available on Dspace: {{DOI|10042/26119}}.

The summary of the results is as follows.

<pre>
File Name PK_GABR3_FREQ_LANL2DZ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set LANL2DZ
Charge 0
Spin Singlet
E(RB3LYP) -41.70082783 a.u.
RMS Gradient Norm 0.00000011 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group D3H
Job cpu time: 0 days 0 hours 0 minutes 12.3 seconds.
</pre>

Convergence was confirmed
<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-6.142862D-13
Optimization completed.
-- Stationary point found.
</pre>

and all vibrations were found to be in the -15 to 15 cm-1 range:
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>

The lowest normal mode is 76.3744cm-1 which corresponds to a combined rocking and scissoring vibration, and is shown in animated form below. This almost has the same energy as the next lowest frequency and is assumed to be degenerate within the boundaries of approximation in the calculation.

[[Image:Pk-ir-gabr3.svg]]

{| class="wikitable"
|+ Vibrations for GaBr3
|-
! Mode
! Frequency (cm-1)
! Intensity
! Image
! Symmetry (D3h point group)
|-
| 1
| 76.37
| 76.38
| [[Image:Pk-gabr3-mode-1.gif|200px]]

Rocking of two bromine atoms, leading to a scissoring effect of third.
| E' (according to log)
|-
| 2
| 76.38
| 3.3447
| [[Image:Pk-gabr3-mode-2.gif|200px]]

Scissoring of two bromine atoms (Br-Ga-Br).
| E' (according to log)
|-
| 3
| 99.70
| 9.2161
| [[Image:Pk-gabr3-mode-3.gif|200px]]

Wag of all bromine atoms.
| A"2 (according to log)
|-
| 4
| 197.34
| 0.0000
| [[Image:Pk-gabr3-mode-4.gif|200px]]

Symmetric stretch of all Ga-Br bonds out in the same direction as the bond.
| A'1 (totally symmetric)
|-
| 5
| 316.18
| 57.0704
| [[Image:Pk-gabr3-mode-5.gif|200px]]

Antisymmetric stretch of Br-Ga-Br group
| E' (according to log)
|-
| 6
| 316.19
| 57.0746
| [[Image:Pk-gabr3-mode-6.gif|200px]]

Antisymmetric stretch of all bromine atoms.
| E' (according to log)
|}

Once again there are fewer peaks than modes - this is for the same reason as observed with BH3. The intensity of 0 for the 4th mode is also due to the same reason why the mode with no intensity for BH3 has no intensity.

=== Comparison to BH3 ===

{| class="wikitable"
|+ Comparisons between BH3 and GaBr3 (modes have been matched by symmetry label and similarity in appearance)
|-
! Mode
! GaBr3 Frequency (cm-1)
! GaBr3 Intensity
! GaBr3 Image
! BH3 Image
! BH3 Frequency (cm-1)
! BH3 Intensity
|-
| 1
| 76.37
| 76.38
| [[Image:Pk-gabr3-mode-1.gif|200px]]
| [[Image:Pk-bh3-2.gif|200px]]
| 1213.12
| 14.0537
|-
| 2
| 76.38
| 3.3447
| [[Image:Pk-gabr3-mode-2.gif|200px]]
| [[Image:Pk-bh3-3.gif|200px]]
| 1213.12
| 14.0532
|-
| 3
| 99.70
| 9.2161
| [[Image:Pk-gabr3-mode-3.gif|200px]]
| [[Image:Pk-bh3-1.gif|200px]]
| 1162.95
| 92.5709
|-
| 4
| 197.34
| 0.0000
| [[Image:Pk-gabr3-mode-4.gif|200px]]
| [[Image:Pk-bh3-4.gif|200px]]
| 2582.68
| 0.0000
|-
| 5
| 316.18
| 57.0704
| [[Image:Pk-gabr3-mode-5.gif|200px]]
| [[Image:Pk-bh3-5.gif|200px]]
| 2715.82
| 126.3288
|-
| 6
| 316.19
| 57.0746
| [[Image:Pk-gabr3-mode-6.gif|200px]]
| [[Image:Pk-bh3-6.gif|200px]]
| 2715.82
| 126.3227
|}

Whilst all the modes which appear in BH3 also appear in GaBr3 there are a number of significant differences:
# The modes are reordered
# The energies are much reduced for GaBr3

Initially, the intensity and wavenumber of the vibrations for GaBr3 is much smaller than BH3 - this is due to the inverse correlation between nuclei mass and the IR frequency - this is because atoms with a lower mass are easier to move around, and hence need a less energetic photon to be excited. This is likely related to the variance in intensity too. This is reflected in the IR spectra, which show a similar distribution in peaks, but the intensities for the BH3 spectra is much bigger.

Secondly, the reordering of modes is due to the same reason - the more atoms which are moved in a mode, the greater the amount of energy is needed to cause a vibration. Thus the A"2 mode has changed position as a significant increase in the amount of energy needed for this mode to oscillate is needed, more than the energy needed to make the two E' modes below it in terms of energy oscillate (as the Ga atoms in these modes do not move as much).

Otherwise the spectra are quite similar, there is an identical number of peaks with a similar distribution, and all the types of vibration seen in BH3 are also seen in GaBr3 - including identical symmetry labels. Also in both cases, there is a large gap between the A"2 and E' modes, and the other two modes. The higher energy modes in both cases are stretching modes and it may be because in doing so the electron density over the molecule is disrupted (and can potentially lead to bond breakage at long displacements as there is no electron density over the bond), which requires significantly more energy than moving the atom but keeping its displacement fixed.

=== Discussion ===

==== Why must you use the same method and basis set for both the optimisation and frequency analysis calculations? ====
The method and basis set give the conditions for the calculation used in either the optimisation or frequency analysis, more specifically the approximations used in solving the Schrodinger equation. The effect of this is that the energy you obtain during the optimisation of a molecule is specific to that method and basis set, as the energy depends on the approximations used. GaussView represents this by showing the energy in terms of the basis set and method.

Thus, when you calculate the frequency analysis, you must use the same method and basis set, as we must analyse the molecule and its energy in the same conditions that it exists in - an analogy would be to optimise in chloroform solvent and then do a frequency analysis in water - the system is different. As the approximations would be different if the models and basis sets differ, the frequency analysis would give bogus results - it would be doing a frequency analysis for a specific case on a molecule not of that case. This is especially important as at the level you optimised the molecule to, the energy the molecule reaches will be a minima, but when you then perform the frequency analysis, if you use a different method and basis set, the energy may no longer correspond to a minima, and thus the frequency analysis is meaningless.

==== What is the purpose of carrying out a frequency analysis? ====
A frequency analysis is important as it shows whether you have reached an energy minima or maxima. When the gradient is zero, it can either be at the peak or trough of a curve, as at these points the gradient is flat and <math>\frac{dy}{dx} = 0</math>. We need to know whether we are at a maximum or minimum as, in the nature of an optimisation, we are looking to find the most accurate representation of a molecule's actual state of existance, and molecules always try to minimise their energy.

In contrast, if we are at a maxima, we are at a transition state (as these are always of the highest energy). Whilst there may be times we are interested in a transition state, we are not here, and thus we must verify we are at a minimum. The frequency analysis finds the second derivative of the gradient, which is positive if we are at a minimum, or negative if we are at a maximum. Thus, by performing a frequency analysis, we can see if any of the vibrations are negative, and if none are we can be sure we are at an energy minimum. It is important to ensure we are at a minimum before we discuss results or perform further calculations.

==== What do the "Low frequencies" represent? ====
The low frequencies refer to the degrees of vibrational freedom within a molecule. For a molecule with 3 (or more) atoms, this is <math>3N-6</math>, which explains why the 4 atom molecules considered previously have 6 low frequencies. Each low frequency refers to one of the vibrational modes for the molecule, which is not necessary IR (or Raman) active, but the molecule would still exhibit this kind of vibration and hence vibrates at that frequency. This is separate to rotational and translational modes of freedom.

== Molecular orbital analysis for BH3 ==
Using the optimised and confirmed minima structure obtained earlier, the molecular orbitals for BH3 have been calculated, which also allows for calculation of NBOs.

An energy calculation was run on the HPC using the pop=full,nbo keyword and the results are available on Dspace: {{DOI|10042/26167}}.

The summary is as follows:

<pre>
File Name PK_BH3_EGY_631GDP
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532361 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 7.4 seconds.
</pre>

All data appears to be identical to the original energy calculation.

MOs 1-8 were calculated in GaussView and plotted on the MO diagram of BH3 shown below:

[[Image:Pk-bh3-mo.png|700px]]

== Molecular orbital and NBO analysis for ammonia ==
Ammonia was optimised and then a frequency calculation run as per the previous method, the choice of keywords and symmetry forcing (but to C3v) was needed in order to get the low frequencies within the acceptable range.

For the optimisation, the final data according to the [[media:Pk-nh3-opt.log|log file]] is:

<pre>
File Name PK_NH3_OPT_631GDP
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -56.55776873 a.u.
RMS Gradient Norm 0.00000323 a.u.
Imaginary Freq
Dipole Moment 1.8465 Debye
Point Group C3V
Job cpu time: 0 days 0 hours 0 minutes 27.0 seconds.
</pre>

and convergence confirmed:
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000015 YES
RMS Force 0.000004 0.000010 YES
Maximum Displacement 0.000012 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-9.846374D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

Low frequencies from the frequency calculation (which differs in energy terms by 0.00000001) [[media:Pk-nh3-freq.log|log file]] are:

<pre>
Low frequencies --- -0.0138 -0.0030 0.0013 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

which show a minima has been obtained. There were no negative frequencies.

'''Summary table:'''

<pre>
File Name PK_NH3_FREQ_631GDP
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -56.55776872 a.u.
RMS Gradient Norm 0.00000322 a.u.
Imaginary Freq 0
Dipole Moment 1.8465 Debye
Point Group C3
Job cpu time: 0 days 0 hours 0 minutes 15.0 seconds.
</pre>

with convergence:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.131338D-10
Optimization completed.
-- Stationary point found.
</pre>

Of concern, the symmetry has become C3, however there has been little change in energy, hence little change in structure, so this is assumed to be a bug in GaussView.

Now being satisfied that a minima has been reached, a MO and NBO calculation was conducted as was done on the BH3 ([[media:Pk-nh3-egy.log|log file]]). The NBO was then plotted from -1.125 to 1.125 and is shown below.

[[Image:Pk-nh3-nbo.PNG]]

'''Energy calculation summary table:'''
<pre>
Ammonia egy
File Name PK_NH3_EGY_631GDP
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -56.55776873 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 1.8465 Debye
Point Group C3V
Job cpu time: 0 days 0 hours 0 minutes 10.0 seconds.
</pre>

As expected, the electronegative nitrogen has a great degree of negative charge - as shown by the red character. The exact charges are -1.125 on the nitrogen and 0.375 on all the protons. The power of NBO for observing the charge density of a molecule is thus seen.

== Energy calculations for NH3BH3 ==
Now optimised energies for NH3 and BH3 have been found, it is now possible to calculate the energy for NH3BH3, find the difference between all three components, and therefore find the energy of association. From this point on it is assumed that the keywords used previously during optimisation are always used. Initially an optimisation was conducted at the same level as before and the [[media:Pk-nh3bh3-opt.log|log file]] reported:

<pre>
File Name PK_NH3BH3_OPT
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -83.22468909 a.u.
RMS Gradient Norm 0.00000047 a.u.
Imaginary Freq
Dipole Moment 5.5646 Debye
Point Group C3V
Job cpu time: 0 days 0 hours 1 minutes 14.0 seconds.
</pre>

and convergence checked:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000007 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.706880D-11
Optimization completed.
-- Stationary point found.
</pre>

A frequency analysis was then conducted. The [[media:Pk-nh3bh3-freq.log|log file]] reported a final energy of -83.22468909, which is identical to what was found in the optimisation, and no frequencies were negative. Low frequencies were in the acceptable range:

<pre>
Low frequencies --- -4.8361 -1.6211 -1.2960 0.0335 0.0539 0.2001
Low frequencies --- 263.3086 632.9964 638.4686
</pre>

Other summary data is as follows:

<pre>
File Name PK_NH3BH3_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -83.22468909 a.u.
RMS Gradient Norm 0.00000052 a.u.
Imaginary Freq 0
Dipole Moment 5.5646 Debye
Point Group C3V
Job cpu time: 0 days 0 hours 0 minutes 48.0 seconds.
</pre>

and convergence:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
Predicted change in Energy=-1.893142D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Calculation of association energy ===
Now that all three components are optimised to the correct level, and are all found as minima, it is possible to find the association energy.

The energies of all 3 components are (in AU):

* E(BH3)=-26.61532361
* E(NH3)=-56.55776873 -83.1730923
* E(NH3BH3)= -83.22468909
* Association energy: -0.0515967

One atomic unit is equal to one Hartree, and the conversion is equal to 1 Hartree = 2625.49962 kJ mol-1<ref name="codata">CODATA 2010</ref>, which gives a final association or dissociation energy of -135.47 kJ mol-1. This is approximately 40 kJ mol-1 below the enthalpy of formation as reported previously<ref name="assoc"> Yu. Kh. Shaulov, G. O. Shmyreva, V. S. Tubyanskaya, ''Zhurnal Fizicheskoi Khimii'', 1966, '''40''', 122</ref>. Considering there are a number of factors not considered in this calculation (for example interactions between the components during the formation or dissocation), the calculation gives a reasonable approximation to the nature of the association process.

= References =
<references />

Rep:Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158

2013-11-22T16:35:12Z

Pk1811: /* Energy calculations for NH3BH3 */

<div style="font-size: 40px"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px"><center>Introductory week 1 work</center></div>
 
<div style="font-size: 30px"><center>[[Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185|To mini project]]</center></div>
 
= Part 1: Basic optimisations and the effect of metals and ligands on bond lengths =
A variety of basic calculations and experimentation have been conducted on BH3 and a number of similar molecules, namely BBr3 and GaBr3. As part of this, energies have been calculated at a variety of optimisation levels. The overall aim is to explore the various facilities available as part of the Gaussian and GaussView suite, in addition to investigating the effect that ligands and metals have on the bond lengths of ML3 structures.

To begin, the molecules of choice need to be optimised to energy minima so that the bond lengths resemble the molecule's reality.

== Optimisation of BH3 ==
BH3 was plotted in GaussView and the structure altered to have bonds 1.54, 1.55, and 1.56Å, so breaking the symmetry of the molecule. An optimisation was then conducted as follows:
* '''Method''': B3LYP
* '''Basis set''': 3-21G
* '''Calculation type''': FOPT

The optimisation completed in 55.0 seconds. Analysis of the log file yielded the following information:
<pre>
File Name PK_BH3_OPT
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 3-21G
Charge 0
Spin Singlet
E(RB3LYP) -26.46226429 a.u.
RMS Gradient Norm 0.00008851 a.u.
Imaginary Freq
Dipole Moment 0.0003 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 55.0 seconds.
</pre>

[[Media:PK_BH3_OPT.LOG|Download log file]]

The molecule was confirmed to converge.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1944 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1947 -DE/DX = -0.0002 !
! R3 R(1,4) 1.1948 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9983 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.986 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0157 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

Strangely, despite apparent convergence, the derivative for the displacements had not reached zero. It was decided not to attempt to rectify this as an additional optimisation would be run shortly after, and any concern from lack of convergence can be had at that point.

The non-D3h point group was somewhat surprising considering the apparent symmetry in the molecule. To verify, all the bond lengths and angles were inspected and reported as follows:
* '''B-H bond lengths (Å)''': 1.9445 (H2 B1), 1.9467 (H3 B1), 1.9480 (H4 B1)
* '''H-B-H bond angles (°)''': 119.986 (H2 B1 H4), 120.016 (H4 B1 H3), 119.998 (H2 B1 H3)

There is quite a significant amount of variance between the bond lengths and angles, explaining the lack of D3h group expected. The molecule is symmetric up to 3dp in the bond lengths and 1° in the angles. A superior optimisation is so required.

A second optimisation was run on the optimised structure. The parameters used are as follows;
* '''Method''': B3LYP
* '''Basis set''': 6-31G(d,p)
* '''Calculation type''': FOPT

The charge was set to 0 and the multiplicity as singlet - this was no change to what was originally specified, but was double checked at this point.

[[Media:PK_BH3_OPT_631GDP.LOG|Download log file]]

Once again, convergence was confirmed.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.068331D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0007 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9938 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0055 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

This time, all gradients have reached zero, hence despite the concern had earlier about the non-zero gradients, there is no issue with convergence when investigating the final conformation of the molecule.

The data obtained from the log file is as follows:
<pre>
File Name PK_BH3_OPT_631GDP
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532361 a.u.
RMS Gradient Norm 0.00000706 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 16.0 seconds.
</pre>

Disappointingly the point group was still found to be CS. Again, all the bond lengths and angles were reported and are as follows:
* '''B-H bond lengths (Å)''': 1.19232 (H2 B1), 1.19231 (H3 B1), 1.19231 (H4 B1)
* '''H-B-H bond angles (°)''': 119.994 (H2 B1 H4), 120.005 (H4 B1 H3), 120.001 (H2 B1 H4)

This time, the bond angles and lengths are much more in agreement, but not yet identical as was expected. Bond lengths are in agreement up to 5dp, but bond angles again 1°. It is unusual to see a dipole moment in a molecule as symmetric as this, however the minor imbalance in the molecule reported above likely leads to a minor dipole moment. CRC notes the experimental bond length as 1.1900Å<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref> which is quite close to what has been computed - the basis set provides an excellent approximation for this molecule. The difference between the computed and experimental bond lengths in the first optimisation is much larger (0.8Å), so vindicating the decision to perform a second optimisation.

== Optimisation of GaBr3 ==
GaBr3 was plotted in GaussView and the symmetry fixed to D3h within 0.00001 tolerance. Optimisation was conducted on the HPC to the LanL2DZ basis set (providing Los Alamos ECP pseudo-potentials on all atoms in the system).
* '''Method''': B3LYP
* '''Basis set''': LanL2DZ
* '''Calculation type''': FOPT
Details from the log file are reported below:

<pre>
File Name PK_GABR3_OPT_LANL2DZ
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set LANL2DZ
Charge 0
Spin Singlet
E(RB3LYP) -41.70082783 a.u.
RMS Gradient Norm 0.00000016 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group D3H
Job cpu time: 0 days 0 hours 0 minutes 13.9 seconds.
</pre>

This calculation can be viewed on Dspace: {{DOI|10042/26081}}.

Convergence was again verified:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282684D-12
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3502 -DE/DX = 0.0 !
! R2 R(1,3) 2.3502 -DE/DX = 0.0 !
! R3 R(1,4) 2.3502 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>
All gradients have reached zero, so the molecule has fully converged.

Bond lengths were 2.35018Å for all bonds, and all angles were exactly 120°. Analysis of the CRC Handbook states<ref name="crc"></ref> an experimental bond length of 2.249Å, 0.1Å is not an insignificant difference, but is reasonable considering the rather basic basis set used.

== Optimisation of BBr3 ==
As a further investigation into pseudo-potentials, a molecule of BBr3 was optimised, with full control on the basis sets used on each atom. Boron was subject to 6-31G(d,p), and the bromine atoms LanL2DZ. Calculation was run on the HPC with an overall DFT B3LYP function. The results can be seen online: {{DOI|10042/26079}} Summary data is as follows, according to the log file:

<pre>
File Name PK_BBR3_OPT_GEN
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set Gen
Charge 0
Spin Singlet
E(RB3LYP) -64.43644897 a.u.
RMS Gradient Norm 0.00001048 a.u.
Imaginary Freq
Dipole Moment 0.0003 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 20.0 seconds.
</pre>

Convergence was once again checked and found to indeed converge, with all parameters reaching a stationary point:
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000115 0.001800 YES
RMS Displacement 0.000063 0.001200 YES
Predicted change in Energy=-2.469464D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9339 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0004 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9975 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0021 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

Once again, there is a lack of symmetry in the optimised molecule, this time the molecule was not configured to have a forced D3h symmetry. This can be seen from the parameters below:
* '''Bond lengths (Å)''': 1.93393 (B1 Br2), 1.93397 (B1 Br3), 1.93401 (B1 Br4)
* '''Bond angles (°)''': 119.997 (Br4 B1 Br2), 120.000 (Br2 B1 Br3), 120.002 (Br3 B1 Br4)

The rather large dipole (compared to the 0 it should be) is likely a result of the slightly elongated B1-Br4 bond, making a net dipole in the molecule. As Br is more electronegative than H, this effect is more pronounced here than it is in BH3. The CRC handbook notes<ref name="crc"></ref> the bond length being 1.893Å, which does not exhibit a huge range from what is calculated here, showing this was a good choice of basis set. Further investigation could be made into alternative basis sets to see if a closer value is obtained.

== Summary ==
In conclusion, all the molecules mentioned previously have been optimised, and the bond lengths have been reported below and compared.

{| class="wikitable" border="1"
|+ Comparison of bond lengths for molecules in this part of the report
! Molecule !! colspan=3 | Bond lengths (M-L) Å
|-
! BH3
| 1.19232 || 1.19231 || 1.19231
|-
! GaBr3
| 2.35018 || 2.35018 || 2.35018
|-
! BBr3
| 1.93393 || 1.93397 || 1.93401
|}

An initial observation is the lack of equality in bond lengths for the two boron molecules. This is not an effect of the boron, but rather the nature of the calculation used. The gallium molecule was configured to force the stereochemistry as D3h, and hence Gaussian ensured that bond lengths are identical to create this symmetry. Thus no conclusions can be drawn from this difference.

It is possible to draw some conclusions from the difference in magnitude between the three molecules. The gallium molecule has a significantly larger bond length than either of the boron molecules - it is thought that this is due to the larger atomic radius of gallium compared to boron (one is in group 4, the other is in group 2), which, by necessity of ensuring the nuclei do not clash with each other, leads to a increased bond length. This leads to the approximate 0.4Å increase in bond length seen. The increase in bond length is not huge, as the increase in nuclear radius is quite small - hence it still remains quite close to the BBr3. If the same calculation was run on TlBr3, which is further down the group, a much larger bond length would be expected compared to BBr3.

Comparing BH3 and BBr3, we can see how a change in ligand affects the bond length. In this case, the main differences between the two ligands are in terms of the size of the nuclei and their electronegativities. While the increase in atomic radius would increase the bond length (as per the change in metal centre), the rather charge in electronegativity causes quite a large change in the bond length. This is because the electronegative atom will polarise the bond as it draws a larger share of the electron density. As a result, electron density is pulled away from the bond to the bromine atom, and when the electron density in a bond is reduced, the bond is weakened and therefore lengthened. This leads to the very large (0.7Å) increase in bond length observed.

This information also makes it possible to examine the nature of a bond. Two questions related to the work done here have been posed and answered below.

=== In some structures, GaussView does not draw bonds where we expect. Does this mean there is no bond? Why? ===
It is reported that GaussView only draws a bond depending on whether the two atoms are close enough for the bond to exist (in addition to the inevitable criteria over whether a bond can exist in a given location - for example if a transition metal has filled its coordination sphere). Hence, even if there is no bond shown, it does not necessarily mean no bond exists.

The existence of a bond depends on a number of criteria, one of which is the length, but other factors must be considered such as whether there is sufficient orbital overlap or whether the antibonding interactions at a given distance outweigh any bonding interactions. Hence, the simple distance criteria that GaussView uses is not sufficient to be absolutely sure if a bond is there or not. To fully ensure if a bond exists, it would be necessary to perform a number of additional calculations, such as investigation of the electron density contour maps and analysis of the molecular orbitals. Only these plots can show whether a bond exists or not, and hence GaussView's approximation is not sufficient proof that a bond does not exist.

=== What is a bond? ===
The IUPAC Gold Book defines a chemical bond as<ref name="goldbook-bond">A. D. McNaught and A. Wilkinson, in ''Compendium of Chemical Terminology'', Blackwell Scientific Publications, Oxford, 2nd ed., 2012, p. CT07009</ref>:
<blockquote>When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups.</blockquote>

Models have been built on top of this to describe specific kinds of bonding, the most common of which are:
* Covalent bond, in terms of a bond where each atom in the bond donates one electron, to form a two-electron bond.
* Ionic bond, a bond where negatively charged anions are electrostatically attracted to positively charged cations, leading to a stabilised arrangement compared to the ions being separate.
* Metallic bond, where positive cations of a metal are in a sea of delocalised electrons.

In the latter two cases, electrostatics are involved, and it is this combination of positive and negative charges combined which lead to a very stable and attractive combination, which massively lowers the energy of the system.

For a covalent bond, modern thinking (which also applies to a variety of inorganic compounds too) makes use of molecular orbitals, a combination of bonding and antibonding orbitals being created when atomic orbitals combine. Generally, according to the Klopman-Salem equation<ref name="klopman">G. Klopman, ''J. Am. Chem. Soc.'', 1968, '''90''', 223–234</ref><ref name="salem">L. Salem, ''J. Am. Chem. Soc.'' 1968, '''90''', 543 & 553</ref>, the bonding orbitals created are of a lower energy than the atomic orbitals they were created from. As a result of this, as these bonding orbitals are filled, the molecule is stabilised, and hence the IUPAC definition of a bond is adhered to.

There are many different ways in which this stabilisation can be created, and the methods discussed here are only a few of them (there may still be other kind of stabilising interactions as yet undiscovered). Hence, it is reasonable to argue that any interaction which causes a stabilising effect in a molecule can be deemed a chemical bond, which the terms 'single' and 'double bond' being associated with interactions of a certain magnitude.

= Part 2: Frequencies, vibrations, orbitals and energies =
On the optimised structures reported previously, a number of advanced calculations have been performed. Initially, frequency analysis has been conducted to ensure that the energies calculated are minima. Once this has been confirmed, more advanced calculations have been performed to help find out more about the nature of these compounds.

== Frequency and vibrational analysis of BH3 ==
Through use of a 6-31G(d,p) frequency analysis of the optimised BH3 structure, it is possible to identify whether a minima has been attained. Initially, the results have been compared to what was obtained from the optimisation, and the frequency results summary from the [[media:Pk-bh3-freq.log|log file]] is found below:

<pre>
File Name PK_BH3_FREQ_631GDP
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532361 a.u.
RMS Gradient Norm 0.00000702 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 18.0 seconds.
</pre>

Other than a minor change in the gradient, the results are the same as was reported previously. Convergence was again confirmed:
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000089 0.001800 YES
RMS Displacement 0.000045 0.001200 YES
Predicted change in Energy=-1.487544D-09
Optimization completed.
-- Stationary point found.
</pre>

Low frequencies were reported as
<pre>
Low frequencies --- -25.0305 -12.9079 0.0006 0.0007 0.0009 15.0420
</pre>

which are outside the range of -15 to +15 cm-1. Hence, the molecule was reoptimised with scf=conver=9 int=ultrafine keywords and a tight convergence to yield the following data in the [[media:Pk_bh3_opt_tight.log|log file]]:

<pre>
File Name PK_BH3_OPT_TIGHT_631GDP
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532360 a.u.
RMS Gradient Norm 0.00000594 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 13.0 seconds.
</pre>

Convergence was obtained on the optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000015 YES
RMS Force 0.000007 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000034 0.000040 YES
Predicted change in Energy=-7.783630D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0008 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9938 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0054 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The frequency calculation was then subsequently run, using the same keywords (but no tight setting). The [[media:Pk-bh3-freq-tight.log|log file]] reported the following data:

<pre>
File Name PK_BH3_FREQ_TIGHT_631GDP
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532360 a.u.
RMS Gradient Norm 0.00000594 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

This time there was convergence:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000086 0.001800 YES
RMS Displacement 0.000043 0.001200 YES
Predicted change in Energy=-1.187652D-09
Optimization completed.
-- Stationary point found.
</pre>

Regrettably the low frequencies were still out of range:

<pre>
Low frequencies --- -19.8568 -17.0127 -9.6394 0.0004 0.0005 0.0007
Low frequencies --- 1162.9117 1213.0852 1213.1686
</pre>

At this point the optimisation was conducted again with the same keywords and forcing a D3h symmetry. The [[media:Pk-bh3-opt-forced.log|log file]] showed:

<pre>
File Name PK_BH3_OPT_FORCED_631GDP
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532364 a.u.
RMS Gradient Norm 0.00000571 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group D3H
Job cpu time: 0 days 0 hours 0 minutes 13.0 seconds.
</pre>

with convergence:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000015 YES
RMS Force 0.000007 0.000010 YES
Maximum Displacement 0.000045 0.000060 YES
RMS Displacement 0.000030 0.000040 YES
Predicted change in Energy=-7.760436D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The frequency calculation was then run again, with the [[media:Pk-bh3-freq-forced.log|log file]] yielding:

<pre>
File Name PK_BH3_FREQ_FORCED_631GDP
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532364
RMS Gradient Norm 0.00000572
Imaginary Freq 0
Dipole Moment 0.0000
Point Group D3H
Job cpu time: 0 days 0 hours 0 minutes 18.0 seconds.
</pre>

with convergence:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000022 0.001200 YES
Predicted change in Energy=-7.723726D-10
Optimization completed.
-- Stationary point found.
</pre>

This time, the low frequencies were found to be within the allowed range.

<pre>
Low frequencies --- -14.8515 -14.8476 -11.2630 0.0012 0.0162 0.3377
Low frequencies --- 1162.9477 1213.1209 1213.1211
</pre>

Vibrations seen were of the symmetry labels A2", E', E', A1', E', E' which matches what the character tables for D3h suggests.

=== Visual representation of vibrational peaks ===
The vibrational peaks can be seen in GaussView and are shown below:

[[Image:Pk-bh3-Ir.svg]]

{| class="wikitable" border="1"
|+ Vibrations for BH3
! Mode !! Frequency (cm-1) || Intensity || Image || Symmetry (D3h point group)
|-
| 1 || 1162.95 || 92.5709
|[[Image:Pk-bh3-1.gif|200px]]
Symmetric wag of all protons.
| A"2 (according to log)
|-
| 2 || 1213.12 || 14.0537
|[[Image:Pk-bh3-2.gif|200px]]
Rock of H-B-H group with associated scissoring of third H.
| E' (according to log)
|-
| 3 || 1213.12 || 14.0532
|[[Image:Pk-bh3-3.gif|200px]]
H-B-H scissoring.
| E' (according to log)
|-
| 4 || 2582.68 || 0.0000
|[[Image:Pk-bh3-4.gif|200px]]
Symmetric stretch of all B-H bonds out in the same direction as the bond.
| A'1 (totally symmetric)
|-
| 5 || 2715.82 || 126.3288
|[[Image:Pk-bh3-5.gif|200px]]
Antisymmetric stretch of H-B-H group
| E' (according to log)
|-
| 6 || 2715.82 || 126.3227
|[[Image:Pk-bh3-6.gif|200px]]
Antisymmetric stretch of all protons.
| E' (according to log)
|}

Of note, there are only three peaks in the IR spectrum, despite there being 6 modes. One of these modes has an intensity of 0, and so it will not show up in the IR spectrum. This intensity is zero as the vibration is totally symmetric, which means there is no change in dipole moment and hence is not IR active. This still leaves 2 peaks missing. The peaks with an E' symmetry are defined as such as they are degenerate, and there are 2 pairs of 2 peaks with the same wavenumber. Hence, both peaks will appear superimposed upon eachother (due to their degeneracy), and the intensities will be added together. The result is that only one peak shows for the two modes for the same wavenumber. All missing peaks are therefore accounted for.

== Vibrational analysis for GaBr3 ==
Frequency analysis from the optimised structure of GaBr3 was conducted on the HPC and the results are available on Dspace: {{DOI|10042/26119}}.

The summary of the results is as follows.

<pre>
File Name PK_GABR3_FREQ_LANL2DZ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set LANL2DZ
Charge 0
Spin Singlet
E(RB3LYP) -41.70082783 a.u.
RMS Gradient Norm 0.00000011 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group D3H
Job cpu time: 0 days 0 hours 0 minutes 12.3 seconds.
</pre>

Convergence was confirmed
<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-6.142862D-13
Optimization completed.
-- Stationary point found.
</pre>

and all vibrations were found to be in the -15 to 15 cm-1 range:
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>

The lowest normal mode is 76.3744cm-1 which corresponds to a combined rocking and scissoring vibration, and is shown in animated form below. This almost has the same energy as the next lowest frequency and is assumed to be degenerate within the boundaries of approximation in the calculation.

[[Image:Pk-ir-gabr3.svg]]

{| class="wikitable"
|+ Vibrations for GaBr3
|-
! Mode
! Frequency (cm-1)
! Intensity
! Image
! Symmetry (D3h point group)
|-
| 1
| 76.37
| 76.38
| [[Image:Pk-gabr3-mode-1.gif|200px]]

Rocking of two bromine atoms, leading to a scissoring effect of third.
| E' (according to log)
|-
| 2
| 76.38
| 3.3447
| [[Image:Pk-gabr3-mode-2.gif|200px]]

Scissoring of two bromine atoms (Br-Ga-Br).
| E' (according to log)
|-
| 3
| 99.70
| 9.2161
| [[Image:Pk-gabr3-mode-3.gif|200px]]

Wag of all bromine atoms.
| A"2 (according to log)
|-
| 4
| 197.34
| 0.0000
| [[Image:Pk-gabr3-mode-4.gif|200px]]

Symmetric stretch of all Ga-Br bonds out in the same direction as the bond.
| A'1 (totally symmetric)
|-
| 5
| 316.18
| 57.0704
| [[Image:Pk-gabr3-mode-5.gif|200px]]

Antisymmetric stretch of Br-Ga-Br group
| E' (according to log)
|-
| 6
| 316.19
| 57.0746
| [[Image:Pk-gabr3-mode-6.gif|200px]]

Antisymmetric stretch of all bromine atoms.
| E' (according to log)
|}

Once again there are fewer peaks than modes - this is for the same reason as observed with BH3. The intensity of 0 for the 4th mode is also due to the same reason why the mode with no intensity for BH3 has no intensity.

=== Comparison to BH3 ===

{| class="wikitable"
|+ Comparisons between BH3 and GaBr3 (modes have been matched by symmetry label and similarity in appearance)
|-
! Mode
! GaBr3 Frequency (cm-1)
! GaBr3 Intensity
! GaBr3 Image
! BH3 Image
! BH3 Frequency (cm-1)
! BH3 Intensity
|-
| 1
| 76.37
| 76.38
| [[Image:Pk-gabr3-mode-1.gif|200px]]
| [[Image:Pk-bh3-2.gif|200px]]
| 1213.12
| 14.0537
|-
| 2
| 76.38
| 3.3447
| [[Image:Pk-gabr3-mode-2.gif|200px]]
| [[Image:Pk-bh3-3.gif|200px]]
| 1213.12
| 14.0532
|-
| 3
| 99.70
| 9.2161
| [[Image:Pk-gabr3-mode-3.gif|200px]]
| [[Image:Pk-bh3-1.gif|200px]]
| 1162.95
| 92.5709
|-
| 4
| 197.34
| 0.0000
| [[Image:Pk-gabr3-mode-4.gif|200px]]
| [[Image:Pk-bh3-4.gif|200px]]
| 2582.68
| 0.0000
|-
| 5
| 316.18
| 57.0704
| [[Image:Pk-gabr3-mode-5.gif|200px]]
| [[Image:Pk-bh3-5.gif|200px]]
| 2715.82
| 126.3288
|-
| 6
| 316.19
| 57.0746
| [[Image:Pk-gabr3-mode-6.gif|200px]]
| [[Image:Pk-bh3-6.gif|200px]]
| 2715.82
| 126.3227
|}

Whilst all the modes which appear in BH3 also appear in GaBr3 there are a number of significant differences:
# The modes are reordered
# The energies are much reduced for GaBr3

Initially, the intensity and wavenumber of the vibrations for GaBr3 is much smaller than BH3 - this is due to the inverse correlation between nuclei mass and the IR frequency - this is because atoms with a lower mass are easier to move around, and hence need a less energetic photon to be excited. This is likely related to the variance in intensity too. This is reflected in the IR spectra, which show a similar distribution in peaks, but the intensities for the BH3 spectra is much bigger.

Secondly, the reordering of modes is due to the same reason - the more atoms which are moved in a mode, the greater the amount of energy is needed to cause a vibration. Thus the A"2 mode has changed position as a significant increase in the amount of energy needed for this mode to oscillate is needed, more than the energy needed to make the two E' modes below it in terms of energy oscillate (as the Ga atoms in these modes do not move as much).

Otherwise the spectra are quite similar, there is an identical number of peaks with a similar distribution, and all the types of vibration seen in BH3 are also seen in GaBr3 - including identical symmetry labels. Also in both cases, there is a large gap between the A"2 and E' modes, and the other two modes. The higher energy modes in both cases are stretching modes and it may be because in doing so the electron density over the molecule is disrupted (and can potentially lead to bond breakage at long displacements as there is no electron density over the bond), which requires significantly more energy than moving the atom but keeping its displacement fixed.

=== Discussion ===

==== Why must you use the same method and basis set for both the optimisation and frequency analysis calculations? ====
The method and basis set give the conditions for the calculation used in either the optimisation or frequency analysis, more specifically the approximations used in solving the Schrodinger equation. The effect of this is that the energy you obtain during the optimisation of a molecule is specific to that method and basis set, as the energy depends on the approximations used. GaussView represents this by showing the energy in terms of the basis set and method.

Thus, when you calculate the frequency analysis, you must use the same method and basis set, as we must analyse the molecule and its energy in the same conditions that it exists in - an analogy would be to optimise in chloroform solvent and then do a frequency analysis in water - the system is different. As the approximations would be different if the models and basis sets differ, the frequency analysis would give bogus results - it would be doing a frequency analysis for a specific case on a molecule not of that case. This is especially important as at the level you optimised the molecule to, the energy the molecule reaches will be a minima, but when you then perform the frequency analysis, if you use a different method and basis set, the energy may no longer correspond to a minima, and thus the frequency analysis is meaningless.

==== What is the purpose of carrying out a frequency analysis? ====
A frequency analysis is important as it shows whether you have reached an energy minima or maxima. When the gradient is zero, it can either be at the peak or trough of a curve, as at these points the gradient is flat and <math>\frac{dy}{dx} = 0</math>. We need to know whether we are at a maximum or minimum as, in the nature of an optimisation, we are looking to find the most accurate representation of a molecule's actual state of existance, and molecules always try to minimise their energy.

In contrast, if we are at a maxima, we are at a transition state (as these are always of the highest energy). Whilst there may be times we are interested in a transition state, we are not here, and thus we must verify we are at a minimum. The frequency analysis finds the second derivative of the gradient, which is positive if we are at a minimum, or negative if we are at a maximum. Thus, by performing a frequency analysis, we can see if any of the vibrations are negative, and if none are we can be sure we are at an energy minimum. It is important to ensure we are at a minimum before we discuss results or perform further calculations.

==== What do the "Low frequencies" represent? ====
The low frequencies refer to the degrees of vibrational freedom within a molecule. For a molecule with 3 (or more) atoms, this is <math>3N-6</math>, which explains why the 4 atom molecules considered previously have 6 low frequencies. Each low frequency refers to one of the vibrational modes for the molecule, which is not necessary IR (or Raman) active, but the molecule would still exhibit this kind of vibration and hence vibrates at that frequency. This is separate to rotational and translational modes of freedom.

== Molecular orbital analysis for BH3 ==
Using the optimised and confirmed minima structure obtained earlier, the molecular orbitals for BH3 have been calculated, which also allows for calculation of NBOs.

An energy calculation was run on the HPC using the pop=full,nbo keyword and the results are available on Dspace: {{DOI|10042/26167}}.

The summary is as follows:

<pre>
File Name PK_BH3_EGY_631GDP
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532361 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 7.4 seconds.
</pre>

All data appears to be identical to the original energy calculation.

MOs 1-8 were calculated in GaussView and plotted on the MO diagram of BH3 shown below:

[[Image:Pk-bh3-mo.png|700px]]

== Molecular orbital and NBO analysis for ammonia ==
Ammonia was optimised and then a frequency calculation run as per the previous method, the choice of keywords and symmetry forcing (but to C3v) was needed in order to get the low frequencies within the acceptable range.

For the optimisation, the final data according to the [[media:Pk-nh3-opt.log|log file]] is:

<pre>
File Name PK_NH3_OPT_631GDP
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -56.55776873 a.u.
RMS Gradient Norm 0.00000323 a.u.
Imaginary Freq
Dipole Moment 1.8465 Debye
Point Group C3V
Job cpu time: 0 days 0 hours 0 minutes 27.0 seconds.
</pre>

and convergence confirmed:
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000015 YES
RMS Force 0.000004 0.000010 YES
Maximum Displacement 0.000012 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-9.846374D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

Low frequencies from the frequency calculation (which differs in energy terms by 0.00000001) [[media:Pk-nh3-freq.log|log file]] are:

<pre>
Low frequencies --- -0.0138 -0.0030 0.0013 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

which show a minima has been obtained. There were no negative frequencies.

'''Summary table:'''

<pre>
File Name PK_NH3_FREQ_631GDP
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -56.55776872 a.u.
RMS Gradient Norm 0.00000322 a.u.
Imaginary Freq 0
Dipole Moment 1.8465 Debye
Point Group C3
Job cpu time: 0 days 0 hours 0 minutes 15.0 seconds.
</pre>

Of concern, the symmetry has become C3, however there has been little change in energy, hence little change in structure, so this is assumed to be a bug in GaussView.

Now being satisfied that a minima has been reached, a MO and NBO calculation was conducted as was done on the BH3 ([[media:Pk-nh3-egy.log|log file]]). The NBO was then plotted from -1.125 to 1.125 and is shown below.

[[Image:Pk-nh3-nbo.PNG]]

'''Energy calculation summary table:'''
<pre>
Ammonia egy
File Name PK_NH3_EGY_631GDP
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -56.55776873 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 1.8465 Debye
Point Group C3V
Job cpu time: 0 days 0 hours 0 minutes 10.0 seconds.
</pre>

As expected, the electronegative nitrogen has a great degree of negative charge - as shown by the red character. The exact charges are -1.125 on the nitrogen and 0.375 on all the protons. The power of NBO for observing the charge density of a molecule is thus seen.

== Energy calculations for NH3BH3 ==
Now optimised energies for NH3 and BH3 have been found, it is now possible to calculate the energy for NH3BH3, find the difference between all three components, and therefore find the energy of association. From this point on it is assumed that the keywords used previously during optimisation are always used. Initially an optimisation was conducted at the same level as before and the [[media:Pk-nh3bh3-opt.log|log file]] reported:

<pre>
File Name PK_NH3BH3_OPT
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -83.22468909 a.u.
RMS Gradient Norm 0.00000047 a.u.
Imaginary Freq
Dipole Moment 5.5646 Debye
Point Group C3V
Job cpu time: 0 days 0 hours 1 minutes 14.0 seconds.
</pre>

and convergence checked:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000007 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.706880D-11
Optimization completed.
-- Stationary point found.
</pre>

A frequency analysis was then conducted. The [[media:Pk-nh3bh3-freq.log|log file]] reported a final energy of -83.22468909, which is identical to what was found in the optimisation, and no frequencies were negative. Low frequencies were in the acceptable range:

<pre>
Low frequencies --- -4.8361 -1.6211 -1.2960 0.0335 0.0539 0.2001
Low frequencies --- 263.3086 632.9964 638.4686
</pre>

Other summary data is as follows:

<pre>
File Name PK_NH3BH3_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -83.22468909 a.u.
RMS Gradient Norm 0.00000052 a.u.
Imaginary Freq 0
Dipole Moment 5.5646 Debye
Point Group C3V
Job cpu time: 0 days 0 hours 0 minutes 48.0 seconds.
</pre>

=== Calculation of association energy ===
Now that all three components are optimised to the correct level, and are all found as minima, it is possible to find the association energy.

The energies of all 3 components are (in AU):

* E(BH3)=-26.61532361
* E(NH3)=-56.55776873 -83.1730923
* E(NH3BH3)= -83.22468909
* Association energy: -0.0515967

One atomic unit is equal to one Hartree, and the conversion is equal to 1 Hartree = 2625.49962 kJ mol-1<ref name="codata">CODATA 2010</ref>, which gives a final association or dissociation energy of -135.47 kJ mol-1. This is approximately 40 kJ mol-1 below the enthalpy of formation as reported previously<ref name="assoc"> Yu. Kh. Shaulov, G. O. Shmyreva, V. S. Tubyanskaya, ''Zhurnal Fizicheskoi Khimii'', 1966, '''40''', 122</ref>. Considering there are a number of factors not considered in this calculation (for example interactions between the components during the formation or dissocation), the calculation gives a reasonable approximation to the nature of the association process.

= References =
<references />

Rep:Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158

2013-11-22T16:26:07Z

Pk1811:

<div style="font-size: 40px"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px"><center>Introductory week 1 work</center></div>
 
<div style="font-size: 30px"><center>[[Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185|To mini project]]</center></div>
 
= Part 1: Basic optimisations and the effect of metals and ligands on bond lengths =
A variety of basic calculations and experimentation have been conducted on BH3 and a number of similar molecules, namely BBr3 and GaBr3. As part of this, energies have been calculated at a variety of optimisation levels. The overall aim is to explore the various facilities available as part of the Gaussian and GaussView suite, in addition to investigating the effect that ligands and metals have on the bond lengths of ML3 structures.

To begin, the molecules of choice need to be optimised to energy minima so that the bond lengths resemble the molecule's reality.

== Optimisation of BH3 ==
BH3 was plotted in GaussView and the structure altered to have bonds 1.54, 1.55, and 1.56Å, so breaking the symmetry of the molecule. An optimisation was then conducted as follows:
* '''Method''': B3LYP
* '''Basis set''': 3-21G
* '''Calculation type''': FOPT

The optimisation completed in 55.0 seconds. Analysis of the log file yielded the following information:
<pre>
File Name PK_BH3_OPT
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 3-21G
Charge 0
Spin Singlet
E(RB3LYP) -26.46226429 a.u.
RMS Gradient Norm 0.00008851 a.u.
Imaginary Freq
Dipole Moment 0.0003 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 55.0 seconds.
</pre>

[[Media:PK_BH3_OPT.LOG|Download log file]]

The molecule was confirmed to converge.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1944 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1947 -DE/DX = -0.0002 !
! R3 R(1,4) 1.1948 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9983 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.986 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0157 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

Strangely, despite apparent convergence, the derivative for the displacements had not reached zero. It was decided not to attempt to rectify this as an additional optimisation would be run shortly after, and any concern from lack of convergence can be had at that point.

The non-D3h point group was somewhat surprising considering the apparent symmetry in the molecule. To verify, all the bond lengths and angles were inspected and reported as follows:
* '''B-H bond lengths (Å)''': 1.9445 (H2 B1), 1.9467 (H3 B1), 1.9480 (H4 B1)
* '''H-B-H bond angles (°)''': 119.986 (H2 B1 H4), 120.016 (H4 B1 H3), 119.998 (H2 B1 H3)

There is quite a significant amount of variance between the bond lengths and angles, explaining the lack of D3h group expected. The molecule is symmetric up to 3dp in the bond lengths and 1° in the angles. A superior optimisation is so required.

A second optimisation was run on the optimised structure. The parameters used are as follows;
* '''Method''': B3LYP
* '''Basis set''': 6-31G(d,p)
* '''Calculation type''': FOPT

The charge was set to 0 and the multiplicity as singlet - this was no change to what was originally specified, but was double checked at this point.

[[Media:PK_BH3_OPT_631GDP.LOG|Download log file]]

Once again, convergence was confirmed.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.068331D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0007 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9938 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0055 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

This time, all gradients have reached zero, hence despite the concern had earlier about the non-zero gradients, there is no issue with convergence when investigating the final conformation of the molecule.

The data obtained from the log file is as follows:
<pre>
File Name PK_BH3_OPT_631GDP
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532361 a.u.
RMS Gradient Norm 0.00000706 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 16.0 seconds.
</pre>

Disappointingly the point group was still found to be CS. Again, all the bond lengths and angles were reported and are as follows:
* '''B-H bond lengths (Å)''': 1.19232 (H2 B1), 1.19231 (H3 B1), 1.19231 (H4 B1)
* '''H-B-H bond angles (°)''': 119.994 (H2 B1 H4), 120.005 (H4 B1 H3), 120.001 (H2 B1 H4)

This time, the bond angles and lengths are much more in agreement, but not yet identical as was expected. Bond lengths are in agreement up to 5dp, but bond angles again 1°. It is unusual to see a dipole moment in a molecule as symmetric as this, however the minor imbalance in the molecule reported above likely leads to a minor dipole moment. CRC notes the experimental bond length as 1.1900Å<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref> which is quite close to what has been computed - the basis set provides an excellent approximation for this molecule. The difference between the computed and experimental bond lengths in the first optimisation is much larger (0.8Å), so vindicating the decision to perform a second optimisation.

== Optimisation of GaBr3 ==
GaBr3 was plotted in GaussView and the symmetry fixed to D3h within 0.00001 tolerance. Optimisation was conducted on the HPC to the LanL2DZ basis set (providing Los Alamos ECP pseudo-potentials on all atoms in the system).
* '''Method''': B3LYP
* '''Basis set''': LanL2DZ
* '''Calculation type''': FOPT
Details from the log file are reported below:

<pre>
File Name PK_GABR3_OPT_LANL2DZ
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set LANL2DZ
Charge 0
Spin Singlet
E(RB3LYP) -41.70082783 a.u.
RMS Gradient Norm 0.00000016 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group D3H
Job cpu time: 0 days 0 hours 0 minutes 13.9 seconds.
</pre>

This calculation can be viewed on Dspace: {{DOI|10042/26081}}.

Convergence was again verified:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282684D-12
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3502 -DE/DX = 0.0 !
! R2 R(1,3) 2.3502 -DE/DX = 0.0 !
! R3 R(1,4) 2.3502 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>
All gradients have reached zero, so the molecule has fully converged.

Bond lengths were 2.35018Å for all bonds, and all angles were exactly 120°. Analysis of the CRC Handbook states<ref name="crc"></ref> an experimental bond length of 2.249Å, 0.1Å is not an insignificant difference, but is reasonable considering the rather basic basis set used.

== Optimisation of BBr3 ==
As a further investigation into pseudo-potentials, a molecule of BBr3 was optimised, with full control on the basis sets used on each atom. Boron was subject to 6-31G(d,p), and the bromine atoms LanL2DZ. Calculation was run on the HPC with an overall DFT B3LYP function. The results can be seen online: {{DOI|10042/26079}} Summary data is as follows, according to the log file:

<pre>
File Name PK_BBR3_OPT_GEN
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set Gen
Charge 0
Spin Singlet
E(RB3LYP) -64.43644897 a.u.
RMS Gradient Norm 0.00001048 a.u.
Imaginary Freq
Dipole Moment 0.0003 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 20.0 seconds.
</pre>

Convergence was once again checked and found to indeed converge, with all parameters reaching a stationary point:
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000115 0.001800 YES
RMS Displacement 0.000063 0.001200 YES
Predicted change in Energy=-2.469464D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9339 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0004 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9975 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0021 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

Once again, there is a lack of symmetry in the optimised molecule, this time the molecule was not configured to have a forced D3h symmetry. This can be seen from the parameters below:
* '''Bond lengths (Å)''': 1.93393 (B1 Br2), 1.93397 (B1 Br3), 1.93401 (B1 Br4)
* '''Bond angles (°)''': 119.997 (Br4 B1 Br2), 120.000 (Br2 B1 Br3), 120.002 (Br3 B1 Br4)

The rather large dipole (compared to the 0 it should be) is likely a result of the slightly elongated B1-Br4 bond, making a net dipole in the molecule. As Br is more electronegative than H, this effect is more pronounced here than it is in BH3. The CRC handbook notes<ref name="crc"></ref> the bond length being 1.893Å, which does not exhibit a huge range from what is calculated here, showing this was a good choice of basis set. Further investigation could be made into alternative basis sets to see if a closer value is obtained.

== Summary ==
In conclusion, all the molecules mentioned previously have been optimised, and the bond lengths have been reported below and compared.

{| class="wikitable" border="1"
|+ Comparison of bond lengths for molecules in this part of the report
! Molecule !! colspan=3 | Bond lengths (M-L) Å
|-
! BH3
| 1.19232 || 1.19231 || 1.19231
|-
! GaBr3
| 2.35018 || 2.35018 || 2.35018
|-
! BBr3
| 1.93393 || 1.93397 || 1.93401
|}

An initial observation is the lack of equality in bond lengths for the two boron molecules. This is not an effect of the boron, but rather the nature of the calculation used. The gallium molecule was configured to force the stereochemistry as D3h, and hence Gaussian ensured that bond lengths are identical to create this symmetry. Thus no conclusions can be drawn from this difference.

It is possible to draw some conclusions from the difference in magnitude between the three molecules. The gallium molecule has a significantly larger bond length than either of the boron molecules - it is thought that this is due to the larger atomic radius of gallium compared to boron (one is in group 4, the other is in group 2), which, by necessity of ensuring the nuclei do not clash with each other, leads to a increased bond length. This leads to the approximate 0.4Å increase in bond length seen. The increase in bond length is not huge, as the increase in nuclear radius is quite small - hence it still remains quite close to the BBr3. If the same calculation was run on TlBr3, which is further down the group, a much larger bond length would be expected compared to BBr3.

Comparing BH3 and BBr3, we can see how a change in ligand affects the bond length. In this case, the main differences between the two ligands are in terms of the size of the nuclei and their electronegativities. While the increase in atomic radius would increase the bond length (as per the change in metal centre), the rather charge in electronegativity causes quite a large change in the bond length. This is because the electronegative atom will polarise the bond as it draws a larger share of the electron density. As a result, electron density is pulled away from the bond to the bromine atom, and when the electron density in a bond is reduced, the bond is weakened and therefore lengthened. This leads to the very large (0.7Å) increase in bond length observed.

This information also makes it possible to examine the nature of a bond. Two questions related to the work done here have been posed and answered below.

=== In some structures, GaussView does not draw bonds where we expect. Does this mean there is no bond? Why? ===
It is reported that GaussView only draws a bond depending on whether the two atoms are close enough for the bond to exist (in addition to the inevitable criteria over whether a bond can exist in a given location - for example if a transition metal has filled its coordination sphere). Hence, even if there is no bond shown, it does not necessarily mean no bond exists.

The existence of a bond depends on a number of criteria, one of which is the length, but other factors must be considered such as whether there is sufficient orbital overlap or whether the antibonding interactions at a given distance outweigh any bonding interactions. Hence, the simple distance criteria that GaussView uses is not sufficient to be absolutely sure if a bond is there or not. To fully ensure if a bond exists, it would be necessary to perform a number of additional calculations, such as investigation of the electron density contour maps and analysis of the molecular orbitals. Only these plots can show whether a bond exists or not, and hence GaussView's approximation is not sufficient proof that a bond does not exist.

=== What is a bond? ===
The IUPAC Gold Book defines a chemical bond as<ref name="goldbook-bond">A. D. McNaught and A. Wilkinson, in ''Compendium of Chemical Terminology'', Blackwell Scientific Publications, Oxford, 2nd ed., 2012, p. CT07009</ref>:
<blockquote>When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups.</blockquote>

Models have been built on top of this to describe specific kinds of bonding, the most common of which are:
* Covalent bond, in terms of a bond where each atom in the bond donates one electron, to form a two-electron bond.
* Ionic bond, a bond where negatively charged anions are electrostatically attracted to positively charged cations, leading to a stabilised arrangement compared to the ions being separate.
* Metallic bond, where positive cations of a metal are in a sea of delocalised electrons.

In the latter two cases, electrostatics are involved, and it is this combination of positive and negative charges combined which lead to a very stable and attractive combination, which massively lowers the energy of the system.

For a covalent bond, modern thinking (which also applies to a variety of inorganic compounds too) makes use of molecular orbitals, a combination of bonding and antibonding orbitals being created when atomic orbitals combine. Generally, according to the Klopman-Salem equation<ref name="klopman">G. Klopman, ''J. Am. Chem. Soc.'', 1968, '''90''', 223–234</ref><ref name="salem">L. Salem, ''J. Am. Chem. Soc.'' 1968, '''90''', 543 & 553</ref>, the bonding orbitals created are of a lower energy than the atomic orbitals they were created from. As a result of this, as these bonding orbitals are filled, the molecule is stabilised, and hence the IUPAC definition of a bond is adhered to.

There are many different ways in which this stabilisation can be created, and the methods discussed here are only a few of them (there may still be other kind of stabilising interactions as yet undiscovered). Hence, it is reasonable to argue that any interaction which causes a stabilising effect in a molecule can be deemed a chemical bond, which the terms 'single' and 'double bond' being associated with interactions of a certain magnitude.

= Part 2: Frequencies, vibrations, orbitals and energies =
On the optimised structures reported previously, a number of advanced calculations have been performed. Initially, frequency analysis has been conducted to ensure that the energies calculated are minima. Once this has been confirmed, more advanced calculations have been performed to help find out more about the nature of these compounds.

== Frequency and vibrational analysis of BH3 ==
Through use of a 6-31G(d,p) frequency analysis of the optimised BH3 structure, it is possible to identify whether a minima has been attained. Initially, the results have been compared to what was obtained from the optimisation, and the frequency results summary from the [[media:Pk-bh3-freq.log|log file]] is found below:

<pre>
File Name PK_BH3_FREQ_631GDP
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532361 a.u.
RMS Gradient Norm 0.00000702 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 18.0 seconds.
</pre>

Other than a minor change in the gradient, the results are the same as was reported previously. Convergence was again confirmed:
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000089 0.001800 YES
RMS Displacement 0.000045 0.001200 YES
Predicted change in Energy=-1.487544D-09
Optimization completed.
-- Stationary point found.
</pre>

Low frequencies were reported as
<pre>
Low frequencies --- -25.0305 -12.9079 0.0006 0.0007 0.0009 15.0420
</pre>

which are outside the range of -15 to +15 cm-1. Hence, the molecule was reoptimised with scf=conver=9 int=ultrafine keywords and a tight convergence to yield the following data in the [[media:Pk_bh3_opt_tight.log|log file]]:

<pre>
File Name PK_BH3_OPT_TIGHT_631GDP
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532360 a.u.
RMS Gradient Norm 0.00000594 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 13.0 seconds.
</pre>

Convergence was obtained on the optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000015 YES
RMS Force 0.000007 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000034 0.000040 YES
Predicted change in Energy=-7.783630D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0008 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9938 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0054 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The frequency calculation was then subsequently run, using the same keywords (but no tight setting). The [[media:Pk-bh3-freq-tight.log|log file]] reported the following data:

<pre>
File Name PK_BH3_FREQ_TIGHT_631GDP
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532360 a.u.
RMS Gradient Norm 0.00000594 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

This time there was convergence:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000086 0.001800 YES
RMS Displacement 0.000043 0.001200 YES
Predicted change in Energy=-1.187652D-09
Optimization completed.
-- Stationary point found.
</pre>

Regrettably the low frequencies were still out of range:

<pre>
Low frequencies --- -19.8568 -17.0127 -9.6394 0.0004 0.0005 0.0007
Low frequencies --- 1162.9117 1213.0852 1213.1686
</pre>

At this point the optimisation was conducted again with the same keywords and forcing a D3h symmetry. The [[media:Pk-bh3-opt-forced.log|log file]] showed:

<pre>
File Name PK_BH3_OPT_FORCED_631GDP
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532364 a.u.
RMS Gradient Norm 0.00000571 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group D3H
Job cpu time: 0 days 0 hours 0 minutes 13.0 seconds.
</pre>

with convergence:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000015 YES
RMS Force 0.000007 0.000010 YES
Maximum Displacement 0.000045 0.000060 YES
RMS Displacement 0.000030 0.000040 YES
Predicted change in Energy=-7.760436D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The frequency calculation was then run again, with the [[media:Pk-bh3-freq-forced.log|log file]] yielding:

<pre>
File Name PK_BH3_FREQ_FORCED_631GDP
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532364
RMS Gradient Norm 0.00000572
Imaginary Freq 0
Dipole Moment 0.0000
Point Group D3H
Job cpu time: 0 days 0 hours 0 minutes 18.0 seconds.
</pre>

with convergence:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000022 0.001200 YES
Predicted change in Energy=-7.723726D-10
Optimization completed.
-- Stationary point found.
</pre>

This time, the low frequencies were found to be within the allowed range.

<pre>
Low frequencies --- -14.8515 -14.8476 -11.2630 0.0012 0.0162 0.3377
Low frequencies --- 1162.9477 1213.1209 1213.1211
</pre>

Vibrations seen were of the symmetry labels A2", E', E', A1', E', E' which matches what the character tables for D3h suggests.

=== Visual representation of vibrational peaks ===
The vibrational peaks can be seen in GaussView and are shown below:

[[Image:Pk-bh3-Ir.svg]]

{| class="wikitable" border="1"
|+ Vibrations for BH3
! Mode !! Frequency (cm-1) || Intensity || Image || Symmetry (D3h point group)
|-
| 1 || 1162.95 || 92.5709
|[[Image:Pk-bh3-1.gif|200px]]
Symmetric wag of all protons.
| A"2 (according to log)
|-
| 2 || 1213.12 || 14.0537
|[[Image:Pk-bh3-2.gif|200px]]
Rock of H-B-H group with associated scissoring of third H.
| E' (according to log)
|-
| 3 || 1213.12 || 14.0532
|[[Image:Pk-bh3-3.gif|200px]]
H-B-H scissoring.
| E' (according to log)
|-
| 4 || 2582.68 || 0.0000
|[[Image:Pk-bh3-4.gif|200px]]
Symmetric stretch of all B-H bonds out in the same direction as the bond.
| A'1 (totally symmetric)
|-
| 5 || 2715.82 || 126.3288
|[[Image:Pk-bh3-5.gif|200px]]
Antisymmetric stretch of H-B-H group
| E' (according to log)
|-
| 6 || 2715.82 || 126.3227
|[[Image:Pk-bh3-6.gif|200px]]
Antisymmetric stretch of all protons.
| E' (according to log)
|}

Of note, there are only three peaks in the IR spectrum, despite there being 6 modes. One of these modes has an intensity of 0, and so it will not show up in the IR spectrum. This intensity is zero as the vibration is totally symmetric, which means there is no change in dipole moment and hence is not IR active. This still leaves 2 peaks missing. The peaks with an E' symmetry are defined as such as they are degenerate, and there are 2 pairs of 2 peaks with the same wavenumber. Hence, both peaks will appear superimposed upon eachother (due to their degeneracy), and the intensities will be added together. The result is that only one peak shows for the two modes for the same wavenumber. All missing peaks are therefore accounted for.

== Vibrational analysis for GaBr3 ==
Frequency analysis from the optimised structure of GaBr3 was conducted on the HPC and the results are available on Dspace: {{DOI|10042/26119}}.

The summary of the results is as follows.

<pre>
File Name PK_GABR3_FREQ_LANL2DZ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set LANL2DZ
Charge 0
Spin Singlet
E(RB3LYP) -41.70082783 a.u.
RMS Gradient Norm 0.00000011 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group D3H
Job cpu time: 0 days 0 hours 0 minutes 12.3 seconds.
</pre>

Convergence was confirmed
<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-6.142862D-13
Optimization completed.
-- Stationary point found.
</pre>

and all vibrations were found to be in the -15 to 15 cm-1 range:
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>

The lowest normal mode is 76.3744cm-1 which corresponds to a combined rocking and scissoring vibration, and is shown in animated form below. This almost has the same energy as the next lowest frequency and is assumed to be degenerate within the boundaries of approximation in the calculation.

[[Image:Pk-ir-gabr3.svg]]

{| class="wikitable"
|+ Vibrations for GaBr3
|-
! Mode
! Frequency (cm-1)
! Intensity
! Image
! Symmetry (D3h point group)
|-
| 1
| 76.37
| 76.38
| [[Image:Pk-gabr3-mode-1.gif|200px]]

Rocking of two bromine atoms, leading to a scissoring effect of third.
| E' (according to log)
|-
| 2
| 76.38
| 3.3447
| [[Image:Pk-gabr3-mode-2.gif|200px]]

Scissoring of two bromine atoms (Br-Ga-Br).
| E' (according to log)
|-
| 3
| 99.70
| 9.2161
| [[Image:Pk-gabr3-mode-3.gif|200px]]

Wag of all bromine atoms.
| A"2 (according to log)
|-
| 4
| 197.34
| 0.0000
| [[Image:Pk-gabr3-mode-4.gif|200px]]

Symmetric stretch of all Ga-Br bonds out in the same direction as the bond.
| A'1 (totally symmetric)
|-
| 5
| 316.18
| 57.0704
| [[Image:Pk-gabr3-mode-5.gif|200px]]

Antisymmetric stretch of Br-Ga-Br group
| E' (according to log)
|-
| 6
| 316.19
| 57.0746
| [[Image:Pk-gabr3-mode-6.gif|200px]]

Antisymmetric stretch of all bromine atoms.
| E' (according to log)
|}

Once again there are fewer peaks than modes - this is for the same reason as observed with BH3. The intensity of 0 for the 4th mode is also due to the same reason why the mode with no intensity for BH3 has no intensity.

=== Comparison to BH3 ===

{| class="wikitable"
|+ Comparisons between BH3 and GaBr3 (modes have been matched by symmetry label and similarity in appearance)
|-
! Mode
! GaBr3 Frequency (cm-1)
! GaBr3 Intensity
! GaBr3 Image
! BH3 Image
! BH3 Frequency (cm-1)
! BH3 Intensity
|-
| 1
| 76.37
| 76.38
| [[Image:Pk-gabr3-mode-1.gif|200px]]
| [[Image:Pk-bh3-2.gif|200px]]
| 1213.12
| 14.0537
|-
| 2
| 76.38
| 3.3447
| [[Image:Pk-gabr3-mode-2.gif|200px]]
| [[Image:Pk-bh3-3.gif|200px]]
| 1213.12
| 14.0532
|-
| 3
| 99.70
| 9.2161
| [[Image:Pk-gabr3-mode-3.gif|200px]]
| [[Image:Pk-bh3-1.gif|200px]]
| 1162.95
| 92.5709
|-
| 4
| 197.34
| 0.0000
| [[Image:Pk-gabr3-mode-4.gif|200px]]
| [[Image:Pk-bh3-4.gif|200px]]
| 2582.68
| 0.0000
|-
| 5
| 316.18
| 57.0704
| [[Image:Pk-gabr3-mode-5.gif|200px]]
| [[Image:Pk-bh3-5.gif|200px]]
| 2715.82
| 126.3288
|-
| 6
| 316.19
| 57.0746
| [[Image:Pk-gabr3-mode-6.gif|200px]]
| [[Image:Pk-bh3-6.gif|200px]]
| 2715.82
| 126.3227
|}

Whilst all the modes which appear in BH3 also appear in GaBr3 there are a number of significant differences:
# The modes are reordered
# The energies are much reduced for GaBr3

Initially, the intensity and wavenumber of the vibrations for GaBr3 is much smaller than BH3 - this is due to the inverse correlation between nuclei mass and the IR frequency - this is because atoms with a lower mass are easier to move around, and hence need a less energetic photon to be excited. This is likely related to the variance in intensity too. This is reflected in the IR spectra, which show a similar distribution in peaks, but the intensities for the BH3 spectra is much bigger.

Secondly, the reordering of modes is due to the same reason - the more atoms which are moved in a mode, the greater the amount of energy is needed to cause a vibration. Thus the A"2 mode has changed position as a significant increase in the amount of energy needed for this mode to oscillate is needed, more than the energy needed to make the two E' modes below it in terms of energy oscillate (as the Ga atoms in these modes do not move as much).

Otherwise the spectra are quite similar, there is an identical number of peaks with a similar distribution, and all the types of vibration seen in BH3 are also seen in GaBr3 - including identical symmetry labels. Also in both cases, there is a large gap between the A"2 and E' modes, and the other two modes. The higher energy modes in both cases are stretching modes and it may be because in doing so the electron density over the molecule is disrupted (and can potentially lead to bond breakage at long displacements as there is no electron density over the bond), which requires significantly more energy than moving the atom but keeping its displacement fixed.

=== Discussion ===

==== Why must you use the same method and basis set for both the optimisation and frequency analysis calculations? ====
The method and basis set give the conditions for the calculation used in either the optimisation or frequency analysis, more specifically the approximations used in solving the Schrodinger equation. The effect of this is that the energy you obtain during the optimisation of a molecule is specific to that method and basis set, as the energy depends on the approximations used. GaussView represents this by showing the energy in terms of the basis set and method.

Thus, when you calculate the frequency analysis, you must use the same method and basis set, as we must analyse the molecule and its energy in the same conditions that it exists in - an analogy would be to optimise in chloroform solvent and then do a frequency analysis in water - the system is different. As the approximations would be different if the models and basis sets differ, the frequency analysis would give bogus results - it would be doing a frequency analysis for a specific case on a molecule not of that case. This is especially important as at the level you optimised the molecule to, the energy the molecule reaches will be a minima, but when you then perform the frequency analysis, if you use a different method and basis set, the energy may no longer correspond to a minima, and thus the frequency analysis is meaningless.

==== What is the purpose of carrying out a frequency analysis? ====
A frequency analysis is important as it shows whether you have reached an energy minima or maxima. When the gradient is zero, it can either be at the peak or trough of a curve, as at these points the gradient is flat and <math>\frac{dy}{dx} = 0</math>. We need to know whether we are at a maximum or minimum as, in the nature of an optimisation, we are looking to find the most accurate representation of a molecule's actual state of existance, and molecules always try to minimise their energy.

In contrast, if we are at a maxima, we are at a transition state (as these are always of the highest energy). Whilst there may be times we are interested in a transition state, we are not here, and thus we must verify we are at a minimum. The frequency analysis finds the second derivative of the gradient, which is positive if we are at a minimum, or negative if we are at a maximum. Thus, by performing a frequency analysis, we can see if any of the vibrations are negative, and if none are we can be sure we are at an energy minimum. It is important to ensure we are at a minimum before we discuss results or perform further calculations.

==== What do the "Low frequencies" represent? ====
The low frequencies refer to the degrees of vibrational freedom within a molecule. For a molecule with 3 (or more) atoms, this is <math>3N-6</math>, which explains why the 4 atom molecules considered previously have 6 low frequencies. Each low frequency refers to one of the vibrational modes for the molecule, which is not necessary IR (or Raman) active, but the molecule would still exhibit this kind of vibration and hence vibrates at that frequency. This is separate to rotational and translational modes of freedom.

== Molecular orbital analysis for BH3 ==
Using the optimised and confirmed minima structure obtained earlier, the molecular orbitals for BH3 have been calculated, which also allows for calculation of NBOs.

An energy calculation was run on the HPC using the pop=full,nbo keyword and the results are available on Dspace: {{DOI|10042/26167}}.

The summary is as follows:

<pre>
File Name PK_BH3_EGY_631GDP
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532361 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 7.4 seconds.
</pre>

All data appears to be identical to the original energy calculation.

MOs 1-8 were calculated in GaussView and plotted on the MO diagram of BH3 shown below:

[[Image:Pk-bh3-mo.png|700px]]

== Molecular orbital and NBO analysis for ammonia ==
Ammonia was optimised and then a frequency calculation run as per the previous method, the choice of keywords and symmetry forcing (but to C3v) was needed in order to get the low frequencies within the acceptable range.

For the optimisation, the final data according to the [[media:Pk-nh3-opt.log|log file]] is:

<pre>
File Name PK_NH3_OPT_631GDP
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -56.55776873 a.u.
RMS Gradient Norm 0.00000323 a.u.
Imaginary Freq
Dipole Moment 1.8465 Debye
Point Group C3V
Job cpu time: 0 days 0 hours 0 minutes 27.0 seconds.
</pre>

and convergence confirmed:
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000015 YES
RMS Force 0.000004 0.000010 YES
Maximum Displacement 0.000012 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-9.846374D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

Low frequencies from the frequency calculation (which differs in energy terms by 0.00000001) [[media:Pk-nh3-freq.log|log file]] are:

<pre>
Low frequencies --- -0.0138 -0.0030 0.0013 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

which show a minima has been obtained. There were no negative frequencies.

'''Summary table:'''

<pre>
File Name PK_NH3_FREQ_631GDP
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -56.55776872 a.u.
RMS Gradient Norm 0.00000322 a.u.
Imaginary Freq 0
Dipole Moment 1.8465 Debye
Point Group C3
Job cpu time: 0 days 0 hours 0 minutes 15.0 seconds.
</pre>

Of concern, the symmetry has become C3, however there has been little change in energy, hence little change in structure, so this is assumed to be a bug in GaussView.

Now being satisfied that a minima has been reached, a MO and NBO calculation was conducted as was done on the BH3 ([[media:Pk-nh3-egy.log|log file]]). The NBO was then plotted from -1.125 to 1.125 and is shown below.

[[Image:Pk-nh3-nbo.PNG]]

'''Energy calculation summary table:'''
<pre>
Ammonia egy
File Name PK_NH3_EGY_631GDP
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -56.55776873 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 1.8465 Debye
Point Group C3V
Job cpu time: 0 days 0 hours 0 minutes 10.0 seconds.
</pre>

As expected, the electronegative nitrogen has a great degree of negative charge - as shown by the red character. The exact charges are -1.125 on the nitrogen and 0.375 on all the protons. The power of NBO for observing the charge density of a molecule is thus seen.

== Energy calculations for NH3BH3 ==
Now optimised energies for NH3 and BH3 have been found, it is now possible to calculate the energy for NH3BH3, find the difference between all three components, and therefore find the energy of association. From this point on it is assumed that the keywords used previously during optimisation are always used. Initially an optimisation was conducted at the same level as before and the [[media:Pk-nh3bh3-opt.log|log file]] reported:

<pre>
File Name PK_NH3BH3_OPT
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -83.22468909 a.u.
RMS Gradient Norm 0.00000047 a.u.
Imaginary Freq
Dipole Moment 5.5646 Debye
Point Group C3V
Job cpu time: 0 days 0 hours 1 minutes 14.0 seconds.
</pre>

and convergence checked:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000007 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.706880D-11
Optimization completed.
-- Stationary point found.
</pre>

A frequency analysis was then conducted. The [[media:Pk-nh3bh3-freq.log|log file]] reported a final energy of -83.22468909, which is identical to what was found in the optimisation, and no frequencies were negative. Low frequencies were in the acceptable range:

<pre>
Low frequencies --- -4.8361 -1.6211 -1.2960 0.0335 0.0539 0.2001
Low frequencies --- 263.3086 632.9964 638.4686
</pre>

Other summary data is as follows:

<pre>
File Name PK_NH3BH3_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -83.22468909 a.u.
RMS Gradient Norm 0.00000052 a.u.
Imaginary Freq 0
Dipole Moment 5.5646 Debye
Point Group C3V
Job cpu time: 0 days 0 hours 0 minutes 48.0 seconds.
</pre>

=== Calculation of association energy ===
Now that all three components are optimised to the correct level, and are all found as minima, it is possible to find the association energy.

The energies of all 3 components are (in AU):

* E(BH3)=-26.61532361
* E(NH3)=-56.55776873 -83.1730923
* E(NH3BH3)= -83.22468909
* Association energy: -0.0515967

One atomic unit is equal to one Hartree, and the conversion is equal to 1 Hartree = 2625.49962 kJ mol-1<ref name="codata">CODATA 2010</ref>, which gives a final association or dissociation energy of -135.47 kJ mol-1.

= References =
<references />

Rep:Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158

2013-11-22T16:25:58Z

Pk1811:

<div style="font-size: 40px"><center>Philip Kent: Inorganic Computational Lab</center></div>
<div style="font-size: 30px"><center>Introductory week 1 work</center></div>
 
<div style="font-size: 30px"><center>[[Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185|To mini project]]</center></div>
 
= Part 1: Basic optimisations and the effect of metals and ligands on bond lengths =
A variety of basic calculations and experimentation have been conducted on BH3 and a number of similar molecules, namely BBr3 and GaBr3. As part of this, energies have been calculated at a variety of optimisation levels. The overall aim is to explore the various facilities available as part of the Gaussian and GaussView suite, in addition to investigating the effect that ligands and metals have on the bond lengths of ML3 structures.

To begin, the molecules of choice need to be optimised to energy minima so that the bond lengths resemble the molecule's reality.

== Optimisation of BH3 ==
BH3 was plotted in GaussView and the structure altered to have bonds 1.54, 1.55, and 1.56Å, so breaking the symmetry of the molecule. An optimisation was then conducted as follows:
* '''Method''': B3LYP
* '''Basis set''': 3-21G
* '''Calculation type''': FOPT

The optimisation completed in 55.0 seconds. Analysis of the log file yielded the following information:
<pre>
File Name PK_BH3_OPT
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 3-21G
Charge 0
Spin Singlet
E(RB3LYP) -26.46226429 a.u.
RMS Gradient Norm 0.00008851 a.u.
Imaginary Freq
Dipole Moment 0.0003 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 55.0 seconds.
</pre>

[[Media:PK_BH3_OPT.LOG|Download log file]]

The molecule was confirmed to converge.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672479D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1944 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1947 -DE/DX = -0.0002 !
! R3 R(1,4) 1.1948 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9983 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.986 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0157 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

Strangely, despite apparent convergence, the derivative for the displacements had not reached zero. It was decided not to attempt to rectify this as an additional optimisation would be run shortly after, and any concern from lack of convergence can be had at that point.

The non-D3h point group was somewhat surprising considering the apparent symmetry in the molecule. To verify, all the bond lengths and angles were inspected and reported as follows:
* '''B-H bond lengths (Å)''': 1.9445 (H2 B1), 1.9467 (H3 B1), 1.9480 (H4 B1)
* '''H-B-H bond angles (°)''': 119.986 (H2 B1 H4), 120.016 (H4 B1 H3), 119.998 (H2 B1 H3)

There is quite a significant amount of variance between the bond lengths and angles, explaining the lack of D3h group expected. The molecule is symmetric up to 3dp in the bond lengths and 1° in the angles. A superior optimisation is so required.

A second optimisation was run on the optimised structure. The parameters used are as follows;
* '''Method''': B3LYP
* '''Basis set''': 6-31G(d,p)
* '''Calculation type''': FOPT

The charge was set to 0 and the multiplicity as singlet - this was no change to what was originally specified, but was double checked at this point.

[[Media:PK_BH3_OPT_631GDP.LOG|Download log file]]

Once again, convergence was confirmed.

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.068331D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0007 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9938 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0055 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

This time, all gradients have reached zero, hence despite the concern had earlier about the non-zero gradients, there is no issue with convergence when investigating the final conformation of the molecule.

The data obtained from the log file is as follows:
<pre>
File Name PK_BH3_OPT_631GDP
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532361 a.u.
RMS Gradient Norm 0.00000706 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 16.0 seconds.
</pre>

Disappointingly the point group was still found to be CS. Again, all the bond lengths and angles were reported and are as follows:
* '''B-H bond lengths (Å)''': 1.19232 (H2 B1), 1.19231 (H3 B1), 1.19231 (H4 B1)
* '''H-B-H bond angles (°)''': 119.994 (H2 B1 H4), 120.005 (H4 B1 H3), 120.001 (H2 B1 H4)

This time, the bond angles and lengths are much more in agreement, but not yet identical as was expected. Bond lengths are in agreement up to 5dp, but bond angles again 1°. It is unusual to see a dipole moment in a molecule as symmetric as this, however the minor imbalance in the molecule reported above likely leads to a minor dipole moment. CRC notes the experimental bond length as 1.1900Å<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref> which is quite close to what has been computed - the basis set provides an excellent approximation for this molecule. The difference between the computed and experimental bond lengths in the first optimisation is much larger (0.8Å), so vindicating the decision to perform a second optimisation.

== Optimisation of GaBr3 ==
GaBr3 was plotted in GaussView and the symmetry fixed to D3h within 0.00001 tolerance. Optimisation was conducted on the HPC to the LanL2DZ basis set (providing Los Alamos ECP pseudo-potentials on all atoms in the system).
* '''Method''': B3LYP
* '''Basis set''': LanL2DZ
* '''Calculation type''': FOPT
Details from the log file are reported below:

<pre>
File Name PK_GABR3_OPT_LANL2DZ
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set LANL2DZ
Charge 0
Spin Singlet
E(RB3LYP) -41.70082783 a.u.
RMS Gradient Norm 0.00000016 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group D3H
Job cpu time: 0 days 0 hours 0 minutes 13.9 seconds.
</pre>

This calculation can be viewed on Dspace: {{DOI|10042/26081}}.

Convergence was again verified:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES
Predicted change in Energy=-1.282684D-12
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.3502 -DE/DX = 0.0 !
! R2 R(1,3) 2.3502 -DE/DX = 0.0 !
! R3 R(1,4) 2.3502 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>
All gradients have reached zero, so the molecule has fully converged.

Bond lengths were 2.35018Å for all bonds, and all angles were exactly 120°. Analysis of the CRC Handbook states<ref name="crc"></ref> an experimental bond length of 2.249Å, 0.1Å is not an insignificant difference, but is reasonable considering the rather basic basis set used.

== Optimisation of BBr3 ==
As a further investigation into pseudo-potentials, a molecule of BBr3 was optimised, with full control on the basis sets used on each atom. Boron was subject to 6-31G(d,p), and the bromine atoms LanL2DZ. Calculation was run on the HPC with an overall DFT B3LYP function. The results can be seen online: {{DOI|10042/26079}} Summary data is as follows, according to the log file:

<pre>
File Name PK_BBR3_OPT_GEN
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set Gen
Charge 0
Spin Singlet
E(RB3LYP) -64.43644897 a.u.
RMS Gradient Norm 0.00001048 a.u.
Imaginary Freq
Dipole Moment 0.0003 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 20.0 seconds.
</pre>

Convergence was once again checked and found to indeed converge, with all parameters reaching a stationary point:
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000115 0.001800 YES
RMS Displacement 0.000063 0.001200 YES
Predicted change in Energy=-2.469464D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9339 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0004 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9975 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0021 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

Once again, there is a lack of symmetry in the optimised molecule, this time the molecule was not configured to have a forced D3h symmetry. This can be seen from the parameters below:
* '''Bond lengths (Å)''': 1.93393 (B1 Br2), 1.93397 (B1 Br3), 1.93401 (B1 Br4)
* '''Bond angles (°)''': 119.997 (Br4 B1 Br2), 120.000 (Br2 B1 Br3), 120.002 (Br3 B1 Br4)

The rather large dipole (compared to the 0 it should be) is likely a result of the slightly elongated B1-Br4 bond, making a net dipole in the molecule. As Br is more electronegative than H, this effect is more pronounced here than it is in BH3. The CRC handbook notes<ref name="crc"></ref> the bond length being 1.893Å, which does not exhibit a huge range from what is calculated here, showing this was a good choice of basis set. Further investigation could be made into alternative basis sets to see if a closer value is obtained.

== Summary ==
In conclusion, all the molecules mentioned previously have been optimised, and the bond lengths have been reported below and compared.

{| class="wikitable" border="1"
|+ Comparison of bond lengths for molecules in this part of the report
! Molecule !! colspan=3 | Bond lengths (M-L) Å
|-
! BH3
| 1.19232 || 1.19231 || 1.19231
|-
! GaBr3
| 2.35018 || 2.35018 || 2.35018
|-
! BBr3
| 1.93393 || 1.93397 || 1.93401
|}

An initial observation is the lack of equality in bond lengths for the two boron molecules. This is not an effect of the boron, but rather the nature of the calculation used. The gallium molecule was configured to force the stereochemistry as D3h, and hence Gaussian ensured that bond lengths are identical to create this symmetry. Thus no conclusions can be drawn from this difference.

It is possible to draw some conclusions from the difference in magnitude between the three molecules. The gallium molecule has a significantly larger bond length than either of the boron molecules - it is thought that this is due to the larger atomic radius of gallium compared to boron (one is in group 4, the other is in group 2), which, by necessity of ensuring the nuclei do not clash with each other, leads to a increased bond length. This leads to the approximate 0.4Å increase in bond length seen. The increase in bond length is not huge, as the increase in nuclear radius is quite small - hence it still remains quite close to the BBr3. If the same calculation was run on TlBr3, which is further down the group, a much larger bond length would be expected compared to BBr3.

Comparing BH3 and BBr3, we can see how a change in ligand affects the bond length. In this case, the main differences between the two ligands are in terms of the size of the nuclei and their electronegativities. While the increase in atomic radius would increase the bond length (as per the change in metal centre), the rather charge in electronegativity causes quite a large change in the bond length. This is because the electronegative atom will polarise the bond as it draws a larger share of the electron density. As a result, electron density is pulled away from the bond to the bromine atom, and when the electron density in a bond is reduced, the bond is weakened and therefore lengthened. This leads to the very large (0.7Å) increase in bond length observed.

This information also makes it possible to examine the nature of a bond. Two questions related to the work done here have been posed and answered below.

=== In some structures, GaussView does not draw bonds where we expect. Does this mean there is no bond? Why? ===
It is reported that GaussView only draws a bond depending on whether the two atoms are close enough for the bond to exist (in addition to the inevitable criteria over whether a bond can exist in a given location - for example if a transition metal has filled its coordination sphere). Hence, even if there is no bond shown, it does not necessarily mean no bond exists.

The existence of a bond depends on a number of criteria, one of which is the length, but other factors must be considered such as whether there is sufficient orbital overlap or whether the antibonding interactions at a given distance outweigh any bonding interactions. Hence, the simple distance criteria that GaussView uses is not sufficient to be absolutely sure if a bond is there or not. To fully ensure if a bond exists, it would be necessary to perform a number of additional calculations, such as investigation of the electron density contour maps and analysis of the molecular orbitals. Only these plots can show whether a bond exists or not, and hence GaussView's approximation is not sufficient proof that a bond does not exist.

=== What is a bond? ===
The IUPAC Gold Book defines a chemical bond as<ref name="goldbook-bond">A. D. McNaught and A. Wilkinson, in ''Compendium of Chemical Terminology'', Blackwell Scientific Publications, Oxford, 2nd ed., 2012, p. CT07009</ref>:
<blockquote>When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups.</blockquote>

Models have been built on top of this to describe specific kinds of bonding, the most common of which are:
* Covalent bond, in terms of a bond where each atom in the bond donates one electron, to form a two-electron bond.
* Ionic bond, a bond where negatively charged anions are electrostatically attracted to positively charged cations, leading to a stabilised arrangement compared to the ions being separate.
* Metallic bond, where positive cations of a metal are in a sea of delocalised electrons.

In the latter two cases, electrostatics are involved, and it is this combination of positive and negative charges combined which lead to a very stable and attractive combination, which massively lowers the energy of the system.

For a covalent bond, modern thinking (which also applies to a variety of inorganic compounds too) makes use of molecular orbitals, a combination of bonding and antibonding orbitals being created when atomic orbitals combine. Generally, according to the Klopman-Salem equation<ref name="klopman">G. Klopman, ''J. Am. Chem. Soc.'', 1968, '''90''', 223–234</ref><ref name="salem">L. Salem, ''J. Am. Chem. Soc.'' 1968, '''90''', 543 & 553</ref>, the bonding orbitals created are of a lower energy than the atomic orbitals they were created from. As a result of this, as these bonding orbitals are filled, the molecule is stabilised, and hence the IUPAC definition of a bond is adhered to.

There are many different ways in which this stabilisation can be created, and the methods discussed here are only a few of them (there may still be other kind of stabilising interactions as yet undiscovered). Hence, it is reasonable to argue that any interaction which causes a stabilising effect in a molecule can be deemed a chemical bond, which the terms 'single' and 'double bond' being associated with interactions of a certain magnitude.

= Part 2: Frequencies, vibrations, orbitals and energies =
On the optimised structures reported previously, a number of advanced calculations have been performed. Initially, frequency analysis has been conducted to ensure that the energies calculated are minima. Once this has been confirmed, more advanced calculations have been performed to help find out more about the nature of these compounds.

== Frequency and vibrational analysis of BH3 ==
Through use of a 6-31G(d,p) frequency analysis of the optimised BH3 structure, it is possible to identify whether a minima has been attained. Initially, the results have been compared to what was obtained from the optimisation, and the frequency results summary from the [[media:Pk-bh3-freq.log|log file]] is found below:

<pre>
File Name PK_BH3_FREQ_631GDP
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532361 a.u.
RMS Gradient Norm 0.00000702 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 18.0 seconds.
</pre>

Other than a minor change in the gradient, the results are the same as was reported previously. Convergence was again confirmed:
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000089 0.001800 YES
RMS Displacement 0.000045 0.001200 YES
Predicted change in Energy=-1.487544D-09
Optimization completed.
-- Stationary point found.
</pre>

Low frequencies were reported as
<pre>
Low frequencies --- -25.0305 -12.9079 0.0006 0.0007 0.0009 15.0420
</pre>

which are outside the range of -15 to +15 cm-1. Hence, the molecule was reoptimised with scf=conver=9 int=ultrafine keywords and a tight convergence to yield the following data in the [[media:Pk_bh3_opt_tight.log|log file]]:

<pre>
File Name PK_BH3_OPT_TIGHT_631GDP
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532360 a.u.
RMS Gradient Norm 0.00000594 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 13.0 seconds.
</pre>

Convergence was obtained on the optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000009 0.000015 YES
RMS Force 0.000007 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000034 0.000040 YES
Predicted change in Energy=-7.783630D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0008 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9938 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0054 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The frequency calculation was then subsequently run, using the same keywords (but no tight setting). The [[media:Pk-bh3-freq-tight.log|log file]] reported the following data:

<pre>
File Name PK_BH3_FREQ_TIGHT_631GDP
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532360 a.u.
RMS Gradient Norm 0.00000594 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

This time there was convergence:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000086 0.001800 YES
RMS Displacement 0.000043 0.001200 YES
Predicted change in Energy=-1.187652D-09
Optimization completed.
-- Stationary point found.
</pre>

Regrettably the low frequencies were still out of range:

<pre>
Low frequencies --- -19.8568 -17.0127 -9.6394 0.0004 0.0005 0.0007
Low frequencies --- 1162.9117 1213.0852 1213.1686
</pre>

At this point the optimisation was conducted again with the same keywords and forcing a D3h symmetry. The [[media:Pk-bh3-opt-forced.log|log file]] showed:

<pre>
File Name PK_BH3_OPT_FORCED_631GDP
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532364 a.u.
RMS Gradient Norm 0.00000571 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group D3H
Job cpu time: 0 days 0 hours 0 minutes 13.0 seconds.
</pre>

with convergence:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000015 YES
RMS Force 0.000007 0.000010 YES
Maximum Displacement 0.000045 0.000060 YES
RMS Displacement 0.000030 0.000040 YES
Predicted change in Energy=-7.760436D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The frequency calculation was then run again, with the [[media:Pk-bh3-freq-forced.log|log file]] yielding:

<pre>
File Name PK_BH3_FREQ_FORCED_631GDP
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532364
RMS Gradient Norm 0.00000572
Imaginary Freq 0
Dipole Moment 0.0000
Point Group D3H
Job cpu time: 0 days 0 hours 0 minutes 18.0 seconds.
</pre>

with convergence:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000045 0.001800 YES
RMS Displacement 0.000022 0.001200 YES
Predicted change in Energy=-7.723726D-10
Optimization completed.
-- Stationary point found.
</pre>

This time, the low frequencies were found to be within the allowed range.

<pre>
Low frequencies --- -14.8515 -14.8476 -11.2630 0.0012 0.0162 0.3377
Low frequencies --- 1162.9477 1213.1209 1213.1211
</pre>

Vibrations seen were of the symmetry labels A2", E', E', A1', E', E' which matches what the character tables for D3h suggests.

=== Visual representation of vibrational peaks ===
The vibrational peaks can be seen in GaussView and are shown below:

[[Image:Pk-bh3-Ir.svg]]

{| class="wikitable" border="1"
|+ Vibrations for BH3
! Mode !! Frequency (cm-1) || Intensity || Image || Symmetry (D3h point group)
|-
| 1 || 1162.95 || 92.5709
|[[Image:Pk-bh3-1.gif|200px]]
Symmetric wag of all protons.
| A"2 (according to log)
|-
| 2 || 1213.12 || 14.0537
|[[Image:Pk-bh3-2.gif|200px]]
Rock of H-B-H group with associated scissoring of third H.
| E' (according to log)
|-
| 3 || 1213.12 || 14.0532
|[[Image:Pk-bh3-3.gif|200px]]
H-B-H scissoring.
| E' (according to log)
|-
| 4 || 2582.68 || 0.0000
|[[Image:Pk-bh3-4.gif|200px]]
Symmetric stretch of all B-H bonds out in the same direction as the bond.
| A'1 (totally symmetric)
|-
| 5 || 2715.82 || 126.3288
|[[Image:Pk-bh3-5.gif|200px]]
Antisymmetric stretch of H-B-H group
| E' (according to log)
|-
| 6 || 2715.82 || 126.3227
|[[Image:Pk-bh3-6.gif|200px]]
Antisymmetric stretch of all protons.
| E' (according to log)
|}

Of note, there are only three peaks in the IR spectrum, despite there being 6 modes. One of these modes has an intensity of 0, and so it will not show up in the IR spectrum. This intensity is zero as the vibration is totally symmetric, which means there is no change in dipole moment and hence is not IR active. This still leaves 2 peaks missing. The peaks with an E' symmetry are defined as such as they are degenerate, and there are 2 pairs of 2 peaks with the same wavenumber. Hence, both peaks will appear superimposed upon eachother (due to their degeneracy), and the intensities will be added together. The result is that only one peak shows for the two modes for the same wavenumber. All missing peaks are therefore accounted for.

== Vibrational analysis for GaBr3 ==
Frequency analysis from the optimised structure of GaBr3 was conducted on the HPC and the results are available on Dspace: {{DOI|10042/26119}}.

The summary of the results is as follows.

<pre>
File Name PK_GABR3_FREQ_LANL2DZ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set LANL2DZ
Charge 0
Spin Singlet
E(RB3LYP) -41.70082783 a.u.
RMS Gradient Norm 0.00000011 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group D3H
Job cpu time: 0 days 0 hours 0 minutes 12.3 seconds.
</pre>

Convergence was confirmed
<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-6.142862D-13
Optimization completed.
-- Stationary point found.
</pre>

and all vibrations were found to be in the -15 to 15 cm-1 range:
<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>

The lowest normal mode is 76.3744cm-1 which corresponds to a combined rocking and scissoring vibration, and is shown in animated form below. This almost has the same energy as the next lowest frequency and is assumed to be degenerate within the boundaries of approximation in the calculation.

[[Image:Pk-ir-gabr3.svg]]

{| class="wikitable"
|+ Vibrations for GaBr3
|-
! Mode
! Frequency (cm-1)
! Intensity
! Image
! Symmetry (D3h point group)
|-
| 1
| 76.37
| 76.38
| [[Image:Pk-gabr3-mode-1.gif|200px]]

Rocking of two bromine atoms, leading to a scissoring effect of third.
| E' (according to log)
|-
| 2
| 76.38
| 3.3447
| [[Image:Pk-gabr3-mode-2.gif|200px]]

Scissoring of two bromine atoms (Br-Ga-Br).
| E' (according to log)
|-
| 3
| 99.70
| 9.2161
| [[Image:Pk-gabr3-mode-3.gif|200px]]

Wag of all bromine atoms.
| A"2 (according to log)
|-
| 4
| 197.34
| 0.0000
| [[Image:Pk-gabr3-mode-4.gif|200px]]

Symmetric stretch of all Ga-Br bonds out in the same direction as the bond.
| A'1 (totally symmetric)
|-
| 5
| 316.18
| 57.0704
| [[Image:Pk-gabr3-mode-5.gif|200px]]

Antisymmetric stretch of Br-Ga-Br group
| E' (according to log)
|-
| 6
| 316.19
| 57.0746
| [[Image:Pk-gabr3-mode-6.gif|200px]]

Antisymmetric stretch of all bromine atoms.
| E' (according to log)
|}

Once again there are fewer peaks than modes - this is for the same reason as observed with BH3. The intensity of 0 for the 4th mode is also due to the same reason why the mode with no intensity for BH3 has no intensity.

=== Comparison to BH3 ===

{| class="wikitable"
|+ Comparisons between BH3 and GaBr3 (modes have been matched by symmetry label and similarity in appearance)
|-
! Mode
! GaBr3 Frequency (cm-1)
! GaBr3 Intensity
! GaBr3 Image
! BH3 Image
! BH3 Frequency (cm-1)
! BH3 Intensity
|-
| 1
| 76.37
| 76.38
| [[Image:Pk-gabr3-mode-1.gif|200px]]
| [[Image:Pk-bh3-2.gif|200px]]
| 1213.12
| 14.0537
|-
| 2
| 76.38
| 3.3447
| [[Image:Pk-gabr3-mode-2.gif|200px]]
| [[Image:Pk-bh3-3.gif|200px]]
| 1213.12
| 14.0532
|-
| 3
| 99.70
| 9.2161
| [[Image:Pk-gabr3-mode-3.gif|200px]]
| [[Image:Pk-bh3-1.gif|200px]]
| 1162.95
| 92.5709
|-
| 4
| 197.34
| 0.0000
| [[Image:Pk-gabr3-mode-4.gif|200px]]
| [[Image:Pk-bh3-4.gif|200px]]
| 2582.68
| 0.0000
|-
| 5
| 316.18
| 57.0704
| [[Image:Pk-gabr3-mode-5.gif|200px]]
| [[Image:Pk-bh3-5.gif|200px]]
| 2715.82
| 126.3288
|-
| 6
| 316.19
| 57.0746
| [[Image:Pk-gabr3-mode-6.gif|200px]]
| [[Image:Pk-bh3-6.gif|200px]]
| 2715.82
| 126.3227
|}

Whilst all the modes which appear in BH3 also appear in GaBr3 there are a number of significant differences:
# The modes are reordered
# The energies are much reduced for GaBr3

Initially, the intensity and wavenumber of the vibrations for GaBr3 is much smaller than BH3 - this is due to the inverse correlation between nuclei mass and the IR frequency - this is because atoms with a lower mass are easier to move around, and hence need a less energetic photon to be excited. This is likely related to the variance in intensity too. This is reflected in the IR spectra, which show a similar distribution in peaks, but the intensities for the BH3 spectra is much bigger.

Secondly, the reordering of modes is due to the same reason - the more atoms which are moved in a mode, the greater the amount of energy is needed to cause a vibration. Thus the A"2 mode has changed position as a significant increase in the amount of energy needed for this mode to oscillate is needed, more than the energy needed to make the two E' modes below it in terms of energy oscillate (as the Ga atoms in these modes do not move as much).

Otherwise the spectra are quite similar, there is an identical number of peaks with a similar distribution, and all the types of vibration seen in BH3 are also seen in GaBr3 - including identical symmetry labels. Also in both cases, there is a large gap between the A"2 and E' modes, and the other two modes. The higher energy modes in both cases are stretching modes and it may be because in doing so the electron density over the molecule is disrupted (and can potentially lead to bond breakage at long displacements as there is no electron density over the bond), which requires significantly more energy than moving the atom but keeping its displacement fixed.

=== Discussion ===

==== Why must you use the same method and basis set for both the optimisation and frequency analysis calculations? ====
The method and basis set give the conditions for the calculation used in either the optimisation or frequency analysis, more specifically the approximations used in solving the Schrodinger equation. The effect of this is that the energy you obtain during the optimisation of a molecule is specific to that method and basis set, as the energy depends on the approximations used. GaussView represents this by showing the energy in terms of the basis set and method.

Thus, when you calculate the frequency analysis, you must use the same method and basis set, as we must analyse the molecule and its energy in the same conditions that it exists in - an analogy would be to optimise in chloroform solvent and then do a frequency analysis in water - the system is different. As the approximations would be different if the models and basis sets differ, the frequency analysis would give bogus results - it would be doing a frequency analysis for a specific case on a molecule not of that case. This is especially important as at the level you optimised the molecule to, the energy the molecule reaches will be a minima, but when you then perform the frequency analysis, if you use a different method and basis set, the energy may no longer correspond to a minima, and thus the frequency analysis is meaningless.

==== What is the purpose of carrying out a frequency analysis? ====
A frequency analysis is important as it shows whether you have reached an energy minima or maxima. When the gradient is zero, it can either be at the peak or trough of a curve, as at these points the gradient is flat and <math>\frac{dy}{dx} = 0</math>. We need to know whether we are at a maximum or minimum as, in the nature of an optimisation, we are looking to find the most accurate representation of a molecule's actual state of existance, and molecules always try to minimise their energy.

In contrast, if we are at a maxima, we are at a transition state (as these are always of the highest energy). Whilst there may be times we are interested in a transition state, we are not here, and thus we must verify we are at a minimum. The frequency analysis finds the second derivative of the gradient, which is positive if we are at a minimum, or negative if we are at a maximum. Thus, by performing a frequency analysis, we can see if any of the vibrations are negative, and if none are we can be sure we are at an energy minimum. It is important to ensure we are at a minimum before we discuss results or perform further calculations.

==== What do the "Low frequencies" represent? ====
The low frequencies refer to the degrees of vibrational freedom within a molecule. For a molecule with 3 (or more) atoms, this is <math>3N-6</math>, which explains why the 4 atom molecules considered previously have 6 low frequencies. Each low frequency refers to one of the vibrational modes for the molecule, which is not necessary IR (or Raman) active, but the molecule would still exhibit this kind of vibration and hence vibrates at that frequency. This is separate to rotational and translational modes of freedom.

== Molecular orbital analysis for BH3 ==
Using the optimised and confirmed minima structure obtained earlier, the molecular orbitals for BH3 have been calculated, which also allows for calculation of NBOs.

An energy calculation was run on the HPC using the pop=full,nbo keyword and the results are available on Dspace: {{DOI|10042/26167}}.

The summary is as follows:

<pre>
File Name PK_BH3_EGY_631GDP
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.61532361 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group CS
Job cpu time: 0 days 0 hours 0 minutes 7.4 seconds.
</pre>

All data appears to be identical to the original energy calculation.

MOs 1-8 were calculated in GaussView and plotted on the MO diagram of BH3 shown below:

[[Image:Pk-bh3-mo.png|700px]]

== Molecular orbital and NBO analysis for ammonia ==
Ammonia was optimised and then a frequency calculation run as per the previous method, the choice of keywords and symmetry forcing (but to C3v) was needed in order to get the low frequencies within the acceptable range.

For the optimisation, the final data according to the [[media:Pk-nh3-opt.log|log file]] is:

<pre>
File Name PK_NH3_OPT_631GDP
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -56.55776873 a.u.
RMS Gradient Norm 0.00000323 a.u.
Imaginary Freq
Dipole Moment 1.8465 Debye
Point Group C3V
Job cpu time: 0 days 0 hours 0 minutes 27.0 seconds.
</pre>

and convergence confirmed:
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000015 YES
RMS Force 0.000004 0.000010 YES
Maximum Displacement 0.000012 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-9.846374D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

Low frequencies from the frequency calculation (which differs in energy terms by 0.00000001) [[media:Pk-nh3-freq.log|log file]] are:

<pre>
Low frequencies --- -0.0138 -0.0030 0.0013 7.0781 8.0927 8.0932
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

which show a minima has been obtained. There were no negative frequencies.

'''Summary table:'''

<pre>
File Name PK_NH3_FREQ_631GDP
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -56.55776872 a.u.
RMS Gradient Norm 0.00000322 a.u.
Imaginary Freq 0
Dipole Moment 1.8465 Debye
Point Group C3
Job cpu time: 0 days 0 hours 0 minutes 15.0 seconds.
</pre>

Of concern, the symmetry has become C3, however there has been little change in energy, hence little change in structure, so this is assumed to be a bug in GaussView.

Now being satisfied that a minima has been reached, a MO and NBO calculation was conducted as was done on the BH3 ([[media:Pk-nh3-egy.log|log file]]). The NBO was then plotted from -1.125 to 1.125 and is shown below.

[[Image:Pk-nh3-nbo.PNG]]

'''Energy calculation summary table:'''
<pre>
Ammonia egy
File Name PK_NH3_EGY_631GDP
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -56.55776873 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 1.8465 Debye
Point Group C3V
Job cpu time: 0 days 0 hours 0 minutes 10.0 seconds.
</pre>

As expected, the electronegative nitrogen has a great degree of negative charge - as shown by the red character. The exact charges are -1.125 on the nitrogen and 0.375 on all the protons. The power of NBO for observing the charge density of a molecule is thus seen.

== Energy calculations for NH3BH3 ==
Now optimised energies for NH3 and BH3 have been found, it is now possible to calculate the energy for NH3BH3, find the difference between all three components, and therefore find the energy of association. From this point on it is assumed that the keywords used previously during optimisation are always used. Initially an optimisation was conducted at the same level as before and the [[media:Pk-nh3bh3-opt.log|log file]] reported:

<pre>
File Name PK_NH3BH3_OPT
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -83.22468909 a.u.
RMS Gradient Norm 0.00000047 a.u.
Imaginary Freq
Dipole Moment 5.5646 Debye
Point Group C3V
Job cpu time: 0 days 0 hours 1 minutes 14.0 seconds.
</pre>

and convergence checked:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000007 0.000060 YES
RMS Displacement 0.000004 0.000040 YES
Predicted change in Energy=-1.706880D-11
Optimization completed.
-- Stationary point found.
</pre>

A frequency analysis was then conducted. The [[media:Pk-nh3bh3-freq.log|log file]] reported a final energy of -83.22468909, which is identical to what was found in the optimisation, and no frequencies were negative. Low frequencies were in the acceptable range:

<pre>
Low frequencies --- -4.8361 -1.6211 -1.2960 0.0335 0.0539 0.2001
Low frequencies --- 263.3086 632.9964 638.4686
</pre>

Other summary data is as follows:

<pre>
File Name PK_NH3BH3_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -83.22468909 a.u.
RMS Gradient Norm 0.00000052 a.u.
Imaginary Freq 0
Dipole Moment 5.5646 Debye
Point Group C3V
Job cpu time: 0 days 0 hours 0 minutes 48.0 seconds.
</pre>

=== Calculation of association energy ===
Now that all three components are optimised to the correct level, and are all found as minima, it is possible to find the association energy.

The energies of all 3 components are (in AU):

* E(BH3)=-26.61532361
* E(NH3)=-56.55776873 -83.1730923
* E(NH3BH3)= -83.22468909
* Association energy: -0.0515967

One atomic unit is equal to one Hartree, and the conversion is equal to 1 Hartree = 2625.49962 kJ mol-1<ref name="codata">CODATA 2010</ref>, which gives a final association or dissociation energy of -135.47 kJ mol-1.

= References =
<references />

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T16:25:21Z

Pk1811:

<div style="font-size: 40px;"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px;"><center>Ionic liquids: Designer solvents</center></div>
 
<div style="font-size: 30px;"><center>[[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|Back to week 1 work]]</center></div>
 
= Introduction =
The aim of this project is to explore the physical nature of ionic liquids, which have application in designing solvents through customisation of the nature of the cation and anion<ref name="abs">M. Freemantle. ''Chem. Eng. News'', 1998, '''76''', 32–37</ref>. In this work, a variety of cations have been investigated to identify what trends are present in the variation in central atom and its ligands.

= Structures of methyl-ligand complexes =
== Optimisations ==
A number of cations have been optimised using Gaussian 09 D.01, namely [N(CH3)4]+, [P(CH3)4]+ and [F(CH3)3]+. All these complexes have been optimised to a DFT B3LYP 6-31G(d,p) level with the <code>int=ultrafine scf=conver=9</code> keywords and tight convergence - this is as a consequence of behaviour seen in previous work<ref name="labintro">P. Kent, unpublished work ([[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|lab intro]])</ref> where low frequencies did not exist within a tight range unless these keywords were specified. All calculations were run on the supplied laptop due to a significant queue of jobs on the HPC (except for [S(CH3)3]+ as it took a very long time), and the log files are available here:

* [N(CH3)4]+: [[media:Pk_log_nch34_opt.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_opt.log]]
* [S(CH3)3]+: The first attempt did not converge: {{DOI|10042/26201}}. A partially optimised structure was resubmitted as a second attempt: {{DOI|10042/26205}}. This also did not converge so a final optimisation was run on this partially optimised structure with the <code>nosymm</code> keyword. This converged: {{DOI|10042/26214}}.

Once done, convergence was verified via inspection of the log file.

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name nch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000090 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 1 minutes 27.0 seconds.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name pch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701126 a.u.
RMS Gradient Norm 0.00000675 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 24 minutes 21.0 seconds.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_opt3
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000101 a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 52.2 seconds.
</pre>

=== Convergence outputs ===

''' [N(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000014 0.000060 YES
RMS Displacement 0.000005 0.000040 YES
Predicted change in Energy=-1.010077D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000015 YES
RMS Force 0.000005 0.000010 YES
Maximum Displacement 0.000026 0.000060 YES
RMS Displacement 0.000009 0.000040 YES
Predicted change in Energy=-1.723206D-06
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''

Initial failed optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000015 NO
RMS Force 0.000006 0.000010 YES
Maximum Displacement 0.002915 0.000060 NO
RMS Displacement 0.000869 0.000040 NO
Predicted change in Energy=-5.685776D-09
Optimization stopped.
-- Number of steps exceeded, NStep= 61
-- Flag reset to prevent archiving.
</pre>

During this failed optimisation, it appears the molecule just spent a large amount of time rotating around the C3 axis through the sulphur.

The final optimisation yielded:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000049 0.000060 YES
RMS Displacement 0.000018 0.000040 YES
Predicted change in Energy=-6.520157D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==
Following this, frequency analysis was conducted with the same keywords and calculation level to ensure a minima has been found. This is ensured by checking there are no negative vibrations in the molecule. Calculations were again run on the laptop, and the log files, summaries, and frequencies are listed below. Actual animations of the modes have not been exported, however a Jmol of the log file is available and the modes can be seen by right clicking and choosing '''model -> the mode you want to see'''. This time, a range of
-30 to +30 cm-1 has been accepted for the low frequencies as molecules investigated are quite complex, and a relatively simple basis set has been used. Optimising to 6-311G(d,p) would likely bring the frequencies within the range used previously however this would be at the expense of much longer computation times.

* [N(CH3)4]+: [[media:Pk_log_nch34_freq.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_freq.log]]
* [S(CH3)3]+: {{DOI|10042/26273}}

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name NCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000085 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 3 minutes 17.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000009 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.014288D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name PCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701149 a.u.
RMS Gradient Norm 0.00000668 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 12 minutes 11.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001774 0.001800 YES
RMS Displacement 0.000659 0.001200 YES
Predicted change in Energy=-3.008780D-08
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000104 a.u.
Imaginary Freq 0
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 9 minutes 6.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000093 0.001800 YES
RMS Displacement 0.000033 0.001200 YES
Predicted change in Energy=-7.179584D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Vibration modes ===

''' [N(CH3)4]+ '''
<pre>
Low frequencies --- 0.0007 0.0011 0.0013 21.5288 21.5288 21.5288
Low frequencies --- 188.5488 292.6546 292.6546
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [P(CH3)4]+ '''
<pre>
Low frequencies --- -15.1139 -0.0002 0.0012 0.0012 5.8940 14.7736
Low frequencies --- 156.2222 191.5376 191.9513
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_pch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [S(CH3)3]+ '''
<pre>
Low frequencies --- -8.5871 0.0029 0.0049 0.0051 5.7111 9.1755
Low frequencies --- 162.4159 200.3446 200.5391
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_sch33_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== Conclusions on molecular structure ==
Investigation of structures is focused on the central atom as this is the only point at which variance should occur. The length of the M-C bonds and the angle between C-M-C on each complex is reported below:

{| class="wikitable" border="1"
! Complex !! M-C Length (Å) !! Angle (°) !! M-C length (lit<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref>) (Å)
|-
| [P(CH3)4]+ || 1.82 || 109.5 || 1.84
|-
| [N(CH3)4]+ || 1.51 || 109.5 || 1.46
|-
| [S(CH3)3]+ || 1.82 || 102.7 || 1.79
|}

''Literature bond lengths are found by adding the covalent radii for the atoms.''

Two key trends are:
* As you go down a group, the bond length decreases
* As you go across a group (so losing a ligand), the bond angle is reduced)

The first trend is straightforward to explain, as bond lengths increase down the group. This is in tandem with the increase in atomic radius down the group as orbitals in a greater shell begin to be filled. Thus, as you move from period 2 (N) to period 3 (P), the length of the bond increases and is in turn the overall size of each ion. There is slight variance in the length of a C-H bond in each complex, however no pattern is immediately discernible (it increases in the order S > P > N) - it is thought this is just some random error in the calculation.

Whilst there is an increase in bond length, there is no change in orientation of the bonds, thus the symmetry of TD is maintained in both the phosphorous and nitrogen molecules. As a result of this, the bond angle is the same for these two complexes. No other arrangement of the ligands is sterically possible, so ensuring that this symmetry label cannot be changed, and therefore the bond angle also cannot change. The bond angle is different for sulphur, as a result of the change of symmetry to C3v, it is not known if the change in metal centre contributes to this change - further investigation would be required.

Of note, the bond length does not appear to change going across the period. There is actually a small increase of 0.01Å if the bond length is reported accurate to 0.001Å, however it is not known if this is just an inherent error in the calculation or not. In any event, it is expected that there is a slight decrease in the bond length as you move towards the right of a period, as the increased nuclear charge better shields the electrons and thus shortens the bond length, but this is not observed here. This may be a result of this complex containing one less ligand, with the arrangement instead taken (along with the lone pair) resulting in some interactions (steric or electronic repulsion) which causes the carbon and metal atoms to move apart from each other. This theory is supported by the large deviation from bond length for the sulphur complex, indicating some feature about the arrangement it has taken is causing the bond length to be artificially lengthened.

Otherwise no strange observations are seen with the structures, with all methyl groups taking the expected tetrahedral structure, and either tetrahedral or C3v structures for the central atom as expected by the number of ligands which are present.

= Molecular orbitals and NBO charges of methyl-ligand complexes =
All three complexes discussed previously have been subject to a full NBO and MO analysis via an energy calculation with the <code>pop=(full,nbo)</code> keyword, retaining any previously used keywords as appropriate. Calculations were performed on the laptop due to load on the HPC, except for the sulphur complex as the calculation took too long on the laptop.

Log files are available as follows:

* '''[N(CH3)4]+''': [[media:Pk_log_nch34_egy.log]]
* '''[P(CH3)4]+''': [[media:Pk_log_pch34_egy.log]]
* '''[S(CH3)3]+''': {{DOI|10042/26274}}
== Calculation output ==

''' [N(CH3)4]+ '''

<pre>
File Name NCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

''' [P(CH3)4]+ '''

<pre>
File Name PCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701105 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 20.0 seconds.
</pre>

''' [S(CH3)3]+ '''

<pre>File Name sch33_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 0 minutes 57.7 seconds.
</pre>

== Sample MOs for [N(CH3)4]+ ==
A variety of 5 molecular orbitals have been calculated and shown below. Only occupied non-core MOs from the totally bonding to totally antibonding are shown.

{| class="wikitable" border="1"
|+ Totally bonding towards the top
! MO number !! Energy (hartree) !! Picture !! Degeneracy !! Notes
|-
| 6 || -1.19645 || [[Image:Pk-n-mo0.png|200px]] || Singly degenerate || This MO exhibits a great degree of strong bonding interactions across the entire molecule up to the protons, the orbitals of which do not appear to be part of this MO. This is seen by the huge red surface containing almost the entirety of the molecule. As a result of the huge amount of delocalisation seen in the MO, there is a lot of through space interactions between adjacent carbon groups, as seen by how the MO forms a 'cage' around the entire molecule - the empty space between two carbon atoms is part of this red object. As there are no other molecular orbitals other than this huge one, there is no concept of a node in this MO diagram.
|-
| 10 || -0.80745 || [[Image:Pk-n-mo1.png|200px]] || Singly degenerate || This is the first MO in this series of 5 to contain a slight degree of antibonding character, as seen by the fact each ligand is in its own (+) phase orbital, whereas the central metal is in a (-) phase one. This leads to a minor degree of antibonding character, and also a node in the centre of the M-C bond where the two MOs end. Through space interactions are present in each ligand MO, with all the protons and the central carbon existing within the boundaries of the MO, and hence there are through-space interactions between the protons. MOs of the same phase interact weakly with each other due to the large distance between each green orbital (seen in the picture), however the interaction between the (+) and (-) orbitals is quite strong as the nodal area is very small in size - the orbitals are nearly touching. The level of delocalisation is reduced, with delocalisation only occurring across each ligand group - the ligands themselves are not delocalised onto one unit.
|-
| 14 || -0.62248 || [[Image:Pk-n-mo2.png|200px]] || Doubly degenerate || For this MO, nodes exist on every carbon atom, as each MO covers two halves of a carbon atom, two protons, and nothing else. This does lead to delocalisationa cross the protons and carbon atoms, however this also does result in strong antibonding interactions at each carbon as the (+) and (-) MOs become quite close. Some protons, and the metal centre are not covered at all by this MO, however from what is delocalised, there is a significant amount of through space interactions between protons on differing methyl ligands - this is of note as the ligand protons are quite a distance away. There may be some weak bonding interactions between orbitals of the same phase, however they are quite a distance away (separated by the metal centre) so this is expected to be quite weak.
|-
| 17 || -0.58035 || [[Image:Pk-n-mo3.png|200px]] || Triply degenerate || This one again has a node on each carbon, however it differs in that each orbital only covers a single proton and half a carbon. This results in there being no through-space interactions in this molecule. Additionally, there are many strong antibonding interactions as all the orbitals are quite close together, with the a (+) orbital being surrounded by a (-) orbital on every side. If there are any bonding interactions, these are going to be very weak.
|-
| 21 || -0.57934 || [[Image:Pk-n-mo4.png|200px]] || Triply degenerate || This MO is similar to the previous, but differs in that each orbital now consists of two protons, so there are no protons which aren't enclosed in an orbital. Again, there are nodes in each carbon, but also a node in the metal center, with orbitals now also covering the metal center. This results in there being strong antibonding interactions over almost the entire molecule, with (+) interacting with (-) almost over the entire surface of every orbital. Through-space interactions are now back with there being two protons in each orbital, making it possible for these to interact, and there is also the potential for protons and metal center to interact as well. This orbital is only slightly higher energy than the previous one, and this is solely because of the increased degree of antibonding interactions present.
|}

== NBO charge distributions ==

NBO charge distributions were calculated from the checkpoint file for a range of -1.750 to 1.750 as this ensured the range of charges for all 3 complexes could be accommodated on the same scale. The charges are as follows:

{| class="wikitable" border="1"
! Complex !! Metal charge (e) !! Carbon charge (e) !! Proton charge (e)
|-
| [P(NH3)4]+ || 1.667 || -1.060 || 0.298
|-
| [N(NH3)4]+ || -0.295 || -0.846 || 0.297
|-
| [S(NH3)3]+ || 0.917 || -0.483 || 0.269
|}

<gallery>
File:Pk-nbo-n.png|Nitrogen complex
File:Pk-nbo-p.png|Phosphorous complex
File:Pk-nbo-s.png|Sulphur complex
</gallery>

There appears to be a slight trend of the metal centre charge with electronegativity, with the charge much lower as it becomes more electronegative (and hence drawing a greater share of electrons to it). This in turn makes the carbon more positive as electron density is removed from it. The protons remain rather positively charged and do not appear to be greatly affected by the metal centre, but this is likely because they are too far away for the inductive effect to occur.

Interestingly, nitrogen is more eletronegative than sulphur, yet sulphur has a greater negative charge. The reduced degree of polarisation in the bond for the nitrogen complex also suggests why the bond length for the nitrogen complex is shorter compared to the sulphur. The reason for this increased amount of negative charge is due to the lone pair present on sulphur (hence the configuration it takes according to the Jmol clip above), and so there is simply more negative charge present on the sulphur.

Thus, for the general complex [NR4]+, the positive charge located on the nitrogen in the picture is indeed located on the nitrogen, however it is somewhat delocalised over the protons too. As the nitrogen contains the greatest degree of positive charge, though, the + sign is conventionally placed here as it gives the indication as to where most of the charge is.

Analysis of the log files show the exact NBO contributions to the bond:

'''[P(NH3)3]+'''
<pre>
1. (1.98031) BD ( 1) P 1 - C 2
( 40.43%) 0.6358* P 1 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.4030 0.0006 0.0000 -0.4429
0.0006 0.0000 0.6188 -0.0009 0.0385
-0.0538 -0.0591 -0.0036 0.0254
( 59.57%) 0.7718* C 2 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.4044
-0.0074 0.4444 -0.0081 -0.6209 0.0114
0.0121 -0.0169 -0.0186 -0.0011 0.0080
</pre>

This shows almost equal contribution from each atom to the bond, with each atom assuming a sp3 arrangement as is expected by the TD symmetry. Carbon is sp3 as expected due to its saturation. As the carbon is slightly more negatively charged according to the charge distributions, the marginal increase in contribution from the carbon vs the phosphorous agrees with the charge distribution seen.

'''[N(NH3)3]+'''
<pre>
4. (1.98452) BD ( 1) C 1 - N 13
( 33.65%) 0.5801* C 1 s( 20.77%)p 3.81( 79.06%)d 0.01( 0.16%)
0.0003 0.4552 -0.0237 0.0026 -0.5129
-0.0218 -0.5129 -0.0218 -0.5129 -0.0218
0.0234 0.0234 0.0234 0.0000 0.0000
( 66.35%) 0.8146* N 13 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 0.5000 -0.0007 0.0000 0.4999
-0.0001 0.4999 -0.0001 0.4999 -0.0001
0.0103 0.0103 0.0103 0.0000 0.0000
</pre>

A similar argument can be made here. The large contribution from the nitrogen is surprising, but considering the smaller bond length for this complex based on the metal, an increased contribution from the nitrogen is not unreasonable. However this does disagree somewhat with the charge distribution which shows there is a much larger electron density on the carbon. It is thus thought that since it is possible to reach orbitals closer to the core on nitrogen rather than phosphorous, it makes nitrogen able to donate a greater share of electrons, and so polarises the bond towards it as a result of its electronegativity.

'''[S(NH3)3]+'''
<pre>
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
-0.0003 -0.4437 -0.0140 0.0033 0.7546
-0.0059 0.3161 -0.0025 0.3634 0.0098
-0.0189 -0.0222 -0.0093 -0.0186 0.0096
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 -0.0001 -0.4117 0.0075 -0.0012
0.0000 -0.7489 0.0330 0.0000 -0.3137
0.0138 0.0000 -0.4037 -0.0260 -0.0353
-0.0572 -0.0240 -0.0347 0.0051
</pre>

Finally, for the sulphur, the bond is an almost equal contribution from each atom in the bond. The charges of the S and C atoms according to the charge distribution are both similar and negative, suggesting little polarisation in this bond, and so the balance seen here is to be expected.

= Ligand influences on nitrogen metal centre complexes =
To investigate how changes to the ligands affects the cation, two variants on the nitrogen complex analysed previously have been used. One has one of the protons on a methyl ligand replaced with CH2OH, the other has the proton replaced with CH2CN. Each complex is then optimised and subject to a frequency analysis so as to allow for investigation of its structure. A MO and NBO calculation is then subsequently run to analyse how the change in ligand affects the ions electronic behaviour.

== Optimisations ==
Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26206}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26207}}

=== Summary output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
File Name nch33ch2oh_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000102 a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 1 hours 22 minutes 37.5 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
File Name nch33ch2cn_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000045 a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 50 minutes 39.5 seconds.
</pre>

=== Convergence output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000034 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-5.591936D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000011 0.000040 YES
Predicted change in Energy=-2.269581D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==

Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26290}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26291}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000106 a.u.
Imaginary Freq 0
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 26 minutes 10.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000102 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-5.078379D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000059 a.u.
Imaginary Freq 0
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 29 minutes 19.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-6.144746D-12
Optimization completed.
-- Stationary point found.
</pre>

=== Vibrational modes ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2oh_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

'''[N(CH3)3(CH2CN)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2cn_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== MO and NBO calculations ==
<code>pop=(nbo,full)</code> energy calculations were then performed on the complexes to generate MOs and NBO charge diagrams, just as has been done previously. All calculations were performed on the HPC and log files are available as follows:

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26294}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26295}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 59.3 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 25.0 seconds.
</pre>

=== NBO charge distributions ===
The main difference between these ligands is that CN is an EWG, and OH is an EDG, the latter due to the lone pairs which make it possible to enolise. Therefore comparison of the charge density of the structure can show how these ligands affect the overall structure of the molecule. The NBO charge distributions from -0.750 to 0.750 are shown below.

<gallery>
File:Pk-nbo-cn.png|CN ligand complex
File:Pk-nbo-oh.png|OH ligand complex
</gallery>

''n.b. the charge for the metal centre in the CN complex is -0.289''

It is seen that, in both cases, the nitrogen makes up the majority of the C-N bond to the C with the substituent:

'''OH case:'''
<pre>
4. (1.98195) BD ( 1) N 1 - C 14
( 67.28%) 0.8202* N 1 s( 23.48%)p 3.26( 76.49%)d 0.00( 0.03%)
0.0000 -0.4845 -0.0026 -0.0002 0.7401
-0.0032 0.3146 -0.0015 0.3438 -0.0026
-0.0092 -0.0105 -0.0043 -0.0088 0.0045
( 32.72%) 0.5720* C 14 s( 20.28%)p 3.92( 79.55%)d 0.01( 0.18%)
-0.0003 -0.4501 0.0135 0.0006 -0.7171
-0.0206 -0.3677 -0.0077 -0.3815 -0.0037
-0.0247 -0.0249 -0.0101 -0.0185 0.0102
</pre>

'''CN case:'''
<pre>
4. (1.97747) BD ( 1) N 1 - C 14
( 64.52%) 0.8033* N 1 s( 24.08%)p 3.15( 75.89%)d 0.00( 0.04%)
0.0000 0.4907 -0.0010 0.0003 0.6601
-0.0021 0.5684 0.0038 0.0000 0.0000
0.0166 0.0000 0.0000 0.0024 -0.0097
( 35.48%) 0.5956* C 14 s( 20.81%)p 3.80( 79.05%)d 0.01( 0.14%)
0.0000 0.4557 -0.0205 0.0000 -0.6428
-0.0249 -0.6135 -0.0174 0.0000 0.0000
0.0320 0.0000 0.0000 -0.0011 -0.0197
</pre>

==== Ligand influence on charge distribution ====

There is quite a significant change in electron density for the OH complex with the carbon between the OH group and the metal centre becoming much more positive. This is surprising considering the OH is a donating group, however this is simply explained. As the carbon is between two electronegative groups, a lot of electron density is withdrawn from it, and hence it becomes very positive. However, the metal centre has become more negatively charged (-0.322 vs -0.295). Hence, the donated electrons are moving straight from the oxygen to the metal centre, while the carbon between's electrons are also donated to both the oxygen and nitrogen as part of the electronegative pull these atoms have on the carbon.

Regarding the CN complex, the electron withdrawal is clearly seen on the carbon the CN ligand is bonded to, as this has become less negatively charged (-0.289 vs -0.295), showing that once again, electron withdrawal is occuring at a distance that causes electrons to travel from the nitrogen through the carbon.

In conclusion, it is seen that the electron inductive effects of the ligands has a direct influence on the the metal centre, as these effects travel through the carbon to directly pull or push electrons from the metal. This is likely due to the large contribution of charge from the nitrogen in the CN bond to the relevant C, so meaning any inductive effects on the C are very likely to influence the N due to the polarisation of the bond towards the N seen.

=== Sample MOs ===
The HOMO and LUMO for these two complexes are reported below:

{| class="wikitable" border="1"
! !! [N(CH3)3(CH2OH)]+ !!
[N(CH3)3(CH2CN)]+
|-
| HOMO || [[Image:Pk-homo-oh.png|200px]] || [[Image:Pk-homo-cn.png|200px]]
|-
| LUMO || [[Image:Pk-lumo-oh.png|200px]] || [[Image:Pk-lumo-cn.png|200px]]
|-
| HOMO Energy (hartree) || -0.48763 || -0.50047
|-
| LUMO Energy (hartree) || -0.12459 || -0.18183
|}

=== Discussion of MOs ===

The most notable change is that there is an increased amount of delocalisation present in the alcohol-containing complex's LUMO vs the cyanide containing one. Whilst it was thought that this is a result of the electron donation, further investigation showed that this is one orbital created by through-space interactions of every proton in the complex. The present of the alcohol group adds protons to fill a space in the molecule where would there otherwise be no protons (see the cyanide complex). This means that the distance between any two protons is small enough for an interaction to occur, and as there are protons around the entirety of the molecule, one orbital surrounds the entire molecule. The original theory was discarded after it was noted that the metal centre has its own orbital of the opposite phase in the centre of the complex, which leads to a very large number of strong antibonding interactions as it comes close to the delocalised proton orbital. Despite the increased degree of through-space interactions, this LUMO is higher in energy than the CN one, simply because of the increased number of antibonding interactions.

The CN complex LUMO does not have such a large delocalisation, and as a result some methyl protons occupy their own orbital of the opposite polarity.

A similar story is seen for the HOMO, which is lower in energy for the CN molecule. The overall volume of orbitals is smaller for the CN molecule, as the CN group is symmetric and simple (pi-bond like) in nature, leading to a very simple arrangement of orbitals at this point. In contrast, for the OH complex, a very complex d-orbital MO is seen over the alcohol group, which then results in some interactions over the nitrogen.

One possible result of this is that it is easier to perform electrophillic attacks on the OH complex at the nitrogen, as the presence of an orbital over the nitrogen would allow for a positively charged group to come in and perform some reaction. These reactions may include ligand substitution or oxidative addition. This kind of attack would not be possible on the CN complex HOMO as no orbital exists on the central nitrogen, and hence cannot be attacked. The only reactions possible on this HOMO would therefore be substitutions on the CN group, which is not as interesting as ligand substitution or oxidative addition on the center of the complex.

Likewise, the OH complex is likely to be more susceptable to attack by nucleophiles. This is however not due to the large delocalised MO (which is present on the CN complex too), as this only covers protons and does not allow any reactions to occur on a ligand or on the metal. However on the CN group, there is an orbital which contains both the metal center and the OH ligand, making it incredibly likely that nucleophillic attack will lead to substitution of the CH2OH group.

Finally, the HOMO-LUMO gap has changed from 0.31864 e (for the CN complex) to 0.36304 e. This makes it harder for an electron to be promoted from the HOMO to the LUMO in the OH complex. Therefore, any photochemical reactivity which is seen would occur in the CN complex but not the OH one. Considering there is a wealth of reported<ref name="photo">F. Crescitelli, B. Karvaly, ''Photochemistry and Photobiology'', 1989, '''50''', 785–791</ref> photoreactivity for CN systems, it is very likely that photochemistry will occur with the cyanide-containing complex.

= Conclusions =
Ionic solvents are formed of a liquid solution of cations and ions, the nature of which massively alter thes behaviour of the solvent. This nature has been shown to be changed by altering the metal, structure, and ligands of various positive complexes, as has been seen. This report examined how the electronegativity and periodicity of the metal, and the electron donating ability of a ligand affects the chemistry of the ion in terms of changing the structure, charge density, and molecular orbitals. Some possible pathways of reactivity of the ions have been proposed, which gives some indication as to how a change of the ion's nature massively changes its solvation properties, as solvation can occur through the coordination of the solute to the solvent ion.

Future work can include investigation into how the different ions coordinate to different substrates added to the calculation, and molecular orbital and NBO calculations can give some idea into whether the theories proposed as to where the ion may be reactive are correct.

= References =
<references />

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T16:25:02Z

Pk1811:

<div style="font-size: 40px;"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px;"><center>Ionic liquids: Designer solvents</center></div>
 
<div style="font-size: 30px;"><center>[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|Back to week 1 work]</center></div>
 
= Introduction =
The aim of this project is to explore the physical nature of ionic liquids, which have application in designing solvents through customisation of the nature of the cation and anion<ref name="abs">M. Freemantle. ''Chem. Eng. News'', 1998, '''76''', 32–37</ref>. In this work, a variety of cations have been investigated to identify what trends are present in the variation in central atom and its ligands.

= Structures of methyl-ligand complexes =
== Optimisations ==
A number of cations have been optimised using Gaussian 09 D.01, namely [N(CH3)4]+, [P(CH3)4]+ and [F(CH3)3]+. All these complexes have been optimised to a DFT B3LYP 6-31G(d,p) level with the <code>int=ultrafine scf=conver=9</code> keywords and tight convergence - this is as a consequence of behaviour seen in previous work<ref name="labintro">P. Kent, unpublished work ([[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|lab intro]])</ref> where low frequencies did not exist within a tight range unless these keywords were specified. All calculations were run on the supplied laptop due to a significant queue of jobs on the HPC (except for [S(CH3)3]+ as it took a very long time), and the log files are available here:

* [N(CH3)4]+: [[media:Pk_log_nch34_opt.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_opt.log]]
* [S(CH3)3]+: The first attempt did not converge: {{DOI|10042/26201}}. A partially optimised structure was resubmitted as a second attempt: {{DOI|10042/26205}}. This also did not converge so a final optimisation was run on this partially optimised structure with the <code>nosymm</code> keyword. This converged: {{DOI|10042/26214}}.

Once done, convergence was verified via inspection of the log file.

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name nch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000090 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 1 minutes 27.0 seconds.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name pch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701126 a.u.
RMS Gradient Norm 0.00000675 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 24 minutes 21.0 seconds.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_opt3
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000101 a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 52.2 seconds.
</pre>

=== Convergence outputs ===

''' [N(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000014 0.000060 YES
RMS Displacement 0.000005 0.000040 YES
Predicted change in Energy=-1.010077D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000015 YES
RMS Force 0.000005 0.000010 YES
Maximum Displacement 0.000026 0.000060 YES
RMS Displacement 0.000009 0.000040 YES
Predicted change in Energy=-1.723206D-06
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''

Initial failed optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000015 NO
RMS Force 0.000006 0.000010 YES
Maximum Displacement 0.002915 0.000060 NO
RMS Displacement 0.000869 0.000040 NO
Predicted change in Energy=-5.685776D-09
Optimization stopped.
-- Number of steps exceeded, NStep= 61
-- Flag reset to prevent archiving.
</pre>

During this failed optimisation, it appears the molecule just spent a large amount of time rotating around the C3 axis through the sulphur.

The final optimisation yielded:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000049 0.000060 YES
RMS Displacement 0.000018 0.000040 YES
Predicted change in Energy=-6.520157D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==
Following this, frequency analysis was conducted with the same keywords and calculation level to ensure a minima has been found. This is ensured by checking there are no negative vibrations in the molecule. Calculations were again run on the laptop, and the log files, summaries, and frequencies are listed below. Actual animations of the modes have not been exported, however a Jmol of the log file is available and the modes can be seen by right clicking and choosing '''model -> the mode you want to see'''. This time, a range of
-30 to +30 cm-1 has been accepted for the low frequencies as molecules investigated are quite complex, and a relatively simple basis set has been used. Optimising to 6-311G(d,p) would likely bring the frequencies within the range used previously however this would be at the expense of much longer computation times.

* [N(CH3)4]+: [[media:Pk_log_nch34_freq.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_freq.log]]
* [S(CH3)3]+: {{DOI|10042/26273}}

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name NCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000085 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 3 minutes 17.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000009 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.014288D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name PCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701149 a.u.
RMS Gradient Norm 0.00000668 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 12 minutes 11.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001774 0.001800 YES
RMS Displacement 0.000659 0.001200 YES
Predicted change in Energy=-3.008780D-08
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000104 a.u.
Imaginary Freq 0
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 9 minutes 6.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000093 0.001800 YES
RMS Displacement 0.000033 0.001200 YES
Predicted change in Energy=-7.179584D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Vibration modes ===

''' [N(CH3)4]+ '''
<pre>
Low frequencies --- 0.0007 0.0011 0.0013 21.5288 21.5288 21.5288
Low frequencies --- 188.5488 292.6546 292.6546
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [P(CH3)4]+ '''
<pre>
Low frequencies --- -15.1139 -0.0002 0.0012 0.0012 5.8940 14.7736
Low frequencies --- 156.2222 191.5376 191.9513
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_pch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [S(CH3)3]+ '''
<pre>
Low frequencies --- -8.5871 0.0029 0.0049 0.0051 5.7111 9.1755
Low frequencies --- 162.4159 200.3446 200.5391
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_sch33_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== Conclusions on molecular structure ==
Investigation of structures is focused on the central atom as this is the only point at which variance should occur. The length of the M-C bonds and the angle between C-M-C on each complex is reported below:

{| class="wikitable" border="1"
! Complex !! M-C Length (Å) !! Angle (°) !! M-C length (lit<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref>) (Å)
|-
| [P(CH3)4]+ || 1.82 || 109.5 || 1.84
|-
| [N(CH3)4]+ || 1.51 || 109.5 || 1.46
|-
| [S(CH3)3]+ || 1.82 || 102.7 || 1.79
|}

''Literature bond lengths are found by adding the covalent radii for the atoms.''

Two key trends are:
* As you go down a group, the bond length decreases
* As you go across a group (so losing a ligand), the bond angle is reduced)

The first trend is straightforward to explain, as bond lengths increase down the group. This is in tandem with the increase in atomic radius down the group as orbitals in a greater shell begin to be filled. Thus, as you move from period 2 (N) to period 3 (P), the length of the bond increases and is in turn the overall size of each ion. There is slight variance in the length of a C-H bond in each complex, however no pattern is immediately discernible (it increases in the order S > P > N) - it is thought this is just some random error in the calculation.

Whilst there is an increase in bond length, there is no change in orientation of the bonds, thus the symmetry of TD is maintained in both the phosphorous and nitrogen molecules. As a result of this, the bond angle is the same for these two complexes. No other arrangement of the ligands is sterically possible, so ensuring that this symmetry label cannot be changed, and therefore the bond angle also cannot change. The bond angle is different for sulphur, as a result of the change of symmetry to C3v, it is not known if the change in metal centre contributes to this change - further investigation would be required.

Of note, the bond length does not appear to change going across the period. There is actually a small increase of 0.01Å if the bond length is reported accurate to 0.001Å, however it is not known if this is just an inherent error in the calculation or not. In any event, it is expected that there is a slight decrease in the bond length as you move towards the right of a period, as the increased nuclear charge better shields the electrons and thus shortens the bond length, but this is not observed here. This may be a result of this complex containing one less ligand, with the arrangement instead taken (along with the lone pair) resulting in some interactions (steric or electronic repulsion) which causes the carbon and metal atoms to move apart from each other. This theory is supported by the large deviation from bond length for the sulphur complex, indicating some feature about the arrangement it has taken is causing the bond length to be artificially lengthened.

Otherwise no strange observations are seen with the structures, with all methyl groups taking the expected tetrahedral structure, and either tetrahedral or C3v structures for the central atom as expected by the number of ligands which are present.

= Molecular orbitals and NBO charges of methyl-ligand complexes =
All three complexes discussed previously have been subject to a full NBO and MO analysis via an energy calculation with the <code>pop=(full,nbo)</code> keyword, retaining any previously used keywords as appropriate. Calculations were performed on the laptop due to load on the HPC, except for the sulphur complex as the calculation took too long on the laptop.

Log files are available as follows:

* '''[N(CH3)4]+''': [[media:Pk_log_nch34_egy.log]]
* '''[P(CH3)4]+''': [[media:Pk_log_pch34_egy.log]]
* '''[S(CH3)3]+''': {{DOI|10042/26274}}
== Calculation output ==

''' [N(CH3)4]+ '''

<pre>
File Name NCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

''' [P(CH3)4]+ '''

<pre>
File Name PCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701105 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 20.0 seconds.
</pre>

''' [S(CH3)3]+ '''

<pre>File Name sch33_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 0 minutes 57.7 seconds.
</pre>

== Sample MOs for [N(CH3)4]+ ==
A variety of 5 molecular orbitals have been calculated and shown below. Only occupied non-core MOs from the totally bonding to totally antibonding are shown.

{| class="wikitable" border="1"
|+ Totally bonding towards the top
! MO number !! Energy (hartree) !! Picture !! Degeneracy !! Notes
|-
| 6 || -1.19645 || [[Image:Pk-n-mo0.png|200px]] || Singly degenerate || This MO exhibits a great degree of strong bonding interactions across the entire molecule up to the protons, the orbitals of which do not appear to be part of this MO. This is seen by the huge red surface containing almost the entirety of the molecule. As a result of the huge amount of delocalisation seen in the MO, there is a lot of through space interactions between adjacent carbon groups, as seen by how the MO forms a 'cage' around the entire molecule - the empty space between two carbon atoms is part of this red object. As there are no other molecular orbitals other than this huge one, there is no concept of a node in this MO diagram.
|-
| 10 || -0.80745 || [[Image:Pk-n-mo1.png|200px]] || Singly degenerate || This is the first MO in this series of 5 to contain a slight degree of antibonding character, as seen by the fact each ligand is in its own (+) phase orbital, whereas the central metal is in a (-) phase one. This leads to a minor degree of antibonding character, and also a node in the centre of the M-C bond where the two MOs end. Through space interactions are present in each ligand MO, with all the protons and the central carbon existing within the boundaries of the MO, and hence there are through-space interactions between the protons. MOs of the same phase interact weakly with each other due to the large distance between each green orbital (seen in the picture), however the interaction between the (+) and (-) orbitals is quite strong as the nodal area is very small in size - the orbitals are nearly touching. The level of delocalisation is reduced, with delocalisation only occurring across each ligand group - the ligands themselves are not delocalised onto one unit.
|-
| 14 || -0.62248 || [[Image:Pk-n-mo2.png|200px]] || Doubly degenerate || For this MO, nodes exist on every carbon atom, as each MO covers two halves of a carbon atom, two protons, and nothing else. This does lead to delocalisationa cross the protons and carbon atoms, however this also does result in strong antibonding interactions at each carbon as the (+) and (-) MOs become quite close. Some protons, and the metal centre are not covered at all by this MO, however from what is delocalised, there is a significant amount of through space interactions between protons on differing methyl ligands - this is of note as the ligand protons are quite a distance away. There may be some weak bonding interactions between orbitals of the same phase, however they are quite a distance away (separated by the metal centre) so this is expected to be quite weak.
|-
| 17 || -0.58035 || [[Image:Pk-n-mo3.png|200px]] || Triply degenerate || This one again has a node on each carbon, however it differs in that each orbital only covers a single proton and half a carbon. This results in there being no through-space interactions in this molecule. Additionally, there are many strong antibonding interactions as all the orbitals are quite close together, with the a (+) orbital being surrounded by a (-) orbital on every side. If there are any bonding interactions, these are going to be very weak.
|-
| 21 || -0.57934 || [[Image:Pk-n-mo4.png|200px]] || Triply degenerate || This MO is similar to the previous, but differs in that each orbital now consists of two protons, so there are no protons which aren't enclosed in an orbital. Again, there are nodes in each carbon, but also a node in the metal center, with orbitals now also covering the metal center. This results in there being strong antibonding interactions over almost the entire molecule, with (+) interacting with (-) almost over the entire surface of every orbital. Through-space interactions are now back with there being two protons in each orbital, making it possible for these to interact, and there is also the potential for protons and metal center to interact as well. This orbital is only slightly higher energy than the previous one, and this is solely because of the increased degree of antibonding interactions present.
|}

== NBO charge distributions ==

NBO charge distributions were calculated from the checkpoint file for a range of -1.750 to 1.750 as this ensured the range of charges for all 3 complexes could be accommodated on the same scale. The charges are as follows:

{| class="wikitable" border="1"
! Complex !! Metal charge (e) !! Carbon charge (e) !! Proton charge (e)
|-
| [P(NH3)4]+ || 1.667 || -1.060 || 0.298
|-
| [N(NH3)4]+ || -0.295 || -0.846 || 0.297
|-
| [S(NH3)3]+ || 0.917 || -0.483 || 0.269
|}

<gallery>
File:Pk-nbo-n.png|Nitrogen complex
File:Pk-nbo-p.png|Phosphorous complex
File:Pk-nbo-s.png|Sulphur complex
</gallery>

There appears to be a slight trend of the metal centre charge with electronegativity, with the charge much lower as it becomes more electronegative (and hence drawing a greater share of electrons to it). This in turn makes the carbon more positive as electron density is removed from it. The protons remain rather positively charged and do not appear to be greatly affected by the metal centre, but this is likely because they are too far away for the inductive effect to occur.

Interestingly, nitrogen is more eletronegative than sulphur, yet sulphur has a greater negative charge. The reduced degree of polarisation in the bond for the nitrogen complex also suggests why the bond length for the nitrogen complex is shorter compared to the sulphur. The reason for this increased amount of negative charge is due to the lone pair present on sulphur (hence the configuration it takes according to the Jmol clip above), and so there is simply more negative charge present on the sulphur.

Thus, for the general complex [NR4]+, the positive charge located on the nitrogen in the picture is indeed located on the nitrogen, however it is somewhat delocalised over the protons too. As the nitrogen contains the greatest degree of positive charge, though, the + sign is conventionally placed here as it gives the indication as to where most of the charge is.

Analysis of the log files show the exact NBO contributions to the bond:

'''[P(NH3)3]+'''
<pre>
1. (1.98031) BD ( 1) P 1 - C 2
( 40.43%) 0.6358* P 1 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.4030 0.0006 0.0000 -0.4429
0.0006 0.0000 0.6188 -0.0009 0.0385
-0.0538 -0.0591 -0.0036 0.0254
( 59.57%) 0.7718* C 2 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.4044
-0.0074 0.4444 -0.0081 -0.6209 0.0114
0.0121 -0.0169 -0.0186 -0.0011 0.0080
</pre>

This shows almost equal contribution from each atom to the bond, with each atom assuming a sp3 arrangement as is expected by the TD symmetry. Carbon is sp3 as expected due to its saturation. As the carbon is slightly more negatively charged according to the charge distributions, the marginal increase in contribution from the carbon vs the phosphorous agrees with the charge distribution seen.

'''[N(NH3)3]+'''
<pre>
4. (1.98452) BD ( 1) C 1 - N 13
( 33.65%) 0.5801* C 1 s( 20.77%)p 3.81( 79.06%)d 0.01( 0.16%)
0.0003 0.4552 -0.0237 0.0026 -0.5129
-0.0218 -0.5129 -0.0218 -0.5129 -0.0218
0.0234 0.0234 0.0234 0.0000 0.0000
( 66.35%) 0.8146* N 13 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 0.5000 -0.0007 0.0000 0.4999
-0.0001 0.4999 -0.0001 0.4999 -0.0001
0.0103 0.0103 0.0103 0.0000 0.0000
</pre>

A similar argument can be made here. The large contribution from the nitrogen is surprising, but considering the smaller bond length for this complex based on the metal, an increased contribution from the nitrogen is not unreasonable. However this does disagree somewhat with the charge distribution which shows there is a much larger electron density on the carbon. It is thus thought that since it is possible to reach orbitals closer to the core on nitrogen rather than phosphorous, it makes nitrogen able to donate a greater share of electrons, and so polarises the bond towards it as a result of its electronegativity.

'''[S(NH3)3]+'''
<pre>
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
-0.0003 -0.4437 -0.0140 0.0033 0.7546
-0.0059 0.3161 -0.0025 0.3634 0.0098
-0.0189 -0.0222 -0.0093 -0.0186 0.0096
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 -0.0001 -0.4117 0.0075 -0.0012
0.0000 -0.7489 0.0330 0.0000 -0.3137
0.0138 0.0000 -0.4037 -0.0260 -0.0353
-0.0572 -0.0240 -0.0347 0.0051
</pre>

Finally, for the sulphur, the bond is an almost equal contribution from each atom in the bond. The charges of the S and C atoms according to the charge distribution are both similar and negative, suggesting little polarisation in this bond, and so the balance seen here is to be expected.

= Ligand influences on nitrogen metal centre complexes =
To investigate how changes to the ligands affects the cation, two variants on the nitrogen complex analysed previously have been used. One has one of the protons on a methyl ligand replaced with CH2OH, the other has the proton replaced with CH2CN. Each complex is then optimised and subject to a frequency analysis so as to allow for investigation of its structure. A MO and NBO calculation is then subsequently run to analyse how the change in ligand affects the ions electronic behaviour.

== Optimisations ==
Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26206}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26207}}

=== Summary output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
File Name nch33ch2oh_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000102 a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 1 hours 22 minutes 37.5 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
File Name nch33ch2cn_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000045 a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 50 minutes 39.5 seconds.
</pre>

=== Convergence output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000034 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-5.591936D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000011 0.000040 YES
Predicted change in Energy=-2.269581D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==

Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26290}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26291}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000106 a.u.
Imaginary Freq 0
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 26 minutes 10.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000102 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-5.078379D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000059 a.u.
Imaginary Freq 0
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 29 minutes 19.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-6.144746D-12
Optimization completed.
-- Stationary point found.
</pre>

=== Vibrational modes ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2oh_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

'''[N(CH3)3(CH2CN)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2cn_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== MO and NBO calculations ==
<code>pop=(nbo,full)</code> energy calculations were then performed on the complexes to generate MOs and NBO charge diagrams, just as has been done previously. All calculations were performed on the HPC and log files are available as follows:

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26294}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26295}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 59.3 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 25.0 seconds.
</pre>

=== NBO charge distributions ===
The main difference between these ligands is that CN is an EWG, and OH is an EDG, the latter due to the lone pairs which make it possible to enolise. Therefore comparison of the charge density of the structure can show how these ligands affect the overall structure of the molecule. The NBO charge distributions from -0.750 to 0.750 are shown below.

<gallery>
File:Pk-nbo-cn.png|CN ligand complex
File:Pk-nbo-oh.png|OH ligand complex
</gallery>

''n.b. the charge for the metal centre in the CN complex is -0.289''

It is seen that, in both cases, the nitrogen makes up the majority of the C-N bond to the C with the substituent:

'''OH case:'''
<pre>
4. (1.98195) BD ( 1) N 1 - C 14
( 67.28%) 0.8202* N 1 s( 23.48%)p 3.26( 76.49%)d 0.00( 0.03%)
0.0000 -0.4845 -0.0026 -0.0002 0.7401
-0.0032 0.3146 -0.0015 0.3438 -0.0026
-0.0092 -0.0105 -0.0043 -0.0088 0.0045
( 32.72%) 0.5720* C 14 s( 20.28%)p 3.92( 79.55%)d 0.01( 0.18%)
-0.0003 -0.4501 0.0135 0.0006 -0.7171
-0.0206 -0.3677 -0.0077 -0.3815 -0.0037
-0.0247 -0.0249 -0.0101 -0.0185 0.0102
</pre>

'''CN case:'''
<pre>
4. (1.97747) BD ( 1) N 1 - C 14
( 64.52%) 0.8033* N 1 s( 24.08%)p 3.15( 75.89%)d 0.00( 0.04%)
0.0000 0.4907 -0.0010 0.0003 0.6601
-0.0021 0.5684 0.0038 0.0000 0.0000
0.0166 0.0000 0.0000 0.0024 -0.0097
( 35.48%) 0.5956* C 14 s( 20.81%)p 3.80( 79.05%)d 0.01( 0.14%)
0.0000 0.4557 -0.0205 0.0000 -0.6428
-0.0249 -0.6135 -0.0174 0.0000 0.0000
0.0320 0.0000 0.0000 -0.0011 -0.0197
</pre>

==== Ligand influence on charge distribution ====

There is quite a significant change in electron density for the OH complex with the carbon between the OH group and the metal centre becoming much more positive. This is surprising considering the OH is a donating group, however this is simply explained. As the carbon is between two electronegative groups, a lot of electron density is withdrawn from it, and hence it becomes very positive. However, the metal centre has become more negatively charged (-0.322 vs -0.295). Hence, the donated electrons are moving straight from the oxygen to the metal centre, while the carbon between's electrons are also donated to both the oxygen and nitrogen as part of the electronegative pull these atoms have on the carbon.

Regarding the CN complex, the electron withdrawal is clearly seen on the carbon the CN ligand is bonded to, as this has become less negatively charged (-0.289 vs -0.295), showing that once again, electron withdrawal is occuring at a distance that causes electrons to travel from the nitrogen through the carbon.

In conclusion, it is seen that the electron inductive effects of the ligands has a direct influence on the the metal centre, as these effects travel through the carbon to directly pull or push electrons from the metal. This is likely due to the large contribution of charge from the nitrogen in the CN bond to the relevant C, so meaning any inductive effects on the C are very likely to influence the N due to the polarisation of the bond towards the N seen.

=== Sample MOs ===
The HOMO and LUMO for these two complexes are reported below:

{| class="wikitable" border="1"
! !! [N(CH3)3(CH2OH)]+ !!
[N(CH3)3(CH2CN)]+
|-
| HOMO || [[Image:Pk-homo-oh.png|200px]] || [[Image:Pk-homo-cn.png|200px]]
|-
| LUMO || [[Image:Pk-lumo-oh.png|200px]] || [[Image:Pk-lumo-cn.png|200px]]
|-
| HOMO Energy (hartree) || -0.48763 || -0.50047
|-
| LUMO Energy (hartree) || -0.12459 || -0.18183
|}

=== Discussion of MOs ===

The most notable change is that there is an increased amount of delocalisation present in the alcohol-containing complex's LUMO vs the cyanide containing one. Whilst it was thought that this is a result of the electron donation, further investigation showed that this is one orbital created by through-space interactions of every proton in the complex. The present of the alcohol group adds protons to fill a space in the molecule where would there otherwise be no protons (see the cyanide complex). This means that the distance between any two protons is small enough for an interaction to occur, and as there are protons around the entirety of the molecule, one orbital surrounds the entire molecule. The original theory was discarded after it was noted that the metal centre has its own orbital of the opposite phase in the centre of the complex, which leads to a very large number of strong antibonding interactions as it comes close to the delocalised proton orbital. Despite the increased degree of through-space interactions, this LUMO is higher in energy than the CN one, simply because of the increased number of antibonding interactions.

The CN complex LUMO does not have such a large delocalisation, and as a result some methyl protons occupy their own orbital of the opposite polarity.

A similar story is seen for the HOMO, which is lower in energy for the CN molecule. The overall volume of orbitals is smaller for the CN molecule, as the CN group is symmetric and simple (pi-bond like) in nature, leading to a very simple arrangement of orbitals at this point. In contrast, for the OH complex, a very complex d-orbital MO is seen over the alcohol group, which then results in some interactions over the nitrogen.

One possible result of this is that it is easier to perform electrophillic attacks on the OH complex at the nitrogen, as the presence of an orbital over the nitrogen would allow for a positively charged group to come in and perform some reaction. These reactions may include ligand substitution or oxidative addition. This kind of attack would not be possible on the CN complex HOMO as no orbital exists on the central nitrogen, and hence cannot be attacked. The only reactions possible on this HOMO would therefore be substitutions on the CN group, which is not as interesting as ligand substitution or oxidative addition on the center of the complex.

Likewise, the OH complex is likely to be more susceptable to attack by nucleophiles. This is however not due to the large delocalised MO (which is present on the CN complex too), as this only covers protons and does not allow any reactions to occur on a ligand or on the metal. However on the CN group, there is an orbital which contains both the metal center and the OH ligand, making it incredibly likely that nucleophillic attack will lead to substitution of the CH2OH group.

Finally, the HOMO-LUMO gap has changed from 0.31864 e (for the CN complex) to 0.36304 e. This makes it harder for an electron to be promoted from the HOMO to the LUMO in the OH complex. Therefore, any photochemical reactivity which is seen would occur in the CN complex but not the OH one. Considering there is a wealth of reported<ref name="photo">F. Crescitelli, B. Karvaly, ''Photochemistry and Photobiology'', 1989, '''50''', 785–791</ref> photoreactivity for CN systems, it is very likely that photochemistry will occur with the cyanide-containing complex.

= Conclusions =
Ionic solvents are formed of a liquid solution of cations and ions, the nature of which massively alter thes behaviour of the solvent. This nature has been shown to be changed by altering the metal, structure, and ligands of various positive complexes, as has been seen. This report examined how the electronegativity and periodicity of the metal, and the electron donating ability of a ligand affects the chemistry of the ion in terms of changing the structure, charge density, and molecular orbitals. Some possible pathways of reactivity of the ions have been proposed, which gives some indication as to how a change of the ion's nature massively changes its solvation properties, as solvation can occur through the coordination of the solute to the solvent ion.

Future work can include investigation into how the different ions coordinate to different substrates added to the calculation, and molecular orbital and NBO calculations can give some idea into whether the theories proposed as to where the ion may be reactive are correct.

= References =
<references />

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T16:24:49Z

Pk1811:

<div style="font-size: 40px;"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px;"><center>Ionic liquids: Designer solvents</center></div>
 
<div style="font-size: 30px;"><center>[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158 Back to week 1 work]</center></div>
 
= Introduction =
The aim of this project is to explore the physical nature of ionic liquids, which have application in designing solvents through customisation of the nature of the cation and anion<ref name="abs">M. Freemantle. ''Chem. Eng. News'', 1998, '''76''', 32–37</ref>. In this work, a variety of cations have been investigated to identify what trends are present in the variation in central atom and its ligands.

= Structures of methyl-ligand complexes =
== Optimisations ==
A number of cations have been optimised using Gaussian 09 D.01, namely [N(CH3)4]+, [P(CH3)4]+ and [F(CH3)3]+. All these complexes have been optimised to a DFT B3LYP 6-31G(d,p) level with the <code>int=ultrafine scf=conver=9</code> keywords and tight convergence - this is as a consequence of behaviour seen in previous work<ref name="labintro">P. Kent, unpublished work ([[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|lab intro]])</ref> where low frequencies did not exist within a tight range unless these keywords were specified. All calculations were run on the supplied laptop due to a significant queue of jobs on the HPC (except for [S(CH3)3]+ as it took a very long time), and the log files are available here:

* [N(CH3)4]+: [[media:Pk_log_nch34_opt.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_opt.log]]
* [S(CH3)3]+: The first attempt did not converge: {{DOI|10042/26201}}. A partially optimised structure was resubmitted as a second attempt: {{DOI|10042/26205}}. This also did not converge so a final optimisation was run on this partially optimised structure with the <code>nosymm</code> keyword. This converged: {{DOI|10042/26214}}.

Once done, convergence was verified via inspection of the log file.

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name nch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000090 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 1 minutes 27.0 seconds.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name pch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701126 a.u.
RMS Gradient Norm 0.00000675 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 24 minutes 21.0 seconds.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_opt3
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000101 a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 52.2 seconds.
</pre>

=== Convergence outputs ===

''' [N(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000014 0.000060 YES
RMS Displacement 0.000005 0.000040 YES
Predicted change in Energy=-1.010077D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000015 YES
RMS Force 0.000005 0.000010 YES
Maximum Displacement 0.000026 0.000060 YES
RMS Displacement 0.000009 0.000040 YES
Predicted change in Energy=-1.723206D-06
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''

Initial failed optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000015 NO
RMS Force 0.000006 0.000010 YES
Maximum Displacement 0.002915 0.000060 NO
RMS Displacement 0.000869 0.000040 NO
Predicted change in Energy=-5.685776D-09
Optimization stopped.
-- Number of steps exceeded, NStep= 61
-- Flag reset to prevent archiving.
</pre>

During this failed optimisation, it appears the molecule just spent a large amount of time rotating around the C3 axis through the sulphur.

The final optimisation yielded:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000049 0.000060 YES
RMS Displacement 0.000018 0.000040 YES
Predicted change in Energy=-6.520157D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==
Following this, frequency analysis was conducted with the same keywords and calculation level to ensure a minima has been found. This is ensured by checking there are no negative vibrations in the molecule. Calculations were again run on the laptop, and the log files, summaries, and frequencies are listed below. Actual animations of the modes have not been exported, however a Jmol of the log file is available and the modes can be seen by right clicking and choosing '''model -> the mode you want to see'''. This time, a range of
-30 to +30 cm-1 has been accepted for the low frequencies as molecules investigated are quite complex, and a relatively simple basis set has been used. Optimising to 6-311G(d,p) would likely bring the frequencies within the range used previously however this would be at the expense of much longer computation times.

* [N(CH3)4]+: [[media:Pk_log_nch34_freq.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_freq.log]]
* [S(CH3)3]+: {{DOI|10042/26273}}

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name NCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000085 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 3 minutes 17.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000009 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.014288D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name PCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701149 a.u.
RMS Gradient Norm 0.00000668 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 12 minutes 11.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001774 0.001800 YES
RMS Displacement 0.000659 0.001200 YES
Predicted change in Energy=-3.008780D-08
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000104 a.u.
Imaginary Freq 0
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 9 minutes 6.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000093 0.001800 YES
RMS Displacement 0.000033 0.001200 YES
Predicted change in Energy=-7.179584D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Vibration modes ===

''' [N(CH3)4]+ '''
<pre>
Low frequencies --- 0.0007 0.0011 0.0013 21.5288 21.5288 21.5288
Low frequencies --- 188.5488 292.6546 292.6546
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [P(CH3)4]+ '''
<pre>
Low frequencies --- -15.1139 -0.0002 0.0012 0.0012 5.8940 14.7736
Low frequencies --- 156.2222 191.5376 191.9513
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_pch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [S(CH3)3]+ '''
<pre>
Low frequencies --- -8.5871 0.0029 0.0049 0.0051 5.7111 9.1755
Low frequencies --- 162.4159 200.3446 200.5391
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_sch33_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== Conclusions on molecular structure ==
Investigation of structures is focused on the central atom as this is the only point at which variance should occur. The length of the M-C bonds and the angle between C-M-C on each complex is reported below:

{| class="wikitable" border="1"
! Complex !! M-C Length (Å) !! Angle (°) !! M-C length (lit<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref>) (Å)
|-
| [P(CH3)4]+ || 1.82 || 109.5 || 1.84
|-
| [N(CH3)4]+ || 1.51 || 109.5 || 1.46
|-
| [S(CH3)3]+ || 1.82 || 102.7 || 1.79
|}

''Literature bond lengths are found by adding the covalent radii for the atoms.''

Two key trends are:
* As you go down a group, the bond length decreases
* As you go across a group (so losing a ligand), the bond angle is reduced)

The first trend is straightforward to explain, as bond lengths increase down the group. This is in tandem with the increase in atomic radius down the group as orbitals in a greater shell begin to be filled. Thus, as you move from period 2 (N) to period 3 (P), the length of the bond increases and is in turn the overall size of each ion. There is slight variance in the length of a C-H bond in each complex, however no pattern is immediately discernible (it increases in the order S > P > N) - it is thought this is just some random error in the calculation.

Whilst there is an increase in bond length, there is no change in orientation of the bonds, thus the symmetry of TD is maintained in both the phosphorous and nitrogen molecules. As a result of this, the bond angle is the same for these two complexes. No other arrangement of the ligands is sterically possible, so ensuring that this symmetry label cannot be changed, and therefore the bond angle also cannot change. The bond angle is different for sulphur, as a result of the change of symmetry to C3v, it is not known if the change in metal centre contributes to this change - further investigation would be required.

Of note, the bond length does not appear to change going across the period. There is actually a small increase of 0.01Å if the bond length is reported accurate to 0.001Å, however it is not known if this is just an inherent error in the calculation or not. In any event, it is expected that there is a slight decrease in the bond length as you move towards the right of a period, as the increased nuclear charge better shields the electrons and thus shortens the bond length, but this is not observed here. This may be a result of this complex containing one less ligand, with the arrangement instead taken (along with the lone pair) resulting in some interactions (steric or electronic repulsion) which causes the carbon and metal atoms to move apart from each other. This theory is supported by the large deviation from bond length for the sulphur complex, indicating some feature about the arrangement it has taken is causing the bond length to be artificially lengthened.

Otherwise no strange observations are seen with the structures, with all methyl groups taking the expected tetrahedral structure, and either tetrahedral or C3v structures for the central atom as expected by the number of ligands which are present.

= Molecular orbitals and NBO charges of methyl-ligand complexes =
All three complexes discussed previously have been subject to a full NBO and MO analysis via an energy calculation with the <code>pop=(full,nbo)</code> keyword, retaining any previously used keywords as appropriate. Calculations were performed on the laptop due to load on the HPC, except for the sulphur complex as the calculation took too long on the laptop.

Log files are available as follows:

* '''[N(CH3)4]+''': [[media:Pk_log_nch34_egy.log]]
* '''[P(CH3)4]+''': [[media:Pk_log_pch34_egy.log]]
* '''[S(CH3)3]+''': {{DOI|10042/26274}}
== Calculation output ==

''' [N(CH3)4]+ '''

<pre>
File Name NCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

''' [P(CH3)4]+ '''

<pre>
File Name PCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701105 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 20.0 seconds.
</pre>

''' [S(CH3)3]+ '''

<pre>File Name sch33_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 0 minutes 57.7 seconds.
</pre>

== Sample MOs for [N(CH3)4]+ ==
A variety of 5 molecular orbitals have been calculated and shown below. Only occupied non-core MOs from the totally bonding to totally antibonding are shown.

{| class="wikitable" border="1"
|+ Totally bonding towards the top
! MO number !! Energy (hartree) !! Picture !! Degeneracy !! Notes
|-
| 6 || -1.19645 || [[Image:Pk-n-mo0.png|200px]] || Singly degenerate || This MO exhibits a great degree of strong bonding interactions across the entire molecule up to the protons, the orbitals of which do not appear to be part of this MO. This is seen by the huge red surface containing almost the entirety of the molecule. As a result of the huge amount of delocalisation seen in the MO, there is a lot of through space interactions between adjacent carbon groups, as seen by how the MO forms a 'cage' around the entire molecule - the empty space between two carbon atoms is part of this red object. As there are no other molecular orbitals other than this huge one, there is no concept of a node in this MO diagram.
|-
| 10 || -0.80745 || [[Image:Pk-n-mo1.png|200px]] || Singly degenerate || This is the first MO in this series of 5 to contain a slight degree of antibonding character, as seen by the fact each ligand is in its own (+) phase orbital, whereas the central metal is in a (-) phase one. This leads to a minor degree of antibonding character, and also a node in the centre of the M-C bond where the two MOs end. Through space interactions are present in each ligand MO, with all the protons and the central carbon existing within the boundaries of the MO, and hence there are through-space interactions between the protons. MOs of the same phase interact weakly with each other due to the large distance between each green orbital (seen in the picture), however the interaction between the (+) and (-) orbitals is quite strong as the nodal area is very small in size - the orbitals are nearly touching. The level of delocalisation is reduced, with delocalisation only occurring across each ligand group - the ligands themselves are not delocalised onto one unit.
|-
| 14 || -0.62248 || [[Image:Pk-n-mo2.png|200px]] || Doubly degenerate || For this MO, nodes exist on every carbon atom, as each MO covers two halves of a carbon atom, two protons, and nothing else. This does lead to delocalisationa cross the protons and carbon atoms, however this also does result in strong antibonding interactions at each carbon as the (+) and (-) MOs become quite close. Some protons, and the metal centre are not covered at all by this MO, however from what is delocalised, there is a significant amount of through space interactions between protons on differing methyl ligands - this is of note as the ligand protons are quite a distance away. There may be some weak bonding interactions between orbitals of the same phase, however they are quite a distance away (separated by the metal centre) so this is expected to be quite weak.
|-
| 17 || -0.58035 || [[Image:Pk-n-mo3.png|200px]] || Triply degenerate || This one again has a node on each carbon, however it differs in that each orbital only covers a single proton and half a carbon. This results in there being no through-space interactions in this molecule. Additionally, there are many strong antibonding interactions as all the orbitals are quite close together, with the a (+) orbital being surrounded by a (-) orbital on every side. If there are any bonding interactions, these are going to be very weak.
|-
| 21 || -0.57934 || [[Image:Pk-n-mo4.png|200px]] || Triply degenerate || This MO is similar to the previous, but differs in that each orbital now consists of two protons, so there are no protons which aren't enclosed in an orbital. Again, there are nodes in each carbon, but also a node in the metal center, with orbitals now also covering the metal center. This results in there being strong antibonding interactions over almost the entire molecule, with (+) interacting with (-) almost over the entire surface of every orbital. Through-space interactions are now back with there being two protons in each orbital, making it possible for these to interact, and there is also the potential for protons and metal center to interact as well. This orbital is only slightly higher energy than the previous one, and this is solely because of the increased degree of antibonding interactions present.
|}

== NBO charge distributions ==

NBO charge distributions were calculated from the checkpoint file for a range of -1.750 to 1.750 as this ensured the range of charges for all 3 complexes could be accommodated on the same scale. The charges are as follows:

{| class="wikitable" border="1"
! Complex !! Metal charge (e) !! Carbon charge (e) !! Proton charge (e)
|-
| [P(NH3)4]+ || 1.667 || -1.060 || 0.298
|-
| [N(NH3)4]+ || -0.295 || -0.846 || 0.297
|-
| [S(NH3)3]+ || 0.917 || -0.483 || 0.269
|}

<gallery>
File:Pk-nbo-n.png|Nitrogen complex
File:Pk-nbo-p.png|Phosphorous complex
File:Pk-nbo-s.png|Sulphur complex
</gallery>

There appears to be a slight trend of the metal centre charge with electronegativity, with the charge much lower as it becomes more electronegative (and hence drawing a greater share of electrons to it). This in turn makes the carbon more positive as electron density is removed from it. The protons remain rather positively charged and do not appear to be greatly affected by the metal centre, but this is likely because they are too far away for the inductive effect to occur.

Interestingly, nitrogen is more eletronegative than sulphur, yet sulphur has a greater negative charge. The reduced degree of polarisation in the bond for the nitrogen complex also suggests why the bond length for the nitrogen complex is shorter compared to the sulphur. The reason for this increased amount of negative charge is due to the lone pair present on sulphur (hence the configuration it takes according to the Jmol clip above), and so there is simply more negative charge present on the sulphur.

Thus, for the general complex [NR4]+, the positive charge located on the nitrogen in the picture is indeed located on the nitrogen, however it is somewhat delocalised over the protons too. As the nitrogen contains the greatest degree of positive charge, though, the + sign is conventionally placed here as it gives the indication as to where most of the charge is.

Analysis of the log files show the exact NBO contributions to the bond:

'''[P(NH3)3]+'''
<pre>
1. (1.98031) BD ( 1) P 1 - C 2
( 40.43%) 0.6358* P 1 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.4030 0.0006 0.0000 -0.4429
0.0006 0.0000 0.6188 -0.0009 0.0385
-0.0538 -0.0591 -0.0036 0.0254
( 59.57%) 0.7718* C 2 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.4044
-0.0074 0.4444 -0.0081 -0.6209 0.0114
0.0121 -0.0169 -0.0186 -0.0011 0.0080
</pre>

This shows almost equal contribution from each atom to the bond, with each atom assuming a sp3 arrangement as is expected by the TD symmetry. Carbon is sp3 as expected due to its saturation. As the carbon is slightly more negatively charged according to the charge distributions, the marginal increase in contribution from the carbon vs the phosphorous agrees with the charge distribution seen.

'''[N(NH3)3]+'''
<pre>
4. (1.98452) BD ( 1) C 1 - N 13
( 33.65%) 0.5801* C 1 s( 20.77%)p 3.81( 79.06%)d 0.01( 0.16%)
0.0003 0.4552 -0.0237 0.0026 -0.5129
-0.0218 -0.5129 -0.0218 -0.5129 -0.0218
0.0234 0.0234 0.0234 0.0000 0.0000
( 66.35%) 0.8146* N 13 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 0.5000 -0.0007 0.0000 0.4999
-0.0001 0.4999 -0.0001 0.4999 -0.0001
0.0103 0.0103 0.0103 0.0000 0.0000
</pre>

A similar argument can be made here. The large contribution from the nitrogen is surprising, but considering the smaller bond length for this complex based on the metal, an increased contribution from the nitrogen is not unreasonable. However this does disagree somewhat with the charge distribution which shows there is a much larger electron density on the carbon. It is thus thought that since it is possible to reach orbitals closer to the core on nitrogen rather than phosphorous, it makes nitrogen able to donate a greater share of electrons, and so polarises the bond towards it as a result of its electronegativity.

'''[S(NH3)3]+'''
<pre>
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
-0.0003 -0.4437 -0.0140 0.0033 0.7546
-0.0059 0.3161 -0.0025 0.3634 0.0098
-0.0189 -0.0222 -0.0093 -0.0186 0.0096
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 -0.0001 -0.4117 0.0075 -0.0012
0.0000 -0.7489 0.0330 0.0000 -0.3137
0.0138 0.0000 -0.4037 -0.0260 -0.0353
-0.0572 -0.0240 -0.0347 0.0051
</pre>

Finally, for the sulphur, the bond is an almost equal contribution from each atom in the bond. The charges of the S and C atoms according to the charge distribution are both similar and negative, suggesting little polarisation in this bond, and so the balance seen here is to be expected.

= Ligand influences on nitrogen metal centre complexes =
To investigate how changes to the ligands affects the cation, two variants on the nitrogen complex analysed previously have been used. One has one of the protons on a methyl ligand replaced with CH2OH, the other has the proton replaced with CH2CN. Each complex is then optimised and subject to a frequency analysis so as to allow for investigation of its structure. A MO and NBO calculation is then subsequently run to analyse how the change in ligand affects the ions electronic behaviour.

== Optimisations ==
Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26206}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26207}}

=== Summary output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
File Name nch33ch2oh_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000102 a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 1 hours 22 minutes 37.5 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
File Name nch33ch2cn_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000045 a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 50 minutes 39.5 seconds.
</pre>

=== Convergence output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000034 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-5.591936D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000011 0.000040 YES
Predicted change in Energy=-2.269581D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==

Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26290}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26291}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000106 a.u.
Imaginary Freq 0
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 26 minutes 10.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000102 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-5.078379D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000059 a.u.
Imaginary Freq 0
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 29 minutes 19.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-6.144746D-12
Optimization completed.
-- Stationary point found.
</pre>

=== Vibrational modes ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2oh_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

'''[N(CH3)3(CH2CN)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2cn_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== MO and NBO calculations ==
<code>pop=(nbo,full)</code> energy calculations were then performed on the complexes to generate MOs and NBO charge diagrams, just as has been done previously. All calculations were performed on the HPC and log files are available as follows:

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26294}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26295}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 59.3 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 25.0 seconds.
</pre>

=== NBO charge distributions ===
The main difference between these ligands is that CN is an EWG, and OH is an EDG, the latter due to the lone pairs which make it possible to enolise. Therefore comparison of the charge density of the structure can show how these ligands affect the overall structure of the molecule. The NBO charge distributions from -0.750 to 0.750 are shown below.

<gallery>
File:Pk-nbo-cn.png|CN ligand complex
File:Pk-nbo-oh.png|OH ligand complex
</gallery>

''n.b. the charge for the metal centre in the CN complex is -0.289''

It is seen that, in both cases, the nitrogen makes up the majority of the C-N bond to the C with the substituent:

'''OH case:'''
<pre>
4. (1.98195) BD ( 1) N 1 - C 14
( 67.28%) 0.8202* N 1 s( 23.48%)p 3.26( 76.49%)d 0.00( 0.03%)
0.0000 -0.4845 -0.0026 -0.0002 0.7401
-0.0032 0.3146 -0.0015 0.3438 -0.0026
-0.0092 -0.0105 -0.0043 -0.0088 0.0045
( 32.72%) 0.5720* C 14 s( 20.28%)p 3.92( 79.55%)d 0.01( 0.18%)
-0.0003 -0.4501 0.0135 0.0006 -0.7171
-0.0206 -0.3677 -0.0077 -0.3815 -0.0037
-0.0247 -0.0249 -0.0101 -0.0185 0.0102
</pre>

'''CN case:'''
<pre>
4. (1.97747) BD ( 1) N 1 - C 14
( 64.52%) 0.8033* N 1 s( 24.08%)p 3.15( 75.89%)d 0.00( 0.04%)
0.0000 0.4907 -0.0010 0.0003 0.6601
-0.0021 0.5684 0.0038 0.0000 0.0000
0.0166 0.0000 0.0000 0.0024 -0.0097
( 35.48%) 0.5956* C 14 s( 20.81%)p 3.80( 79.05%)d 0.01( 0.14%)
0.0000 0.4557 -0.0205 0.0000 -0.6428
-0.0249 -0.6135 -0.0174 0.0000 0.0000
0.0320 0.0000 0.0000 -0.0011 -0.0197
</pre>

==== Ligand influence on charge distribution ====

There is quite a significant change in electron density for the OH complex with the carbon between the OH group and the metal centre becoming much more positive. This is surprising considering the OH is a donating group, however this is simply explained. As the carbon is between two electronegative groups, a lot of electron density is withdrawn from it, and hence it becomes very positive. However, the metal centre has become more negatively charged (-0.322 vs -0.295). Hence, the donated electrons are moving straight from the oxygen to the metal centre, while the carbon between's electrons are also donated to both the oxygen and nitrogen as part of the electronegative pull these atoms have on the carbon.

Regarding the CN complex, the electron withdrawal is clearly seen on the carbon the CN ligand is bonded to, as this has become less negatively charged (-0.289 vs -0.295), showing that once again, electron withdrawal is occuring at a distance that causes electrons to travel from the nitrogen through the carbon.

In conclusion, it is seen that the electron inductive effects of the ligands has a direct influence on the the metal centre, as these effects travel through the carbon to directly pull or push electrons from the metal. This is likely due to the large contribution of charge from the nitrogen in the CN bond to the relevant C, so meaning any inductive effects on the C are very likely to influence the N due to the polarisation of the bond towards the N seen.

=== Sample MOs ===
The HOMO and LUMO for these two complexes are reported below:

{| class="wikitable" border="1"
! !! [N(CH3)3(CH2OH)]+ !!
[N(CH3)3(CH2CN)]+
|-
| HOMO || [[Image:Pk-homo-oh.png|200px]] || [[Image:Pk-homo-cn.png|200px]]
|-
| LUMO || [[Image:Pk-lumo-oh.png|200px]] || [[Image:Pk-lumo-cn.png|200px]]
|-
| HOMO Energy (hartree) || -0.48763 || -0.50047
|-
| LUMO Energy (hartree) || -0.12459 || -0.18183
|}

=== Discussion of MOs ===

The most notable change is that there is an increased amount of delocalisation present in the alcohol-containing complex's LUMO vs the cyanide containing one. Whilst it was thought that this is a result of the electron donation, further investigation showed that this is one orbital created by through-space interactions of every proton in the complex. The present of the alcohol group adds protons to fill a space in the molecule where would there otherwise be no protons (see the cyanide complex). This means that the distance between any two protons is small enough for an interaction to occur, and as there are protons around the entirety of the molecule, one orbital surrounds the entire molecule. The original theory was discarded after it was noted that the metal centre has its own orbital of the opposite phase in the centre of the complex, which leads to a very large number of strong antibonding interactions as it comes close to the delocalised proton orbital. Despite the increased degree of through-space interactions, this LUMO is higher in energy than the CN one, simply because of the increased number of antibonding interactions.

The CN complex LUMO does not have such a large delocalisation, and as a result some methyl protons occupy their own orbital of the opposite polarity.

A similar story is seen for the HOMO, which is lower in energy for the CN molecule. The overall volume of orbitals is smaller for the CN molecule, as the CN group is symmetric and simple (pi-bond like) in nature, leading to a very simple arrangement of orbitals at this point. In contrast, for the OH complex, a very complex d-orbital MO is seen over the alcohol group, which then results in some interactions over the nitrogen.

One possible result of this is that it is easier to perform electrophillic attacks on the OH complex at the nitrogen, as the presence of an orbital over the nitrogen would allow for a positively charged group to come in and perform some reaction. These reactions may include ligand substitution or oxidative addition. This kind of attack would not be possible on the CN complex HOMO as no orbital exists on the central nitrogen, and hence cannot be attacked. The only reactions possible on this HOMO would therefore be substitutions on the CN group, which is not as interesting as ligand substitution or oxidative addition on the center of the complex.

Likewise, the OH complex is likely to be more susceptable to attack by nucleophiles. This is however not due to the large delocalised MO (which is present on the CN complex too), as this only covers protons and does not allow any reactions to occur on a ligand or on the metal. However on the CN group, there is an orbital which contains both the metal center and the OH ligand, making it incredibly likely that nucleophillic attack will lead to substitution of the CH2OH group.

Finally, the HOMO-LUMO gap has changed from 0.31864 e (for the CN complex) to 0.36304 e. This makes it harder for an electron to be promoted from the HOMO to the LUMO in the OH complex. Therefore, any photochemical reactivity which is seen would occur in the CN complex but not the OH one. Considering there is a wealth of reported<ref name="photo">F. Crescitelli, B. Karvaly, ''Photochemistry and Photobiology'', 1989, '''50''', 785–791</ref> photoreactivity for CN systems, it is very likely that photochemistry will occur with the cyanide-containing complex.

= Conclusions =
Ionic solvents are formed of a liquid solution of cations and ions, the nature of which massively alter thes behaviour of the solvent. This nature has been shown to be changed by altering the metal, structure, and ligands of various positive complexes, as has been seen. This report examined how the electronegativity and periodicity of the metal, and the electron donating ability of a ligand affects the chemistry of the ion in terms of changing the structure, charge density, and molecular orbitals. Some possible pathways of reactivity of the ions have been proposed, which gives some indication as to how a change of the ion's nature massively changes its solvation properties, as solvation can occur through the coordination of the solute to the solvent ion.

Future work can include investigation into how the different ions coordinate to different substrates added to the calculation, and molecular orbital and NBO calculations can give some idea into whether the theories proposed as to where the ion may be reactive are correct.

= References =
<references />

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T16:22:54Z

Pk1811: /* Discussion of MOs */

<div style="font-size: 40px;"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px;"><center>Ionic liquids: Designer solvents</center></div>
 
= Introduction =
The aim of this project is to explore the physical nature of ionic liquids, which have application in designing solvents through customisation of the nature of the cation and anion<ref name="abs">M. Freemantle. ''Chem. Eng. News'', 1998, '''76''', 32–37</ref>. In this work, a variety of cations have been investigated to identify what trends are present in the variation in central atom and its ligands.

= Structures of methyl-ligand complexes =
== Optimisations ==
A number of cations have been optimised using Gaussian 09 D.01, namely [N(CH3)4]+, [P(CH3)4]+ and [F(CH3)3]+. All these complexes have been optimised to a DFT B3LYP 6-31G(d,p) level with the <code>int=ultrafine scf=conver=9</code> keywords and tight convergence - this is as a consequence of behaviour seen in previous work<ref name="labintro">P. Kent, unpublished work ([[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|lab intro]])</ref> where low frequencies did not exist within a tight range unless these keywords were specified. All calculations were run on the supplied laptop due to a significant queue of jobs on the HPC (except for [S(CH3)3]+ as it took a very long time), and the log files are available here:

* [N(CH3)4]+: [[media:Pk_log_nch34_opt.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_opt.log]]
* [S(CH3)3]+: The first attempt did not converge: {{DOI|10042/26201}}. A partially optimised structure was resubmitted as a second attempt: {{DOI|10042/26205}}. This also did not converge so a final optimisation was run on this partially optimised structure with the <code>nosymm</code> keyword. This converged: {{DOI|10042/26214}}.

Once done, convergence was verified via inspection of the log file.

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name nch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000090 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 1 minutes 27.0 seconds.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name pch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701126 a.u.
RMS Gradient Norm 0.00000675 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 24 minutes 21.0 seconds.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_opt3
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000101 a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 52.2 seconds.
</pre>

=== Convergence outputs ===

''' [N(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000014 0.000060 YES
RMS Displacement 0.000005 0.000040 YES
Predicted change in Energy=-1.010077D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000015 YES
RMS Force 0.000005 0.000010 YES
Maximum Displacement 0.000026 0.000060 YES
RMS Displacement 0.000009 0.000040 YES
Predicted change in Energy=-1.723206D-06
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''

Initial failed optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000015 NO
RMS Force 0.000006 0.000010 YES
Maximum Displacement 0.002915 0.000060 NO
RMS Displacement 0.000869 0.000040 NO
Predicted change in Energy=-5.685776D-09
Optimization stopped.
-- Number of steps exceeded, NStep= 61
-- Flag reset to prevent archiving.
</pre>

During this failed optimisation, it appears the molecule just spent a large amount of time rotating around the C3 axis through the sulphur.

The final optimisation yielded:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000049 0.000060 YES
RMS Displacement 0.000018 0.000040 YES
Predicted change in Energy=-6.520157D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==
Following this, frequency analysis was conducted with the same keywords and calculation level to ensure a minima has been found. This is ensured by checking there are no negative vibrations in the molecule. Calculations were again run on the laptop, and the log files, summaries, and frequencies are listed below. Actual animations of the modes have not been exported, however a Jmol of the log file is available and the modes can be seen by right clicking and choosing '''model -> the mode you want to see'''. This time, a range of
-30 to +30 cm-1 has been accepted for the low frequencies as molecules investigated are quite complex, and a relatively simple basis set has been used. Optimising to 6-311G(d,p) would likely bring the frequencies within the range used previously however this would be at the expense of much longer computation times.

* [N(CH3)4]+: [[media:Pk_log_nch34_freq.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_freq.log]]
* [S(CH3)3]+: {{DOI|10042/26273}}

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name NCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000085 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 3 minutes 17.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000009 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.014288D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name PCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701149 a.u.
RMS Gradient Norm 0.00000668 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 12 minutes 11.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001774 0.001800 YES
RMS Displacement 0.000659 0.001200 YES
Predicted change in Energy=-3.008780D-08
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000104 a.u.
Imaginary Freq 0
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 9 minutes 6.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000093 0.001800 YES
RMS Displacement 0.000033 0.001200 YES
Predicted change in Energy=-7.179584D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Vibration modes ===

''' [N(CH3)4]+ '''
<pre>
Low frequencies --- 0.0007 0.0011 0.0013 21.5288 21.5288 21.5288
Low frequencies --- 188.5488 292.6546 292.6546
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [P(CH3)4]+ '''
<pre>
Low frequencies --- -15.1139 -0.0002 0.0012 0.0012 5.8940 14.7736
Low frequencies --- 156.2222 191.5376 191.9513
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_pch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [S(CH3)3]+ '''
<pre>
Low frequencies --- -8.5871 0.0029 0.0049 0.0051 5.7111 9.1755
Low frequencies --- 162.4159 200.3446 200.5391
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_sch33_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== Conclusions on molecular structure ==
Investigation of structures is focused on the central atom as this is the only point at which variance should occur. The length of the M-C bonds and the angle between C-M-C on each complex is reported below:

{| class="wikitable" border="1"
! Complex !! M-C Length (Å) !! Angle (°) !! M-C length (lit<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref>) (Å)
|-
| [P(CH3)4]+ || 1.82 || 109.5 || 1.84
|-
| [N(CH3)4]+ || 1.51 || 109.5 || 1.46
|-
| [S(CH3)3]+ || 1.82 || 102.7 || 1.79
|}

''Literature bond lengths are found by adding the covalent radii for the atoms.''

Two key trends are:
* As you go down a group, the bond length decreases
* As you go across a group (so losing a ligand), the bond angle is reduced)

The first trend is straightforward to explain, as bond lengths increase down the group. This is in tandem with the increase in atomic radius down the group as orbitals in a greater shell begin to be filled. Thus, as you move from period 2 (N) to period 3 (P), the length of the bond increases and is in turn the overall size of each ion. There is slight variance in the length of a C-H bond in each complex, however no pattern is immediately discernible (it increases in the order S > P > N) - it is thought this is just some random error in the calculation.

Whilst there is an increase in bond length, there is no change in orientation of the bonds, thus the symmetry of TD is maintained in both the phosphorous and nitrogen molecules. As a result of this, the bond angle is the same for these two complexes. No other arrangement of the ligands is sterically possible, so ensuring that this symmetry label cannot be changed, and therefore the bond angle also cannot change. The bond angle is different for sulphur, as a result of the change of symmetry to C3v, it is not known if the change in metal centre contributes to this change - further investigation would be required.

Of note, the bond length does not appear to change going across the period. There is actually a small increase of 0.01Å if the bond length is reported accurate to 0.001Å, however it is not known if this is just an inherent error in the calculation or not. In any event, it is expected that there is a slight decrease in the bond length as you move towards the right of a period, as the increased nuclear charge better shields the electrons and thus shortens the bond length, but this is not observed here. This may be a result of this complex containing one less ligand, with the arrangement instead taken (along with the lone pair) resulting in some interactions (steric or electronic repulsion) which causes the carbon and metal atoms to move apart from each other. This theory is supported by the large deviation from bond length for the sulphur complex, indicating some feature about the arrangement it has taken is causing the bond length to be artificially lengthened.

Otherwise no strange observations are seen with the structures, with all methyl groups taking the expected tetrahedral structure, and either tetrahedral or C3v structures for the central atom as expected by the number of ligands which are present.

= Molecular orbitals and NBO charges of methyl-ligand complexes =
All three complexes discussed previously have been subject to a full NBO and MO analysis via an energy calculation with the <code>pop=(full,nbo)</code> keyword, retaining any previously used keywords as appropriate. Calculations were performed on the laptop due to load on the HPC, except for the sulphur complex as the calculation took too long on the laptop.

Log files are available as follows:

* '''[N(CH3)4]+''': [[media:Pk_log_nch34_egy.log]]
* '''[P(CH3)4]+''': [[media:Pk_log_pch34_egy.log]]
* '''[S(CH3)3]+''': {{DOI|10042/26274}}
== Calculation output ==

''' [N(CH3)4]+ '''

<pre>
File Name NCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

''' [P(CH3)4]+ '''

<pre>
File Name PCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701105 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 20.0 seconds.
</pre>

''' [S(CH3)3]+ '''

<pre>File Name sch33_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 0 minutes 57.7 seconds.
</pre>

== Sample MOs for [N(CH3)4]+ ==
A variety of 5 molecular orbitals have been calculated and shown below. Only occupied non-core MOs from the totally bonding to totally antibonding are shown.

{| class="wikitable" border="1"
|+ Totally bonding towards the top
! MO number !! Energy (hartree) !! Picture !! Degeneracy !! Notes
|-
| 6 || -1.19645 || [[Image:Pk-n-mo0.png|200px]] || Singly degenerate || This MO exhibits a great degree of strong bonding interactions across the entire molecule up to the protons, the orbitals of which do not appear to be part of this MO. This is seen by the huge red surface containing almost the entirety of the molecule. As a result of the huge amount of delocalisation seen in the MO, there is a lot of through space interactions between adjacent carbon groups, as seen by how the MO forms a 'cage' around the entire molecule - the empty space between two carbon atoms is part of this red object. As there are no other molecular orbitals other than this huge one, there is no concept of a node in this MO diagram.
|-
| 10 || -0.80745 || [[Image:Pk-n-mo1.png|200px]] || Singly degenerate || This is the first MO in this series of 5 to contain a slight degree of antibonding character, as seen by the fact each ligand is in its own (+) phase orbital, whereas the central metal is in a (-) phase one. This leads to a minor degree of antibonding character, and also a node in the centre of the M-C bond where the two MOs end. Through space interactions are present in each ligand MO, with all the protons and the central carbon existing within the boundaries of the MO, and hence there are through-space interactions between the protons. MOs of the same phase interact weakly with each other due to the large distance between each green orbital (seen in the picture), however the interaction between the (+) and (-) orbitals is quite strong as the nodal area is very small in size - the orbitals are nearly touching. The level of delocalisation is reduced, with delocalisation only occurring across each ligand group - the ligands themselves are not delocalised onto one unit.
|-
| 14 || -0.62248 || [[Image:Pk-n-mo2.png|200px]] || Doubly degenerate || For this MO, nodes exist on every carbon atom, as each MO covers two halves of a carbon atom, two protons, and nothing else. This does lead to delocalisationa cross the protons and carbon atoms, however this also does result in strong antibonding interactions at each carbon as the (+) and (-) MOs become quite close. Some protons, and the metal centre are not covered at all by this MO, however from what is delocalised, there is a significant amount of through space interactions between protons on differing methyl ligands - this is of note as the ligand protons are quite a distance away. There may be some weak bonding interactions between orbitals of the same phase, however they are quite a distance away (separated by the metal centre) so this is expected to be quite weak.
|-
| 17 || -0.58035 || [[Image:Pk-n-mo3.png|200px]] || Triply degenerate || This one again has a node on each carbon, however it differs in that each orbital only covers a single proton and half a carbon. This results in there being no through-space interactions in this molecule. Additionally, there are many strong antibonding interactions as all the orbitals are quite close together, with the a (+) orbital being surrounded by a (-) orbital on every side. If there are any bonding interactions, these are going to be very weak.
|-
| 21 || -0.57934 || [[Image:Pk-n-mo4.png|200px]] || Triply degenerate || This MO is similar to the previous, but differs in that each orbital now consists of two protons, so there are no protons which aren't enclosed in an orbital. Again, there are nodes in each carbon, but also a node in the metal center, with orbitals now also covering the metal center. This results in there being strong antibonding interactions over almost the entire molecule, with (+) interacting with (-) almost over the entire surface of every orbital. Through-space interactions are now back with there being two protons in each orbital, making it possible for these to interact, and there is also the potential for protons and metal center to interact as well. This orbital is only slightly higher energy than the previous one, and this is solely because of the increased degree of antibonding interactions present.
|}

== NBO charge distributions ==

NBO charge distributions were calculated from the checkpoint file for a range of -1.750 to 1.750 as this ensured the range of charges for all 3 complexes could be accommodated on the same scale. The charges are as follows:

{| class="wikitable" border="1"
! Complex !! Metal charge (e) !! Carbon charge (e) !! Proton charge (e)
|-
| [P(NH3)4]+ || 1.667 || -1.060 || 0.298
|-
| [N(NH3)4]+ || -0.295 || -0.846 || 0.297
|-
| [S(NH3)3]+ || 0.917 || -0.483 || 0.269
|}

<gallery>
File:Pk-nbo-n.png|Nitrogen complex
File:Pk-nbo-p.png|Phosphorous complex
File:Pk-nbo-s.png|Sulphur complex
</gallery>

There appears to be a slight trend of the metal centre charge with electronegativity, with the charge much lower as it becomes more electronegative (and hence drawing a greater share of electrons to it). This in turn makes the carbon more positive as electron density is removed from it. The protons remain rather positively charged and do not appear to be greatly affected by the metal centre, but this is likely because they are too far away for the inductive effect to occur.

Interestingly, nitrogen is more eletronegative than sulphur, yet sulphur has a greater negative charge. The reduced degree of polarisation in the bond for the nitrogen complex also suggests why the bond length for the nitrogen complex is shorter compared to the sulphur. The reason for this increased amount of negative charge is due to the lone pair present on sulphur (hence the configuration it takes according to the Jmol clip above), and so there is simply more negative charge present on the sulphur.

Thus, for the general complex [NR4]+, the positive charge located on the nitrogen in the picture is indeed located on the nitrogen, however it is somewhat delocalised over the protons too. As the nitrogen contains the greatest degree of positive charge, though, the + sign is conventionally placed here as it gives the indication as to where most of the charge is.

Analysis of the log files show the exact NBO contributions to the bond:

'''[P(NH3)3]+'''
<pre>
1. (1.98031) BD ( 1) P 1 - C 2
( 40.43%) 0.6358* P 1 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.4030 0.0006 0.0000 -0.4429
0.0006 0.0000 0.6188 -0.0009 0.0385
-0.0538 -0.0591 -0.0036 0.0254
( 59.57%) 0.7718* C 2 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.4044
-0.0074 0.4444 -0.0081 -0.6209 0.0114
0.0121 -0.0169 -0.0186 -0.0011 0.0080
</pre>

This shows almost equal contribution from each atom to the bond, with each atom assuming a sp3 arrangement as is expected by the TD symmetry. Carbon is sp3 as expected due to its saturation. As the carbon is slightly more negatively charged according to the charge distributions, the marginal increase in contribution from the carbon vs the phosphorous agrees with the charge distribution seen.

'''[N(NH3)3]+'''
<pre>
4. (1.98452) BD ( 1) C 1 - N 13
( 33.65%) 0.5801* C 1 s( 20.77%)p 3.81( 79.06%)d 0.01( 0.16%)
0.0003 0.4552 -0.0237 0.0026 -0.5129
-0.0218 -0.5129 -0.0218 -0.5129 -0.0218
0.0234 0.0234 0.0234 0.0000 0.0000
( 66.35%) 0.8146* N 13 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 0.5000 -0.0007 0.0000 0.4999
-0.0001 0.4999 -0.0001 0.4999 -0.0001
0.0103 0.0103 0.0103 0.0000 0.0000
</pre>

A similar argument can be made here. The large contribution from the nitrogen is surprising, but considering the smaller bond length for this complex based on the metal, an increased contribution from the nitrogen is not unreasonable. However this does disagree somewhat with the charge distribution which shows there is a much larger electron density on the carbon. It is thus thought that since it is possible to reach orbitals closer to the core on nitrogen rather than phosphorous, it makes nitrogen able to donate a greater share of electrons, and so polarises the bond towards it as a result of its electronegativity.

'''[S(NH3)3]+'''
<pre>
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
-0.0003 -0.4437 -0.0140 0.0033 0.7546
-0.0059 0.3161 -0.0025 0.3634 0.0098
-0.0189 -0.0222 -0.0093 -0.0186 0.0096
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 -0.0001 -0.4117 0.0075 -0.0012
0.0000 -0.7489 0.0330 0.0000 -0.3137
0.0138 0.0000 -0.4037 -0.0260 -0.0353
-0.0572 -0.0240 -0.0347 0.0051
</pre>

Finally, for the sulphur, the bond is an almost equal contribution from each atom in the bond. The charges of the S and C atoms according to the charge distribution are both similar and negative, suggesting little polarisation in this bond, and so the balance seen here is to be expected.

= Ligand influences on nitrogen metal centre complexes =
To investigate how changes to the ligands affects the cation, two variants on the nitrogen complex analysed previously have been used. One has one of the protons on a methyl ligand replaced with CH2OH, the other has the proton replaced with CH2CN. Each complex is then optimised and subject to a frequency analysis so as to allow for investigation of its structure. A MO and NBO calculation is then subsequently run to analyse how the change in ligand affects the ions electronic behaviour.

== Optimisations ==
Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26206}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26207}}

=== Summary output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
File Name nch33ch2oh_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000102 a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 1 hours 22 minutes 37.5 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
File Name nch33ch2cn_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000045 a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 50 minutes 39.5 seconds.
</pre>

=== Convergence output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000034 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-5.591936D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000011 0.000040 YES
Predicted change in Energy=-2.269581D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==

Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26290}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26291}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000106 a.u.
Imaginary Freq 0
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 26 minutes 10.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000102 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-5.078379D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000059 a.u.
Imaginary Freq 0
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 29 minutes 19.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-6.144746D-12
Optimization completed.
-- Stationary point found.
</pre>

=== Vibrational modes ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2oh_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

'''[N(CH3)3(CH2CN)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2cn_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== MO and NBO calculations ==
<code>pop=(nbo,full)</code> energy calculations were then performed on the complexes to generate MOs and NBO charge diagrams, just as has been done previously. All calculations were performed on the HPC and log files are available as follows:

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26294}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26295}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 59.3 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 25.0 seconds.
</pre>

=== NBO charge distributions ===
The main difference between these ligands is that CN is an EWG, and OH is an EDG, the latter due to the lone pairs which make it possible to enolise. Therefore comparison of the charge density of the structure can show how these ligands affect the overall structure of the molecule. The NBO charge distributions from -0.750 to 0.750 are shown below.

<gallery>
File:Pk-nbo-cn.png|CN ligand complex
File:Pk-nbo-oh.png|OH ligand complex
</gallery>

''n.b. the charge for the metal centre in the CN complex is -0.289''

It is seen that, in both cases, the nitrogen makes up the majority of the C-N bond to the C with the substituent:

'''OH case:'''
<pre>
4. (1.98195) BD ( 1) N 1 - C 14
( 67.28%) 0.8202* N 1 s( 23.48%)p 3.26( 76.49%)d 0.00( 0.03%)
0.0000 -0.4845 -0.0026 -0.0002 0.7401
-0.0032 0.3146 -0.0015 0.3438 -0.0026
-0.0092 -0.0105 -0.0043 -0.0088 0.0045
( 32.72%) 0.5720* C 14 s( 20.28%)p 3.92( 79.55%)d 0.01( 0.18%)
-0.0003 -0.4501 0.0135 0.0006 -0.7171
-0.0206 -0.3677 -0.0077 -0.3815 -0.0037
-0.0247 -0.0249 -0.0101 -0.0185 0.0102
</pre>

'''CN case:'''
<pre>
4. (1.97747) BD ( 1) N 1 - C 14
( 64.52%) 0.8033* N 1 s( 24.08%)p 3.15( 75.89%)d 0.00( 0.04%)
0.0000 0.4907 -0.0010 0.0003 0.6601
-0.0021 0.5684 0.0038 0.0000 0.0000
0.0166 0.0000 0.0000 0.0024 -0.0097
( 35.48%) 0.5956* C 14 s( 20.81%)p 3.80( 79.05%)d 0.01( 0.14%)
0.0000 0.4557 -0.0205 0.0000 -0.6428
-0.0249 -0.6135 -0.0174 0.0000 0.0000
0.0320 0.0000 0.0000 -0.0011 -0.0197
</pre>

==== Ligand influence on charge distribution ====

There is quite a significant change in electron density for the OH complex with the carbon between the OH group and the metal centre becoming much more positive. This is surprising considering the OH is a donating group, however this is simply explained. As the carbon is between two electronegative groups, a lot of electron density is withdrawn from it, and hence it becomes very positive. However, the metal centre has become more negatively charged (-0.322 vs -0.295). Hence, the donated electrons are moving straight from the oxygen to the metal centre, while the carbon between's electrons are also donated to both the oxygen and nitrogen as part of the electronegative pull these atoms have on the carbon.

Regarding the CN complex, the electron withdrawal is clearly seen on the carbon the CN ligand is bonded to, as this has become less negatively charged (-0.289 vs -0.295), showing that once again, electron withdrawal is occuring at a distance that causes electrons to travel from the nitrogen through the carbon.

In conclusion, it is seen that the electron inductive effects of the ligands has a direct influence on the the metal centre, as these effects travel through the carbon to directly pull or push electrons from the metal. This is likely due to the large contribution of charge from the nitrogen in the CN bond to the relevant C, so meaning any inductive effects on the C are very likely to influence the N due to the polarisation of the bond towards the N seen.

=== Sample MOs ===
The HOMO and LUMO for these two complexes are reported below:

{| class="wikitable" border="1"
! !! [N(CH3)3(CH2OH)]+ !!
[N(CH3)3(CH2CN)]+
|-
| HOMO || [[Image:Pk-homo-oh.png|200px]] || [[Image:Pk-homo-cn.png|200px]]
|-
| LUMO || [[Image:Pk-lumo-oh.png|200px]] || [[Image:Pk-lumo-cn.png|200px]]
|-
| HOMO Energy (hartree) || -0.48763 || -0.50047
|-
| LUMO Energy (hartree) || -0.12459 || -0.18183
|}

=== Discussion of MOs ===

The most notable change is that there is an increased amount of delocalisation present in the alcohol-containing complex's LUMO vs the cyanide containing one. Whilst it was thought that this is a result of the electron donation, further investigation showed that this is one orbital created by through-space interactions of every proton in the complex. The present of the alcohol group adds protons to fill a space in the molecule where would there otherwise be no protons (see the cyanide complex). This means that the distance between any two protons is small enough for an interaction to occur, and as there are protons around the entirety of the molecule, one orbital surrounds the entire molecule. The original theory was discarded after it was noted that the metal centre has its own orbital of the opposite phase in the centre of the complex, which leads to a very large number of strong antibonding interactions as it comes close to the delocalised proton orbital. Despite the increased degree of through-space interactions, this LUMO is higher in energy than the CN one, simply because of the increased number of antibonding interactions.

The CN complex LUMO does not have such a large delocalisation, and as a result some methyl protons occupy their own orbital of the opposite polarity.

A similar story is seen for the HOMO, which is lower in energy for the CN molecule. The overall volume of orbitals is smaller for the CN molecule, as the CN group is symmetric and simple (pi-bond like) in nature, leading to a very simple arrangement of orbitals at this point. In contrast, for the OH complex, a very complex d-orbital MO is seen over the alcohol group, which then results in some interactions over the nitrogen.

One possible result of this is that it is easier to perform electrophillic attacks on the OH complex at the nitrogen, as the presence of an orbital over the nitrogen would allow for a positively charged group to come in and perform some reaction. These reactions may include ligand substitution or oxidative addition. This kind of attack would not be possible on the CN complex HOMO as no orbital exists on the central nitrogen, and hence cannot be attacked. The only reactions possible on this HOMO would therefore be substitutions on the CN group, which is not as interesting as ligand substitution or oxidative addition on the center of the complex.

Likewise, the OH complex is likely to be more susceptable to attack by nucleophiles. This is however not due to the large delocalised MO (which is present on the CN complex too), as this only covers protons and does not allow any reactions to occur on a ligand or on the metal. However on the CN group, there is an orbital which contains both the metal center and the OH ligand, making it incredibly likely that nucleophillic attack will lead to substitution of the CH2OH group.

Finally, the HOMO-LUMO gap has changed from 0.31864 e (for the CN complex) to 0.36304 e. This makes it harder for an electron to be promoted from the HOMO to the LUMO in the OH complex. Therefore, any photochemical reactivity which is seen would occur in the CN complex but not the OH one. Considering there is a wealth of reported<ref name="photo">F. Crescitelli, B. Karvaly, ''Photochemistry and Photobiology'', 1989, '''50''', 785–791</ref> photoreactivity for CN systems, it is very likely that photochemistry will occur with the cyanide-containing complex.

= Conclusions =
Ionic solvents are formed of a liquid solution of cations and ions, the nature of which massively alter thes behaviour of the solvent. This nature has been shown to be changed by altering the metal, structure, and ligands of various positive complexes, as has been seen. This report examined how the electronegativity and periodicity of the metal, and the electron donating ability of a ligand affects the chemistry of the ion in terms of changing the structure, charge density, and molecular orbitals. Some possible pathways of reactivity of the ions have been proposed, which gives some indication as to how a change of the ion's nature massively changes its solvation properties, as solvation can occur through the coordination of the solute to the solvent ion.

Future work can include investigation into how the different ions coordinate to different substrates added to the calculation, and molecular orbital and NBO calculations can give some idea into whether the theories proposed as to where the ion may be reactive are correct.

= References =
<references />

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T16:17:40Z

Pk1811: /* Discussion of MOs */

<div style="font-size: 40px;"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px;"><center>Ionic liquids: Designer solvents</center></div>
 
= Introduction =
The aim of this project is to explore the physical nature of ionic liquids, which have application in designing solvents through customisation of the nature of the cation and anion<ref name="abs">M. Freemantle. ''Chem. Eng. News'', 1998, '''76''', 32–37</ref>. In this work, a variety of cations have been investigated to identify what trends are present in the variation in central atom and its ligands.

= Structures of methyl-ligand complexes =
== Optimisations ==
A number of cations have been optimised using Gaussian 09 D.01, namely [N(CH3)4]+, [P(CH3)4]+ and [F(CH3)3]+. All these complexes have been optimised to a DFT B3LYP 6-31G(d,p) level with the <code>int=ultrafine scf=conver=9</code> keywords and tight convergence - this is as a consequence of behaviour seen in previous work<ref name="labintro">P. Kent, unpublished work ([[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|lab intro]])</ref> where low frequencies did not exist within a tight range unless these keywords were specified. All calculations were run on the supplied laptop due to a significant queue of jobs on the HPC (except for [S(CH3)3]+ as it took a very long time), and the log files are available here:

* [N(CH3)4]+: [[media:Pk_log_nch34_opt.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_opt.log]]
* [S(CH3)3]+: The first attempt did not converge: {{DOI|10042/26201}}. A partially optimised structure was resubmitted as a second attempt: {{DOI|10042/26205}}. This also did not converge so a final optimisation was run on this partially optimised structure with the <code>nosymm</code> keyword. This converged: {{DOI|10042/26214}}.

Once done, convergence was verified via inspection of the log file.

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name nch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000090 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 1 minutes 27.0 seconds.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name pch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701126 a.u.
RMS Gradient Norm 0.00000675 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 24 minutes 21.0 seconds.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_opt3
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000101 a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 52.2 seconds.
</pre>

=== Convergence outputs ===

''' [N(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000014 0.000060 YES
RMS Displacement 0.000005 0.000040 YES
Predicted change in Energy=-1.010077D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000015 YES
RMS Force 0.000005 0.000010 YES
Maximum Displacement 0.000026 0.000060 YES
RMS Displacement 0.000009 0.000040 YES
Predicted change in Energy=-1.723206D-06
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''

Initial failed optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000015 NO
RMS Force 0.000006 0.000010 YES
Maximum Displacement 0.002915 0.000060 NO
RMS Displacement 0.000869 0.000040 NO
Predicted change in Energy=-5.685776D-09
Optimization stopped.
-- Number of steps exceeded, NStep= 61
-- Flag reset to prevent archiving.
</pre>

During this failed optimisation, it appears the molecule just spent a large amount of time rotating around the C3 axis through the sulphur.

The final optimisation yielded:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000049 0.000060 YES
RMS Displacement 0.000018 0.000040 YES
Predicted change in Energy=-6.520157D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==
Following this, frequency analysis was conducted with the same keywords and calculation level to ensure a minima has been found. This is ensured by checking there are no negative vibrations in the molecule. Calculations were again run on the laptop, and the log files, summaries, and frequencies are listed below. Actual animations of the modes have not been exported, however a Jmol of the log file is available and the modes can be seen by right clicking and choosing '''model -> the mode you want to see'''. This time, a range of
-30 to +30 cm-1 has been accepted for the low frequencies as molecules investigated are quite complex, and a relatively simple basis set has been used. Optimising to 6-311G(d,p) would likely bring the frequencies within the range used previously however this would be at the expense of much longer computation times.

* [N(CH3)4]+: [[media:Pk_log_nch34_freq.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_freq.log]]
* [S(CH3)3]+: {{DOI|10042/26273}}

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name NCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000085 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 3 minutes 17.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000009 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.014288D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name PCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701149 a.u.
RMS Gradient Norm 0.00000668 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 12 minutes 11.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001774 0.001800 YES
RMS Displacement 0.000659 0.001200 YES
Predicted change in Energy=-3.008780D-08
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000104 a.u.
Imaginary Freq 0
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 9 minutes 6.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000093 0.001800 YES
RMS Displacement 0.000033 0.001200 YES
Predicted change in Energy=-7.179584D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Vibration modes ===

''' [N(CH3)4]+ '''
<pre>
Low frequencies --- 0.0007 0.0011 0.0013 21.5288 21.5288 21.5288
Low frequencies --- 188.5488 292.6546 292.6546
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [P(CH3)4]+ '''
<pre>
Low frequencies --- -15.1139 -0.0002 0.0012 0.0012 5.8940 14.7736
Low frequencies --- 156.2222 191.5376 191.9513
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_pch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [S(CH3)3]+ '''
<pre>
Low frequencies --- -8.5871 0.0029 0.0049 0.0051 5.7111 9.1755
Low frequencies --- 162.4159 200.3446 200.5391
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_sch33_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== Conclusions on molecular structure ==
Investigation of structures is focused on the central atom as this is the only point at which variance should occur. The length of the M-C bonds and the angle between C-M-C on each complex is reported below:

{| class="wikitable" border="1"
! Complex !! M-C Length (Å) !! Angle (°) !! M-C length (lit<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref>) (Å)
|-
| [P(CH3)4]+ || 1.82 || 109.5 || 1.84
|-
| [N(CH3)4]+ || 1.51 || 109.5 || 1.46
|-
| [S(CH3)3]+ || 1.82 || 102.7 || 1.79
|}

''Literature bond lengths are found by adding the covalent radii for the atoms.''

Two key trends are:
* As you go down a group, the bond length decreases
* As you go across a group (so losing a ligand), the bond angle is reduced)

The first trend is straightforward to explain, as bond lengths increase down the group. This is in tandem with the increase in atomic radius down the group as orbitals in a greater shell begin to be filled. Thus, as you move from period 2 (N) to period 3 (P), the length of the bond increases and is in turn the overall size of each ion. There is slight variance in the length of a C-H bond in each complex, however no pattern is immediately discernible (it increases in the order S > P > N) - it is thought this is just some random error in the calculation.

Whilst there is an increase in bond length, there is no change in orientation of the bonds, thus the symmetry of TD is maintained in both the phosphorous and nitrogen molecules. As a result of this, the bond angle is the same for these two complexes. No other arrangement of the ligands is sterically possible, so ensuring that this symmetry label cannot be changed, and therefore the bond angle also cannot change. The bond angle is different for sulphur, as a result of the change of symmetry to C3v, it is not known if the change in metal centre contributes to this change - further investigation would be required.

Of note, the bond length does not appear to change going across the period. There is actually a small increase of 0.01Å if the bond length is reported accurate to 0.001Å, however it is not known if this is just an inherent error in the calculation or not. In any event, it is expected that there is a slight decrease in the bond length as you move towards the right of a period, as the increased nuclear charge better shields the electrons and thus shortens the bond length, but this is not observed here. This may be a result of this complex containing one less ligand, with the arrangement instead taken (along with the lone pair) resulting in some interactions (steric or electronic repulsion) which causes the carbon and metal atoms to move apart from each other. This theory is supported by the large deviation from bond length for the sulphur complex, indicating some feature about the arrangement it has taken is causing the bond length to be artificially lengthened.

Otherwise no strange observations are seen with the structures, with all methyl groups taking the expected tetrahedral structure, and either tetrahedral or C3v structures for the central atom as expected by the number of ligands which are present.

= Molecular orbitals and NBO charges of methyl-ligand complexes =
All three complexes discussed previously have been subject to a full NBO and MO analysis via an energy calculation with the <code>pop=(full,nbo)</code> keyword, retaining any previously used keywords as appropriate. Calculations were performed on the laptop due to load on the HPC, except for the sulphur complex as the calculation took too long on the laptop.

Log files are available as follows:

* '''[N(CH3)4]+''': [[media:Pk_log_nch34_egy.log]]
* '''[P(CH3)4]+''': [[media:Pk_log_pch34_egy.log]]
* '''[S(CH3)3]+''': {{DOI|10042/26274}}
== Calculation output ==

''' [N(CH3)4]+ '''

<pre>
File Name NCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

''' [P(CH3)4]+ '''

<pre>
File Name PCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701105 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 20.0 seconds.
</pre>

''' [S(CH3)3]+ '''

<pre>File Name sch33_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 0 minutes 57.7 seconds.
</pre>

== Sample MOs for [N(CH3)4]+ ==
A variety of 5 molecular orbitals have been calculated and shown below. Only occupied non-core MOs from the totally bonding to totally antibonding are shown.

{| class="wikitable" border="1"
|+ Totally bonding towards the top
! MO number !! Energy (hartree) !! Picture !! Degeneracy !! Notes
|-
| 6 || -1.19645 || [[Image:Pk-n-mo0.png|200px]] || Singly degenerate || This MO exhibits a great degree of strong bonding interactions across the entire molecule up to the protons, the orbitals of which do not appear to be part of this MO. This is seen by the huge red surface containing almost the entirety of the molecule. As a result of the huge amount of delocalisation seen in the MO, there is a lot of through space interactions between adjacent carbon groups, as seen by how the MO forms a 'cage' around the entire molecule - the empty space between two carbon atoms is part of this red object. As there are no other molecular orbitals other than this huge one, there is no concept of a node in this MO diagram.
|-
| 10 || -0.80745 || [[Image:Pk-n-mo1.png|200px]] || Singly degenerate || This is the first MO in this series of 5 to contain a slight degree of antibonding character, as seen by the fact each ligand is in its own (+) phase orbital, whereas the central metal is in a (-) phase one. This leads to a minor degree of antibonding character, and also a node in the centre of the M-C bond where the two MOs end. Through space interactions are present in each ligand MO, with all the protons and the central carbon existing within the boundaries of the MO, and hence there are through-space interactions between the protons. MOs of the same phase interact weakly with each other due to the large distance between each green orbital (seen in the picture), however the interaction between the (+) and (-) orbitals is quite strong as the nodal area is very small in size - the orbitals are nearly touching. The level of delocalisation is reduced, with delocalisation only occurring across each ligand group - the ligands themselves are not delocalised onto one unit.
|-
| 14 || -0.62248 || [[Image:Pk-n-mo2.png|200px]] || Doubly degenerate || For this MO, nodes exist on every carbon atom, as each MO covers two halves of a carbon atom, two protons, and nothing else. This does lead to delocalisationa cross the protons and carbon atoms, however this also does result in strong antibonding interactions at each carbon as the (+) and (-) MOs become quite close. Some protons, and the metal centre are not covered at all by this MO, however from what is delocalised, there is a significant amount of through space interactions between protons on differing methyl ligands - this is of note as the ligand protons are quite a distance away. There may be some weak bonding interactions between orbitals of the same phase, however they are quite a distance away (separated by the metal centre) so this is expected to be quite weak.
|-
| 17 || -0.58035 || [[Image:Pk-n-mo3.png|200px]] || Triply degenerate || This one again has a node on each carbon, however it differs in that each orbital only covers a single proton and half a carbon. This results in there being no through-space interactions in this molecule. Additionally, there are many strong antibonding interactions as all the orbitals are quite close together, with the a (+) orbital being surrounded by a (-) orbital on every side. If there are any bonding interactions, these are going to be very weak.
|-
| 21 || -0.57934 || [[Image:Pk-n-mo4.png|200px]] || Triply degenerate || This MO is similar to the previous, but differs in that each orbital now consists of two protons, so there are no protons which aren't enclosed in an orbital. Again, there are nodes in each carbon, but also a node in the metal center, with orbitals now also covering the metal center. This results in there being strong antibonding interactions over almost the entire molecule, with (+) interacting with (-) almost over the entire surface of every orbital. Through-space interactions are now back with there being two protons in each orbital, making it possible for these to interact, and there is also the potential for protons and metal center to interact as well. This orbital is only slightly higher energy than the previous one, and this is solely because of the increased degree of antibonding interactions present.
|}

== NBO charge distributions ==

NBO charge distributions were calculated from the checkpoint file for a range of -1.750 to 1.750 as this ensured the range of charges for all 3 complexes could be accommodated on the same scale. The charges are as follows:

{| class="wikitable" border="1"
! Complex !! Metal charge (e) !! Carbon charge (e) !! Proton charge (e)
|-
| [P(NH3)4]+ || 1.667 || -1.060 || 0.298
|-
| [N(NH3)4]+ || -0.295 || -0.846 || 0.297
|-
| [S(NH3)3]+ || 0.917 || -0.483 || 0.269
|}

<gallery>
File:Pk-nbo-n.png|Nitrogen complex
File:Pk-nbo-p.png|Phosphorous complex
File:Pk-nbo-s.png|Sulphur complex
</gallery>

There appears to be a slight trend of the metal centre charge with electronegativity, with the charge much lower as it becomes more electronegative (and hence drawing a greater share of electrons to it). This in turn makes the carbon more positive as electron density is removed from it. The protons remain rather positively charged and do not appear to be greatly affected by the metal centre, but this is likely because they are too far away for the inductive effect to occur.

Interestingly, nitrogen is more eletronegative than sulphur, yet sulphur has a greater negative charge. The reduced degree of polarisation in the bond for the nitrogen complex also suggests why the bond length for the nitrogen complex is shorter compared to the sulphur. The reason for this increased amount of negative charge is due to the lone pair present on sulphur (hence the configuration it takes according to the Jmol clip above), and so there is simply more negative charge present on the sulphur.

Thus, for the general complex [NR4]+, the positive charge located on the nitrogen in the picture is indeed located on the nitrogen, however it is somewhat delocalised over the protons too. As the nitrogen contains the greatest degree of positive charge, though, the + sign is conventionally placed here as it gives the indication as to where most of the charge is.

Analysis of the log files show the exact NBO contributions to the bond:

'''[P(NH3)3]+'''
<pre>
1. (1.98031) BD ( 1) P 1 - C 2
( 40.43%) 0.6358* P 1 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.4030 0.0006 0.0000 -0.4429
0.0006 0.0000 0.6188 -0.0009 0.0385
-0.0538 -0.0591 -0.0036 0.0254
( 59.57%) 0.7718* C 2 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.4044
-0.0074 0.4444 -0.0081 -0.6209 0.0114
0.0121 -0.0169 -0.0186 -0.0011 0.0080
</pre>

This shows almost equal contribution from each atom to the bond, with each atom assuming a sp3 arrangement as is expected by the TD symmetry. Carbon is sp3 as expected due to its saturation. As the carbon is slightly more negatively charged according to the charge distributions, the marginal increase in contribution from the carbon vs the phosphorous agrees with the charge distribution seen.

'''[N(NH3)3]+'''
<pre>
4. (1.98452) BD ( 1) C 1 - N 13
( 33.65%) 0.5801* C 1 s( 20.77%)p 3.81( 79.06%)d 0.01( 0.16%)
0.0003 0.4552 -0.0237 0.0026 -0.5129
-0.0218 -0.5129 -0.0218 -0.5129 -0.0218
0.0234 0.0234 0.0234 0.0000 0.0000
( 66.35%) 0.8146* N 13 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 0.5000 -0.0007 0.0000 0.4999
-0.0001 0.4999 -0.0001 0.4999 -0.0001
0.0103 0.0103 0.0103 0.0000 0.0000
</pre>

A similar argument can be made here. The large contribution from the nitrogen is surprising, but considering the smaller bond length for this complex based on the metal, an increased contribution from the nitrogen is not unreasonable. However this does disagree somewhat with the charge distribution which shows there is a much larger electron density on the carbon. It is thus thought that since it is possible to reach orbitals closer to the core on nitrogen rather than phosphorous, it makes nitrogen able to donate a greater share of electrons, and so polarises the bond towards it as a result of its electronegativity.

'''[S(NH3)3]+'''
<pre>
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
-0.0003 -0.4437 -0.0140 0.0033 0.7546
-0.0059 0.3161 -0.0025 0.3634 0.0098
-0.0189 -0.0222 -0.0093 -0.0186 0.0096
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 -0.0001 -0.4117 0.0075 -0.0012
0.0000 -0.7489 0.0330 0.0000 -0.3137
0.0138 0.0000 -0.4037 -0.0260 -0.0353
-0.0572 -0.0240 -0.0347 0.0051
</pre>

Finally, for the sulphur, the bond is an almost equal contribution from each atom in the bond. The charges of the S and C atoms according to the charge distribution are both similar and negative, suggesting little polarisation in this bond, and so the balance seen here is to be expected.

= Ligand influences on nitrogen metal centre complexes =
To investigate how changes to the ligands affects the cation, two variants on the nitrogen complex analysed previously have been used. One has one of the protons on a methyl ligand replaced with CH2OH, the other has the proton replaced with CH2CN. Each complex is then optimised and subject to a frequency analysis so as to allow for investigation of its structure. A MO and NBO calculation is then subsequently run to analyse how the change in ligand affects the ions electronic behaviour.

== Optimisations ==
Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26206}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26207}}

=== Summary output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
File Name nch33ch2oh_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000102 a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 1 hours 22 minutes 37.5 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
File Name nch33ch2cn_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000045 a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 50 minutes 39.5 seconds.
</pre>

=== Convergence output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000034 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-5.591936D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000011 0.000040 YES
Predicted change in Energy=-2.269581D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==

Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26290}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26291}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000106 a.u.
Imaginary Freq 0
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 26 minutes 10.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000102 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-5.078379D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000059 a.u.
Imaginary Freq 0
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 29 minutes 19.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-6.144746D-12
Optimization completed.
-- Stationary point found.
</pre>

=== Vibrational modes ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2oh_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

'''[N(CH3)3(CH2CN)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2cn_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== MO and NBO calculations ==
<code>pop=(nbo,full)</code> energy calculations were then performed on the complexes to generate MOs and NBO charge diagrams, just as has been done previously. All calculations were performed on the HPC and log files are available as follows:

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26294}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26295}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 59.3 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 25.0 seconds.
</pre>

=== NBO charge distributions ===
The main difference between these ligands is that CN is an EWG, and OH is an EDG, the latter due to the lone pairs which make it possible to enolise. Therefore comparison of the charge density of the structure can show how these ligands affect the overall structure of the molecule. The NBO charge distributions from -0.750 to 0.750 are shown below.

<gallery>
File:Pk-nbo-cn.png|CN ligand complex
File:Pk-nbo-oh.png|OH ligand complex
</gallery>

''n.b. the charge for the metal centre in the CN complex is -0.289''

It is seen that, in both cases, the nitrogen makes up the majority of the C-N bond to the C with the substituent:

'''OH case:'''
<pre>
4. (1.98195) BD ( 1) N 1 - C 14
( 67.28%) 0.8202* N 1 s( 23.48%)p 3.26( 76.49%)d 0.00( 0.03%)
0.0000 -0.4845 -0.0026 -0.0002 0.7401
-0.0032 0.3146 -0.0015 0.3438 -0.0026
-0.0092 -0.0105 -0.0043 -0.0088 0.0045
( 32.72%) 0.5720* C 14 s( 20.28%)p 3.92( 79.55%)d 0.01( 0.18%)
-0.0003 -0.4501 0.0135 0.0006 -0.7171
-0.0206 -0.3677 -0.0077 -0.3815 -0.0037
-0.0247 -0.0249 -0.0101 -0.0185 0.0102
</pre>

'''CN case:'''
<pre>
4. (1.97747) BD ( 1) N 1 - C 14
( 64.52%) 0.8033* N 1 s( 24.08%)p 3.15( 75.89%)d 0.00( 0.04%)
0.0000 0.4907 -0.0010 0.0003 0.6601
-0.0021 0.5684 0.0038 0.0000 0.0000
0.0166 0.0000 0.0000 0.0024 -0.0097
( 35.48%) 0.5956* C 14 s( 20.81%)p 3.80( 79.05%)d 0.01( 0.14%)
0.0000 0.4557 -0.0205 0.0000 -0.6428
-0.0249 -0.6135 -0.0174 0.0000 0.0000
0.0320 0.0000 0.0000 -0.0011 -0.0197
</pre>

==== Ligand influence on charge distribution ====

There is quite a significant change in electron density for the OH complex with the carbon between the OH group and the metal centre becoming much more positive. This is surprising considering the OH is a donating group, however this is simply explained. As the carbon is between two electronegative groups, a lot of electron density is withdrawn from it, and hence it becomes very positive. However, the metal centre has become more negatively charged (-0.322 vs -0.295). Hence, the donated electrons are moving straight from the oxygen to the metal centre, while the carbon between's electrons are also donated to both the oxygen and nitrogen as part of the electronegative pull these atoms have on the carbon.

Regarding the CN complex, the electron withdrawal is clearly seen on the carbon the CN ligand is bonded to, as this has become less negatively charged (-0.289 vs -0.295), showing that once again, electron withdrawal is occuring at a distance that causes electrons to travel from the nitrogen through the carbon.

In conclusion, it is seen that the electron inductive effects of the ligands has a direct influence on the the metal centre, as these effects travel through the carbon to directly pull or push electrons from the metal. This is likely due to the large contribution of charge from the nitrogen in the CN bond to the relevant C, so meaning any inductive effects on the C are very likely to influence the N due to the polarisation of the bond towards the N seen.

=== Sample MOs ===
The HOMO and LUMO for these two complexes are reported below:

{| class="wikitable" border="1"
! !! [N(CH3)3(CH2OH)]+ !!
[N(CH3)3(CH2CN)]+
|-
| HOMO || [[Image:Pk-homo-oh.png|200px]] || [[Image:Pk-homo-cn.png|200px]]
|-
| LUMO || [[Image:Pk-lumo-oh.png|200px]] || [[Image:Pk-lumo-cn.png|200px]]
|-
| HOMO Energy (hartree) || -0.48763 || -0.50047
|-
| LUMO Energy (hartree) || -0.12459 || -0.18183
|}

=== Discussion of MOs ===

The most notable change is that there is an increased amount of delocalisation present in the alcohol-containing complex's LUMO vs the cyanide containing one. Whilst it was thought that this is a result of the electron donation, further investigation showed that this is one orbital created by through-space interactions of every proton in the complex. The present of the alcohol group adds protons to fill a space in the molecule where would there otherwise be no protons (see the cyanide complex). This means that the distance between any two protons is small enough for an interaction to occur, and as there are protons around the entirety of the molecule, one orbital surrounds the entire molecule. The original theory was discarded after it was noted that the metal centre has its own orbital of the opposite phase in the centre of the complex, which leads to a very large number of strong antibonding interactions as it comes close to the delocalised proton orbital. Despite the increased degree of through-space interactions, this LUMO is higher in energy than the CN one, simply because of the increased number of antibonding interactions.

The CN complex LUMO does not have such a large delocalisation, and as a result some methyl protons occupy their own orbital of the opposite polarity.

A similar story is seen for the HOMO, which is lower in energy for the CN molecule. The overall volume of orbitals is smaller for the CN molecule, as the CN group is symmetric and simple (pi-bond like) in nature, leading to a very simple arrangement of orbitals at this point. In contrast, for the OH complex, a very complex d-orbital MO is seen over the alcohol group, which then results in some interactions over the nitrogen.

One possible result of this is that it is easier to perform electrophillic attacks on the OH complex at the nitrogen, as the presence of an orbital over the nitrogen would allow for a positively charged group to come in and perform some reaction. These reactions may include ligand substitution or oxidative addition. This kind of attack would not be possible on the CN complex HOMO as no orbital exists on the central nitrogen, and hence cannot be attacked. The only reactions possible on this HOMO would therefore be substitutions on the CN group, which is not as interesting as ligand substitution or oxidative addition on the center of the complex.

Likewise, the OH complex is likely to be more susceptable to attack by nucleophiles. This is however not due to the large delocalised MO (which is present on the CN complex too), as this only covers protons and does not allow any reactions to occur on a ligand or on the metal. However on the CN group, there is an orbital which contains both the metal center and the OH ligand, making it incredibly likely that nucleophillic attack will lead to substitution of the CH2OH group.

Finally, the HOMO-LUMO gap has changed from 0.31864 e (for the CN complex) to 0.36304 e. This makes it harder for an electron to be promoted from the HOMO to the LUMO in the OH complex. Therefore, any photochemical reactivity which is seen would occur in the CN complex but not the OH one. Considering there is a wealth of reported<ref name="photo">F. Crescitelli, B. Karvaly(1989), ''Photochemistry and Photobiology'', '''50''' 785–791</ref> photoreactivity for CN systems, it is very likely that photochemistry will occur with the cyanide-containing complex.

= References =
<references />

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T15:53:25Z

Pk1811: /* Sample MOs */

<div style="font-size: 40px;"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px;"><center>Ionic liquids: Designer solvents</center></div>
 
= Introduction =
The aim of this project is to explore the physical nature of ionic liquids, which have application in designing solvents through customisation of the nature of the cation and anion<ref name="abs">M. Freemantle. ''Chem. Eng. News'', 1998, '''76''', 32–37</ref>. In this work, a variety of cations have been investigated to identify what trends are present in the variation in central atom and its ligands.

= Structures of methyl-ligand complexes =
== Optimisations ==
A number of cations have been optimised using Gaussian 09 D.01, namely [N(CH3)4]+, [P(CH3)4]+ and [F(CH3)3]+. All these complexes have been optimised to a DFT B3LYP 6-31G(d,p) level with the <code>int=ultrafine scf=conver=9</code> keywords and tight convergence - this is as a consequence of behaviour seen in previous work<ref name="labintro">P. Kent, unpublished work ([[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|lab intro]])</ref> where low frequencies did not exist within a tight range unless these keywords were specified. All calculations were run on the supplied laptop due to a significant queue of jobs on the HPC (except for [S(CH3)3]+ as it took a very long time), and the log files are available here:

* [N(CH3)4]+: [[media:Pk_log_nch34_opt.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_opt.log]]
* [S(CH3)3]+: The first attempt did not converge: {{DOI|10042/26201}}. A partially optimised structure was resubmitted as a second attempt: {{DOI|10042/26205}}. This also did not converge so a final optimisation was run on this partially optimised structure with the <code>nosymm</code> keyword. This converged: {{DOI|10042/26214}}.

Once done, convergence was verified via inspection of the log file.

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name nch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000090 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 1 minutes 27.0 seconds.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name pch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701126 a.u.
RMS Gradient Norm 0.00000675 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 24 minutes 21.0 seconds.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_opt3
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000101 a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 52.2 seconds.
</pre>

=== Convergence outputs ===

''' [N(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000014 0.000060 YES
RMS Displacement 0.000005 0.000040 YES
Predicted change in Energy=-1.010077D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000015 YES
RMS Force 0.000005 0.000010 YES
Maximum Displacement 0.000026 0.000060 YES
RMS Displacement 0.000009 0.000040 YES
Predicted change in Energy=-1.723206D-06
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''

Initial failed optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000015 NO
RMS Force 0.000006 0.000010 YES
Maximum Displacement 0.002915 0.000060 NO
RMS Displacement 0.000869 0.000040 NO
Predicted change in Energy=-5.685776D-09
Optimization stopped.
-- Number of steps exceeded, NStep= 61
-- Flag reset to prevent archiving.
</pre>

During this failed optimisation, it appears the molecule just spent a large amount of time rotating around the C3 axis through the sulphur.

The final optimisation yielded:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000049 0.000060 YES
RMS Displacement 0.000018 0.000040 YES
Predicted change in Energy=-6.520157D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==
Following this, frequency analysis was conducted with the same keywords and calculation level to ensure a minima has been found. This is ensured by checking there are no negative vibrations in the molecule. Calculations were again run on the laptop, and the log files, summaries, and frequencies are listed below. Actual animations of the modes have not been exported, however a Jmol of the log file is available and the modes can be seen by right clicking and choosing '''model -> the mode you want to see'''. This time, a range of
-30 to +30 cm-1 has been accepted for the low frequencies as molecules investigated are quite complex, and a relatively simple basis set has been used. Optimising to 6-311G(d,p) would likely bring the frequencies within the range used previously however this would be at the expense of much longer computation times.

* [N(CH3)4]+: [[media:Pk_log_nch34_freq.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_freq.log]]
* [S(CH3)3]+: {{DOI|10042/26273}}

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name NCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000085 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 3 minutes 17.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000009 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.014288D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name PCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701149 a.u.
RMS Gradient Norm 0.00000668 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 12 minutes 11.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001774 0.001800 YES
RMS Displacement 0.000659 0.001200 YES
Predicted change in Energy=-3.008780D-08
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000104 a.u.
Imaginary Freq 0
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 9 minutes 6.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000093 0.001800 YES
RMS Displacement 0.000033 0.001200 YES
Predicted change in Energy=-7.179584D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Vibration modes ===

''' [N(CH3)4]+ '''
<pre>
Low frequencies --- 0.0007 0.0011 0.0013 21.5288 21.5288 21.5288
Low frequencies --- 188.5488 292.6546 292.6546
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [P(CH3)4]+ '''
<pre>
Low frequencies --- -15.1139 -0.0002 0.0012 0.0012 5.8940 14.7736
Low frequencies --- 156.2222 191.5376 191.9513
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_pch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [S(CH3)3]+ '''
<pre>
Low frequencies --- -8.5871 0.0029 0.0049 0.0051 5.7111 9.1755
Low frequencies --- 162.4159 200.3446 200.5391
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_sch33_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== Conclusions on molecular structure ==
Investigation of structures is focused on the central atom as this is the only point at which variance should occur. The length of the M-C bonds and the angle between C-M-C on each complex is reported below:

{| class="wikitable" border="1"
! Complex !! M-C Length (Å) !! Angle (°) !! M-C length (lit<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref>) (Å)
|-
| [P(CH3)4]+ || 1.82 || 109.5 || 1.84
|-
| [N(CH3)4]+ || 1.51 || 109.5 || 1.46
|-
| [S(CH3)3]+ || 1.82 || 102.7 || 1.79
|}

''Literature bond lengths are found by adding the covalent radii for the atoms.''

Two key trends are:
* As you go down a group, the bond length decreases
* As you go across a group (so losing a ligand), the bond angle is reduced)

The first trend is straightforward to explain, as bond lengths increase down the group. This is in tandem with the increase in atomic radius down the group as orbitals in a greater shell begin to be filled. Thus, as you move from period 2 (N) to period 3 (P), the length of the bond increases and is in turn the overall size of each ion. There is slight variance in the length of a C-H bond in each complex, however no pattern is immediately discernible (it increases in the order S > P > N) - it is thought this is just some random error in the calculation.

Whilst there is an increase in bond length, there is no change in orientation of the bonds, thus the symmetry of TD is maintained in both the phosphorous and nitrogen molecules. As a result of this, the bond angle is the same for these two complexes. No other arrangement of the ligands is sterically possible, so ensuring that this symmetry label cannot be changed, and therefore the bond angle also cannot change. The bond angle is different for sulphur, as a result of the change of symmetry to C3v, it is not known if the change in metal centre contributes to this change - further investigation would be required.

Of note, the bond length does not appear to change going across the period. There is actually a small increase of 0.01Å if the bond length is reported accurate to 0.001Å, however it is not known if this is just an inherent error in the calculation or not. In any event, it is expected that there is a slight decrease in the bond length as you move towards the right of a period, as the increased nuclear charge better shields the electrons and thus shortens the bond length, but this is not observed here. This may be a result of this complex containing one less ligand, with the arrangement instead taken (along with the lone pair) resulting in some interactions (steric or electronic repulsion) which causes the carbon and metal atoms to move apart from each other. This theory is supported by the large deviation from bond length for the sulphur complex, indicating some feature about the arrangement it has taken is causing the bond length to be artificially lengthened.

Otherwise no strange observations are seen with the structures, with all methyl groups taking the expected tetrahedral structure, and either tetrahedral or C3v structures for the central atom as expected by the number of ligands which are present.

= Molecular orbitals and NBO charges of methyl-ligand complexes =
All three complexes discussed previously have been subject to a full NBO and MO analysis via an energy calculation with the <code>pop=(full,nbo)</code> keyword, retaining any previously used keywords as appropriate. Calculations were performed on the laptop due to load on the HPC, except for the sulphur complex as the calculation took too long on the laptop.

Log files are available as follows:

* '''[N(CH3)4]+''': [[media:Pk_log_nch34_egy.log]]
* '''[P(CH3)4]+''': [[media:Pk_log_pch34_egy.log]]
* '''[S(CH3)3]+''': {{DOI|10042/26274}}
== Calculation output ==

''' [N(CH3)4]+ '''

<pre>
File Name NCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

''' [P(CH3)4]+ '''

<pre>
File Name PCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701105 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 20.0 seconds.
</pre>

''' [S(CH3)3]+ '''

<pre>File Name sch33_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 0 minutes 57.7 seconds.
</pre>

== Sample MOs for [N(CH3)4]+ ==
A variety of 5 molecular orbitals have been calculated and shown below. Only occupied non-core MOs from the totally bonding to totally antibonding are shown.

{| class="wikitable" border="1"
|+ Totally bonding towards the top
! MO number !! Energy (hartree) !! Picture !! Degeneracy !! Notes
|-
| 6 || -1.19645 || [[Image:Pk-n-mo0.png|200px]] || Singly degenerate || This MO exhibits a great degree of strong bonding interactions across the entire molecule up to the protons, the orbitals of which do not appear to be part of this MO. This is seen by the huge red surface containing almost the entirety of the molecule. As a result of the huge amount of delocalisation seen in the MO, there is a lot of through space interactions between adjacent carbon groups, as seen by how the MO forms a 'cage' around the entire molecule - the empty space between two carbon atoms is part of this red object. As there are no other molecular orbitals other than this huge one, there is no concept of a node in this MO diagram.
|-
| 10 || -0.80745 || [[Image:Pk-n-mo1.png|200px]] || Singly degenerate || This is the first MO in this series of 5 to contain a slight degree of antibonding character, as seen by the fact each ligand is in its own (+) phase orbital, whereas the central metal is in a (-) phase one. This leads to a minor degree of antibonding character, and also a node in the centre of the M-C bond where the two MOs end. Through space interactions are present in each ligand MO, with all the protons and the central carbon existing within the boundaries of the MO, and hence there are through-space interactions between the protons. MOs of the same phase interact weakly with each other due to the large distance between each green orbital (seen in the picture), however the interaction between the (+) and (-) orbitals is quite strong as the nodal area is very small in size - the orbitals are nearly touching. The level of delocalisation is reduced, with delocalisation only occurring across each ligand group - the ligands themselves are not delocalised onto one unit.
|-
| 14 || -0.62248 || [[Image:Pk-n-mo2.png|200px]] || Doubly degenerate || For this MO, nodes exist on every carbon atom, as each MO covers two halves of a carbon atom, two protons, and nothing else. This does lead to delocalisationa cross the protons and carbon atoms, however this also does result in strong antibonding interactions at each carbon as the (+) and (-) MOs become quite close. Some protons, and the metal centre are not covered at all by this MO, however from what is delocalised, there is a significant amount of through space interactions between protons on differing methyl ligands - this is of note as the ligand protons are quite a distance away. There may be some weak bonding interactions between orbitals of the same phase, however they are quite a distance away (separated by the metal centre) so this is expected to be quite weak.
|-
| 17 || -0.58035 || [[Image:Pk-n-mo3.png|200px]] || Triply degenerate || This one again has a node on each carbon, however it differs in that each orbital only covers a single proton and half a carbon. This results in there being no through-space interactions in this molecule. Additionally, there are many strong antibonding interactions as all the orbitals are quite close together, with the a (+) orbital being surrounded by a (-) orbital on every side. If there are any bonding interactions, these are going to be very weak.
|-
| 21 || -0.57934 || [[Image:Pk-n-mo4.png|200px]] || Triply degenerate || This MO is similar to the previous, but differs in that each orbital now consists of two protons, so there are no protons which aren't enclosed in an orbital. Again, there are nodes in each carbon, but also a node in the metal center, with orbitals now also covering the metal center. This results in there being strong antibonding interactions over almost the entire molecule, with (+) interacting with (-) almost over the entire surface of every orbital. Through-space interactions are now back with there being two protons in each orbital, making it possible for these to interact, and there is also the potential for protons and metal center to interact as well. This orbital is only slightly higher energy than the previous one, and this is solely because of the increased degree of antibonding interactions present.
|}

== NBO charge distributions ==

NBO charge distributions were calculated from the checkpoint file for a range of -1.750 to 1.750 as this ensured the range of charges for all 3 complexes could be accommodated on the same scale. The charges are as follows:

{| class="wikitable" border="1"
! Complex !! Metal charge (e) !! Carbon charge (e) !! Proton charge (e)
|-
| [P(NH3)4]+ || 1.667 || -1.060 || 0.298
|-
| [N(NH3)4]+ || -0.295 || -0.846 || 0.297
|-
| [S(NH3)3]+ || 0.917 || -0.483 || 0.269
|}

<gallery>
File:Pk-nbo-n.png|Nitrogen complex
File:Pk-nbo-p.png|Phosphorous complex
File:Pk-nbo-s.png|Sulphur complex
</gallery>

There appears to be a slight trend of the metal centre charge with electronegativity, with the charge much lower as it becomes more electronegative (and hence drawing a greater share of electrons to it). This in turn makes the carbon more positive as electron density is removed from it. The protons remain rather positively charged and do not appear to be greatly affected by the metal centre, but this is likely because they are too far away for the inductive effect to occur.

Interestingly, nitrogen is more eletronegative than sulphur, yet sulphur has a greater negative charge. The reduced degree of polarisation in the bond for the nitrogen complex also suggests why the bond length for the nitrogen complex is shorter compared to the sulphur. The reason for this increased amount of negative charge is due to the lone pair present on sulphur (hence the configuration it takes according to the Jmol clip above), and so there is simply more negative charge present on the sulphur.

Thus, for the general complex [NR4]+, the positive charge located on the nitrogen in the picture is indeed located on the nitrogen, however it is somewhat delocalised over the protons too. As the nitrogen contains the greatest degree of positive charge, though, the + sign is conventionally placed here as it gives the indication as to where most of the charge is.

Analysis of the log files show the exact NBO contributions to the bond:

'''[P(NH3)3]+'''
<pre>
1. (1.98031) BD ( 1) P 1 - C 2
( 40.43%) 0.6358* P 1 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.4030 0.0006 0.0000 -0.4429
0.0006 0.0000 0.6188 -0.0009 0.0385
-0.0538 -0.0591 -0.0036 0.0254
( 59.57%) 0.7718* C 2 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.4044
-0.0074 0.4444 -0.0081 -0.6209 0.0114
0.0121 -0.0169 -0.0186 -0.0011 0.0080
</pre>

This shows almost equal contribution from each atom to the bond, with each atom assuming a sp3 arrangement as is expected by the TD symmetry. Carbon is sp3 as expected due to its saturation. As the carbon is slightly more negatively charged according to the charge distributions, the marginal increase in contribution from the carbon vs the phosphorous agrees with the charge distribution seen.

'''[N(NH3)3]+'''
<pre>
4. (1.98452) BD ( 1) C 1 - N 13
( 33.65%) 0.5801* C 1 s( 20.77%)p 3.81( 79.06%)d 0.01( 0.16%)
0.0003 0.4552 -0.0237 0.0026 -0.5129
-0.0218 -0.5129 -0.0218 -0.5129 -0.0218
0.0234 0.0234 0.0234 0.0000 0.0000
( 66.35%) 0.8146* N 13 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 0.5000 -0.0007 0.0000 0.4999
-0.0001 0.4999 -0.0001 0.4999 -0.0001
0.0103 0.0103 0.0103 0.0000 0.0000
</pre>

A similar argument can be made here. The large contribution from the nitrogen is surprising, but considering the smaller bond length for this complex based on the metal, an increased contribution from the nitrogen is not unreasonable. However this does disagree somewhat with the charge distribution which shows there is a much larger electron density on the carbon. It is thus thought that since it is possible to reach orbitals closer to the core on nitrogen rather than phosphorous, it makes nitrogen able to donate a greater share of electrons, and so polarises the bond towards it as a result of its electronegativity.

'''[S(NH3)3]+'''
<pre>
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
-0.0003 -0.4437 -0.0140 0.0033 0.7546
-0.0059 0.3161 -0.0025 0.3634 0.0098
-0.0189 -0.0222 -0.0093 -0.0186 0.0096
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 -0.0001 -0.4117 0.0075 -0.0012
0.0000 -0.7489 0.0330 0.0000 -0.3137
0.0138 0.0000 -0.4037 -0.0260 -0.0353
-0.0572 -0.0240 -0.0347 0.0051
</pre>

Finally, for the sulphur, the bond is an almost equal contribution from each atom in the bond. The charges of the S and C atoms according to the charge distribution are both similar and negative, suggesting little polarisation in this bond, and so the balance seen here is to be expected.

= Ligand influences on nitrogen metal centre complexes =
To investigate how changes to the ligands affects the cation, two variants on the nitrogen complex analysed previously have been used. One has one of the protons on a methyl ligand replaced with CH2OH, the other has the proton replaced with CH2CN. Each complex is then optimised and subject to a frequency analysis so as to allow for investigation of its structure. A MO and NBO calculation is then subsequently run to analyse how the change in ligand affects the ions electronic behaviour.

== Optimisations ==
Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26206}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26207}}

=== Summary output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
File Name nch33ch2oh_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000102 a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 1 hours 22 minutes 37.5 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
File Name nch33ch2cn_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000045 a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 50 minutes 39.5 seconds.
</pre>

=== Convergence output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000034 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-5.591936D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000011 0.000040 YES
Predicted change in Energy=-2.269581D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==

Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26290}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26291}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000106 a.u.
Imaginary Freq 0
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 26 minutes 10.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000102 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-5.078379D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000059 a.u.
Imaginary Freq 0
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 29 minutes 19.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-6.144746D-12
Optimization completed.
-- Stationary point found.
</pre>

=== Vibrational modes ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2oh_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

'''[N(CH3)3(CH2CN)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2cn_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== MO and NBO calculations ==
<code>pop=(nbo,full)</code> energy calculations were then performed on the complexes to generate MOs and NBO charge diagrams, just as has been done previously. All calculations were performed on the HPC and log files are available as follows:

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26294}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26295}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 59.3 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 25.0 seconds.
</pre>

=== NBO charge distributions ===
The main difference between these ligands is that CN is an EWG, and OH is an EDG, the latter due to the lone pairs which make it possible to enolise. Therefore comparison of the charge density of the structure can show how these ligands affect the overall structure of the molecule. The NBO charge distributions from -0.750 to 0.750 are shown below.

<gallery>
File:Pk-nbo-cn.png|CN ligand complex
File:Pk-nbo-oh.png|OH ligand complex
</gallery>

''n.b. the charge for the metal centre in the CN complex is -0.289''

It is seen that, in both cases, the nitrogen makes up the majority of the C-N bond to the C with the substituent:

'''OH case:'''
<pre>
4. (1.98195) BD ( 1) N 1 - C 14
( 67.28%) 0.8202* N 1 s( 23.48%)p 3.26( 76.49%)d 0.00( 0.03%)
0.0000 -0.4845 -0.0026 -0.0002 0.7401
-0.0032 0.3146 -0.0015 0.3438 -0.0026
-0.0092 -0.0105 -0.0043 -0.0088 0.0045
( 32.72%) 0.5720* C 14 s( 20.28%)p 3.92( 79.55%)d 0.01( 0.18%)
-0.0003 -0.4501 0.0135 0.0006 -0.7171
-0.0206 -0.3677 -0.0077 -0.3815 -0.0037
-0.0247 -0.0249 -0.0101 -0.0185 0.0102
</pre>

'''CN case:'''
<pre>
4. (1.97747) BD ( 1) N 1 - C 14
( 64.52%) 0.8033* N 1 s( 24.08%)p 3.15( 75.89%)d 0.00( 0.04%)
0.0000 0.4907 -0.0010 0.0003 0.6601
-0.0021 0.5684 0.0038 0.0000 0.0000
0.0166 0.0000 0.0000 0.0024 -0.0097
( 35.48%) 0.5956* C 14 s( 20.81%)p 3.80( 79.05%)d 0.01( 0.14%)
0.0000 0.4557 -0.0205 0.0000 -0.6428
-0.0249 -0.6135 -0.0174 0.0000 0.0000
0.0320 0.0000 0.0000 -0.0011 -0.0197
</pre>

==== Ligand influence on charge distribution ====

There is quite a significant change in electron density for the OH complex with the carbon between the OH group and the metal centre becoming much more positive. This is surprising considering the OH is a donating group, however this is simply explained. As the carbon is between two electronegative groups, a lot of electron density is withdrawn from it, and hence it becomes very positive. However, the metal centre has become more negatively charged (-0.322 vs -0.295). Hence, the donated electrons are moving straight from the oxygen to the metal centre, while the carbon between's electrons are also donated to both the oxygen and nitrogen as part of the electronegative pull these atoms have on the carbon.

Regarding the CN complex, the electron withdrawal is clearly seen on the carbon the CN ligand is bonded to, as this has become less negatively charged (-0.289 vs -0.295), showing that once again, electron withdrawal is occuring at a distance that causes electrons to travel from the nitrogen through the carbon.

In conclusion, it is seen that the electron inductive effects of the ligands has a direct influence on the the metal centre, as these effects travel through the carbon to directly pull or push electrons from the metal. This is likely due to the large contribution of charge from the nitrogen in the CN bond to the relevant C, so meaning any inductive effects on the C are very likely to influence the N due to the polarisation of the bond towards the N seen.

=== Sample MOs ===
The HOMO and LUMO for these two complexes are reported below:

{| class="wikitable" border="1"
! !! [N(CH3)3(CH2OH)]+ !!
[N(CH3)3(CH2CN)]+
|-
| HOMO || [[Image:Pk-homo-oh.png|200px]] || [[Image:Pk-homo-cn.png|200px]]
|-
| LUMO || [[Image:Pk-lumo-oh.png|200px]] || [[Image:Pk-lumo-cn.png|200px]]
|-
| HOMO Energy (hartree) || -0.48763 || -0.50047
|-
| LUMO Energy (hartree) || -0.12459 || -0.18183
|}

=== Discussion of MOs ===

= References =
<references />

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T14:59:22Z

Pk1811: /* Discussion of MOs */

<div style="font-size: 40px;"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px;"><center>Ionic liquids: Designer solvents</center></div>
 
= Introduction =
The aim of this project is to explore the physical nature of ionic liquids, which have application in designing solvents through customisation of the nature of the cation and anion<ref name="abs">M. Freemantle. ''Chem. Eng. News'', 1998, '''76''', 32–37</ref>. In this work, a variety of cations have been investigated to identify what trends are present in the variation in central atom and its ligands.

= Structures of methyl-ligand complexes =
== Optimisations ==
A number of cations have been optimised using Gaussian 09 D.01, namely [N(CH3)4]+, [P(CH3)4]+ and [F(CH3)3]+. All these complexes have been optimised to a DFT B3LYP 6-31G(d,p) level with the <code>int=ultrafine scf=conver=9</code> keywords and tight convergence - this is as a consequence of behaviour seen in previous work<ref name="labintro">P. Kent, unpublished work ([[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|lab intro]])</ref> where low frequencies did not exist within a tight range unless these keywords were specified. All calculations were run on the supplied laptop due to a significant queue of jobs on the HPC (except for [S(CH3)3]+ as it took a very long time), and the log files are available here:

* [N(CH3)4]+: [[media:Pk_log_nch34_opt.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_opt.log]]
* [S(CH3)3]+: The first attempt did not converge: {{DOI|10042/26201}}. A partially optimised structure was resubmitted as a second attempt: {{DOI|10042/26205}}. This also did not converge so a final optimisation was run on this partially optimised structure with the <code>nosymm</code> keyword. This converged: {{DOI|10042/26214}}.

Once done, convergence was verified via inspection of the log file.

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name nch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000090 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 1 minutes 27.0 seconds.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name pch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701126 a.u.
RMS Gradient Norm 0.00000675 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 24 minutes 21.0 seconds.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_opt3
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000101 a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 52.2 seconds.
</pre>

=== Convergence outputs ===

''' [N(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000014 0.000060 YES
RMS Displacement 0.000005 0.000040 YES
Predicted change in Energy=-1.010077D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000015 YES
RMS Force 0.000005 0.000010 YES
Maximum Displacement 0.000026 0.000060 YES
RMS Displacement 0.000009 0.000040 YES
Predicted change in Energy=-1.723206D-06
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''

Initial failed optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000015 NO
RMS Force 0.000006 0.000010 YES
Maximum Displacement 0.002915 0.000060 NO
RMS Displacement 0.000869 0.000040 NO
Predicted change in Energy=-5.685776D-09
Optimization stopped.
-- Number of steps exceeded, NStep= 61
-- Flag reset to prevent archiving.
</pre>

During this failed optimisation, it appears the molecule just spent a large amount of time rotating around the C3 axis through the sulphur.

The final optimisation yielded:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000049 0.000060 YES
RMS Displacement 0.000018 0.000040 YES
Predicted change in Energy=-6.520157D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==
Following this, frequency analysis was conducted with the same keywords and calculation level to ensure a minima has been found. This is ensured by checking there are no negative vibrations in the molecule. Calculations were again run on the laptop, and the log files, summaries, and frequencies are listed below. Actual animations of the modes have not been exported, however a Jmol of the log file is available and the modes can be seen by right clicking and choosing '''model -> the mode you want to see'''. This time, a range of
-30 to +30 cm-1 has been accepted for the low frequencies as molecules investigated are quite complex, and a relatively simple basis set has been used. Optimising to 6-311G(d,p) would likely bring the frequencies within the range used previously however this would be at the expense of much longer computation times.

* [N(CH3)4]+: [[media:Pk_log_nch34_freq.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_freq.log]]
* [S(CH3)3]+: {{DOI|10042/26273}}

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name NCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000085 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 3 minutes 17.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000009 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.014288D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name PCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701149 a.u.
RMS Gradient Norm 0.00000668 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 12 minutes 11.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001774 0.001800 YES
RMS Displacement 0.000659 0.001200 YES
Predicted change in Energy=-3.008780D-08
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000104 a.u.
Imaginary Freq 0
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 9 minutes 6.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000093 0.001800 YES
RMS Displacement 0.000033 0.001200 YES
Predicted change in Energy=-7.179584D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Vibration modes ===

''' [N(CH3)4]+ '''
<pre>
Low frequencies --- 0.0007 0.0011 0.0013 21.5288 21.5288 21.5288
Low frequencies --- 188.5488 292.6546 292.6546
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [P(CH3)4]+ '''
<pre>
Low frequencies --- -15.1139 -0.0002 0.0012 0.0012 5.8940 14.7736
Low frequencies --- 156.2222 191.5376 191.9513
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_pch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [S(CH3)3]+ '''
<pre>
Low frequencies --- -8.5871 0.0029 0.0049 0.0051 5.7111 9.1755
Low frequencies --- 162.4159 200.3446 200.5391
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_sch33_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== Conclusions on molecular structure ==
Investigation of structures is focused on the central atom as this is the only point at which variance should occur. The length of the M-C bonds and the angle between C-M-C on each complex is reported below:

{| class="wikitable" border="1"
! Complex !! M-C Length (Å) !! Angle (°) !! M-C length (lit<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref>) (Å)
|-
| [P(CH3)4]+ || 1.82 || 109.5 || 1.84
|-
| [N(CH3)4]+ || 1.51 || 109.5 || 1.46
|-
| [S(CH3)3]+ || 1.82 || 102.7 || 1.79
|}

''Literature bond lengths are found by adding the covalent radii for the atoms.''

Two key trends are:
* As you go down a group, the bond length decreases
* As you go across a group (so losing a ligand), the bond angle is reduced)

The first trend is straightforward to explain, as bond lengths increase down the group. This is in tandem with the increase in atomic radius down the group as orbitals in a greater shell begin to be filled. Thus, as you move from period 2 (N) to period 3 (P), the length of the bond increases and is in turn the overall size of each ion. There is slight variance in the length of a C-H bond in each complex, however no pattern is immediately discernible (it increases in the order S > P > N) - it is thought this is just some random error in the calculation.

Whilst there is an increase in bond length, there is no change in orientation of the bonds, thus the symmetry of TD is maintained in both the phosphorous and nitrogen molecules. As a result of this, the bond angle is the same for these two complexes. No other arrangement of the ligands is sterically possible, so ensuring that this symmetry label cannot be changed, and therefore the bond angle also cannot change. The bond angle is different for sulphur, as a result of the change of symmetry to C3v, it is not known if the change in metal centre contributes to this change - further investigation would be required.

Of note, the bond length does not appear to change going across the period. There is actually a small increase of 0.01Å if the bond length is reported accurate to 0.001Å, however it is not known if this is just an inherent error in the calculation or not. In any event, it is expected that there is a slight decrease in the bond length as you move towards the right of a period, as the increased nuclear charge better shields the electrons and thus shortens the bond length, but this is not observed here. This may be a result of this complex containing one less ligand, with the arrangement instead taken (along with the lone pair) resulting in some interactions (steric or electronic repulsion) which causes the carbon and metal atoms to move apart from each other. This theory is supported by the large deviation from bond length for the sulphur complex, indicating some feature about the arrangement it has taken is causing the bond length to be artificially lengthened.

Otherwise no strange observations are seen with the structures, with all methyl groups taking the expected tetrahedral structure, and either tetrahedral or C3v structures for the central atom as expected by the number of ligands which are present.

= Molecular orbitals and NBO charges of methyl-ligand complexes =
All three complexes discussed previously have been subject to a full NBO and MO analysis via an energy calculation with the <code>pop=(full,nbo)</code> keyword, retaining any previously used keywords as appropriate. Calculations were performed on the laptop due to load on the HPC, except for the sulphur complex as the calculation took too long on the laptop.

Log files are available as follows:

* '''[N(CH3)4]+''': [[media:Pk_log_nch34_egy.log]]
* '''[P(CH3)4]+''': [[media:Pk_log_pch34_egy.log]]
* '''[S(CH3)3]+''': {{DOI|10042/26274}}
== Calculation output ==

''' [N(CH3)4]+ '''

<pre>
File Name NCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

''' [P(CH3)4]+ '''

<pre>
File Name PCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701105 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 20.0 seconds.
</pre>

''' [S(CH3)3]+ '''

<pre>File Name sch33_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 0 minutes 57.7 seconds.
</pre>

== Sample MOs for [N(CH3)4]+ ==
A variety of 5 molecular orbitals have been calculated and shown below. Only occupied non-core MOs from the totally bonding to totally antibonding are shown.

{| class="wikitable" border="1"
|+ Totally bonding towards the top
! MO number !! Energy (hartree) !! Picture !! Degeneracy !! Notes
|-
| 6 || -1.19645 || [[Image:Pk-n-mo0.png|200px]] || Singly degenerate || This MO exhibits a great degree of strong bonding interactions across the entire molecule up to the protons, the orbitals of which do not appear to be part of this MO. This is seen by the huge red surface containing almost the entirety of the molecule. As a result of the huge amount of delocalisation seen in the MO, there is a lot of through space interactions between adjacent carbon groups, as seen by how the MO forms a 'cage' around the entire molecule - the empty space between two carbon atoms is part of this red object. As there are no other molecular orbitals other than this huge one, there is no concept of a node in this MO diagram.
|-
| 10 || -0.80745 || [[Image:Pk-n-mo1.png|200px]] || Singly degenerate || This is the first MO in this series of 5 to contain a slight degree of antibonding character, as seen by the fact each ligand is in its own (+) phase orbital, whereas the central metal is in a (-) phase one. This leads to a minor degree of antibonding character, and also a node in the centre of the M-C bond where the two MOs end. Through space interactions are present in each ligand MO, with all the protons and the central carbon existing within the boundaries of the MO, and hence there are through-space interactions between the protons. MOs of the same phase interact weakly with each other due to the large distance between each green orbital (seen in the picture), however the interaction between the (+) and (-) orbitals is quite strong as the nodal area is very small in size - the orbitals are nearly touching. The level of delocalisation is reduced, with delocalisation only occurring across each ligand group - the ligands themselves are not delocalised onto one unit.
|-
| 14 || -0.62248 || [[Image:Pk-n-mo2.png|200px]] || Doubly degenerate || For this MO, nodes exist on every carbon atom, as each MO covers two halves of a carbon atom, two protons, and nothing else. This does lead to delocalisationa cross the protons and carbon atoms, however this also does result in strong antibonding interactions at each carbon as the (+) and (-) MOs become quite close. Some protons, and the metal centre are not covered at all by this MO, however from what is delocalised, there is a significant amount of through space interactions between protons on differing methyl ligands - this is of note as the ligand protons are quite a distance away. There may be some weak bonding interactions between orbitals of the same phase, however they are quite a distance away (separated by the metal centre) so this is expected to be quite weak.
|-
| 17 || -0.58035 || [[Image:Pk-n-mo3.png|200px]] || Triply degenerate || This one again has a node on each carbon, however it differs in that each orbital only covers a single proton and half a carbon. This results in there being no through-space interactions in this molecule. Additionally, there are many strong antibonding interactions as all the orbitals are quite close together, with the a (+) orbital being surrounded by a (-) orbital on every side. If there are any bonding interactions, these are going to be very weak.
|-
| 21 || -0.57934 || [[Image:Pk-n-mo4.png|200px]] || Triply degenerate || This MO is similar to the previous, but differs in that each orbital now consists of two protons, so there are no protons which aren't enclosed in an orbital. Again, there are nodes in each carbon, but also a node in the metal center, with orbitals now also covering the metal center. This results in there being strong antibonding interactions over almost the entire molecule, with (+) interacting with (-) almost over the entire surface of every orbital. Through-space interactions are now back with there being two protons in each orbital, making it possible for these to interact, and there is also the potential for protons and metal center to interact as well. This orbital is only slightly higher energy than the previous one, and this is solely because of the increased degree of antibonding interactions present.
|}

== NBO charge distributions ==

NBO charge distributions were calculated from the checkpoint file for a range of -1.750 to 1.750 as this ensured the range of charges for all 3 complexes could be accommodated on the same scale. The charges are as follows:

{| class="wikitable" border="1"
! Complex !! Metal charge (e) !! Carbon charge (e) !! Proton charge (e)
|-
| [P(NH3)4]+ || 1.667 || -1.060 || 0.298
|-
| [N(NH3)4]+ || -0.295 || -0.846 || 0.297
|-
| [S(NH3)3]+ || 0.917 || -0.483 || 0.269
|}

<gallery>
File:Pk-nbo-n.png|Nitrogen complex
File:Pk-nbo-p.png|Phosphorous complex
File:Pk-nbo-s.png|Sulphur complex
</gallery>

There appears to be a slight trend of the metal centre charge with electronegativity, with the charge much lower as it becomes more electronegative (and hence drawing a greater share of electrons to it). This in turn makes the carbon more positive as electron density is removed from it. The protons remain rather positively charged and do not appear to be greatly affected by the metal centre, but this is likely because they are too far away for the inductive effect to occur.

Interestingly, nitrogen is more eletronegative than sulphur, yet sulphur has a greater negative charge. The reduced degree of polarisation in the bond for the nitrogen complex also suggests why the bond length for the nitrogen complex is shorter compared to the sulphur. The reason for this increased amount of negative charge is due to the lone pair present on sulphur (hence the configuration it takes according to the Jmol clip above), and so there is simply more negative charge present on the sulphur.

Thus, for the general complex [NR4]+, the positive charge located on the nitrogen in the picture is indeed located on the nitrogen, however it is somewhat delocalised over the protons too. As the nitrogen contains the greatest degree of positive charge, though, the + sign is conventionally placed here as it gives the indication as to where most of the charge is.

Analysis of the log files show the exact NBO contributions to the bond:

'''[P(NH3)3]+'''
<pre>
1. (1.98031) BD ( 1) P 1 - C 2
( 40.43%) 0.6358* P 1 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.4030 0.0006 0.0000 -0.4429
0.0006 0.0000 0.6188 -0.0009 0.0385
-0.0538 -0.0591 -0.0036 0.0254
( 59.57%) 0.7718* C 2 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.4044
-0.0074 0.4444 -0.0081 -0.6209 0.0114
0.0121 -0.0169 -0.0186 -0.0011 0.0080
</pre>

This shows almost equal contribution from each atom to the bond, with each atom assuming a sp3 arrangement as is expected by the TD symmetry. Carbon is sp3 as expected due to its saturation. As the carbon is slightly more negatively charged according to the charge distributions, the marginal increase in contribution from the carbon vs the phosphorous agrees with the charge distribution seen.

'''[N(NH3)3]+'''
<pre>
4. (1.98452) BD ( 1) C 1 - N 13
( 33.65%) 0.5801* C 1 s( 20.77%)p 3.81( 79.06%)d 0.01( 0.16%)
0.0003 0.4552 -0.0237 0.0026 -0.5129
-0.0218 -0.5129 -0.0218 -0.5129 -0.0218
0.0234 0.0234 0.0234 0.0000 0.0000
( 66.35%) 0.8146* N 13 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 0.5000 -0.0007 0.0000 0.4999
-0.0001 0.4999 -0.0001 0.4999 -0.0001
0.0103 0.0103 0.0103 0.0000 0.0000
</pre>

A similar argument can be made here. The large contribution from the nitrogen is surprising, but considering the smaller bond length for this complex based on the metal, an increased contribution from the nitrogen is not unreasonable. However this does disagree somewhat with the charge distribution which shows there is a much larger electron density on the carbon. It is thus thought that since it is possible to reach orbitals closer to the core on nitrogen rather than phosphorous, it makes nitrogen able to donate a greater share of electrons, and so polarises the bond towards it as a result of its electronegativity.

'''[S(NH3)3]+'''
<pre>
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
-0.0003 -0.4437 -0.0140 0.0033 0.7546
-0.0059 0.3161 -0.0025 0.3634 0.0098
-0.0189 -0.0222 -0.0093 -0.0186 0.0096
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 -0.0001 -0.4117 0.0075 -0.0012
0.0000 -0.7489 0.0330 0.0000 -0.3137
0.0138 0.0000 -0.4037 -0.0260 -0.0353
-0.0572 -0.0240 -0.0347 0.0051
</pre>

Finally, for the sulphur, the bond is an almost equal contribution from each atom in the bond. The charges of the S and C atoms according to the charge distribution are both similar and negative, suggesting little polarisation in this bond, and so the balance seen here is to be expected.

= Ligand influences on nitrogen metal centre complexes =
To investigate how changes to the ligands affects the cation, two variants on the nitrogen complex analysed previously have been used. One has one of the protons on a methyl ligand replaced with CH2OH, the other has the proton replaced with CH2CN. Each complex is then optimised and subject to a frequency analysis so as to allow for investigation of its structure. A MO and NBO calculation is then subsequently run to analyse how the change in ligand affects the ions electronic behaviour.

== Optimisations ==
Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26206}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26207}}

=== Summary output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
File Name nch33ch2oh_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000102 a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 1 hours 22 minutes 37.5 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
File Name nch33ch2cn_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000045 a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 50 minutes 39.5 seconds.
</pre>

=== Convergence output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000034 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-5.591936D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000011 0.000040 YES
Predicted change in Energy=-2.269581D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==

Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26290}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26291}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000106 a.u.
Imaginary Freq 0
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 26 minutes 10.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000102 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-5.078379D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000059 a.u.
Imaginary Freq 0
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 29 minutes 19.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-6.144746D-12
Optimization completed.
-- Stationary point found.
</pre>

=== Vibrational modes ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2oh_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

'''[N(CH3)3(CH2CN)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2cn_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== MO and NBO calculations ==
<code>pop=(nbo,full)</code> energy calculations were then performed on the complexes to generate MOs and NBO charge diagrams, just as has been done previously. All calculations were performed on the HPC and log files are available as follows:

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26294}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26295}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 59.3 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 25.0 seconds.
</pre>

=== NBO charge distributions ===
The main difference between these ligands is that CN is an EWG, and OH is an EDG, the latter due to the lone pairs which make it possible to enolise. Therefore comparison of the charge density of the structure can show how these ligands affect the overall structure of the molecule. The NBO charge distributions from -0.750 to 0.750 are shown below.

<gallery>
File:Pk-nbo-cn.png|CN ligand complex
File:Pk-nbo-oh.png|OH ligand complex
</gallery>

''n.b. the charge for the metal centre in the CN complex is -0.289''

It is seen that, in both cases, the nitrogen makes up the majority of the C-N bond to the C with the substituent:

'''OH case:'''
<pre>
4. (1.98195) BD ( 1) N 1 - C 14
( 67.28%) 0.8202* N 1 s( 23.48%)p 3.26( 76.49%)d 0.00( 0.03%)
0.0000 -0.4845 -0.0026 -0.0002 0.7401
-0.0032 0.3146 -0.0015 0.3438 -0.0026
-0.0092 -0.0105 -0.0043 -0.0088 0.0045
( 32.72%) 0.5720* C 14 s( 20.28%)p 3.92( 79.55%)d 0.01( 0.18%)
-0.0003 -0.4501 0.0135 0.0006 -0.7171
-0.0206 -0.3677 -0.0077 -0.3815 -0.0037
-0.0247 -0.0249 -0.0101 -0.0185 0.0102
</pre>

'''CN case:'''
<pre>
4. (1.97747) BD ( 1) N 1 - C 14
( 64.52%) 0.8033* N 1 s( 24.08%)p 3.15( 75.89%)d 0.00( 0.04%)
0.0000 0.4907 -0.0010 0.0003 0.6601
-0.0021 0.5684 0.0038 0.0000 0.0000
0.0166 0.0000 0.0000 0.0024 -0.0097
( 35.48%) 0.5956* C 14 s( 20.81%)p 3.80( 79.05%)d 0.01( 0.14%)
0.0000 0.4557 -0.0205 0.0000 -0.6428
-0.0249 -0.6135 -0.0174 0.0000 0.0000
0.0320 0.0000 0.0000 -0.0011 -0.0197
</pre>

==== Ligand influence on charge distribution ====

There is quite a significant change in electron density for the OH complex with the carbon between the OH group and the metal centre becoming much more positive. This is surprising considering the OH is a donating group, however this is simply explained. As the carbon is between two electronegative groups, a lot of electron density is withdrawn from it, and hence it becomes very positive. However, the metal centre has become more negatively charged (-0.322 vs -0.295). Hence, the donated electrons are moving straight from the oxygen to the metal centre, while the carbon between's electrons are also donated to both the oxygen and nitrogen as part of the electronegative pull these atoms have on the carbon.

Regarding the CN complex, the electron withdrawal is clearly seen on the carbon the CN ligand is bonded to, as this has become less negatively charged (-0.289 vs -0.295), showing that once again, electron withdrawal is occuring at a distance that causes electrons to travel from the nitrogen through the carbon.

In conclusion, it is seen that the electron inductive effects of the ligands has a direct influence on the the metal centre, as these effects travel through the carbon to directly pull or push electrons from the metal. This is likely due to the large contribution of charge from the nitrogen in the CN bond to the relevant C, so meaning any inductive effects on the C are very likely to influence the N due to the polarisation of the bond towards the N seen.

=== Sample MOs ===

{| class="wikitable" border="1"
! !! [N(CH3)3(CH2OH)]+ !!
[N(CH3)3(CH2CN)]+
|-
| HOMO || [[Image:Pk-homo-oh.png|200px]] || [[Image:Pk-homo-cn.png|200px]]
|-
| LUMO || [[Image:Pk-lumo-oh.png|200px]] || [[Image:Pk-lumo-cn.png|200px]]
|-
| HOMO Energy (hartree) || -0.48763 || -0.50047
|-
| LUMO Energy (hartree) || -0.12459 || -0.18183
|}

=== Discussion of MOs ===

= References =
<references />

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T14:58:44Z

Pk1811: /* NBO charge distributions */

<div style="font-size: 40px;"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px;"><center>Ionic liquids: Designer solvents</center></div>
 
= Introduction =
The aim of this project is to explore the physical nature of ionic liquids, which have application in designing solvents through customisation of the nature of the cation and anion<ref name="abs">M. Freemantle. ''Chem. Eng. News'', 1998, '''76''', 32–37</ref>. In this work, a variety of cations have been investigated to identify what trends are present in the variation in central atom and its ligands.

= Structures of methyl-ligand complexes =
== Optimisations ==
A number of cations have been optimised using Gaussian 09 D.01, namely [N(CH3)4]+, [P(CH3)4]+ and [F(CH3)3]+. All these complexes have been optimised to a DFT B3LYP 6-31G(d,p) level with the <code>int=ultrafine scf=conver=9</code> keywords and tight convergence - this is as a consequence of behaviour seen in previous work<ref name="labintro">P. Kent, unpublished work ([[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|lab intro]])</ref> where low frequencies did not exist within a tight range unless these keywords were specified. All calculations were run on the supplied laptop due to a significant queue of jobs on the HPC (except for [S(CH3)3]+ as it took a very long time), and the log files are available here:

* [N(CH3)4]+: [[media:Pk_log_nch34_opt.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_opt.log]]
* [S(CH3)3]+: The first attempt did not converge: {{DOI|10042/26201}}. A partially optimised structure was resubmitted as a second attempt: {{DOI|10042/26205}}. This also did not converge so a final optimisation was run on this partially optimised structure with the <code>nosymm</code> keyword. This converged: {{DOI|10042/26214}}.

Once done, convergence was verified via inspection of the log file.

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name nch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000090 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 1 minutes 27.0 seconds.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name pch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701126 a.u.
RMS Gradient Norm 0.00000675 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 24 minutes 21.0 seconds.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_opt3
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000101 a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 52.2 seconds.
</pre>

=== Convergence outputs ===

''' [N(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000014 0.000060 YES
RMS Displacement 0.000005 0.000040 YES
Predicted change in Energy=-1.010077D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000015 YES
RMS Force 0.000005 0.000010 YES
Maximum Displacement 0.000026 0.000060 YES
RMS Displacement 0.000009 0.000040 YES
Predicted change in Energy=-1.723206D-06
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''

Initial failed optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000015 NO
RMS Force 0.000006 0.000010 YES
Maximum Displacement 0.002915 0.000060 NO
RMS Displacement 0.000869 0.000040 NO
Predicted change in Energy=-5.685776D-09
Optimization stopped.
-- Number of steps exceeded, NStep= 61
-- Flag reset to prevent archiving.
</pre>

During this failed optimisation, it appears the molecule just spent a large amount of time rotating around the C3 axis through the sulphur.

The final optimisation yielded:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000049 0.000060 YES
RMS Displacement 0.000018 0.000040 YES
Predicted change in Energy=-6.520157D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==
Following this, frequency analysis was conducted with the same keywords and calculation level to ensure a minima has been found. This is ensured by checking there are no negative vibrations in the molecule. Calculations were again run on the laptop, and the log files, summaries, and frequencies are listed below. Actual animations of the modes have not been exported, however a Jmol of the log file is available and the modes can be seen by right clicking and choosing '''model -> the mode you want to see'''. This time, a range of
-30 to +30 cm-1 has been accepted for the low frequencies as molecules investigated are quite complex, and a relatively simple basis set has been used. Optimising to 6-311G(d,p) would likely bring the frequencies within the range used previously however this would be at the expense of much longer computation times.

* [N(CH3)4]+: [[media:Pk_log_nch34_freq.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_freq.log]]
* [S(CH3)3]+: {{DOI|10042/26273}}

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name NCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000085 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 3 minutes 17.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000009 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.014288D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name PCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701149 a.u.
RMS Gradient Norm 0.00000668 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 12 minutes 11.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001774 0.001800 YES
RMS Displacement 0.000659 0.001200 YES
Predicted change in Energy=-3.008780D-08
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000104 a.u.
Imaginary Freq 0
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 9 minutes 6.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000093 0.001800 YES
RMS Displacement 0.000033 0.001200 YES
Predicted change in Energy=-7.179584D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Vibration modes ===

''' [N(CH3)4]+ '''
<pre>
Low frequencies --- 0.0007 0.0011 0.0013 21.5288 21.5288 21.5288
Low frequencies --- 188.5488 292.6546 292.6546
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [P(CH3)4]+ '''
<pre>
Low frequencies --- -15.1139 -0.0002 0.0012 0.0012 5.8940 14.7736
Low frequencies --- 156.2222 191.5376 191.9513
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_pch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [S(CH3)3]+ '''
<pre>
Low frequencies --- -8.5871 0.0029 0.0049 0.0051 5.7111 9.1755
Low frequencies --- 162.4159 200.3446 200.5391
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_sch33_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== Conclusions on molecular structure ==
Investigation of structures is focused on the central atom as this is the only point at which variance should occur. The length of the M-C bonds and the angle between C-M-C on each complex is reported below:

{| class="wikitable" border="1"
! Complex !! M-C Length (Å) !! Angle (°) !! M-C length (lit<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref>) (Å)
|-
| [P(CH3)4]+ || 1.82 || 109.5 || 1.84
|-
| [N(CH3)4]+ || 1.51 || 109.5 || 1.46
|-
| [S(CH3)3]+ || 1.82 || 102.7 || 1.79
|}

''Literature bond lengths are found by adding the covalent radii for the atoms.''

Two key trends are:
* As you go down a group, the bond length decreases
* As you go across a group (so losing a ligand), the bond angle is reduced)

The first trend is straightforward to explain, as bond lengths increase down the group. This is in tandem with the increase in atomic radius down the group as orbitals in a greater shell begin to be filled. Thus, as you move from period 2 (N) to period 3 (P), the length of the bond increases and is in turn the overall size of each ion. There is slight variance in the length of a C-H bond in each complex, however no pattern is immediately discernible (it increases in the order S > P > N) - it is thought this is just some random error in the calculation.

Whilst there is an increase in bond length, there is no change in orientation of the bonds, thus the symmetry of TD is maintained in both the phosphorous and nitrogen molecules. As a result of this, the bond angle is the same for these two complexes. No other arrangement of the ligands is sterically possible, so ensuring that this symmetry label cannot be changed, and therefore the bond angle also cannot change. The bond angle is different for sulphur, as a result of the change of symmetry to C3v, it is not known if the change in metal centre contributes to this change - further investigation would be required.

Of note, the bond length does not appear to change going across the period. There is actually a small increase of 0.01Å if the bond length is reported accurate to 0.001Å, however it is not known if this is just an inherent error in the calculation or not. In any event, it is expected that there is a slight decrease in the bond length as you move towards the right of a period, as the increased nuclear charge better shields the electrons and thus shortens the bond length, but this is not observed here. This may be a result of this complex containing one less ligand, with the arrangement instead taken (along with the lone pair) resulting in some interactions (steric or electronic repulsion) which causes the carbon and metal atoms to move apart from each other. This theory is supported by the large deviation from bond length for the sulphur complex, indicating some feature about the arrangement it has taken is causing the bond length to be artificially lengthened.

Otherwise no strange observations are seen with the structures, with all methyl groups taking the expected tetrahedral structure, and either tetrahedral or C3v structures for the central atom as expected by the number of ligands which are present.

= Molecular orbitals and NBO charges of methyl-ligand complexes =
All three complexes discussed previously have been subject to a full NBO and MO analysis via an energy calculation with the <code>pop=(full,nbo)</code> keyword, retaining any previously used keywords as appropriate. Calculations were performed on the laptop due to load on the HPC, except for the sulphur complex as the calculation took too long on the laptop.

Log files are available as follows:

* '''[N(CH3)4]+''': [[media:Pk_log_nch34_egy.log]]
* '''[P(CH3)4]+''': [[media:Pk_log_pch34_egy.log]]
* '''[S(CH3)3]+''': {{DOI|10042/26274}}
== Calculation output ==

''' [N(CH3)4]+ '''

<pre>
File Name NCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

''' [P(CH3)4]+ '''

<pre>
File Name PCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701105 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 20.0 seconds.
</pre>

''' [S(CH3)3]+ '''

<pre>File Name sch33_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 0 minutes 57.7 seconds.
</pre>

== Sample MOs for [N(CH3)4]+ ==
A variety of 5 molecular orbitals have been calculated and shown below. Only occupied non-core MOs from the totally bonding to totally antibonding are shown.

{| class="wikitable" border="1"
|+ Totally bonding towards the top
! MO number !! Energy (hartree) !! Picture !! Degeneracy !! Notes
|-
| 6 || -1.19645 || [[Image:Pk-n-mo0.png|200px]] || Singly degenerate || This MO exhibits a great degree of strong bonding interactions across the entire molecule up to the protons, the orbitals of which do not appear to be part of this MO. This is seen by the huge red surface containing almost the entirety of the molecule. As a result of the huge amount of delocalisation seen in the MO, there is a lot of through space interactions between adjacent carbon groups, as seen by how the MO forms a 'cage' around the entire molecule - the empty space between two carbon atoms is part of this red object. As there are no other molecular orbitals other than this huge one, there is no concept of a node in this MO diagram.
|-
| 10 || -0.80745 || [[Image:Pk-n-mo1.png|200px]] || Singly degenerate || This is the first MO in this series of 5 to contain a slight degree of antibonding character, as seen by the fact each ligand is in its own (+) phase orbital, whereas the central metal is in a (-) phase one. This leads to a minor degree of antibonding character, and also a node in the centre of the M-C bond where the two MOs end. Through space interactions are present in each ligand MO, with all the protons and the central carbon existing within the boundaries of the MO, and hence there are through-space interactions between the protons. MOs of the same phase interact weakly with each other due to the large distance between each green orbital (seen in the picture), however the interaction between the (+) and (-) orbitals is quite strong as the nodal area is very small in size - the orbitals are nearly touching. The level of delocalisation is reduced, with delocalisation only occurring across each ligand group - the ligands themselves are not delocalised onto one unit.
|-
| 14 || -0.62248 || [[Image:Pk-n-mo2.png|200px]] || Doubly degenerate || For this MO, nodes exist on every carbon atom, as each MO covers two halves of a carbon atom, two protons, and nothing else. This does lead to delocalisationa cross the protons and carbon atoms, however this also does result in strong antibonding interactions at each carbon as the (+) and (-) MOs become quite close. Some protons, and the metal centre are not covered at all by this MO, however from what is delocalised, there is a significant amount of through space interactions between protons on differing methyl ligands - this is of note as the ligand protons are quite a distance away. There may be some weak bonding interactions between orbitals of the same phase, however they are quite a distance away (separated by the metal centre) so this is expected to be quite weak.
|-
| 17 || -0.58035 || [[Image:Pk-n-mo3.png|200px]] || Triply degenerate || This one again has a node on each carbon, however it differs in that each orbital only covers a single proton and half a carbon. This results in there being no through-space interactions in this molecule. Additionally, there are many strong antibonding interactions as all the orbitals are quite close together, with the a (+) orbital being surrounded by a (-) orbital on every side. If there are any bonding interactions, these are going to be very weak.
|-
| 21 || -0.57934 || [[Image:Pk-n-mo4.png|200px]] || Triply degenerate || This MO is similar to the previous, but differs in that each orbital now consists of two protons, so there are no protons which aren't enclosed in an orbital. Again, there are nodes in each carbon, but also a node in the metal center, with orbitals now also covering the metal center. This results in there being strong antibonding interactions over almost the entire molecule, with (+) interacting with (-) almost over the entire surface of every orbital. Through-space interactions are now back with there being two protons in each orbital, making it possible for these to interact, and there is also the potential for protons and metal center to interact as well. This orbital is only slightly higher energy than the previous one, and this is solely because of the increased degree of antibonding interactions present.
|}

== NBO charge distributions ==

NBO charge distributions were calculated from the checkpoint file for a range of -1.750 to 1.750 as this ensured the range of charges for all 3 complexes could be accommodated on the same scale. The charges are as follows:

{| class="wikitable" border="1"
! Complex !! Metal charge (e) !! Carbon charge (e) !! Proton charge (e)
|-
| [P(NH3)4]+ || 1.667 || -1.060 || 0.298
|-
| [N(NH3)4]+ || -0.295 || -0.846 || 0.297
|-
| [S(NH3)3]+ || 0.917 || -0.483 || 0.269
|}

<gallery>
File:Pk-nbo-n.png|Nitrogen complex
File:Pk-nbo-p.png|Phosphorous complex
File:Pk-nbo-s.png|Sulphur complex
</gallery>

There appears to be a slight trend of the metal centre charge with electronegativity, with the charge much lower as it becomes more electronegative (and hence drawing a greater share of electrons to it). This in turn makes the carbon more positive as electron density is removed from it. The protons remain rather positively charged and do not appear to be greatly affected by the metal centre, but this is likely because they are too far away for the inductive effect to occur.

Interestingly, nitrogen is more eletronegative than sulphur, yet sulphur has a greater negative charge. The reduced degree of polarisation in the bond for the nitrogen complex also suggests why the bond length for the nitrogen complex is shorter compared to the sulphur. The reason for this increased amount of negative charge is due to the lone pair present on sulphur (hence the configuration it takes according to the Jmol clip above), and so there is simply more negative charge present on the sulphur.

Thus, for the general complex [NR4]+, the positive charge located on the nitrogen in the picture is indeed located on the nitrogen, however it is somewhat delocalised over the protons too. As the nitrogen contains the greatest degree of positive charge, though, the + sign is conventionally placed here as it gives the indication as to where most of the charge is.

Analysis of the log files show the exact NBO contributions to the bond:

'''[P(NH3)3]+'''
<pre>
1. (1.98031) BD ( 1) P 1 - C 2
( 40.43%) 0.6358* P 1 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.4030 0.0006 0.0000 -0.4429
0.0006 0.0000 0.6188 -0.0009 0.0385
-0.0538 -0.0591 -0.0036 0.0254
( 59.57%) 0.7718* C 2 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.4044
-0.0074 0.4444 -0.0081 -0.6209 0.0114
0.0121 -0.0169 -0.0186 -0.0011 0.0080
</pre>

This shows almost equal contribution from each atom to the bond, with each atom assuming a sp3 arrangement as is expected by the TD symmetry. Carbon is sp3 as expected due to its saturation. As the carbon is slightly more negatively charged according to the charge distributions, the marginal increase in contribution from the carbon vs the phosphorous agrees with the charge distribution seen.

'''[N(NH3)3]+'''
<pre>
4. (1.98452) BD ( 1) C 1 - N 13
( 33.65%) 0.5801* C 1 s( 20.77%)p 3.81( 79.06%)d 0.01( 0.16%)
0.0003 0.4552 -0.0237 0.0026 -0.5129
-0.0218 -0.5129 -0.0218 -0.5129 -0.0218
0.0234 0.0234 0.0234 0.0000 0.0000
( 66.35%) 0.8146* N 13 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 0.5000 -0.0007 0.0000 0.4999
-0.0001 0.4999 -0.0001 0.4999 -0.0001
0.0103 0.0103 0.0103 0.0000 0.0000
</pre>

A similar argument can be made here. The large contribution from the nitrogen is surprising, but considering the smaller bond length for this complex based on the metal, an increased contribution from the nitrogen is not unreasonable. However this does disagree somewhat with the charge distribution which shows there is a much larger electron density on the carbon. It is thus thought that since it is possible to reach orbitals closer to the core on nitrogen rather than phosphorous, it makes nitrogen able to donate a greater share of electrons, and so polarises the bond towards it as a result of its electronegativity.

'''[S(NH3)3]+'''
<pre>
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
-0.0003 -0.4437 -0.0140 0.0033 0.7546
-0.0059 0.3161 -0.0025 0.3634 0.0098
-0.0189 -0.0222 -0.0093 -0.0186 0.0096
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 -0.0001 -0.4117 0.0075 -0.0012
0.0000 -0.7489 0.0330 0.0000 -0.3137
0.0138 0.0000 -0.4037 -0.0260 -0.0353
-0.0572 -0.0240 -0.0347 0.0051
</pre>

Finally, for the sulphur, the bond is an almost equal contribution from each atom in the bond. The charges of the S and C atoms according to the charge distribution are both similar and negative, suggesting little polarisation in this bond, and so the balance seen here is to be expected.

= Ligand influences on nitrogen metal centre complexes =
To investigate how changes to the ligands affects the cation, two variants on the nitrogen complex analysed previously have been used. One has one of the protons on a methyl ligand replaced with CH2OH, the other has the proton replaced with CH2CN. Each complex is then optimised and subject to a frequency analysis so as to allow for investigation of its structure. A MO and NBO calculation is then subsequently run to analyse how the change in ligand affects the ions electronic behaviour.

== Optimisations ==
Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26206}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26207}}

=== Summary output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
File Name nch33ch2oh_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000102 a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 1 hours 22 minutes 37.5 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
File Name nch33ch2cn_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000045 a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 50 minutes 39.5 seconds.
</pre>

=== Convergence output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000034 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-5.591936D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000011 0.000040 YES
Predicted change in Energy=-2.269581D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==

Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26290}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26291}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000106 a.u.
Imaginary Freq 0
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 26 minutes 10.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000102 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-5.078379D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000059 a.u.
Imaginary Freq 0
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 29 minutes 19.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-6.144746D-12
Optimization completed.
-- Stationary point found.
</pre>

=== Vibrational modes ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2oh_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

'''[N(CH3)3(CH2CN)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2cn_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== MO and NBO calculations ==
<code>pop=(nbo,full)</code> energy calculations were then performed on the complexes to generate MOs and NBO charge diagrams, just as has been done previously. All calculations were performed on the HPC and log files are available as follows:

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26294}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26295}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 59.3 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 25.0 seconds.
</pre>

=== NBO charge distributions ===
The main difference between these ligands is that CN is an EWG, and OH is an EDG, the latter due to the lone pairs which make it possible to enolise. Therefore comparison of the charge density of the structure can show how these ligands affect the overall structure of the molecule. The NBO charge distributions from -0.750 to 0.750 are shown below.

<gallery>
File:Pk-nbo-cn.png|CN ligand complex
File:Pk-nbo-oh.png|OH ligand complex
</gallery>

''n.b. the charge for the metal centre in the CN complex is -0.289''

It is seen that, in both cases, the nitrogen makes up the majority of the C-N bond to the C with the substituent:

'''OH case:'''
<pre>
4. (1.98195) BD ( 1) N 1 - C 14
( 67.28%) 0.8202* N 1 s( 23.48%)p 3.26( 76.49%)d 0.00( 0.03%)
0.0000 -0.4845 -0.0026 -0.0002 0.7401
-0.0032 0.3146 -0.0015 0.3438 -0.0026
-0.0092 -0.0105 -0.0043 -0.0088 0.0045
( 32.72%) 0.5720* C 14 s( 20.28%)p 3.92( 79.55%)d 0.01( 0.18%)
-0.0003 -0.4501 0.0135 0.0006 -0.7171
-0.0206 -0.3677 -0.0077 -0.3815 -0.0037
-0.0247 -0.0249 -0.0101 -0.0185 0.0102
</pre>

'''CN case:'''
<pre>
4. (1.97747) BD ( 1) N 1 - C 14
( 64.52%) 0.8033* N 1 s( 24.08%)p 3.15( 75.89%)d 0.00( 0.04%)
0.0000 0.4907 -0.0010 0.0003 0.6601
-0.0021 0.5684 0.0038 0.0000 0.0000
0.0166 0.0000 0.0000 0.0024 -0.0097
( 35.48%) 0.5956* C 14 s( 20.81%)p 3.80( 79.05%)d 0.01( 0.14%)
0.0000 0.4557 -0.0205 0.0000 -0.6428
-0.0249 -0.6135 -0.0174 0.0000 0.0000
0.0320 0.0000 0.0000 -0.0011 -0.0197
</pre>

==== Ligand influence on charge distribution ====

There is quite a significant change in electron density for the OH complex with the carbon between the OH group and the metal centre becoming much more positive. This is surprising considering the OH is a donating group, however this is simply explained. As the carbon is between two electronegative groups, a lot of electron density is withdrawn from it, and hence it becomes very positive. However, the metal centre has become more negatively charged (-0.322 vs -0.295). Hence, the donated electrons are moving straight from the oxygen to the metal centre, while the carbon between's electrons are also donated to both the oxygen and nitrogen as part of the electronegative pull these atoms have on the carbon.

Regarding the CN complex, the electron withdrawal is clearly seen on the carbon the CN ligand is bonded to, as this has become less negatively charged (-0.289 vs -0.295), showing that once again, electron withdrawal is occuring at a distance that causes electrons to travel from the nitrogen through the carbon.

In conclusion, it is seen that the electron inductive effects of the ligands has a direct influence on the the metal centre, as these effects travel through the carbon to directly pull or push electrons from the metal. This is likely due to the large contribution of charge from the nitrogen in the CN bond to the relevant C, so meaning any inductive effects on the C are very likely to influence the N due to the polarisation of the bond towards the N seen.

=== Sample MOs ===

{| class="wikitable" border="1"
! !! [N(CH3)3(CH2OH)]+ !!
[N(CH3)3(CH2CN)]+
|-
| HOMO || [[Image:Pk-homo-oh.png|200px]] || [[Image:Pk-homo-cn.png|200px]]
|-
| LUMO || [[Image:Pk-lumo-oh.png|200px]] || [[Image:Pk-lumo-cn.png|200px]]
|-
| HOMO Energy (hartree) || -0.48763 || -0.50047
|-
| LUMO Energy (hartree) || -0.12459 || -0.18183
|}

=== Discussion of MOs ===

==== Ligand influence on structure ====

==== Ligand influence on charge distribution ====

==== Ligand influence on molecular orbitals ====

= References =
<references />

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T14:52:51Z

Pk1811: /* NBO charge distributions */

<div style="font-size: 40px;"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px;"><center>Ionic liquids: Designer solvents</center></div>
 
= Introduction =
The aim of this project is to explore the physical nature of ionic liquids, which have application in designing solvents through customisation of the nature of the cation and anion<ref name="abs">M. Freemantle. ''Chem. Eng. News'', 1998, '''76''', 32–37</ref>. In this work, a variety of cations have been investigated to identify what trends are present in the variation in central atom and its ligands.

= Structures of methyl-ligand complexes =
== Optimisations ==
A number of cations have been optimised using Gaussian 09 D.01, namely [N(CH3)4]+, [P(CH3)4]+ and [F(CH3)3]+. All these complexes have been optimised to a DFT B3LYP 6-31G(d,p) level with the <code>int=ultrafine scf=conver=9</code> keywords and tight convergence - this is as a consequence of behaviour seen in previous work<ref name="labintro">P. Kent, unpublished work ([[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|lab intro]])</ref> where low frequencies did not exist within a tight range unless these keywords were specified. All calculations were run on the supplied laptop due to a significant queue of jobs on the HPC (except for [S(CH3)3]+ as it took a very long time), and the log files are available here:

* [N(CH3)4]+: [[media:Pk_log_nch34_opt.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_opt.log]]
* [S(CH3)3]+: The first attempt did not converge: {{DOI|10042/26201}}. A partially optimised structure was resubmitted as a second attempt: {{DOI|10042/26205}}. This also did not converge so a final optimisation was run on this partially optimised structure with the <code>nosymm</code> keyword. This converged: {{DOI|10042/26214}}.

Once done, convergence was verified via inspection of the log file.

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name nch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000090 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 1 minutes 27.0 seconds.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name pch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701126 a.u.
RMS Gradient Norm 0.00000675 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 24 minutes 21.0 seconds.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_opt3
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000101 a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 52.2 seconds.
</pre>

=== Convergence outputs ===

''' [N(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000014 0.000060 YES
RMS Displacement 0.000005 0.000040 YES
Predicted change in Energy=-1.010077D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000015 YES
RMS Force 0.000005 0.000010 YES
Maximum Displacement 0.000026 0.000060 YES
RMS Displacement 0.000009 0.000040 YES
Predicted change in Energy=-1.723206D-06
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''

Initial failed optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000015 NO
RMS Force 0.000006 0.000010 YES
Maximum Displacement 0.002915 0.000060 NO
RMS Displacement 0.000869 0.000040 NO
Predicted change in Energy=-5.685776D-09
Optimization stopped.
-- Number of steps exceeded, NStep= 61
-- Flag reset to prevent archiving.
</pre>

During this failed optimisation, it appears the molecule just spent a large amount of time rotating around the C3 axis through the sulphur.

The final optimisation yielded:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000049 0.000060 YES
RMS Displacement 0.000018 0.000040 YES
Predicted change in Energy=-6.520157D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==
Following this, frequency analysis was conducted with the same keywords and calculation level to ensure a minima has been found. This is ensured by checking there are no negative vibrations in the molecule. Calculations were again run on the laptop, and the log files, summaries, and frequencies are listed below. Actual animations of the modes have not been exported, however a Jmol of the log file is available and the modes can be seen by right clicking and choosing '''model -> the mode you want to see'''. This time, a range of
-30 to +30 cm-1 has been accepted for the low frequencies as molecules investigated are quite complex, and a relatively simple basis set has been used. Optimising to 6-311G(d,p) would likely bring the frequencies within the range used previously however this would be at the expense of much longer computation times.

* [N(CH3)4]+: [[media:Pk_log_nch34_freq.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_freq.log]]
* [S(CH3)3]+: {{DOI|10042/26273}}

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name NCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000085 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 3 minutes 17.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000009 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.014288D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name PCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701149 a.u.
RMS Gradient Norm 0.00000668 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 12 minutes 11.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001774 0.001800 YES
RMS Displacement 0.000659 0.001200 YES
Predicted change in Energy=-3.008780D-08
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000104 a.u.
Imaginary Freq 0
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 9 minutes 6.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000093 0.001800 YES
RMS Displacement 0.000033 0.001200 YES
Predicted change in Energy=-7.179584D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Vibration modes ===

''' [N(CH3)4]+ '''
<pre>
Low frequencies --- 0.0007 0.0011 0.0013 21.5288 21.5288 21.5288
Low frequencies --- 188.5488 292.6546 292.6546
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [P(CH3)4]+ '''
<pre>
Low frequencies --- -15.1139 -0.0002 0.0012 0.0012 5.8940 14.7736
Low frequencies --- 156.2222 191.5376 191.9513
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_pch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [S(CH3)3]+ '''
<pre>
Low frequencies --- -8.5871 0.0029 0.0049 0.0051 5.7111 9.1755
Low frequencies --- 162.4159 200.3446 200.5391
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_sch33_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== Conclusions on molecular structure ==
Investigation of structures is focused on the central atom as this is the only point at which variance should occur. The length of the M-C bonds and the angle between C-M-C on each complex is reported below:

{| class="wikitable" border="1"
! Complex !! M-C Length (Å) !! Angle (°) !! M-C length (lit<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref>) (Å)
|-
| [P(CH3)4]+ || 1.82 || 109.5 || 1.84
|-
| [N(CH3)4]+ || 1.51 || 109.5 || 1.46
|-
| [S(CH3)3]+ || 1.82 || 102.7 || 1.79
|}

''Literature bond lengths are found by adding the covalent radii for the atoms.''

Two key trends are:
* As you go down a group, the bond length decreases
* As you go across a group (so losing a ligand), the bond angle is reduced)

The first trend is straightforward to explain, as bond lengths increase down the group. This is in tandem with the increase in atomic radius down the group as orbitals in a greater shell begin to be filled. Thus, as you move from period 2 (N) to period 3 (P), the length of the bond increases and is in turn the overall size of each ion. There is slight variance in the length of a C-H bond in each complex, however no pattern is immediately discernible (it increases in the order S > P > N) - it is thought this is just some random error in the calculation.

Whilst there is an increase in bond length, there is no change in orientation of the bonds, thus the symmetry of TD is maintained in both the phosphorous and nitrogen molecules. As a result of this, the bond angle is the same for these two complexes. No other arrangement of the ligands is sterically possible, so ensuring that this symmetry label cannot be changed, and therefore the bond angle also cannot change. The bond angle is different for sulphur, as a result of the change of symmetry to C3v, it is not known if the change in metal centre contributes to this change - further investigation would be required.

Of note, the bond length does not appear to change going across the period. There is actually a small increase of 0.01Å if the bond length is reported accurate to 0.001Å, however it is not known if this is just an inherent error in the calculation or not. In any event, it is expected that there is a slight decrease in the bond length as you move towards the right of a period, as the increased nuclear charge better shields the electrons and thus shortens the bond length, but this is not observed here. This may be a result of this complex containing one less ligand, with the arrangement instead taken (along with the lone pair) resulting in some interactions (steric or electronic repulsion) which causes the carbon and metal atoms to move apart from each other. This theory is supported by the large deviation from bond length for the sulphur complex, indicating some feature about the arrangement it has taken is causing the bond length to be artificially lengthened.

Otherwise no strange observations are seen with the structures, with all methyl groups taking the expected tetrahedral structure, and either tetrahedral or C3v structures for the central atom as expected by the number of ligands which are present.

= Molecular orbitals and NBO charges of methyl-ligand complexes =
All three complexes discussed previously have been subject to a full NBO and MO analysis via an energy calculation with the <code>pop=(full,nbo)</code> keyword, retaining any previously used keywords as appropriate. Calculations were performed on the laptop due to load on the HPC, except for the sulphur complex as the calculation took too long on the laptop.

Log files are available as follows:

* '''[N(CH3)4]+''': [[media:Pk_log_nch34_egy.log]]
* '''[P(CH3)4]+''': [[media:Pk_log_pch34_egy.log]]
* '''[S(CH3)3]+''': {{DOI|10042/26274}}
== Calculation output ==

''' [N(CH3)4]+ '''

<pre>
File Name NCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

''' [P(CH3)4]+ '''

<pre>
File Name PCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701105 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 20.0 seconds.
</pre>

''' [S(CH3)3]+ '''

<pre>File Name sch33_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 0 minutes 57.7 seconds.
</pre>

== Sample MOs for [N(CH3)4]+ ==
A variety of 5 molecular orbitals have been calculated and shown below. Only occupied non-core MOs from the totally bonding to totally antibonding are shown.

{| class="wikitable" border="1"
|+ Totally bonding towards the top
! MO number !! Energy (hartree) !! Picture !! Degeneracy !! Notes
|-
| 6 || -1.19645 || [[Image:Pk-n-mo0.png|200px]] || Singly degenerate || This MO exhibits a great degree of strong bonding interactions across the entire molecule up to the protons, the orbitals of which do not appear to be part of this MO. This is seen by the huge red surface containing almost the entirety of the molecule. As a result of the huge amount of delocalisation seen in the MO, there is a lot of through space interactions between adjacent carbon groups, as seen by how the MO forms a 'cage' around the entire molecule - the empty space between two carbon atoms is part of this red object. As there are no other molecular orbitals other than this huge one, there is no concept of a node in this MO diagram.
|-
| 10 || -0.80745 || [[Image:Pk-n-mo1.png|200px]] || Singly degenerate || This is the first MO in this series of 5 to contain a slight degree of antibonding character, as seen by the fact each ligand is in its own (+) phase orbital, whereas the central metal is in a (-) phase one. This leads to a minor degree of antibonding character, and also a node in the centre of the M-C bond where the two MOs end. Through space interactions are present in each ligand MO, with all the protons and the central carbon existing within the boundaries of the MO, and hence there are through-space interactions between the protons. MOs of the same phase interact weakly with each other due to the large distance between each green orbital (seen in the picture), however the interaction between the (+) and (-) orbitals is quite strong as the nodal area is very small in size - the orbitals are nearly touching. The level of delocalisation is reduced, with delocalisation only occurring across each ligand group - the ligands themselves are not delocalised onto one unit.
|-
| 14 || -0.62248 || [[Image:Pk-n-mo2.png|200px]] || Doubly degenerate || For this MO, nodes exist on every carbon atom, as each MO covers two halves of a carbon atom, two protons, and nothing else. This does lead to delocalisationa cross the protons and carbon atoms, however this also does result in strong antibonding interactions at each carbon as the (+) and (-) MOs become quite close. Some protons, and the metal centre are not covered at all by this MO, however from what is delocalised, there is a significant amount of through space interactions between protons on differing methyl ligands - this is of note as the ligand protons are quite a distance away. There may be some weak bonding interactions between orbitals of the same phase, however they are quite a distance away (separated by the metal centre) so this is expected to be quite weak.
|-
| 17 || -0.58035 || [[Image:Pk-n-mo3.png|200px]] || Triply degenerate || This one again has a node on each carbon, however it differs in that each orbital only covers a single proton and half a carbon. This results in there being no through-space interactions in this molecule. Additionally, there are many strong antibonding interactions as all the orbitals are quite close together, with the a (+) orbital being surrounded by a (-) orbital on every side. If there are any bonding interactions, these are going to be very weak.
|-
| 21 || -0.57934 || [[Image:Pk-n-mo4.png|200px]] || Triply degenerate || This MO is similar to the previous, but differs in that each orbital now consists of two protons, so there are no protons which aren't enclosed in an orbital. Again, there are nodes in each carbon, but also a node in the metal center, with orbitals now also covering the metal center. This results in there being strong antibonding interactions over almost the entire molecule, with (+) interacting with (-) almost over the entire surface of every orbital. Through-space interactions are now back with there being two protons in each orbital, making it possible for these to interact, and there is also the potential for protons and metal center to interact as well. This orbital is only slightly higher energy than the previous one, and this is solely because of the increased degree of antibonding interactions present.
|}

== NBO charge distributions ==

NBO charge distributions were calculated from the checkpoint file for a range of -1.750 to 1.750 as this ensured the range of charges for all 3 complexes could be accommodated on the same scale. The charges are as follows:

{| class="wikitable" border="1"
! Complex !! Metal charge (e) !! Carbon charge (e) !! Proton charge (e)
|-
| [P(NH3)4]+ || 1.667 || -1.060 || 0.298
|-
| [N(NH3)4]+ || -0.295 || -0.846 || 0.297
|-
| [S(NH3)3]+ || 0.917 || -0.483 || 0.269
|}

<gallery>
File:Pk-nbo-n.png|Nitrogen complex
File:Pk-nbo-p.png|Phosphorous complex
File:Pk-nbo-s.png|Sulphur complex
</gallery>

There appears to be a slight trend of the metal centre charge with electronegativity, with the charge much lower as it becomes more electronegative (and hence drawing a greater share of electrons to it). This in turn makes the carbon more positive as electron density is removed from it. The protons remain rather positively charged and do not appear to be greatly affected by the metal centre, but this is likely because they are too far away for the inductive effect to occur.

Interestingly, nitrogen is more eletronegative than sulphur, yet sulphur has a greater negative charge. The reduced degree of polarisation in the bond for the nitrogen complex also suggests why the bond length for the nitrogen complex is shorter compared to the sulphur. The reason for this increased amount of negative charge is due to the lone pair present on sulphur (hence the configuration it takes according to the Jmol clip above), and so there is simply more negative charge present on the sulphur.

Thus, for the general complex [NR4]+, the positive charge located on the nitrogen in the picture is indeed located on the nitrogen, however it is somewhat delocalised over the protons too. As the nitrogen contains the greatest degree of positive charge, though, the + sign is conventionally placed here as it gives the indication as to where most of the charge is.

Analysis of the log files show the exact NBO contributions to the bond:

'''[P(NH3)3]+'''
<pre>
1. (1.98031) BD ( 1) P 1 - C 2
( 40.43%) 0.6358* P 1 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.4030 0.0006 0.0000 -0.4429
0.0006 0.0000 0.6188 -0.0009 0.0385
-0.0538 -0.0591 -0.0036 0.0254
( 59.57%) 0.7718* C 2 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.4044
-0.0074 0.4444 -0.0081 -0.6209 0.0114
0.0121 -0.0169 -0.0186 -0.0011 0.0080
</pre>

This shows almost equal contribution from each atom to the bond, with each atom assuming a sp3 arrangement as is expected by the TD symmetry. Carbon is sp3 as expected due to its saturation. As the carbon is slightly more negatively charged according to the charge distributions, the marginal increase in contribution from the carbon vs the phosphorous agrees with the charge distribution seen.

'''[N(NH3)3]+'''
<pre>
4. (1.98452) BD ( 1) C 1 - N 13
( 33.65%) 0.5801* C 1 s( 20.77%)p 3.81( 79.06%)d 0.01( 0.16%)
0.0003 0.4552 -0.0237 0.0026 -0.5129
-0.0218 -0.5129 -0.0218 -0.5129 -0.0218
0.0234 0.0234 0.0234 0.0000 0.0000
( 66.35%) 0.8146* N 13 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 0.5000 -0.0007 0.0000 0.4999
-0.0001 0.4999 -0.0001 0.4999 -0.0001
0.0103 0.0103 0.0103 0.0000 0.0000
</pre>

A similar argument can be made here. The large contribution from the nitrogen is surprising, but considering the smaller bond length for this complex based on the metal, an increased contribution from the nitrogen is not unreasonable. However this does disagree somewhat with the charge distribution which shows there is a much larger electron density on the carbon. It is thus thought that since it is possible to reach orbitals closer to the core on nitrogen rather than phosphorous, it makes nitrogen able to donate a greater share of electrons, and so polarises the bond towards it as a result of its electronegativity.

'''[S(NH3)3]+'''
<pre>
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
-0.0003 -0.4437 -0.0140 0.0033 0.7546
-0.0059 0.3161 -0.0025 0.3634 0.0098
-0.0189 -0.0222 -0.0093 -0.0186 0.0096
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 -0.0001 -0.4117 0.0075 -0.0012
0.0000 -0.7489 0.0330 0.0000 -0.3137
0.0138 0.0000 -0.4037 -0.0260 -0.0353
-0.0572 -0.0240 -0.0347 0.0051
</pre>

Finally, for the sulphur, the bond is an almost equal contribution from each atom in the bond. The charges of the S and C atoms according to the charge distribution are both similar and negative, suggesting little polarisation in this bond, and so the balance seen here is to be expected.

= Ligand influences on nitrogen metal centre complexes =
To investigate how changes to the ligands affects the cation, two variants on the nitrogen complex analysed previously have been used. One has one of the protons on a methyl ligand replaced with CH2OH, the other has the proton replaced with CH2CN. Each complex is then optimised and subject to a frequency analysis so as to allow for investigation of its structure. A MO and NBO calculation is then subsequently run to analyse how the change in ligand affects the ions electronic behaviour.

== Optimisations ==
Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26206}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26207}}

=== Summary output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
File Name nch33ch2oh_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000102 a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 1 hours 22 minutes 37.5 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
File Name nch33ch2cn_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000045 a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 50 minutes 39.5 seconds.
</pre>

=== Convergence output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000034 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-5.591936D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000011 0.000040 YES
Predicted change in Energy=-2.269581D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==

Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26290}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26291}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000106 a.u.
Imaginary Freq 0
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 26 minutes 10.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000102 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-5.078379D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000059 a.u.
Imaginary Freq 0
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 29 minutes 19.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-6.144746D-12
Optimization completed.
-- Stationary point found.
</pre>

=== Vibrational modes ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2oh_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

'''[N(CH3)3(CH2CN)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2cn_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== MO and NBO calculations ==
<code>pop=(nbo,full)</code> energy calculations were then performed on the complexes to generate MOs and NBO charge diagrams, just as has been done previously. All calculations were performed on the HPC and log files are available as follows:

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26294}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26295}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 59.3 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 25.0 seconds.
</pre>

=== NBO charge distributions ===
The main difference between these ligands is that CN is an EWG, and OH is an EDG, the latter due to the lone pairs which make it possible to enolise. Therefore comparison of the charge density of the structure can show how these ligands affect the overall structure of the molecule. The NBO charge distributions from -0.750 to 0.750 are shown below.

<gallery>
File:Pk-nbo-cn.png|CN ligand complex
File:Pk-nbo-oh.png|OH ligand complex
</gallery>

''n.b. the charge for the metal centre in the CN complex is -0.289''

There is quite a significant change in electron density for the OH complex with the carbon between the OH group and the metal centre becoming much more positive. This is surprising considering the OH is a donating group, however this is simply explained. As the carbon is between two electronegative groups, a lot of electron density is withdrawn from it, and hence it becomes very positive. However, the metal centre has become more negatively charged (-0.322 vs -0.295). Hence, the donated electrons are moving straight from the oxygen to the metal centre, while the carbon between's electrons are also donated to both the oxygen and nitrogen as part of the electronegative pull these atoms have on the carbon.

Regarding the CN complex, the electron withdrawal is clearly seen on the carbon the CN ligand is bonded to, as this has become less negatively charged (-0.289 vs -0.295), showing that once again, electron withdrawal is occuring at a distance that causes electrons to travel from the nitrogen through the carbon.

=== Sample MOs ===

{| class="wikitable" border="1"
! !! [N(CH3)3(CH2OH)]+ !!
[N(CH3)3(CH2CN)]+
|-
| HOMO || [[Image:Pk-homo-oh.png|200px]] || [[Image:Pk-homo-cn.png|200px]]
|-
| LUMO || [[Image:Pk-lumo-oh.png|200px]] || [[Image:Pk-lumo-cn.png|200px]]
|-
| HOMO Energy (hartree) || -0.48763 || -0.50047
|-
| LUMO Energy (hartree) || -0.12459 || -0.18183
|}

=== Discussion of MOs ===

==== Ligand influence on structure ====

==== Ligand influence on charge distribution ====

==== Ligand influence on molecular orbitals ====

= References =
<references />

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T14:51:18Z

Pk1811: /* NBO charge distributions */

<div style="font-size: 40px;"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px;"><center>Ionic liquids: Designer solvents</center></div>
 
= Introduction =
The aim of this project is to explore the physical nature of ionic liquids, which have application in designing solvents through customisation of the nature of the cation and anion<ref name="abs">M. Freemantle. ''Chem. Eng. News'', 1998, '''76''', 32–37</ref>. In this work, a variety of cations have been investigated to identify what trends are present in the variation in central atom and its ligands.

= Structures of methyl-ligand complexes =
== Optimisations ==
A number of cations have been optimised using Gaussian 09 D.01, namely [N(CH3)4]+, [P(CH3)4]+ and [F(CH3)3]+. All these complexes have been optimised to a DFT B3LYP 6-31G(d,p) level with the <code>int=ultrafine scf=conver=9</code> keywords and tight convergence - this is as a consequence of behaviour seen in previous work<ref name="labintro">P. Kent, unpublished work ([[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|lab intro]])</ref> where low frequencies did not exist within a tight range unless these keywords were specified. All calculations were run on the supplied laptop due to a significant queue of jobs on the HPC (except for [S(CH3)3]+ as it took a very long time), and the log files are available here:

* [N(CH3)4]+: [[media:Pk_log_nch34_opt.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_opt.log]]
* [S(CH3)3]+: The first attempt did not converge: {{DOI|10042/26201}}. A partially optimised structure was resubmitted as a second attempt: {{DOI|10042/26205}}. This also did not converge so a final optimisation was run on this partially optimised structure with the <code>nosymm</code> keyword. This converged: {{DOI|10042/26214}}.

Once done, convergence was verified via inspection of the log file.

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name nch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000090 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 1 minutes 27.0 seconds.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name pch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701126 a.u.
RMS Gradient Norm 0.00000675 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 24 minutes 21.0 seconds.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_opt3
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000101 a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 52.2 seconds.
</pre>

=== Convergence outputs ===

''' [N(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000014 0.000060 YES
RMS Displacement 0.000005 0.000040 YES
Predicted change in Energy=-1.010077D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000015 YES
RMS Force 0.000005 0.000010 YES
Maximum Displacement 0.000026 0.000060 YES
RMS Displacement 0.000009 0.000040 YES
Predicted change in Energy=-1.723206D-06
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''

Initial failed optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000015 NO
RMS Force 0.000006 0.000010 YES
Maximum Displacement 0.002915 0.000060 NO
RMS Displacement 0.000869 0.000040 NO
Predicted change in Energy=-5.685776D-09
Optimization stopped.
-- Number of steps exceeded, NStep= 61
-- Flag reset to prevent archiving.
</pre>

During this failed optimisation, it appears the molecule just spent a large amount of time rotating around the C3 axis through the sulphur.

The final optimisation yielded:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000049 0.000060 YES
RMS Displacement 0.000018 0.000040 YES
Predicted change in Energy=-6.520157D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==
Following this, frequency analysis was conducted with the same keywords and calculation level to ensure a minima has been found. This is ensured by checking there are no negative vibrations in the molecule. Calculations were again run on the laptop, and the log files, summaries, and frequencies are listed below. Actual animations of the modes have not been exported, however a Jmol of the log file is available and the modes can be seen by right clicking and choosing '''model -> the mode you want to see'''. This time, a range of
-30 to +30 cm-1 has been accepted for the low frequencies as molecules investigated are quite complex, and a relatively simple basis set has been used. Optimising to 6-311G(d,p) would likely bring the frequencies within the range used previously however this would be at the expense of much longer computation times.

* [N(CH3)4]+: [[media:Pk_log_nch34_freq.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_freq.log]]
* [S(CH3)3]+: {{DOI|10042/26273}}

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name NCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000085 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 3 minutes 17.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000009 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.014288D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name PCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701149 a.u.
RMS Gradient Norm 0.00000668 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 12 minutes 11.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001774 0.001800 YES
RMS Displacement 0.000659 0.001200 YES
Predicted change in Energy=-3.008780D-08
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000104 a.u.
Imaginary Freq 0
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 9 minutes 6.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000093 0.001800 YES
RMS Displacement 0.000033 0.001200 YES
Predicted change in Energy=-7.179584D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Vibration modes ===

''' [N(CH3)4]+ '''
<pre>
Low frequencies --- 0.0007 0.0011 0.0013 21.5288 21.5288 21.5288
Low frequencies --- 188.5488 292.6546 292.6546
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [P(CH3)4]+ '''
<pre>
Low frequencies --- -15.1139 -0.0002 0.0012 0.0012 5.8940 14.7736
Low frequencies --- 156.2222 191.5376 191.9513
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_pch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [S(CH3)3]+ '''
<pre>
Low frequencies --- -8.5871 0.0029 0.0049 0.0051 5.7111 9.1755
Low frequencies --- 162.4159 200.3446 200.5391
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_sch33_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== Conclusions on molecular structure ==
Investigation of structures is focused on the central atom as this is the only point at which variance should occur. The length of the M-C bonds and the angle between C-M-C on each complex is reported below:

{| class="wikitable" border="1"
! Complex !! M-C Length (Å) !! Angle (°) !! M-C length (lit<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref>) (Å)
|-
| [P(CH3)4]+ || 1.82 || 109.5 || 1.84
|-
| [N(CH3)4]+ || 1.51 || 109.5 || 1.46
|-
| [S(CH3)3]+ || 1.82 || 102.7 || 1.79
|}

''Literature bond lengths are found by adding the covalent radii for the atoms.''

Two key trends are:
* As you go down a group, the bond length decreases
* As you go across a group (so losing a ligand), the bond angle is reduced)

The first trend is straightforward to explain, as bond lengths increase down the group. This is in tandem with the increase in atomic radius down the group as orbitals in a greater shell begin to be filled. Thus, as you move from period 2 (N) to period 3 (P), the length of the bond increases and is in turn the overall size of each ion. There is slight variance in the length of a C-H bond in each complex, however no pattern is immediately discernible (it increases in the order S > P > N) - it is thought this is just some random error in the calculation.

Whilst there is an increase in bond length, there is no change in orientation of the bonds, thus the symmetry of TD is maintained in both the phosphorous and nitrogen molecules. As a result of this, the bond angle is the same for these two complexes. No other arrangement of the ligands is sterically possible, so ensuring that this symmetry label cannot be changed, and therefore the bond angle also cannot change. The bond angle is different for sulphur, as a result of the change of symmetry to C3v, it is not known if the change in metal centre contributes to this change - further investigation would be required.

Of note, the bond length does not appear to change going across the period. There is actually a small increase of 0.01Å if the bond length is reported accurate to 0.001Å, however it is not known if this is just an inherent error in the calculation or not. In any event, it is expected that there is a slight decrease in the bond length as you move towards the right of a period, as the increased nuclear charge better shields the electrons and thus shortens the bond length, but this is not observed here. This may be a result of this complex containing one less ligand, with the arrangement instead taken (along with the lone pair) resulting in some interactions (steric or electronic repulsion) which causes the carbon and metal atoms to move apart from each other. This theory is supported by the large deviation from bond length for the sulphur complex, indicating some feature about the arrangement it has taken is causing the bond length to be artificially lengthened.

Otherwise no strange observations are seen with the structures, with all methyl groups taking the expected tetrahedral structure, and either tetrahedral or C3v structures for the central atom as expected by the number of ligands which are present.

= Molecular orbitals and NBO charges of methyl-ligand complexes =
All three complexes discussed previously have been subject to a full NBO and MO analysis via an energy calculation with the <code>pop=(full,nbo)</code> keyword, retaining any previously used keywords as appropriate. Calculations were performed on the laptop due to load on the HPC, except for the sulphur complex as the calculation took too long on the laptop.

Log files are available as follows:

* '''[N(CH3)4]+''': [[media:Pk_log_nch34_egy.log]]
* '''[P(CH3)4]+''': [[media:Pk_log_pch34_egy.log]]
* '''[S(CH3)3]+''': {{DOI|10042/26274}}
== Calculation output ==

''' [N(CH3)4]+ '''

<pre>
File Name NCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

''' [P(CH3)4]+ '''

<pre>
File Name PCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701105 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 20.0 seconds.
</pre>

''' [S(CH3)3]+ '''

<pre>File Name sch33_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 0 minutes 57.7 seconds.
</pre>

== Sample MOs for [N(CH3)4]+ ==
A variety of 5 molecular orbitals have been calculated and shown below. Only occupied non-core MOs from the totally bonding to totally antibonding are shown.

{| class="wikitable" border="1"
|+ Totally bonding towards the top
! MO number !! Energy (hartree) !! Picture !! Degeneracy !! Notes
|-
| 6 || -1.19645 || [[Image:Pk-n-mo0.png|200px]] || Singly degenerate || This MO exhibits a great degree of strong bonding interactions across the entire molecule up to the protons, the orbitals of which do not appear to be part of this MO. This is seen by the huge red surface containing almost the entirety of the molecule. As a result of the huge amount of delocalisation seen in the MO, there is a lot of through space interactions between adjacent carbon groups, as seen by how the MO forms a 'cage' around the entire molecule - the empty space between two carbon atoms is part of this red object. As there are no other molecular orbitals other than this huge one, there is no concept of a node in this MO diagram.
|-
| 10 || -0.80745 || [[Image:Pk-n-mo1.png|200px]] || Singly degenerate || This is the first MO in this series of 5 to contain a slight degree of antibonding character, as seen by the fact each ligand is in its own (+) phase orbital, whereas the central metal is in a (-) phase one. This leads to a minor degree of antibonding character, and also a node in the centre of the M-C bond where the two MOs end. Through space interactions are present in each ligand MO, with all the protons and the central carbon existing within the boundaries of the MO, and hence there are through-space interactions between the protons. MOs of the same phase interact weakly with each other due to the large distance between each green orbital (seen in the picture), however the interaction between the (+) and (-) orbitals is quite strong as the nodal area is very small in size - the orbitals are nearly touching. The level of delocalisation is reduced, with delocalisation only occurring across each ligand group - the ligands themselves are not delocalised onto one unit.
|-
| 14 || -0.62248 || [[Image:Pk-n-mo2.png|200px]] || Doubly degenerate || For this MO, nodes exist on every carbon atom, as each MO covers two halves of a carbon atom, two protons, and nothing else. This does lead to delocalisationa cross the protons and carbon atoms, however this also does result in strong antibonding interactions at each carbon as the (+) and (-) MOs become quite close. Some protons, and the metal centre are not covered at all by this MO, however from what is delocalised, there is a significant amount of through space interactions between protons on differing methyl ligands - this is of note as the ligand protons are quite a distance away. There may be some weak bonding interactions between orbitals of the same phase, however they are quite a distance away (separated by the metal centre) so this is expected to be quite weak.
|-
| 17 || -0.58035 || [[Image:Pk-n-mo3.png|200px]] || Triply degenerate || This one again has a node on each carbon, however it differs in that each orbital only covers a single proton and half a carbon. This results in there being no through-space interactions in this molecule. Additionally, there are many strong antibonding interactions as all the orbitals are quite close together, with the a (+) orbital being surrounded by a (-) orbital on every side. If there are any bonding interactions, these are going to be very weak.
|-
| 21 || -0.57934 || [[Image:Pk-n-mo4.png|200px]] || Triply degenerate || This MO is similar to the previous, but differs in that each orbital now consists of two protons, so there are no protons which aren't enclosed in an orbital. Again, there are nodes in each carbon, but also a node in the metal center, with orbitals now also covering the metal center. This results in there being strong antibonding interactions over almost the entire molecule, with (+) interacting with (-) almost over the entire surface of every orbital. Through-space interactions are now back with there being two protons in each orbital, making it possible for these to interact, and there is also the potential for protons and metal center to interact as well. This orbital is only slightly higher energy than the previous one, and this is solely because of the increased degree of antibonding interactions present.
|}

== NBO charge distributions ==

NBO charge distributions were calculated from the checkpoint file for a range of -1.750 to 1.750 as this ensured the range of charges for all 3 complexes could be accommodated on the same scale. The charges are as follows:

{| class="wikitable" border="1"
! Complex !! Metal charge (e) !! Carbon charge (e) !! Proton charge (e)
|-
| [P(NH3)4]+ || 1.667 || -1.060 || 0.298
|-
| [N(NH3)4]+ || -0.295 || -0.846 || 0.297
|-
| [S(NH3)3]+ || 0.917 || -0.483 || 0.269
|}

<gallery>
File:Pk-nbo-n.png|Nitrogen complex
File:Pk-nbo-p.png|Phosphorous complex
File:Pk-nbo-s.png|Sulphur complex
</gallery>

There appears to be a slight trend of the metal centre charge with electronegativity, with the charge much lower as it becomes more electronegative (and hence drawing a greater share of electrons to it). This in turn makes the carbon more positive as electron density is removed from it. The protons remain rather positively charged and do not appear to be greatly affected by the metal centre, but this is likely because they are too far away for the inductive effect to occur.

Interestingly, nitrogen is more eletronegative than sulphur, yet sulphur has a greater negative charge. The reduced degree of polarisation in the bond for the nitrogen complex also suggests why the bond length for the nitrogen complex is shorter compared to the sulphur. The reason for this increased amount of negative charge is due to the lone pair present on sulphur (hence the configuration it takes according to the Jmol clip above), and so there is simply more negative charge present on the sulphur.

Thus, for the general complex [NR4]+, the positive charge located on the nitrogen in the picture is indeed located on the nitrogen, however it is somewhat delocalised over the protons too. As the nitrogen contains the greatest degree of positive charge, though, the + sign is conventionally placed here as it gives the indication as to where most of the charge is.

Analysis of the log files show the exact NBO contributions to the bond:

'''[P(NH3)3]+'''
<pre>
1. (1.98031) BD ( 1) P 1 - C 2
( 40.43%) 0.6358* P 1 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.4030 0.0006 0.0000 -0.4429
0.0006 0.0000 0.6188 -0.0009 0.0385
-0.0538 -0.0591 -0.0036 0.0254
( 59.57%) 0.7718* C 2 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.4044
-0.0074 0.4444 -0.0081 -0.6209 0.0114
0.0121 -0.0169 -0.0186 -0.0011 0.0080
</pre>

This shows almost equal contribution from each atom to the bond, with each atom assuming a sp3 arrangement as is expected by the TD symmetry. Carbon is sp3 as expected due to its saturation. As the carbon is slightly more negatively charged according to the charge distributions, the marginal increase in contribution from the carbon vs the phosphorous agrees with the charge distribution seen.

'''[N(NH3)3]+'''
<pre>
4. (1.98452) BD ( 1) C 1 - N 13
( 33.65%) 0.5801* C 1 s( 20.77%)p 3.81( 79.06%)d 0.01( 0.16%)
0.0003 0.4552 -0.0237 0.0026 -0.5129
-0.0218 -0.5129 -0.0218 -0.5129 -0.0218
0.0234 0.0234 0.0234 0.0000 0.0000
( 66.35%) 0.8146* N 13 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 0.5000 -0.0007 0.0000 0.4999
-0.0001 0.4999 -0.0001 0.4999 -0.0001
0.0103 0.0103 0.0103 0.0000 0.0000
</pre>

A similar argument can be made here. The large contribution from the nitrogen is surprising, but considering the smaller bond length for this complex based on the metal, an increased contribution from the nitrogen is not unreasonable. However this does disagree somewhat with the charge distribution which shows there is a much larger electron density on the carbon. It is thus thought that since it is possible to reach orbitals closer to the core on nitrogen rather than phosphorous, it makes nitrogen able to donate a greater share of electrons, and so polarises the bond towards it as a result of its electronegativity.

'''[S(NH3)3]+'''
<pre>
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
-0.0003 -0.4437 -0.0140 0.0033 0.7546
-0.0059 0.3161 -0.0025 0.3634 0.0098
-0.0189 -0.0222 -0.0093 -0.0186 0.0096
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 -0.0001 -0.4117 0.0075 -0.0012
0.0000 -0.7489 0.0330 0.0000 -0.3137
0.0138 0.0000 -0.4037 -0.0260 -0.0353
-0.0572 -0.0240 -0.0347 0.0051
</pre>

Finally, for the sulphur, the bond is an almost equal contribution from each atom in the bond. The charges of the S and C atoms according to the charge distribution are both similar and negative, suggesting little polarisation in this bond, and so the balance seen here is to be expected.

= Ligand influences on nitrogen metal centre complexes =
To investigate how changes to the ligands affects the cation, two variants on the nitrogen complex analysed previously have been used. One has one of the protons on a methyl ligand replaced with CH2OH, the other has the proton replaced with CH2CN. Each complex is then optimised and subject to a frequency analysis so as to allow for investigation of its structure. A MO and NBO calculation is then subsequently run to analyse how the change in ligand affects the ions electronic behaviour.

== Optimisations ==
Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26206}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26207}}

=== Summary output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
File Name nch33ch2oh_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000102 a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 1 hours 22 minutes 37.5 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
File Name nch33ch2cn_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000045 a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 50 minutes 39.5 seconds.
</pre>

=== Convergence output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000034 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-5.591936D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000011 0.000040 YES
Predicted change in Energy=-2.269581D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==

Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26290}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26291}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000106 a.u.
Imaginary Freq 0
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 26 minutes 10.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000102 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-5.078379D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000059 a.u.
Imaginary Freq 0
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 29 minutes 19.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-6.144746D-12
Optimization completed.
-- Stationary point found.
</pre>

=== Vibrational modes ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2oh_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

'''[N(CH3)3(CH2CN)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2cn_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== MO and NBO calculations ==
<code>pop=(nbo,full)</code> energy calculations were then performed on the complexes to generate MOs and NBO charge diagrams, just as has been done previously. All calculations were performed on the HPC and log files are available as follows:

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26294}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26295}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 59.3 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 25.0 seconds.
</pre>

=== NBO charge distributions ===
The main difference between these ligands is that CN is an EWG, and OH is an EDG, the latter due to the lone pairs which make it possible to enolise. Therefore comparison of the charge density of the structure can show how these ligands affect the overall structure of the molecule. The NBO charge distributions from -0.750 to 0.750 are shown below.

<gallery>
File:Pk-nbo-cn.png|CN ligand complex
File:Pk-nbo-oh.png|OH ligand complex
</gallery>

=== Sample MOs ===

{| class="wikitable" border="1"
! !! [N(CH3)3(CH2OH)]+ !!
[N(CH3)3(CH2CN)]+
|-
| HOMO || [[Image:Pk-homo-oh.png|200px]] || [[Image:Pk-homo-cn.png|200px]]
|-
| LUMO || [[Image:Pk-lumo-oh.png|200px]] || [[Image:Pk-lumo-cn.png|200px]]
|-
| HOMO Energy (hartree) || -0.48763 || -0.50047
|-
| LUMO Energy (hartree) || -0.12459 || -0.18183
|}

=== Discussion of MOs ===

==== Ligand influence on structure ====

==== Ligand influence on charge distribution ====

==== Ligand influence on molecular orbitals ====

= References =
<references />

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T14:33:35Z

Pk1811: /* NBO charge distributions */

<div style="font-size: 40px;"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px;"><center>Ionic liquids: Designer solvents</center></div>
 
= Introduction =
The aim of this project is to explore the physical nature of ionic liquids, which have application in designing solvents through customisation of the nature of the cation and anion<ref name="abs">M. Freemantle. ''Chem. Eng. News'', 1998, '''76''', 32–37</ref>. In this work, a variety of cations have been investigated to identify what trends are present in the variation in central atom and its ligands.

= Structures of methyl-ligand complexes =
== Optimisations ==
A number of cations have been optimised using Gaussian 09 D.01, namely [N(CH3)4]+, [P(CH3)4]+ and [F(CH3)3]+. All these complexes have been optimised to a DFT B3LYP 6-31G(d,p) level with the <code>int=ultrafine scf=conver=9</code> keywords and tight convergence - this is as a consequence of behaviour seen in previous work<ref name="labintro">P. Kent, unpublished work ([[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|lab intro]])</ref> where low frequencies did not exist within a tight range unless these keywords were specified. All calculations were run on the supplied laptop due to a significant queue of jobs on the HPC (except for [S(CH3)3]+ as it took a very long time), and the log files are available here:

* [N(CH3)4]+: [[media:Pk_log_nch34_opt.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_opt.log]]
* [S(CH3)3]+: The first attempt did not converge: {{DOI|10042/26201}}. A partially optimised structure was resubmitted as a second attempt: {{DOI|10042/26205}}. This also did not converge so a final optimisation was run on this partially optimised structure with the <code>nosymm</code> keyword. This converged: {{DOI|10042/26214}}.

Once done, convergence was verified via inspection of the log file.

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name nch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000090 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 1 minutes 27.0 seconds.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name pch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701126 a.u.
RMS Gradient Norm 0.00000675 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 24 minutes 21.0 seconds.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_opt3
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000101 a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 52.2 seconds.
</pre>

=== Convergence outputs ===

''' [N(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000014 0.000060 YES
RMS Displacement 0.000005 0.000040 YES
Predicted change in Energy=-1.010077D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000015 YES
RMS Force 0.000005 0.000010 YES
Maximum Displacement 0.000026 0.000060 YES
RMS Displacement 0.000009 0.000040 YES
Predicted change in Energy=-1.723206D-06
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''

Initial failed optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000015 NO
RMS Force 0.000006 0.000010 YES
Maximum Displacement 0.002915 0.000060 NO
RMS Displacement 0.000869 0.000040 NO
Predicted change in Energy=-5.685776D-09
Optimization stopped.
-- Number of steps exceeded, NStep= 61
-- Flag reset to prevent archiving.
</pre>

During this failed optimisation, it appears the molecule just spent a large amount of time rotating around the C3 axis through the sulphur.

The final optimisation yielded:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000049 0.000060 YES
RMS Displacement 0.000018 0.000040 YES
Predicted change in Energy=-6.520157D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==
Following this, frequency analysis was conducted with the same keywords and calculation level to ensure a minima has been found. This is ensured by checking there are no negative vibrations in the molecule. Calculations were again run on the laptop, and the log files, summaries, and frequencies are listed below. Actual animations of the modes have not been exported, however a Jmol of the log file is available and the modes can be seen by right clicking and choosing '''model -> the mode you want to see'''. This time, a range of
-30 to +30 cm-1 has been accepted for the low frequencies as molecules investigated are quite complex, and a relatively simple basis set has been used. Optimising to 6-311G(d,p) would likely bring the frequencies within the range used previously however this would be at the expense of much longer computation times.

* [N(CH3)4]+: [[media:Pk_log_nch34_freq.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_freq.log]]
* [S(CH3)3]+: {{DOI|10042/26273}}

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name NCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000085 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 3 minutes 17.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000009 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.014288D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name PCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701149 a.u.
RMS Gradient Norm 0.00000668 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 12 minutes 11.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001774 0.001800 YES
RMS Displacement 0.000659 0.001200 YES
Predicted change in Energy=-3.008780D-08
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000104 a.u.
Imaginary Freq 0
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 9 minutes 6.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000093 0.001800 YES
RMS Displacement 0.000033 0.001200 YES
Predicted change in Energy=-7.179584D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Vibration modes ===

''' [N(CH3)4]+ '''
<pre>
Low frequencies --- 0.0007 0.0011 0.0013 21.5288 21.5288 21.5288
Low frequencies --- 188.5488 292.6546 292.6546
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [P(CH3)4]+ '''
<pre>
Low frequencies --- -15.1139 -0.0002 0.0012 0.0012 5.8940 14.7736
Low frequencies --- 156.2222 191.5376 191.9513
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_pch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [S(CH3)3]+ '''
<pre>
Low frequencies --- -8.5871 0.0029 0.0049 0.0051 5.7111 9.1755
Low frequencies --- 162.4159 200.3446 200.5391
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_sch33_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== Conclusions on molecular structure ==
Investigation of structures is focused on the central atom as this is the only point at which variance should occur. The length of the M-C bonds and the angle between C-M-C on each complex is reported below:

{| class="wikitable" border="1"
! Complex !! M-C Length (Å) !! Angle (°) !! M-C length (lit<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref>) (Å)
|-
| [P(CH3)4]+ || 1.82 || 109.5 || 1.84
|-
| [N(CH3)4]+ || 1.51 || 109.5 || 1.46
|-
| [S(CH3)3]+ || 1.82 || 102.7 || 1.79
|}

''Literature bond lengths are found by adding the covalent radii for the atoms.''

Two key trends are:
* As you go down a group, the bond length decreases
* As you go across a group (so losing a ligand), the bond angle is reduced)

The first trend is straightforward to explain, as bond lengths increase down the group. This is in tandem with the increase in atomic radius down the group as orbitals in a greater shell begin to be filled. Thus, as you move from period 2 (N) to period 3 (P), the length of the bond increases and is in turn the overall size of each ion. There is slight variance in the length of a C-H bond in each complex, however no pattern is immediately discernible (it increases in the order S > P > N) - it is thought this is just some random error in the calculation.

Whilst there is an increase in bond length, there is no change in orientation of the bonds, thus the symmetry of TD is maintained in both the phosphorous and nitrogen molecules. As a result of this, the bond angle is the same for these two complexes. No other arrangement of the ligands is sterically possible, so ensuring that this symmetry label cannot be changed, and therefore the bond angle also cannot change. The bond angle is different for sulphur, as a result of the change of symmetry to C3v, it is not known if the change in metal centre contributes to this change - further investigation would be required.

Of note, the bond length does not appear to change going across the period. There is actually a small increase of 0.01Å if the bond length is reported accurate to 0.001Å, however it is not known if this is just an inherent error in the calculation or not. In any event, it is expected that there is a slight decrease in the bond length as you move towards the right of a period, as the increased nuclear charge better shields the electrons and thus shortens the bond length, but this is not observed here. This may be a result of this complex containing one less ligand, with the arrangement instead taken (along with the lone pair) resulting in some interactions (steric or electronic repulsion) which causes the carbon and metal atoms to move apart from each other. This theory is supported by the large deviation from bond length for the sulphur complex, indicating some feature about the arrangement it has taken is causing the bond length to be artificially lengthened.

Otherwise no strange observations are seen with the structures, with all methyl groups taking the expected tetrahedral structure, and either tetrahedral or C3v structures for the central atom as expected by the number of ligands which are present.

= Molecular orbitals and NBO charges of methyl-ligand complexes =
All three complexes discussed previously have been subject to a full NBO and MO analysis via an energy calculation with the <code>pop=(full,nbo)</code> keyword, retaining any previously used keywords as appropriate. Calculations were performed on the laptop due to load on the HPC, except for the sulphur complex as the calculation took too long on the laptop.

Log files are available as follows:

* '''[N(CH3)4]+''': [[media:Pk_log_nch34_egy.log]]
* '''[P(CH3)4]+''': [[media:Pk_log_pch34_egy.log]]
* '''[S(CH3)3]+''': {{DOI|10042/26274}}
== Calculation output ==

''' [N(CH3)4]+ '''

<pre>
File Name NCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

''' [P(CH3)4]+ '''

<pre>
File Name PCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701105 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 20.0 seconds.
</pre>

''' [S(CH3)3]+ '''

<pre>File Name sch33_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 0 minutes 57.7 seconds.
</pre>

== Sample MOs for [N(CH3)4]+ ==
A variety of 5 molecular orbitals have been calculated and shown below. Only occupied non-core MOs from the totally bonding to totally antibonding are shown.

{| class="wikitable" border="1"
|+ Totally bonding towards the top
! MO number !! Energy (hartree) !! Picture !! Degeneracy !! Notes
|-
| 6 || -1.19645 || [[Image:Pk-n-mo0.png|200px]] || Singly degenerate || This MO exhibits a great degree of strong bonding interactions across the entire molecule up to the protons, the orbitals of which do not appear to be part of this MO. This is seen by the huge red surface containing almost the entirety of the molecule. As a result of the huge amount of delocalisation seen in the MO, there is a lot of through space interactions between adjacent carbon groups, as seen by how the MO forms a 'cage' around the entire molecule - the empty space between two carbon atoms is part of this red object. As there are no other molecular orbitals other than this huge one, there is no concept of a node in this MO diagram.
|-
| 10 || -0.80745 || [[Image:Pk-n-mo1.png|200px]] || Singly degenerate || This is the first MO in this series of 5 to contain a slight degree of antibonding character, as seen by the fact each ligand is in its own (+) phase orbital, whereas the central metal is in a (-) phase one. This leads to a minor degree of antibonding character, and also a node in the centre of the M-C bond where the two MOs end. Through space interactions are present in each ligand MO, with all the protons and the central carbon existing within the boundaries of the MO, and hence there are through-space interactions between the protons. MOs of the same phase interact weakly with each other due to the large distance between each green orbital (seen in the picture), however the interaction between the (+) and (-) orbitals is quite strong as the nodal area is very small in size - the orbitals are nearly touching. The level of delocalisation is reduced, with delocalisation only occurring across each ligand group - the ligands themselves are not delocalised onto one unit.
|-
| 14 || -0.62248 || [[Image:Pk-n-mo2.png|200px]] || Doubly degenerate || For this MO, nodes exist on every carbon atom, as each MO covers two halves of a carbon atom, two protons, and nothing else. This does lead to delocalisationa cross the protons and carbon atoms, however this also does result in strong antibonding interactions at each carbon as the (+) and (-) MOs become quite close. Some protons, and the metal centre are not covered at all by this MO, however from what is delocalised, there is a significant amount of through space interactions between protons on differing methyl ligands - this is of note as the ligand protons are quite a distance away. There may be some weak bonding interactions between orbitals of the same phase, however they are quite a distance away (separated by the metal centre) so this is expected to be quite weak.
|-
| 17 || -0.58035 || [[Image:Pk-n-mo3.png|200px]] || Triply degenerate || This one again has a node on each carbon, however it differs in that each orbital only covers a single proton and half a carbon. This results in there being no through-space interactions in this molecule. Additionally, there are many strong antibonding interactions as all the orbitals are quite close together, with the a (+) orbital being surrounded by a (-) orbital on every side. If there are any bonding interactions, these are going to be very weak.
|-
| 21 || -0.57934 || [[Image:Pk-n-mo4.png|200px]] || Triply degenerate || This MO is similar to the previous, but differs in that each orbital now consists of two protons, so there are no protons which aren't enclosed in an orbital. Again, there are nodes in each carbon, but also a node in the metal center, with orbitals now also covering the metal center. This results in there being strong antibonding interactions over almost the entire molecule, with (+) interacting with (-) almost over the entire surface of every orbital. Through-space interactions are now back with there being two protons in each orbital, making it possible for these to interact, and there is also the potential for protons and metal center to interact as well. This orbital is only slightly higher energy than the previous one, and this is solely because of the increased degree of antibonding interactions present.
|}

== NBO charge distributions ==

NBO charge distributions were calculated from the checkpoint file for a range of -1.750 to 1.750 as this ensured the range of charges for all 3 complexes could be accommodated on the same scale. The charges are as follows:

{| class="wikitable" border="1"
! Complex !! Metal charge (e) !! Carbon charge (e) !! Proton charge (e)
|-
| [P(NH3)4]+ || 1.667 || -1.060 || 0.298
|-
| [N(NH3)4]+ || 0.917 || -0.846 || 0.297
|-
| [S(NH3)3]+ || -0.295 || -0.483 || 0.269
|}

<gallery>
File:Pk-nbo-n.png|Nitrogen complex
File:Pk-nbo-p.png|Phosphorous complex
File:Pk-nbo-s.png|Sulphur complex
</gallery>

There appears to be a slight trend of the metal centre charge with electronegativity, with the charge much lower as it becomes more electronegative (and hence drawing a greater share of electrons to it). This in turn makes the carbon more positive as electron density is removed from it. The protons remain rather positively charged and do not appear to be greatly affected by the metal centre, but this is likely because they are too far away for the inductive effect to occur.

Interestingly, nitrogen is more eletronegative than sulphur, yet sulphur has a greater negative charge. The reduced degree of polarisation in the bond for the nitrogen complex also suggests why the bond length for the nitrogen complex is shorter compared to the sulphur. The reason for this increased amount of negative charge is due to the lone pair present on sulphur (hence the configuration it takes according to the Jmol clip above), and so there is simply more negative charge present on the sulphur.

Thus, for the general complex [NR4]+, the positive charge located on the nitrogen in the picture is indeed located on the nitrogen, however it is somewhat delocalised over the protons too. As the nitrogen contains the greatest degree of positive charge, though, the + sign is conventionally placed here as it gives the indication as to where most of the charge is.

Analysis of the log files show the exact NBO contributions to the bond:

'''[P(NH3)3]+'''
<pre>
1. (1.98031) BD ( 1) P 1 - C 2
( 40.43%) 0.6358* P 1 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.4030 0.0006 0.0000 -0.4429
0.0006 0.0000 0.6188 -0.0009 0.0385
-0.0538 -0.0591 -0.0036 0.0254
( 59.57%) 0.7718* C 2 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.4044
-0.0074 0.4444 -0.0081 -0.6209 0.0114
0.0121 -0.0169 -0.0186 -0.0011 0.0080
</pre>

This shows almost equal contribution from each atom to the bond, with each atom assuming a sp3 arrangement as is expected by the TD symmetry. Carbon is sp3 as expected due to its saturation. As the carbon is slightly more negatively charged according to the charge distributions, the marginal increase in contribution from the carbon vs the phosphorous agrees with the charge distribution seen.

'''[N(NH3)3]+'''
<pre>
4. (1.98452) BD ( 1) C 1 - N 13
( 33.65%) 0.5801* C 1 s( 20.77%)p 3.81( 79.06%)d 0.01( 0.16%)
0.0003 0.4552 -0.0237 0.0026 -0.5129
-0.0218 -0.5129 -0.0218 -0.5129 -0.0218
0.0234 0.0234 0.0234 0.0000 0.0000
( 66.35%) 0.8146* N 13 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 0.5000 -0.0007 0.0000 0.4999
-0.0001 0.4999 -0.0001 0.4999 -0.0001
0.0103 0.0103 0.0103 0.0000 0.0000
</pre>

A similar argument can be made here. The large contribution from the nitrogen is surprising, but considering the smaller bond length for this complex based on the metal, an increased contribution from the nitrogen is not unreasonable. However this does disagree somewhat with the charge distribution which shows there is a much larger electron density on the carbon. It is thus thought that since it is possible to reach orbitals closer to the core on nitrogen rather than phosphorous, it makes nitrogen able to donate a greater share of electrons, and so polarises the bond towards it as a result of its electronegativity.

'''[S(NH3)3]+'''
<pre>
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
-0.0003 -0.4437 -0.0140 0.0033 0.7546
-0.0059 0.3161 -0.0025 0.3634 0.0098
-0.0189 -0.0222 -0.0093 -0.0186 0.0096
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 -0.0001 -0.4117 0.0075 -0.0012
0.0000 -0.7489 0.0330 0.0000 -0.3137
0.0138 0.0000 -0.4037 -0.0260 -0.0353
-0.0572 -0.0240 -0.0347 0.0051
</pre>

Finally, for the sulphur, the bond is an almost equal contribution from each atom in the bond. The charges of the S and C atoms according to the charge distribution are both similar and negative, suggesting little polarisation in this bond, and so the balance seen here is to be expected.

= Ligand influences on nitrogen metal centre complexes =
To investigate how changes to the ligands affects the cation, two variants on the nitrogen complex analysed previously have been used. One has one of the protons on a methyl ligand replaced with CH2OH, the other has the proton replaced with CH2CN. Each complex is then optimised and subject to a frequency analysis so as to allow for investigation of its structure. A MO and NBO calculation is then subsequently run to analyse how the change in ligand affects the ions electronic behaviour.

== Optimisations ==
Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26206}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26207}}

=== Summary output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
File Name nch33ch2oh_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000102 a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 1 hours 22 minutes 37.5 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
File Name nch33ch2cn_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000045 a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 50 minutes 39.5 seconds.
</pre>

=== Convergence output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000034 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-5.591936D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000011 0.000040 YES
Predicted change in Energy=-2.269581D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==

Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26290}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26291}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000106 a.u.
Imaginary Freq 0
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 26 minutes 10.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000102 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-5.078379D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000059 a.u.
Imaginary Freq 0
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 29 minutes 19.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-6.144746D-12
Optimization completed.
-- Stationary point found.
</pre>

=== Vibrational modes ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2oh_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

'''[N(CH3)3(CH2CN)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2cn_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== MO and NBO calculations ==
<code>pop=(nbo,full)</code> energy calculations were then performed on the complexes to generate MOs and NBO charge diagrams, just as has been done previously. All calculations were performed on the HPC and log files are available as follows:

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26294}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26295}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 59.3 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 25.0 seconds.
</pre>

=== NBO charge distributions ===
The main difference between these ligands is that CN is an EWG, and OH is an EDG, the latter due to the lone pairs which make it possible to enolise. Therefore comparison of the charge density of the structure can show how these ligands affect the overall structure of the molecule. The NBO charge distributions from -0.750 to 0.750 are shown below.

<gallery>
File:Pk-nbo-cn.png|CN ligand complex
File:Pk-nbo-oh.png|OH ligand complex
</gallery>

=== Sample MOs ===

{| class="wikitable" border="1"
! !! [N(CH3)3(CH2OH)]+ !!
[N(CH3)3(CH2CN)]+
|-
| HOMO || [[Image:Pk-homo-oh.png|200px]] || [[Image:Pk-homo-cn.png|200px]]
|-
| LUMO || [[Image:Pk-lumo-oh.png|200px]] || [[Image:Pk-lumo-cn.png|200px]]
|-
| HOMO Energy (hartree) || -0.48763 || -0.50047
|-
| LUMO Energy (hartree) || -0.12459 || -0.18183
|}

=== Discussion of MOs ===

==== Ligand influence on structure ====

==== Ligand influence on charge distribution ====

==== Ligand influence on molecular orbitals ====

= References =
<references />

File:Pk-lumo-oh.png

2013-11-22T14:33:13Z

Pk1811:

File:Pk-lumo-cn.png

2013-11-22T14:33:12Z

Pk1811:

File:Pk-homo-oh.png

2013-11-22T14:33:11Z

Pk1811:

File:Pk-homo-cn.png

2013-11-22T14:33:11Z

Pk1811:

File:Pk-nbo-oh.png

2013-11-22T14:33:10Z

Pk1811:

File:Pk-nbo-cn.png

2013-11-22T14:33:10Z

Pk1811:

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T13:48:47Z

Pk1811:

<div style="font-size: 40px;"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px;"><center>Ionic liquids: Designer solvents</center></div>
 
= Introduction =
The aim of this project is to explore the physical nature of ionic liquids, which have application in designing solvents through customisation of the nature of the cation and anion<ref name="abs">M. Freemantle. ''Chem. Eng. News'', 1998, '''76''', 32–37</ref>. In this work, a variety of cations have been investigated to identify what trends are present in the variation in central atom and its ligands.

= Structures of methyl-ligand complexes =
== Optimisations ==
A number of cations have been optimised using Gaussian 09 D.01, namely [N(CH3)4]+, [P(CH3)4]+ and [F(CH3)3]+. All these complexes have been optimised to a DFT B3LYP 6-31G(d,p) level with the <code>int=ultrafine scf=conver=9</code> keywords and tight convergence - this is as a consequence of behaviour seen in previous work<ref name="labintro">P. Kent, unpublished work ([[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|lab intro]])</ref> where low frequencies did not exist within a tight range unless these keywords were specified. All calculations were run on the supplied laptop due to a significant queue of jobs on the HPC (except for [S(CH3)3]+ as it took a very long time), and the log files are available here:

* [N(CH3)4]+: [[media:Pk_log_nch34_opt.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_opt.log]]
* [S(CH3)3]+: The first attempt did not converge: {{DOI|10042/26201}}. A partially optimised structure was resubmitted as a second attempt: {{DOI|10042/26205}}. This also did not converge so a final optimisation was run on this partially optimised structure with the <code>nosymm</code> keyword. This converged: {{DOI|10042/26214}}.

Once done, convergence was verified via inspection of the log file.

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name nch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000090 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 1 minutes 27.0 seconds.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name pch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701126 a.u.
RMS Gradient Norm 0.00000675 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 24 minutes 21.0 seconds.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_opt3
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000101 a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 52.2 seconds.
</pre>

=== Convergence outputs ===

''' [N(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000014 0.000060 YES
RMS Displacement 0.000005 0.000040 YES
Predicted change in Energy=-1.010077D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000015 YES
RMS Force 0.000005 0.000010 YES
Maximum Displacement 0.000026 0.000060 YES
RMS Displacement 0.000009 0.000040 YES
Predicted change in Energy=-1.723206D-06
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''

Initial failed optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000015 NO
RMS Force 0.000006 0.000010 YES
Maximum Displacement 0.002915 0.000060 NO
RMS Displacement 0.000869 0.000040 NO
Predicted change in Energy=-5.685776D-09
Optimization stopped.
-- Number of steps exceeded, NStep= 61
-- Flag reset to prevent archiving.
</pre>

During this failed optimisation, it appears the molecule just spent a large amount of time rotating around the C3 axis through the sulphur.

The final optimisation yielded:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000049 0.000060 YES
RMS Displacement 0.000018 0.000040 YES
Predicted change in Energy=-6.520157D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==
Following this, frequency analysis was conducted with the same keywords and calculation level to ensure a minima has been found. This is ensured by checking there are no negative vibrations in the molecule. Calculations were again run on the laptop, and the log files, summaries, and frequencies are listed below. Actual animations of the modes have not been exported, however a Jmol of the log file is available and the modes can be seen by right clicking and choosing '''model -> the mode you want to see'''. This time, a range of
-30 to +30 cm-1 has been accepted for the low frequencies as molecules investigated are quite complex, and a relatively simple basis set has been used. Optimising to 6-311G(d,p) would likely bring the frequencies within the range used previously however this would be at the expense of much longer computation times.

* [N(CH3)4]+: [[media:Pk_log_nch34_freq.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_freq.log]]
* [S(CH3)3]+: {{DOI|10042/26273}}

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name NCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000085 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 3 minutes 17.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000009 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.014288D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name PCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701149 a.u.
RMS Gradient Norm 0.00000668 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 12 minutes 11.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001774 0.001800 YES
RMS Displacement 0.000659 0.001200 YES
Predicted change in Energy=-3.008780D-08
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000104 a.u.
Imaginary Freq 0
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 9 minutes 6.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000093 0.001800 YES
RMS Displacement 0.000033 0.001200 YES
Predicted change in Energy=-7.179584D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Vibration modes ===

''' [N(CH3)4]+ '''
<pre>
Low frequencies --- 0.0007 0.0011 0.0013 21.5288 21.5288 21.5288
Low frequencies --- 188.5488 292.6546 292.6546
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [P(CH3)4]+ '''
<pre>
Low frequencies --- -15.1139 -0.0002 0.0012 0.0012 5.8940 14.7736
Low frequencies --- 156.2222 191.5376 191.9513
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_pch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [S(CH3)3]+ '''
<pre>
Low frequencies --- -8.5871 0.0029 0.0049 0.0051 5.7111 9.1755
Low frequencies --- 162.4159 200.3446 200.5391
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_sch33_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== Conclusions on molecular structure ==
Investigation of structures is focused on the central atom as this is the only point at which variance should occur. The length of the M-C bonds and the angle between C-M-C on each complex is reported below:

{| class="wikitable" border="1"
! Complex !! M-C Length (Å) !! Angle (°) !! M-C length (lit<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref>) (Å)
|-
| [P(CH3)4]+ || 1.82 || 109.5 || 1.84
|-
| [N(CH3)4]+ || 1.51 || 109.5 || 1.46
|-
| [S(CH3)3]+ || 1.82 || 102.7 || 1.79
|}

''Literature bond lengths are found by adding the covalent radii for the atoms.''

Two key trends are:
* As you go down a group, the bond length decreases
* As you go across a group (so losing a ligand), the bond angle is reduced)

The first trend is straightforward to explain, as bond lengths increase down the group. This is in tandem with the increase in atomic radius down the group as orbitals in a greater shell begin to be filled. Thus, as you move from period 2 (N) to period 3 (P), the length of the bond increases and is in turn the overall size of each ion. There is slight variance in the length of a C-H bond in each complex, however no pattern is immediately discernible (it increases in the order S > P > N) - it is thought this is just some random error in the calculation.

Whilst there is an increase in bond length, there is no change in orientation of the bonds, thus the symmetry of TD is maintained in both the phosphorous and nitrogen molecules. As a result of this, the bond angle is the same for these two complexes. No other arrangement of the ligands is sterically possible, so ensuring that this symmetry label cannot be changed, and therefore the bond angle also cannot change. The bond angle is different for sulphur, as a result of the change of symmetry to C3v, it is not known if the change in metal centre contributes to this change - further investigation would be required.

Of note, the bond length does not appear to change going across the period. There is actually a small increase of 0.01Å if the bond length is reported accurate to 0.001Å, however it is not known if this is just an inherent error in the calculation or not. In any event, it is expected that there is a slight decrease in the bond length as you move towards the right of a period, as the increased nuclear charge better shields the electrons and thus shortens the bond length, but this is not observed here. This may be a result of this complex containing one less ligand, with the arrangement instead taken (along with the lone pair) resulting in some interactions (steric or electronic repulsion) which causes the carbon and metal atoms to move apart from each other. This theory is supported by the large deviation from bond length for the sulphur complex, indicating some feature about the arrangement it has taken is causing the bond length to be artificially lengthened.

Otherwise no strange observations are seen with the structures, with all methyl groups taking the expected tetrahedral structure, and either tetrahedral or C3v structures for the central atom as expected by the number of ligands which are present.

= Molecular orbitals and NBO charges of methyl-ligand complexes =
All three complexes discussed previously have been subject to a full NBO and MO analysis via an energy calculation with the <code>pop=(full,nbo)</code> keyword, retaining any previously used keywords as appropriate. Calculations were performed on the laptop due to load on the HPC, except for the sulphur complex as the calculation took too long on the laptop.

Log files are available as follows:

* '''[N(CH3)4]+''': [[media:Pk_log_nch34_egy.log]]
* '''[P(CH3)4]+''': [[media:Pk_log_pch34_egy.log]]
* '''[S(CH3)3]+''': {{DOI|10042/26274}}
== Calculation output ==

''' [N(CH3)4]+ '''

<pre>
File Name NCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

''' [P(CH3)4]+ '''

<pre>
File Name PCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701105 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 20.0 seconds.
</pre>

''' [S(CH3)3]+ '''

<pre>File Name sch33_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 0 minutes 57.7 seconds.
</pre>

== Sample MOs for [N(CH3)4]+ ==
A variety of 5 molecular orbitals have been calculated and shown below. Only occupied non-core MOs from the totally bonding to totally antibonding are shown.

{| class="wikitable" border="1"
|+ Totally bonding towards the top
! MO number !! Energy (hartree) !! Picture !! Degeneracy !! Notes
|-
| 6 || -1.19645 || [[Image:Pk-n-mo0.png|200px]] || Singly degenerate || This MO exhibits a great degree of strong bonding interactions across the entire molecule up to the protons, the orbitals of which do not appear to be part of this MO. This is seen by the huge red surface containing almost the entirety of the molecule. As a result of the huge amount of delocalisation seen in the MO, there is a lot of through space interactions between adjacent carbon groups, as seen by how the MO forms a 'cage' around the entire molecule - the empty space between two carbon atoms is part of this red object. As there are no other molecular orbitals other than this huge one, there is no concept of a node in this MO diagram.
|-
| 10 || -0.80745 || [[Image:Pk-n-mo1.png|200px]] || Singly degenerate || This is the first MO in this series of 5 to contain a slight degree of antibonding character, as seen by the fact each ligand is in its own (+) phase orbital, whereas the central metal is in a (-) phase one. This leads to a minor degree of antibonding character, and also a node in the centre of the M-C bond where the two MOs end. Through space interactions are present in each ligand MO, with all the protons and the central carbon existing within the boundaries of the MO, and hence there are through-space interactions between the protons. MOs of the same phase interact weakly with each other due to the large distance between each green orbital (seen in the picture), however the interaction between the (+) and (-) orbitals is quite strong as the nodal area is very small in size - the orbitals are nearly touching. The level of delocalisation is reduced, with delocalisation only occurring across each ligand group - the ligands themselves are not delocalised onto one unit.
|-
| 14 || -0.62248 || [[Image:Pk-n-mo2.png|200px]] || Doubly degenerate || For this MO, nodes exist on every carbon atom, as each MO covers two halves of a carbon atom, two protons, and nothing else. This does lead to delocalisationa cross the protons and carbon atoms, however this also does result in strong antibonding interactions at each carbon as the (+) and (-) MOs become quite close. Some protons, and the metal centre are not covered at all by this MO, however from what is delocalised, there is a significant amount of through space interactions between protons on differing methyl ligands - this is of note as the ligand protons are quite a distance away. There may be some weak bonding interactions between orbitals of the same phase, however they are quite a distance away (separated by the metal centre) so this is expected to be quite weak.
|-
| 17 || -0.58035 || [[Image:Pk-n-mo3.png|200px]] || Triply degenerate || This one again has a node on each carbon, however it differs in that each orbital only covers a single proton and half a carbon. This results in there being no through-space interactions in this molecule. Additionally, there are many strong antibonding interactions as all the orbitals are quite close together, with the a (+) orbital being surrounded by a (-) orbital on every side. If there are any bonding interactions, these are going to be very weak.
|-
| 21 || -0.57934 || [[Image:Pk-n-mo4.png|200px]] || Triply degenerate || This MO is similar to the previous, but differs in that each orbital now consists of two protons, so there are no protons which aren't enclosed in an orbital. Again, there are nodes in each carbon, but also a node in the metal center, with orbitals now also covering the metal center. This results in there being strong antibonding interactions over almost the entire molecule, with (+) interacting with (-) almost over the entire surface of every orbital. Through-space interactions are now back with there being two protons in each orbital, making it possible for these to interact, and there is also the potential for protons and metal center to interact as well. This orbital is only slightly higher energy than the previous one, and this is solely because of the increased degree of antibonding interactions present.
|}

== NBO charge distributions ==

NBO charge distributions were calculated from the checkpoint file for a range of -1.750 to 1.750 as this ensured the range of charges for all 3 complexes could be accommodated on the same scale. The charges are as follows:

{| class="wikitable" border="1"
! Complex !! Metal charge (e) !! Carbon charge (e) !! Proton charge (e)
|-
| [P(NH3)4]+ || 1.667 || -1.060 || 0.298
|-
| [N(NH3)4]+ || 0.917 || -0.846 || 0.297
|-
| [S(NH3)3]+ || -0.295 || -0.483 || 0.269
|}

<gallery>
File:Pk-nbo-n.png|Nitrogen complex
File:Pk-nbo-p.png|Phosphorous complex
File:Pk-nbo-s.png|Sulphur complex
</gallery>

There appears to be a slight trend of the metal centre charge with electronegativity, with the charge much lower as it becomes more electronegative (and hence drawing a greater share of electrons to it). This in turn makes the carbon more positive as electron density is removed from it. The protons remain rather positively charged and do not appear to be greatly affected by the metal centre, but this is likely because they are too far away for the inductive effect to occur.

Interestingly, nitrogen is more eletronegative than sulphur, yet sulphur has a greater negative charge. The reduced degree of polarisation in the bond for the nitrogen complex also suggests why the bond length for the nitrogen complex is shorter compared to the sulphur. The reason for this increased amount of negative charge is due to the lone pair present on sulphur (hence the configuration it takes according to the Jmol clip above), and so there is simply more negative charge present on the sulphur.

Thus, for the general complex [NR4]+, the positive charge located on the nitrogen in the picture is indeed located on the nitrogen, however it is somewhat delocalised over the protons too. As the nitrogen contains the greatest degree of positive charge, though, the + sign is conventionally placed here as it gives the indication as to where most of the charge is.

Analysis of the log files show the exact NBO contributions to the bond:

'''[P(NH3)3]+'''
<pre>
1. (1.98031) BD ( 1) P 1 - C 2
( 40.43%) 0.6358* P 1 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.4030 0.0006 0.0000 -0.4429
0.0006 0.0000 0.6188 -0.0009 0.0385
-0.0538 -0.0591 -0.0036 0.0254
( 59.57%) 0.7718* C 2 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.4044
-0.0074 0.4444 -0.0081 -0.6209 0.0114
0.0121 -0.0169 -0.0186 -0.0011 0.0080
</pre>

This shows almost equal contribution from each atom to the bond, with each atom assuming a sp3 arrangement as is expected by the TD symmetry. Carbon is sp3 as expected due to its saturation. As the carbon is slightly more negatively charged according to the charge distributions, the marginal increase in contribution from the carbon vs the phosphorous agrees with the charge distribution seen.

'''[N(NH3)3]+'''
<pre>
4. (1.98452) BD ( 1) C 1 - N 13
( 33.65%) 0.5801* C 1 s( 20.77%)p 3.81( 79.06%)d 0.01( 0.16%)
0.0003 0.4552 -0.0237 0.0026 -0.5129
-0.0218 -0.5129 -0.0218 -0.5129 -0.0218
0.0234 0.0234 0.0234 0.0000 0.0000
( 66.35%) 0.8146* N 13 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 0.5000 -0.0007 0.0000 0.4999
-0.0001 0.4999 -0.0001 0.4999 -0.0001
0.0103 0.0103 0.0103 0.0000 0.0000
</pre>

A similar argument can be made here. The large contribution from the nitrogen is surprising, but considering the smaller bond length for this complex based on the metal, an increased contribution from the nitrogen is not unreasonable. However this does disagree somewhat with the charge distribution which shows there is a much larger electron density on the carbon. It is thus thought that since it is possible to reach orbitals closer to the core on nitrogen rather than phosphorous, it makes nitrogen able to donate a greater share of electrons, and so polarises the bond towards it as a result of its electronegativity.

'''[S(NH3)3]+'''
<pre>
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
-0.0003 -0.4437 -0.0140 0.0033 0.7546
-0.0059 0.3161 -0.0025 0.3634 0.0098
-0.0189 -0.0222 -0.0093 -0.0186 0.0096
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 -0.0001 -0.4117 0.0075 -0.0012
0.0000 -0.7489 0.0330 0.0000 -0.3137
0.0138 0.0000 -0.4037 -0.0260 -0.0353
-0.0572 -0.0240 -0.0347 0.0051
</pre>

Finally, for the sulphur, the bond is an almost equal contribution from each atom in the bond. The charges of the S and C atoms according to the charge distribution are both similar and negative, suggesting little polarisation in this bond, and so the balance seen here is to be expected.

= Ligand influences on nitrogen metal centre complexes =
To investigate how changes to the ligands affects the cation, two variants on the nitrogen complex analysed previously have been used. One has one of the protons on a methyl ligand replaced with CH2OH, the other has the proton replaced with CH2CN. Each complex is then optimised and subject to a frequency analysis so as to allow for investigation of its structure. A MO and NBO calculation is then subsequently run to analyse how the change in ligand affects the ions electronic behaviour.

== Optimisations ==
Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26206}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26207}}

=== Summary output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
File Name nch33ch2oh_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000102 a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 1 hours 22 minutes 37.5 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
File Name nch33ch2cn_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000045 a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 50 minutes 39.5 seconds.
</pre>

=== Convergence output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000034 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-5.591936D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000011 0.000040 YES
Predicted change in Energy=-2.269581D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==

Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26290}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26291}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000106 a.u.
Imaginary Freq 0
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 26 minutes 10.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000102 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-5.078379D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000059 a.u.
Imaginary Freq 0
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 29 minutes 19.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-6.144746D-12
Optimization completed.
-- Stationary point found.
</pre>

=== Vibrational modes ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2oh_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

'''[N(CH3)3(CH2CN)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2cn_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== MO and NBO calculations ==
<code>pop=(nbo,full)</code> energy calculations were then performed on the complexes to generate MOs and NBO charge diagrams, just as has been done previously. All calculations were performed on the HPC and log files are available as follows:

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26294}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26295}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 59.3 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 25.0 seconds.
</pre>

=== NBO charge distributions ===
The main difference between these ligands is that CN is an EWG, and OH is an EDG, the latter due to the lone pairs which make it possible to enolise. Therefore comparison of the charge density of the structure can show how these ligands affect the overall structure of the molecule. The NBO charge distributions from -0.750 to 0.750 are shown below.

<gallery>
File:Pk-nbo-nc.png|CN ligand complex
File:Pk-nbo-oh.png|OH ligand complex
</gallery>

=== Sample MOs ===

{| class="wikitable" border="1"
! !! [N(CH3)3(CH2OH)]+ !!
[N(CH3)3(CH2CN)]+
|-
| HOMO || [[Image:Pk-homo-oh.png|200px]] || [[Image:Pk-homo-cn.png|200px]]
|-
| LUMO || [[Image:Pk-lumo-oh.png|200px]] || [[Image:Pk-lumo-cn.png|200px]]
|-
| HOMO Energy (hartree) || -0.48763 || -0.50047
|-
| LUMO Energy (hartree) || -0.12459 || -0.18183
|}

=== Discussion of MOs ===

==== Ligand influence on structure ====

==== Ligand influence on charge distribution ====

==== Ligand influence on molecular orbitals ====

= References =
<references />

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T13:47:44Z

Pk1811: /* NBO charge distributions */

<div style="font-size: 40px;"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px;"><center>Ionic liquids: Designer solvents</center></div>
 
= Introduction =
The aim of this project is to explore the physical nature of ionic liquids, which have application in designing solvents through customisation of the nature of the cation and anion<ref name="abs">M. Freemantle. ''Chem. Eng. News'', 1998, '''76''', 32–37</ref>. In this work, a variety of cations have been investigated to identify what trends are present in the variation in central atom and its ligands.

= Structures of methyl-ligand complexes =
== Optimisations ==
A number of cations have been optimised using Gaussian 09 D.01, namely [N(CH3)4]+, [P(CH3)4]+ and [F(CH3)3]+. All these complexes have been optimised to a DFT B3LYP 6-31G(d,p) level with the <code>int=ultrafine scf=conver=9</code> keywords and tight convergence - this is as a consequence of behaviour seen in previous work<ref name="labintro">P. Kent, unpublished work ([[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|lab intro]])</ref> where low frequencies did not exist within a tight range unless these keywords were specified. All calculations were run on the supplied laptop due to a significant queue of jobs on the HPC (except for [S(CH3)3]+ as it took a very long time), and the log files are available here:

* [N(CH3)4]+: [[media:Pk_log_nch34_opt.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_opt.log]]
* [S(CH3)3]+: The first attempt did not converge: {{DOI|10042/26201}}. A partially optimised structure was resubmitted as a second attempt: {{DOI|10042/26205}}. This also did not converge so a final optimisation was run on this partially optimised structure with the <code>nosymm</code> keyword. This converged: {{DOI|10042/26214}}.

Once done, convergence was verified via inspection of the log file.

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name nch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000090 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 1 minutes 27.0 seconds.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name pch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701126 a.u.
RMS Gradient Norm 0.00000675 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 24 minutes 21.0 seconds.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_opt3
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000101 a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 52.2 seconds.
</pre>

=== Convergence outputs ===

''' [N(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000014 0.000060 YES
RMS Displacement 0.000005 0.000040 YES
Predicted change in Energy=-1.010077D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000015 YES
RMS Force 0.000005 0.000010 YES
Maximum Displacement 0.000026 0.000060 YES
RMS Displacement 0.000009 0.000040 YES
Predicted change in Energy=-1.723206D-06
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''

Initial failed optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000015 NO
RMS Force 0.000006 0.000010 YES
Maximum Displacement 0.002915 0.000060 NO
RMS Displacement 0.000869 0.000040 NO
Predicted change in Energy=-5.685776D-09
Optimization stopped.
-- Number of steps exceeded, NStep= 61
-- Flag reset to prevent archiving.
</pre>

During this failed optimisation, it appears the molecule just spent a large amount of time rotating around the C3 axis through the sulphur.

The final optimisation yielded:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000049 0.000060 YES
RMS Displacement 0.000018 0.000040 YES
Predicted change in Energy=-6.520157D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==
Following this, frequency analysis was conducted with the same keywords and calculation level to ensure a minima has been found. This is ensured by checking there are no negative vibrations in the molecule. Calculations were again run on the laptop, and the log files, summaries, and frequencies are listed below. Actual animations of the modes have not been exported, however a Jmol of the log file is available and the modes can be seen by right clicking and choosing '''model -> the mode you want to see'''. This time, a range of
-30 to +30 cm-1 has been accepted for the low frequencies as molecules investigated are quite complex, and a relatively simple basis set has been used. Optimising to 6-311G(d,p) would likely bring the frequencies within the range used previously however this would be at the expense of much longer computation times.

* [N(CH3)4]+: [[media:Pk_log_nch34_freq.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_freq.log]]
* [S(CH3)3]+: {{DOI|10042/26273}}

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name NCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000085 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 3 minutes 17.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000009 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.014288D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name PCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701149 a.u.
RMS Gradient Norm 0.00000668 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 12 minutes 11.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001774 0.001800 YES
RMS Displacement 0.000659 0.001200 YES
Predicted change in Energy=-3.008780D-08
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000104 a.u.
Imaginary Freq 0
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 9 minutes 6.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000093 0.001800 YES
RMS Displacement 0.000033 0.001200 YES
Predicted change in Energy=-7.179584D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Vibration modes ===

''' [N(CH3)4]+ '''
<pre>
Low frequencies --- 0.0007 0.0011 0.0013 21.5288 21.5288 21.5288
Low frequencies --- 188.5488 292.6546 292.6546
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [P(CH3)4]+ '''
<pre>
Low frequencies --- -15.1139 -0.0002 0.0012 0.0012 5.8940 14.7736
Low frequencies --- 156.2222 191.5376 191.9513
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_pch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [S(CH3)3]+ '''
<pre>
Low frequencies --- -8.5871 0.0029 0.0049 0.0051 5.7111 9.1755
Low frequencies --- 162.4159 200.3446 200.5391
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_sch33_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== Conclusions on molecular structure ==
Investigation of structures is focused on the central atom as this is the only point at which variance should occur. The length of the M-C bonds and the angle between C-M-C on each complex is reported below:

{| class="wikitable" border="1"
! Complex !! M-C Length (Å) !! Angle (°) !! M-C length (lit<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref>) (Å)
|-
| [P(CH3)4]+ || 1.82 || 109.5 || 1.84
|-
| [N(CH3)4]+ || 1.51 || 109.5 || 1.46
|-
| [S(CH3)3]+ || 1.82 || 102.7 || 1.79
|}

''Literature bond lengths are found by adding the covalent radii for the atoms.''

Two key trends are:
* As you go down a group, the bond length decreases
* As you go across a group (so losing a ligand), the bond angle is reduced)

The first trend is straightforward to explain, as bond lengths increase down the group. This is in tandem with the increase in atomic radius down the group as orbitals in a greater shell begin to be filled. Thus, as you move from period 2 (N) to period 3 (P), the length of the bond increases and is in turn the overall size of each ion. There is slight variance in the length of a C-H bond in each complex, however no pattern is immediately discernible (it increases in the order S > P > N) - it is thought this is just some random error in the calculation.

Whilst there is an increase in bond length, there is no change in orientation of the bonds, thus the symmetry of TD is maintained in both the phosphorous and nitrogen molecules. As a result of this, the bond angle is the same for these two complexes. No other arrangement of the ligands is sterically possible, so ensuring that this symmetry label cannot be changed, and therefore the bond angle also cannot change. The bond angle is different for sulphur, as a result of the change of symmetry to C3v, it is not known if the change in metal centre contributes to this change - further investigation would be required.

Of note, the bond length does not appear to change going across the period. There is actually a small increase of 0.01Å if the bond length is reported accurate to 0.001Å, however it is not known if this is just an inherent error in the calculation or not. In any event, it is expected that there is a slight decrease in the bond length as you move towards the right of a period, as the increased nuclear charge better shields the electrons and thus shortens the bond length, but this is not observed here. This may be a result of this complex containing one less ligand, with the arrangement instead taken (along with the lone pair) resulting in some interactions (steric or electronic repulsion) which causes the carbon and metal atoms to move apart from each other. This theory is supported by the large deviation from bond length for the sulphur complex, indicating some feature about the arrangement it has taken is causing the bond length to be artificially lengthened.

Otherwise no strange observations are seen with the structures, with all methyl groups taking the expected tetrahedral structure, and either tetrahedral or C3v structures for the central atom as expected by the number of ligands which are present.

= Molecular orbitals and NBO charges of methyl-ligand complexes =
All three complexes discussed previously have been subject to a full NBO and MO analysis via an energy calculation with the <code>pop=(full,nbo)</code> keyword, retaining any previously used keywords as appropriate. Calculations were performed on the laptop due to load on the HPC, except for the sulphur complex as the calculation took too long on the laptop.

Log files are available as follows:

* '''[N(CH3)4]+''': [[media:Pk_log_nch34_egy.log]]
* '''[P(CH3)4]+''': [[media:Pk_log_pch34_egy.log]]
* '''[S(CH3)3]+''': {{DOI|10042/26274}}
== Calculation output ==

''' [N(CH3)4]+ '''

<pre>
File Name NCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

''' [P(CH3)4]+ '''

<pre>
File Name PCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701105 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 20.0 seconds.
</pre>

''' [S(CH3)3]+ '''

<pre>File Name sch33_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 0 minutes 57.7 seconds.
</pre>

== Sample MOs for [N(CH3)4]+ ==
A variety of 5 molecular orbitals have been calculated and shown below. Only occupied non-core MOs from the totally bonding to totally antibonding are shown.

{| class="wikitable" border="1"
|+ Totally bonding towards the top
! MO number !! Energy (hartree) !! Picture !! Degeneracy !! Notes
|-
| 6 || -1.19645 || [[Image:Pk-n-mo0.png|200px]] || Singly degenerate || This MO exhibits a great degree of strong bonding interactions across the entire molecule up to the protons, the orbitals of which do not appear to be part of this MO. This is seen by the huge red surface containing almost the entirety of the molecule. As a result of the huge amount of delocalisation seen in the MO, there is a lot of through space interactions between adjacent carbon groups, as seen by how the MO forms a 'cage' around the entire molecule - the empty space between two carbon atoms is part of this red object. As there are no other molecular orbitals other than this huge one, there is no concept of a node in this MO diagram.
|-
| 10 || -0.80745 || [[Image:Pk-n-mo1.png|200px]] || Singly degenerate || This is the first MO in this series of 5 to contain a slight degree of antibonding character, as seen by the fact each ligand is in its own (+) phase orbital, whereas the central metal is in a (-) phase one. This leads to a minor degree of antibonding character, and also a node in the centre of the M-C bond where the two MOs end. Through space interactions are present in each ligand MO, with all the protons and the central carbon existing within the boundaries of the MO, and hence there are through-space interactions between the protons. MOs of the same phase interact weakly with each other due to the large distance between each green orbital (seen in the picture), however the interaction between the (+) and (-) orbitals is quite strong as the nodal area is very small in size - the orbitals are nearly touching. The level of delocalisation is reduced, with delocalisation only occurring across each ligand group - the ligands themselves are not delocalised onto one unit.
|-
| 14 || -0.62248 || [[Image:Pk-n-mo2.png|200px]] || Doubly degenerate || For this MO, nodes exist on every carbon atom, as each MO covers two halves of a carbon atom, two protons, and nothing else. This does lead to delocalisationa cross the protons and carbon atoms, however this also does result in strong antibonding interactions at each carbon as the (+) and (-) MOs become quite close. Some protons, and the metal centre are not covered at all by this MO, however from what is delocalised, there is a significant amount of through space interactions between protons on differing methyl ligands - this is of note as the ligand protons are quite a distance away. There may be some weak bonding interactions between orbitals of the same phase, however they are quite a distance away (separated by the metal centre) so this is expected to be quite weak.
|-
| 17 || -0.58035 || [[Image:Pk-n-mo3.png|200px]] || Triply degenerate || This one again has a node on each carbon, however it differs in that each orbital only covers a single proton and half a carbon. This results in there being no through-space interactions in this molecule. Additionally, there are many strong antibonding interactions as all the orbitals are quite close together, with the a (+) orbital being surrounded by a (-) orbital on every side. If there are any bonding interactions, these are going to be very weak.
|-
| 21 || -0.57934 || [[Image:Pk-n-mo4.png|200px]] || Triply degenerate || This MO is similar to the previous, but differs in that each orbital now consists of two protons, so there are no protons which aren't enclosed in an orbital. Again, there are nodes in each carbon, but also a node in the metal center, with orbitals now also covering the metal center. This results in there being strong antibonding interactions over almost the entire molecule, with (+) interacting with (-) almost over the entire surface of every orbital. Through-space interactions are now back with there being two protons in each orbital, making it possible for these to interact, and there is also the potential for protons and metal center to interact as well. This orbital is only slightly higher energy than the previous one, and this is solely because of the increased degree of antibonding interactions present.
|}

== NBO charge distributions ==

NBO charge distributions were calculated from the checkpoint file for a range of -1.750 to 1.750 as this ensured the range of charges for all 3 complexes could be accommodated on the same scale. The charges are as follows:

{| class="wikitable" border="1"
! Complex !! Metal charge (e) !! Carbon charge (e) !! Proton charge (e)
|-
| [P(NH3)4]+ || 1.667 || -1.060 || 0.298
|-
| [N(NH3)4]+ || 0.917 || -0.846 || 0.297
|-
| [S(NH3)3]+ || -0.295 || -0.483 || 0.269
|}

<gallery>
File:Pk-nbo-n.png|Nitrogen complex
File:Pk-nbo-p.png|Phosphorous complex
File:Pk-nbo-s.png|Sulphur complex
</gallery>

There appears to be a slight trend of the metal centre charge with electronegativity, with the charge much lower as it becomes more electronegative (and hence drawing a greater share of electrons to it). This in turn makes the carbon more positive as electron density is removed from it. The protons remain rather positively charged and do not appear to be greatly affected by the metal centre, but this is likely because they are too far away for the inductive effect to occur.

Interestingly, nitrogen is more eletronegative than sulphur, yet sulphur has a greater negative charge. The reduced degree of polarisation in the bond for the nitrogen complex also suggests why the bond length for the nitrogen complex is shorter compared to the sulphur. The reason for this increased amount of negative charge is due to the lone pair present on sulphur (hence the configuration it takes according to the Jmol clip above), and so there is simply more negative charge present on the sulphur.

Thus, for the general complex [NR4]+, the positive charge located on the nitrogen in the picture is indeed located on the nitrogen, however it is somewhat delocalised over the protons too. As the nitrogen contains the greatest degree of positive charge, though, the + sign is conventionally placed here as it gives the indication as to where most of the charge is.

Analysis of the log files show the exact NBO contributions to the bond:

'''[P(NH3)3]+'''
<pre>
1. (1.98031) BD ( 1) P 1 - C 2
( 40.43%) 0.6358* P 1 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.4030 0.0006 0.0000 -0.4429
0.0006 0.0000 0.6188 -0.0009 0.0385
-0.0538 -0.0591 -0.0036 0.0254
( 59.57%) 0.7718* C 2 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.4044
-0.0074 0.4444 -0.0081 -0.6209 0.0114
0.0121 -0.0169 -0.0186 -0.0011 0.0080
</pre>

This shows almost equal contribution from each atom to the bond, with each atom assuming a sp3 arrangement as is expected by the TD symmetry. Carbon is sp3 as expected due to its saturation. As the carbon is slightly more negatively charged according to the charge distributions, the marginal increase in contribution from the carbon vs the phosphorous agrees with the charge distribution seen.

'''[N(NH3)3]+'''
<pre>
4. (1.98452) BD ( 1) C 1 - N 13
( 33.65%) 0.5801* C 1 s( 20.77%)p 3.81( 79.06%)d 0.01( 0.16%)
0.0003 0.4552 -0.0237 0.0026 -0.5129
-0.0218 -0.5129 -0.0218 -0.5129 -0.0218
0.0234 0.0234 0.0234 0.0000 0.0000
( 66.35%) 0.8146* N 13 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 0.5000 -0.0007 0.0000 0.4999
-0.0001 0.4999 -0.0001 0.4999 -0.0001
0.0103 0.0103 0.0103 0.0000 0.0000
</pre>

A similar argument can be made here. The large contribution from the nitrogen is surprising, but considering the smaller bond length for this complex based on the metal, an increased contribution from the nitrogen is not unreasonable. However this does disagree somewhat with the charge distribution which shows there is a much larger electron density on the carbon. It is thus thought that since it is possible to reach orbitals closer to the core on nitrogen rather than phosphorous, it makes nitrogen able to donate a greater share of electrons, and so polarises the bond towards it as a result of its electronegativity.

'''[S(NH3)3]+'''
<pre>
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
-0.0003 -0.4437 -0.0140 0.0033 0.7546
-0.0059 0.3161 -0.0025 0.3634 0.0098
-0.0189 -0.0222 -0.0093 -0.0186 0.0096
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 -0.0001 -0.4117 0.0075 -0.0012
0.0000 -0.7489 0.0330 0.0000 -0.3137
0.0138 0.0000 -0.4037 -0.0260 -0.0353
-0.0572 -0.0240 -0.0347 0.0051
</pre>

Finally, for the sulphur, the bond is an almost equal contribution from each atom in the bond. The charges of the S and C atoms according to the charge distribution are both similar and negative, suggesting little polarisation in this bond, and so the balance seen here is to be expected.

= Ligand influences on nitrogen metal centre complexes =
To investigate how changes to the ligands affects the cation, two variants on the nitrogen complex analysed previously have been used. One has one of the protons on a methyl ligand replaced with CH2OH, the other has the proton replaced with CH2CN. Each complex is then optimised and subject to a frequency analysis so as to allow for investigation of its structure. A MO and NBO calculation is then subsequently run to analyse how the change in ligand affects the ions electronic behaviour.

== Optimisations ==
Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26206}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26207}}

=== Summary output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
File Name nch33ch2oh_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000102 a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 1 hours 22 minutes 37.5 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
File Name nch33ch2cn_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000045 a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 50 minutes 39.5 seconds.
</pre>

=== Convergence output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000034 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-5.591936D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000011 0.000040 YES
Predicted change in Energy=-2.269581D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==

Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26290}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26291}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000106 a.u.
Imaginary Freq 0
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 26 minutes 10.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000102 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-5.078379D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000059 a.u.
Imaginary Freq 0
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 29 minutes 19.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-6.144746D-12
Optimization completed.
-- Stationary point found.
</pre>

=== Vibrational modes ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2oh_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

'''[N(CH3)3(CH2CN)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2cn_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== MO and NBO calculations ==
<code>pop=(nbo,full)</code> energy calculations were then performed on the complexes to generate MOs and NBO charge diagrams, just as has been done previously. All calculations were performed on the HPC and log files are available as follows:

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26294}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26295}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 59.3 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 25.0 seconds.
</pre>

=== NBO charge distributions ===
The main difference between these ligands is that CN is an EWG, and OH is an EDG, the latter due to the lone pairs which make it possible to enolise. Therefore comparison of the charge density of the structure can show how these ligands affect the overall structure of the molecule. The NBO charge distributions from -0.750 to 0.750 are shown below.

<gallery>
File:Pk-nbo-nc.png|CN ligand complex
File:Pk-nbo-oh.png|OH ligand complex
</gallery>

=== Sample MOs ===

{| class="wikitable" border="1"
! !! [N(CH3)3(CH2OH)]+ !!
[N(CH3)3(CH2CN)]+
|-
| HOMO || [[Image:Pk-homo-oh.png|200px]] || [[Image:Pk-homo-cn.png|200px]]
|-
| LUMO || [[Image:Pk-lumo-oh.png|200px]] || [[Image:Pk-lumo-cn.png|200px]]
|-
| HOMO Energy (hartree) || -0.48763 || -0.50047
|-
| LUMO Energy (hartree) || -0.12459 || -0.18183
|}

=== Discussion of MOs ===

== Ligand influence on structure ==

== Ligand influence on charge distribution ==

== Ligand influence on molecular orbitals ==

= References =
<references />

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T13:46:22Z

Pk1811: /* MO and NBO calculations */

<div style="font-size: 40px;"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px;"><center>Ionic liquids: Designer solvents</center></div>
 
= Introduction =
The aim of this project is to explore the physical nature of ionic liquids, which have application in designing solvents through customisation of the nature of the cation and anion<ref name="abs">M. Freemantle. ''Chem. Eng. News'', 1998, '''76''', 32–37</ref>. In this work, a variety of cations have been investigated to identify what trends are present in the variation in central atom and its ligands.

= Structures of methyl-ligand complexes =
== Optimisations ==
A number of cations have been optimised using Gaussian 09 D.01, namely [N(CH3)4]+, [P(CH3)4]+ and [F(CH3)3]+. All these complexes have been optimised to a DFT B3LYP 6-31G(d,p) level with the <code>int=ultrafine scf=conver=9</code> keywords and tight convergence - this is as a consequence of behaviour seen in previous work<ref name="labintro">P. Kent, unpublished work ([[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|lab intro]])</ref> where low frequencies did not exist within a tight range unless these keywords were specified. All calculations were run on the supplied laptop due to a significant queue of jobs on the HPC (except for [S(CH3)3]+ as it took a very long time), and the log files are available here:

* [N(CH3)4]+: [[media:Pk_log_nch34_opt.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_opt.log]]
* [S(CH3)3]+: The first attempt did not converge: {{DOI|10042/26201}}. A partially optimised structure was resubmitted as a second attempt: {{DOI|10042/26205}}. This also did not converge so a final optimisation was run on this partially optimised structure with the <code>nosymm</code> keyword. This converged: {{DOI|10042/26214}}.

Once done, convergence was verified via inspection of the log file.

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name nch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000090 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 1 minutes 27.0 seconds.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name pch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701126 a.u.
RMS Gradient Norm 0.00000675 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 24 minutes 21.0 seconds.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_opt3
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000101 a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 52.2 seconds.
</pre>

=== Convergence outputs ===

''' [N(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000014 0.000060 YES
RMS Displacement 0.000005 0.000040 YES
Predicted change in Energy=-1.010077D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000015 YES
RMS Force 0.000005 0.000010 YES
Maximum Displacement 0.000026 0.000060 YES
RMS Displacement 0.000009 0.000040 YES
Predicted change in Energy=-1.723206D-06
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''

Initial failed optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000015 NO
RMS Force 0.000006 0.000010 YES
Maximum Displacement 0.002915 0.000060 NO
RMS Displacement 0.000869 0.000040 NO
Predicted change in Energy=-5.685776D-09
Optimization stopped.
-- Number of steps exceeded, NStep= 61
-- Flag reset to prevent archiving.
</pre>

During this failed optimisation, it appears the molecule just spent a large amount of time rotating around the C3 axis through the sulphur.

The final optimisation yielded:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000049 0.000060 YES
RMS Displacement 0.000018 0.000040 YES
Predicted change in Energy=-6.520157D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==
Following this, frequency analysis was conducted with the same keywords and calculation level to ensure a minima has been found. This is ensured by checking there are no negative vibrations in the molecule. Calculations were again run on the laptop, and the log files, summaries, and frequencies are listed below. Actual animations of the modes have not been exported, however a Jmol of the log file is available and the modes can be seen by right clicking and choosing '''model -> the mode you want to see'''. This time, a range of
-30 to +30 cm-1 has been accepted for the low frequencies as molecules investigated are quite complex, and a relatively simple basis set has been used. Optimising to 6-311G(d,p) would likely bring the frequencies within the range used previously however this would be at the expense of much longer computation times.

* [N(CH3)4]+: [[media:Pk_log_nch34_freq.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_freq.log]]
* [S(CH3)3]+: {{DOI|10042/26273}}

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name NCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000085 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 3 minutes 17.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000009 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.014288D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name PCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701149 a.u.
RMS Gradient Norm 0.00000668 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 12 minutes 11.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001774 0.001800 YES
RMS Displacement 0.000659 0.001200 YES
Predicted change in Energy=-3.008780D-08
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000104 a.u.
Imaginary Freq 0
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 9 minutes 6.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000093 0.001800 YES
RMS Displacement 0.000033 0.001200 YES
Predicted change in Energy=-7.179584D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Vibration modes ===

''' [N(CH3)4]+ '''
<pre>
Low frequencies --- 0.0007 0.0011 0.0013 21.5288 21.5288 21.5288
Low frequencies --- 188.5488 292.6546 292.6546
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [P(CH3)4]+ '''
<pre>
Low frequencies --- -15.1139 -0.0002 0.0012 0.0012 5.8940 14.7736
Low frequencies --- 156.2222 191.5376 191.9513
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_pch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [S(CH3)3]+ '''
<pre>
Low frequencies --- -8.5871 0.0029 0.0049 0.0051 5.7111 9.1755
Low frequencies --- 162.4159 200.3446 200.5391
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_sch33_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== Conclusions on molecular structure ==
Investigation of structures is focused on the central atom as this is the only point at which variance should occur. The length of the M-C bonds and the angle between C-M-C on each complex is reported below:

{| class="wikitable" border="1"
! Complex !! M-C Length (Å) !! Angle (°) !! M-C length (lit<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref>) (Å)
|-
| [P(CH3)4]+ || 1.82 || 109.5 || 1.84
|-
| [N(CH3)4]+ || 1.51 || 109.5 || 1.46
|-
| [S(CH3)3]+ || 1.82 || 102.7 || 1.79
|}

''Literature bond lengths are found by adding the covalent radii for the atoms.''

Two key trends are:
* As you go down a group, the bond length decreases
* As you go across a group (so losing a ligand), the bond angle is reduced)

The first trend is straightforward to explain, as bond lengths increase down the group. This is in tandem with the increase in atomic radius down the group as orbitals in a greater shell begin to be filled. Thus, as you move from period 2 (N) to period 3 (P), the length of the bond increases and is in turn the overall size of each ion. There is slight variance in the length of a C-H bond in each complex, however no pattern is immediately discernible (it increases in the order S > P > N) - it is thought this is just some random error in the calculation.

Whilst there is an increase in bond length, there is no change in orientation of the bonds, thus the symmetry of TD is maintained in both the phosphorous and nitrogen molecules. As a result of this, the bond angle is the same for these two complexes. No other arrangement of the ligands is sterically possible, so ensuring that this symmetry label cannot be changed, and therefore the bond angle also cannot change. The bond angle is different for sulphur, as a result of the change of symmetry to C3v, it is not known if the change in metal centre contributes to this change - further investigation would be required.

Of note, the bond length does not appear to change going across the period. There is actually a small increase of 0.01Å if the bond length is reported accurate to 0.001Å, however it is not known if this is just an inherent error in the calculation or not. In any event, it is expected that there is a slight decrease in the bond length as you move towards the right of a period, as the increased nuclear charge better shields the electrons and thus shortens the bond length, but this is not observed here. This may be a result of this complex containing one less ligand, with the arrangement instead taken (along with the lone pair) resulting in some interactions (steric or electronic repulsion) which causes the carbon and metal atoms to move apart from each other. This theory is supported by the large deviation from bond length for the sulphur complex, indicating some feature about the arrangement it has taken is causing the bond length to be artificially lengthened.

Otherwise no strange observations are seen with the structures, with all methyl groups taking the expected tetrahedral structure, and either tetrahedral or C3v structures for the central atom as expected by the number of ligands which are present.

= Molecular orbitals and NBO charges of methyl-ligand complexes =
All three complexes discussed previously have been subject to a full NBO and MO analysis via an energy calculation with the <code>pop=(full,nbo)</code> keyword, retaining any previously used keywords as appropriate. Calculations were performed on the laptop due to load on the HPC, except for the sulphur complex as the calculation took too long on the laptop.

Log files are available as follows:

* '''[N(CH3)4]+''': [[media:Pk_log_nch34_egy.log]]
* '''[P(CH3)4]+''': [[media:Pk_log_pch34_egy.log]]
* '''[S(CH3)3]+''': {{DOI|10042/26274}}
== Calculation output ==

''' [N(CH3)4]+ '''

<pre>
File Name NCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

''' [P(CH3)4]+ '''

<pre>
File Name PCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701105 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 20.0 seconds.
</pre>

''' [S(CH3)3]+ '''

<pre>File Name sch33_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 0 minutes 57.7 seconds.
</pre>

== Sample MOs for [N(CH3)4]+ ==
A variety of 5 molecular orbitals have been calculated and shown below. Only occupied non-core MOs from the totally bonding to totally antibonding are shown.

{| class="wikitable" border="1"
|+ Totally bonding towards the top
! MO number !! Energy (hartree) !! Picture !! Degeneracy !! Notes
|-
| 6 || -1.19645 || [[Image:Pk-n-mo0.png|200px]] || Singly degenerate || This MO exhibits a great degree of strong bonding interactions across the entire molecule up to the protons, the orbitals of which do not appear to be part of this MO. This is seen by the huge red surface containing almost the entirety of the molecule. As a result of the huge amount of delocalisation seen in the MO, there is a lot of through space interactions between adjacent carbon groups, as seen by how the MO forms a 'cage' around the entire molecule - the empty space between two carbon atoms is part of this red object. As there are no other molecular orbitals other than this huge one, there is no concept of a node in this MO diagram.
|-
| 10 || -0.80745 || [[Image:Pk-n-mo1.png|200px]] || Singly degenerate || This is the first MO in this series of 5 to contain a slight degree of antibonding character, as seen by the fact each ligand is in its own (+) phase orbital, whereas the central metal is in a (-) phase one. This leads to a minor degree of antibonding character, and also a node in the centre of the M-C bond where the two MOs end. Through space interactions are present in each ligand MO, with all the protons and the central carbon existing within the boundaries of the MO, and hence there are through-space interactions between the protons. MOs of the same phase interact weakly with each other due to the large distance between each green orbital (seen in the picture), however the interaction between the (+) and (-) orbitals is quite strong as the nodal area is very small in size - the orbitals are nearly touching. The level of delocalisation is reduced, with delocalisation only occurring across each ligand group - the ligands themselves are not delocalised onto one unit.
|-
| 14 || -0.62248 || [[Image:Pk-n-mo2.png|200px]] || Doubly degenerate || For this MO, nodes exist on every carbon atom, as each MO covers two halves of a carbon atom, two protons, and nothing else. This does lead to delocalisationa cross the protons and carbon atoms, however this also does result in strong antibonding interactions at each carbon as the (+) and (-) MOs become quite close. Some protons, and the metal centre are not covered at all by this MO, however from what is delocalised, there is a significant amount of through space interactions between protons on differing methyl ligands - this is of note as the ligand protons are quite a distance away. There may be some weak bonding interactions between orbitals of the same phase, however they are quite a distance away (separated by the metal centre) so this is expected to be quite weak.
|-
| 17 || -0.58035 || [[Image:Pk-n-mo3.png|200px]] || Triply degenerate || This one again has a node on each carbon, however it differs in that each orbital only covers a single proton and half a carbon. This results in there being no through-space interactions in this molecule. Additionally, there are many strong antibonding interactions as all the orbitals are quite close together, with the a (+) orbital being surrounded by a (-) orbital on every side. If there are any bonding interactions, these are going to be very weak.
|-
| 21 || -0.57934 || [[Image:Pk-n-mo4.png|200px]] || Triply degenerate || This MO is similar to the previous, but differs in that each orbital now consists of two protons, so there are no protons which aren't enclosed in an orbital. Again, there are nodes in each carbon, but also a node in the metal center, with orbitals now also covering the metal center. This results in there being strong antibonding interactions over almost the entire molecule, with (+) interacting with (-) almost over the entire surface of every orbital. Through-space interactions are now back with there being two protons in each orbital, making it possible for these to interact, and there is also the potential for protons and metal center to interact as well. This orbital is only slightly higher energy than the previous one, and this is solely because of the increased degree of antibonding interactions present.
|}

== NBO charge distributions ==

NBO charge distributions were calculated from the checkpoint file for a range of -1.750 to 1.750 as this ensured the range of charges for all 3 complexes could be accommodated on the same scale. The charges are as follows:

{| class="wikitable" border="1"
! Complex !! Metal charge (e) !! Carbon charge (e) !! Proton charge (e)
|-
| [P(NH3)4]+ || 1.667 || -1.060 || 0.298
|-
| [N(NH3)4]+ || 0.917 || -0.846 || 0.297
|-
| [S(NH3)3]+ || -0.295 || -0.483 || 0.269
|}

<gallery>
File:Pk-nbo-n.png|Nitrogen complex
File:Pk-nbo-p.png|Phosphorous complex
File:Pk-nbo-s.png|Sulphur complex
</gallery>

There appears to be a slight trend of the metal centre charge with electronegativity, with the charge much lower as it becomes more electronegative (and hence drawing a greater share of electrons to it). This in turn makes the carbon more positive as electron density is removed from it. The protons remain rather positively charged and do not appear to be greatly affected by the metal centre, but this is likely because they are too far away for the inductive effect to occur.

Interestingly, nitrogen is more eletronegative than sulphur, yet sulphur has a greater negative charge. The reduced degree of polarisation in the bond for the nitrogen complex also suggests why the bond length for the nitrogen complex is shorter compared to the sulphur. The reason for this increased amount of negative charge is due to the lone pair present on sulphur (hence the configuration it takes according to the Jmol clip above), and so there is simply more negative charge present on the sulphur.

Thus, for the general complex [NR4]+, the positive charge located on the nitrogen in the picture is indeed located on the nitrogen, however it is somewhat delocalised over the protons too. As the nitrogen contains the greatest degree of positive charge, though, the + sign is conventionally placed here as it gives the indication as to where most of the charge is.

Analysis of the log files show the exact NBO contributions to the bond:

'''[P(NH3)3]+'''
<pre>
1. (1.98031) BD ( 1) P 1 - C 2
( 40.43%) 0.6358* P 1 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.4030 0.0006 0.0000 -0.4429
0.0006 0.0000 0.6188 -0.0009 0.0385
-0.0538 -0.0591 -0.0036 0.0254
( 59.57%) 0.7718* C 2 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.4044
-0.0074 0.4444 -0.0081 -0.6209 0.0114
0.0121 -0.0169 -0.0186 -0.0011 0.0080
</pre>

This shows almost equal contribution from each atom to the bond, with each atom assuming a sp3 arrangement as is expected by the TD symmetry. Carbon is sp3 as expected due to its saturation. As the carbon is slightly more negatively charged according to the charge distributions, the marginal increase in contribution from the carbon vs the phosphorous agrees with the charge distribution seen.

'''[N(NH3)3]+'''
<pre>
4. (1.98452) BD ( 1) C 1 - N 13
( 33.65%) 0.5801* C 1 s( 20.77%)p 3.81( 79.06%)d 0.01( 0.16%)
0.0003 0.4552 -0.0237 0.0026 -0.5129
-0.0218 -0.5129 -0.0218 -0.5129 -0.0218
0.0234 0.0234 0.0234 0.0000 0.0000
( 66.35%) 0.8146* N 13 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 0.5000 -0.0007 0.0000 0.4999
-0.0001 0.4999 -0.0001 0.4999 -0.0001
0.0103 0.0103 0.0103 0.0000 0.0000
</pre>

A similar argument can be made here. The large contribution from the nitrogen is surprising, but considering the smaller bond length for this complex based on the metal, an increased contribution from the nitrogen is not unreasonable. However this does disagree somewhat with the charge distribution which shows there is a much larger electron density on the carbon. It is thus thought that since it is possible to reach orbitals closer to the core on nitrogen rather than phosphorous, it makes nitrogen able to donate a greater share of electrons, and so polarises the bond towards it as a result of its electronegativity.

'''[S(NH3)3]+'''
<pre>
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
-0.0003 -0.4437 -0.0140 0.0033 0.7546
-0.0059 0.3161 -0.0025 0.3634 0.0098
-0.0189 -0.0222 -0.0093 -0.0186 0.0096
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 -0.0001 -0.4117 0.0075 -0.0012
0.0000 -0.7489 0.0330 0.0000 -0.3137
0.0138 0.0000 -0.4037 -0.0260 -0.0353
-0.0572 -0.0240 -0.0347 0.0051
</pre>

Finally, for the sulphur, the bond is an almost equal contribution from each atom in the bond. The charges of the S and C atoms according to the charge distribution are both similar and negative, suggesting little polarisation in this bond, and so the balance seen here is to be expected.

= Ligand influences on nitrogen metal centre complexes =
To investigate how changes to the ligands affects the cation, two variants on the nitrogen complex analysed previously have been used. One has one of the protons on a methyl ligand replaced with CH2OH, the other has the proton replaced with CH2CN. Each complex is then optimised and subject to a frequency analysis so as to allow for investigation of its structure. A MO and NBO calculation is then subsequently run to analyse how the change in ligand affects the ions electronic behaviour.

== Optimisations ==
Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26206}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26207}}

=== Summary output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
File Name nch33ch2oh_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000102 a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 1 hours 22 minutes 37.5 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
File Name nch33ch2cn_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000045 a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 50 minutes 39.5 seconds.
</pre>

=== Convergence output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000034 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-5.591936D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000011 0.000040 YES
Predicted change in Energy=-2.269581D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==

Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26290}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26291}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000106 a.u.
Imaginary Freq 0
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 26 minutes 10.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000102 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-5.078379D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000059 a.u.
Imaginary Freq 0
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 29 minutes 19.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-6.144746D-12
Optimization completed.
-- Stationary point found.
</pre>

=== Vibrational modes ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2oh_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

'''[N(CH3)3(CH2CN)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2cn_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== MO and NBO calculations ==
<code>pop=(nbo,full)</code> energy calculations were then performed on the complexes to generate MOs and NBO charge diagrams, just as has been done previously. All calculations were performed on the HPC and log files are available as follows:

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26294}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26295}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 59.3 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 25.0 seconds.
</pre>

=== NBO charge distributions ===
The main difference between these ligands is that CN is an EWG, and OH is an EDG, the latter due to the lone pairs which make it possible to enolise. Therefore comparison of the charge density of the structure can show how these ligands affect the overall structure of the molecule. The NBO charge distributions from -0.750 to 0.750 are shown below.

=== Sample MOs ===

{| class="wikitable" border="1"
! !! [N(CH3)3(CH2OH)]+ !!
[N(CH3)3(CH2CN)]+
|-
| HOMO || [[Image:Pk-homo-oh.png|200px]] || [[Image:Pk-homo-cn.png|200px]]
|-
| LUMO || [[Image:Pk-lumo-oh.png|200px]] || [[Image:Pk-lumo-cn.png|200px]]
|-
| HOMO Energy (hartree) || -0.48763 || -0.50047
|-
| LUMO Energy (hartree) || -0.12459 || -0.18183
|}

=== Discussion of MOs ===

== Ligand influence on structure ==

== Ligand influence on charge distribution ==

== Ligand influence on molecular orbitals ==

= References =
<references />

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T13:41:57Z

Pk1811: /* Sample MOs */

<div style="font-size: 40px;"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px;"><center>Ionic liquids: Designer solvents</center></div>
 
= Introduction =
The aim of this project is to explore the physical nature of ionic liquids, which have application in designing solvents through customisation of the nature of the cation and anion<ref name="abs">M. Freemantle. ''Chem. Eng. News'', 1998, '''76''', 32–37</ref>. In this work, a variety of cations have been investigated to identify what trends are present in the variation in central atom and its ligands.

= Structures of methyl-ligand complexes =
== Optimisations ==
A number of cations have been optimised using Gaussian 09 D.01, namely [N(CH3)4]+, [P(CH3)4]+ and [F(CH3)3]+. All these complexes have been optimised to a DFT B3LYP 6-31G(d,p) level with the <code>int=ultrafine scf=conver=9</code> keywords and tight convergence - this is as a consequence of behaviour seen in previous work<ref name="labintro">P. Kent, unpublished work ([[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|lab intro]])</ref> where low frequencies did not exist within a tight range unless these keywords were specified. All calculations were run on the supplied laptop due to a significant queue of jobs on the HPC (except for [S(CH3)3]+ as it took a very long time), and the log files are available here:

* [N(CH3)4]+: [[media:Pk_log_nch34_opt.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_opt.log]]
* [S(CH3)3]+: The first attempt did not converge: {{DOI|10042/26201}}. A partially optimised structure was resubmitted as a second attempt: {{DOI|10042/26205}}. This also did not converge so a final optimisation was run on this partially optimised structure with the <code>nosymm</code> keyword. This converged: {{DOI|10042/26214}}.

Once done, convergence was verified via inspection of the log file.

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name nch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000090 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 1 minutes 27.0 seconds.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name pch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701126 a.u.
RMS Gradient Norm 0.00000675 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 24 minutes 21.0 seconds.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_opt3
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000101 a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 52.2 seconds.
</pre>

=== Convergence outputs ===

''' [N(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000014 0.000060 YES
RMS Displacement 0.000005 0.000040 YES
Predicted change in Energy=-1.010077D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000015 YES
RMS Force 0.000005 0.000010 YES
Maximum Displacement 0.000026 0.000060 YES
RMS Displacement 0.000009 0.000040 YES
Predicted change in Energy=-1.723206D-06
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''

Initial failed optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000015 NO
RMS Force 0.000006 0.000010 YES
Maximum Displacement 0.002915 0.000060 NO
RMS Displacement 0.000869 0.000040 NO
Predicted change in Energy=-5.685776D-09
Optimization stopped.
-- Number of steps exceeded, NStep= 61
-- Flag reset to prevent archiving.
</pre>

During this failed optimisation, it appears the molecule just spent a large amount of time rotating around the C3 axis through the sulphur.

The final optimisation yielded:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000049 0.000060 YES
RMS Displacement 0.000018 0.000040 YES
Predicted change in Energy=-6.520157D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==
Following this, frequency analysis was conducted with the same keywords and calculation level to ensure a minima has been found. This is ensured by checking there are no negative vibrations in the molecule. Calculations were again run on the laptop, and the log files, summaries, and frequencies are listed below. Actual animations of the modes have not been exported, however a Jmol of the log file is available and the modes can be seen by right clicking and choosing '''model -> the mode you want to see'''. This time, a range of
-30 to +30 cm-1 has been accepted for the low frequencies as molecules investigated are quite complex, and a relatively simple basis set has been used. Optimising to 6-311G(d,p) would likely bring the frequencies within the range used previously however this would be at the expense of much longer computation times.

* [N(CH3)4]+: [[media:Pk_log_nch34_freq.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_freq.log]]
* [S(CH3)3]+: {{DOI|10042/26273}}

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name NCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000085 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 3 minutes 17.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000009 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.014288D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name PCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701149 a.u.
RMS Gradient Norm 0.00000668 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 12 minutes 11.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001774 0.001800 YES
RMS Displacement 0.000659 0.001200 YES
Predicted change in Energy=-3.008780D-08
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000104 a.u.
Imaginary Freq 0
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 9 minutes 6.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000093 0.001800 YES
RMS Displacement 0.000033 0.001200 YES
Predicted change in Energy=-7.179584D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Vibration modes ===

''' [N(CH3)4]+ '''
<pre>
Low frequencies --- 0.0007 0.0011 0.0013 21.5288 21.5288 21.5288
Low frequencies --- 188.5488 292.6546 292.6546
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [P(CH3)4]+ '''
<pre>
Low frequencies --- -15.1139 -0.0002 0.0012 0.0012 5.8940 14.7736
Low frequencies --- 156.2222 191.5376 191.9513
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_pch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [S(CH3)3]+ '''
<pre>
Low frequencies --- -8.5871 0.0029 0.0049 0.0051 5.7111 9.1755
Low frequencies --- 162.4159 200.3446 200.5391
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_sch33_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== Conclusions on molecular structure ==
Investigation of structures is focused on the central atom as this is the only point at which variance should occur. The length of the M-C bonds and the angle between C-M-C on each complex is reported below:

{| class="wikitable" border="1"
! Complex !! M-C Length (Å) !! Angle (°) !! M-C length (lit<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref>) (Å)
|-
| [P(CH3)4]+ || 1.82 || 109.5 || 1.84
|-
| [N(CH3)4]+ || 1.51 || 109.5 || 1.46
|-
| [S(CH3)3]+ || 1.82 || 102.7 || 1.79
|}

''Literature bond lengths are found by adding the covalent radii for the atoms.''

Two key trends are:
* As you go down a group, the bond length decreases
* As you go across a group (so losing a ligand), the bond angle is reduced)

The first trend is straightforward to explain, as bond lengths increase down the group. This is in tandem with the increase in atomic radius down the group as orbitals in a greater shell begin to be filled. Thus, as you move from period 2 (N) to period 3 (P), the length of the bond increases and is in turn the overall size of each ion. There is slight variance in the length of a C-H bond in each complex, however no pattern is immediately discernible (it increases in the order S > P > N) - it is thought this is just some random error in the calculation.

Whilst there is an increase in bond length, there is no change in orientation of the bonds, thus the symmetry of TD is maintained in both the phosphorous and nitrogen molecules. As a result of this, the bond angle is the same for these two complexes. No other arrangement of the ligands is sterically possible, so ensuring that this symmetry label cannot be changed, and therefore the bond angle also cannot change. The bond angle is different for sulphur, as a result of the change of symmetry to C3v, it is not known if the change in metal centre contributes to this change - further investigation would be required.

Of note, the bond length does not appear to change going across the period. There is actually a small increase of 0.01Å if the bond length is reported accurate to 0.001Å, however it is not known if this is just an inherent error in the calculation or not. In any event, it is expected that there is a slight decrease in the bond length as you move towards the right of a period, as the increased nuclear charge better shields the electrons and thus shortens the bond length, but this is not observed here. This may be a result of this complex containing one less ligand, with the arrangement instead taken (along with the lone pair) resulting in some interactions (steric or electronic repulsion) which causes the carbon and metal atoms to move apart from each other. This theory is supported by the large deviation from bond length for the sulphur complex, indicating some feature about the arrangement it has taken is causing the bond length to be artificially lengthened.

Otherwise no strange observations are seen with the structures, with all methyl groups taking the expected tetrahedral structure, and either tetrahedral or C3v structures for the central atom as expected by the number of ligands which are present.

= Molecular orbitals and NBO charges of methyl-ligand complexes =
All three complexes discussed previously have been subject to a full NBO and MO analysis via an energy calculation with the <code>pop=(full,nbo)</code> keyword, retaining any previously used keywords as appropriate. Calculations were performed on the laptop due to load on the HPC, except for the sulphur complex as the calculation took too long on the laptop.

Log files are available as follows:

* '''[N(CH3)4]+''': [[media:Pk_log_nch34_egy.log]]
* '''[P(CH3)4]+''': [[media:Pk_log_pch34_egy.log]]
* '''[S(CH3)3]+''': {{DOI|10042/26274}}
== Calculation output ==

''' [N(CH3)4]+ '''

<pre>
File Name NCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

''' [P(CH3)4]+ '''

<pre>
File Name PCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701105 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 20.0 seconds.
</pre>

''' [S(CH3)3]+ '''

<pre>File Name sch33_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 0 minutes 57.7 seconds.
</pre>

== Sample MOs for [N(CH3)4]+ ==
A variety of 5 molecular orbitals have been calculated and shown below. Only occupied non-core MOs from the totally bonding to totally antibonding are shown.

{| class="wikitable" border="1"
|+ Totally bonding towards the top
! MO number !! Energy (hartree) !! Picture !! Degeneracy !! Notes
|-
| 6 || -1.19645 || [[Image:Pk-n-mo0.png|200px]] || Singly degenerate || This MO exhibits a great degree of strong bonding interactions across the entire molecule up to the protons, the orbitals of which do not appear to be part of this MO. This is seen by the huge red surface containing almost the entirety of the molecule. As a result of the huge amount of delocalisation seen in the MO, there is a lot of through space interactions between adjacent carbon groups, as seen by how the MO forms a 'cage' around the entire molecule - the empty space between two carbon atoms is part of this red object. As there are no other molecular orbitals other than this huge one, there is no concept of a node in this MO diagram.
|-
| 10 || -0.80745 || [[Image:Pk-n-mo1.png|200px]] || Singly degenerate || This is the first MO in this series of 5 to contain a slight degree of antibonding character, as seen by the fact each ligand is in its own (+) phase orbital, whereas the central metal is in a (-) phase one. This leads to a minor degree of antibonding character, and also a node in the centre of the M-C bond where the two MOs end. Through space interactions are present in each ligand MO, with all the protons and the central carbon existing within the boundaries of the MO, and hence there are through-space interactions between the protons. MOs of the same phase interact weakly with each other due to the large distance between each green orbital (seen in the picture), however the interaction between the (+) and (-) orbitals is quite strong as the nodal area is very small in size - the orbitals are nearly touching. The level of delocalisation is reduced, with delocalisation only occurring across each ligand group - the ligands themselves are not delocalised onto one unit.
|-
| 14 || -0.62248 || [[Image:Pk-n-mo2.png|200px]] || Doubly degenerate || For this MO, nodes exist on every carbon atom, as each MO covers two halves of a carbon atom, two protons, and nothing else. This does lead to delocalisationa cross the protons and carbon atoms, however this also does result in strong antibonding interactions at each carbon as the (+) and (-) MOs become quite close. Some protons, and the metal centre are not covered at all by this MO, however from what is delocalised, there is a significant amount of through space interactions between protons on differing methyl ligands - this is of note as the ligand protons are quite a distance away. There may be some weak bonding interactions between orbitals of the same phase, however they are quite a distance away (separated by the metal centre) so this is expected to be quite weak.
|-
| 17 || -0.58035 || [[Image:Pk-n-mo3.png|200px]] || Triply degenerate || This one again has a node on each carbon, however it differs in that each orbital only covers a single proton and half a carbon. This results in there being no through-space interactions in this molecule. Additionally, there are many strong antibonding interactions as all the orbitals are quite close together, with the a (+) orbital being surrounded by a (-) orbital on every side. If there are any bonding interactions, these are going to be very weak.
|-
| 21 || -0.57934 || [[Image:Pk-n-mo4.png|200px]] || Triply degenerate || This MO is similar to the previous, but differs in that each orbital now consists of two protons, so there are no protons which aren't enclosed in an orbital. Again, there are nodes in each carbon, but also a node in the metal center, with orbitals now also covering the metal center. This results in there being strong antibonding interactions over almost the entire molecule, with (+) interacting with (-) almost over the entire surface of every orbital. Through-space interactions are now back with there being two protons in each orbital, making it possible for these to interact, and there is also the potential for protons and metal center to interact as well. This orbital is only slightly higher energy than the previous one, and this is solely because of the increased degree of antibonding interactions present.
|}

== NBO charge distributions ==

NBO charge distributions were calculated from the checkpoint file for a range of -1.750 to 1.750 as this ensured the range of charges for all 3 complexes could be accommodated on the same scale. The charges are as follows:

{| class="wikitable" border="1"
! Complex !! Metal charge (e) !! Carbon charge (e) !! Proton charge (e)
|-
| [P(NH3)4]+ || 1.667 || -1.060 || 0.298
|-
| [N(NH3)4]+ || 0.917 || -0.846 || 0.297
|-
| [S(NH3)3]+ || -0.295 || -0.483 || 0.269
|}

<gallery>
File:Pk-nbo-n.png|Nitrogen complex
File:Pk-nbo-p.png|Phosphorous complex
File:Pk-nbo-s.png|Sulphur complex
</gallery>

There appears to be a slight trend of the metal centre charge with electronegativity, with the charge much lower as it becomes more electronegative (and hence drawing a greater share of electrons to it). This in turn makes the carbon more positive as electron density is removed from it. The protons remain rather positively charged and do not appear to be greatly affected by the metal centre, but this is likely because they are too far away for the inductive effect to occur.

Interestingly, nitrogen is more eletronegative than sulphur, yet sulphur has a greater negative charge. The reduced degree of polarisation in the bond for the nitrogen complex also suggests why the bond length for the nitrogen complex is shorter compared to the sulphur. The reason for this increased amount of negative charge is due to the lone pair present on sulphur (hence the configuration it takes according to the Jmol clip above), and so there is simply more negative charge present on the sulphur.

Thus, for the general complex [NR4]+, the positive charge located on the nitrogen in the picture is indeed located on the nitrogen, however it is somewhat delocalised over the protons too. As the nitrogen contains the greatest degree of positive charge, though, the + sign is conventionally placed here as it gives the indication as to where most of the charge is.

Analysis of the log files show the exact NBO contributions to the bond:

'''[P(NH3)3]+'''
<pre>
1. (1.98031) BD ( 1) P 1 - C 2
( 40.43%) 0.6358* P 1 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.4030 0.0006 0.0000 -0.4429
0.0006 0.0000 0.6188 -0.0009 0.0385
-0.0538 -0.0591 -0.0036 0.0254
( 59.57%) 0.7718* C 2 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.4044
-0.0074 0.4444 -0.0081 -0.6209 0.0114
0.0121 -0.0169 -0.0186 -0.0011 0.0080
</pre>

This shows almost equal contribution from each atom to the bond, with each atom assuming a sp3 arrangement as is expected by the TD symmetry. Carbon is sp3 as expected due to its saturation. As the carbon is slightly more negatively charged according to the charge distributions, the marginal increase in contribution from the carbon vs the phosphorous agrees with the charge distribution seen.

'''[N(NH3)3]+'''
<pre>
4. (1.98452) BD ( 1) C 1 - N 13
( 33.65%) 0.5801* C 1 s( 20.77%)p 3.81( 79.06%)d 0.01( 0.16%)
0.0003 0.4552 -0.0237 0.0026 -0.5129
-0.0218 -0.5129 -0.0218 -0.5129 -0.0218
0.0234 0.0234 0.0234 0.0000 0.0000
( 66.35%) 0.8146* N 13 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 0.5000 -0.0007 0.0000 0.4999
-0.0001 0.4999 -0.0001 0.4999 -0.0001
0.0103 0.0103 0.0103 0.0000 0.0000
</pre>

A similar argument can be made here. The large contribution from the nitrogen is surprising, but considering the smaller bond length for this complex based on the metal, an increased contribution from the nitrogen is not unreasonable. However this does disagree somewhat with the charge distribution which shows there is a much larger electron density on the carbon. It is thus thought that since it is possible to reach orbitals closer to the core on nitrogen rather than phosphorous, it makes nitrogen able to donate a greater share of electrons, and so polarises the bond towards it as a result of its electronegativity.

'''[S(NH3)3]+'''
<pre>
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
-0.0003 -0.4437 -0.0140 0.0033 0.7546
-0.0059 0.3161 -0.0025 0.3634 0.0098
-0.0189 -0.0222 -0.0093 -0.0186 0.0096
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 -0.0001 -0.4117 0.0075 -0.0012
0.0000 -0.7489 0.0330 0.0000 -0.3137
0.0138 0.0000 -0.4037 -0.0260 -0.0353
-0.0572 -0.0240 -0.0347 0.0051
</pre>

Finally, for the sulphur, the bond is an almost equal contribution from each atom in the bond. The charges of the S and C atoms according to the charge distribution are both similar and negative, suggesting little polarisation in this bond, and so the balance seen here is to be expected.

= Ligand influences on nitrogen metal centre complexes =
To investigate how changes to the ligands affects the cation, two variants on the nitrogen complex analysed previously have been used. One has one of the protons on a methyl ligand replaced with CH2OH, the other has the proton replaced with CH2CN. Each complex is then optimised and subject to a frequency analysis so as to allow for investigation of its structure. A MO and NBO calculation is then subsequently run to analyse how the change in ligand affects the ions electronic behaviour.

== Optimisations ==
Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26206}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26207}}

=== Summary output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
File Name nch33ch2oh_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000102 a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 1 hours 22 minutes 37.5 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
File Name nch33ch2cn_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000045 a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 50 minutes 39.5 seconds.
</pre>

=== Convergence output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000034 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-5.591936D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000011 0.000040 YES
Predicted change in Energy=-2.269581D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==

Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26290}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26291}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000106 a.u.
Imaginary Freq 0
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 26 minutes 10.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000102 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-5.078379D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000059 a.u.
Imaginary Freq 0
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 29 minutes 19.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-6.144746D-12
Optimization completed.
-- Stationary point found.
</pre>

=== Vibrational modes ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2oh_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

'''[N(CH3)3(CH2CN)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2cn_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== MO and NBO calculations ==
<code>pop=(nbo,full)</code> energy calculations were then performed on the complexes to generate MOs and NBO charge diagrams, just as has been done previously. All calculations were performed on the HPC and log files are available as follows:

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26294}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26295}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 59.3 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 25.0 seconds.
</pre>

=== Sample MOs ===

{| class="wikitable" border="1"
! !! [N(CH3)3(CH2OH)]+ !!
[N(CH3)3(CH2CN)]+
|-
| HOMO || [[Image:Pk-homo-oh.png|200px]] || [[Image:Pk-homo-cn.png|200px]]
|-
| LUMO || [[Image:Pk-lumo-oh.png|200px]] || [[Image:Pk-lumo-cn.png|200px]]
|-
| HOMO Energy (hartree) || -0.48763 || -0.50047
|-
| LUMO Energy (hartree) || -0.12459 || -0.18183
|}

=== NBO energy distributions ===

=== Discussion ===

== Ligand influence on structure ==

== Ligand influence on charge distribution ==

== Ligand influence on molecular orbitals ==

= References =
<references />

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T13:10:53Z

Pk1811: /* NBO charge distributions */

<div style="font-size: 40px;"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px;"><center>Ionic liquids: Designer solvents</center></div>
 
= Introduction =
The aim of this project is to explore the physical nature of ionic liquids, which have application in designing solvents through customisation of the nature of the cation and anion<ref name="abs">M. Freemantle. ''Chem. Eng. News'', 1998, '''76''', 32–37</ref>. In this work, a variety of cations have been investigated to identify what trends are present in the variation in central atom and its ligands.

= Structures of methyl-ligand complexes =
== Optimisations ==
A number of cations have been optimised using Gaussian 09 D.01, namely [N(CH3)4]+, [P(CH3)4]+ and [F(CH3)3]+. All these complexes have been optimised to a DFT B3LYP 6-31G(d,p) level with the <code>int=ultrafine scf=conver=9</code> keywords and tight convergence - this is as a consequence of behaviour seen in previous work<ref name="labintro">P. Kent, unpublished work ([[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|lab intro]])</ref> where low frequencies did not exist within a tight range unless these keywords were specified. All calculations were run on the supplied laptop due to a significant queue of jobs on the HPC (except for [S(CH3)3]+ as it took a very long time), and the log files are available here:

* [N(CH3)4]+: [[media:Pk_log_nch34_opt.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_opt.log]]
* [S(CH3)3]+: The first attempt did not converge: {{DOI|10042/26201}}. A partially optimised structure was resubmitted as a second attempt: {{DOI|10042/26205}}. This also did not converge so a final optimisation was run on this partially optimised structure with the <code>nosymm</code> keyword. This converged: {{DOI|10042/26214}}.

Once done, convergence was verified via inspection of the log file.

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name nch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000090 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 1 minutes 27.0 seconds.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name pch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701126 a.u.
RMS Gradient Norm 0.00000675 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 24 minutes 21.0 seconds.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_opt3
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000101 a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 52.2 seconds.
</pre>

=== Convergence outputs ===

''' [N(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000014 0.000060 YES
RMS Displacement 0.000005 0.000040 YES
Predicted change in Energy=-1.010077D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000015 YES
RMS Force 0.000005 0.000010 YES
Maximum Displacement 0.000026 0.000060 YES
RMS Displacement 0.000009 0.000040 YES
Predicted change in Energy=-1.723206D-06
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''

Initial failed optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000015 NO
RMS Force 0.000006 0.000010 YES
Maximum Displacement 0.002915 0.000060 NO
RMS Displacement 0.000869 0.000040 NO
Predicted change in Energy=-5.685776D-09
Optimization stopped.
-- Number of steps exceeded, NStep= 61
-- Flag reset to prevent archiving.
</pre>

During this failed optimisation, it appears the molecule just spent a large amount of time rotating around the C3 axis through the sulphur.

The final optimisation yielded:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000049 0.000060 YES
RMS Displacement 0.000018 0.000040 YES
Predicted change in Energy=-6.520157D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==
Following this, frequency analysis was conducted with the same keywords and calculation level to ensure a minima has been found. This is ensured by checking there are no negative vibrations in the molecule. Calculations were again run on the laptop, and the log files, summaries, and frequencies are listed below. Actual animations of the modes have not been exported, however a Jmol of the log file is available and the modes can be seen by right clicking and choosing '''model -> the mode you want to see'''. This time, a range of
-30 to +30 cm-1 has been accepted for the low frequencies as molecules investigated are quite complex, and a relatively simple basis set has been used. Optimising to 6-311G(d,p) would likely bring the frequencies within the range used previously however this would be at the expense of much longer computation times.

* [N(CH3)4]+: [[media:Pk_log_nch34_freq.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_freq.log]]
* [S(CH3)3]+: {{DOI|10042/26273}}

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name NCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000085 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 3 minutes 17.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000009 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.014288D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name PCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701149 a.u.
RMS Gradient Norm 0.00000668 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 12 minutes 11.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001774 0.001800 YES
RMS Displacement 0.000659 0.001200 YES
Predicted change in Energy=-3.008780D-08
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000104 a.u.
Imaginary Freq 0
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 9 minutes 6.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000093 0.001800 YES
RMS Displacement 0.000033 0.001200 YES
Predicted change in Energy=-7.179584D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Vibration modes ===

''' [N(CH3)4]+ '''
<pre>
Low frequencies --- 0.0007 0.0011 0.0013 21.5288 21.5288 21.5288
Low frequencies --- 188.5488 292.6546 292.6546
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [P(CH3)4]+ '''
<pre>
Low frequencies --- -15.1139 -0.0002 0.0012 0.0012 5.8940 14.7736
Low frequencies --- 156.2222 191.5376 191.9513
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_pch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [S(CH3)3]+ '''
<pre>
Low frequencies --- -8.5871 0.0029 0.0049 0.0051 5.7111 9.1755
Low frequencies --- 162.4159 200.3446 200.5391
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_sch33_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== Conclusions on molecular structure ==
Investigation of structures is focused on the central atom as this is the only point at which variance should occur. The length of the M-C bonds and the angle between C-M-C on each complex is reported below:

{| class="wikitable" border="1"
! Complex !! M-C Length (Å) !! Angle (°) !! M-C length (lit<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref>) (Å)
|-
| [P(CH3)4]+ || 1.82 || 109.5 || 1.84
|-
| [N(CH3)4]+ || 1.51 || 109.5 || 1.46
|-
| [S(CH3)3]+ || 1.82 || 102.7 || 1.79
|}

''Literature bond lengths are found by adding the covalent radii for the atoms.''

Two key trends are:
* As you go down a group, the bond length decreases
* As you go across a group (so losing a ligand), the bond angle is reduced)

The first trend is straightforward to explain, as bond lengths increase down the group. This is in tandem with the increase in atomic radius down the group as orbitals in a greater shell begin to be filled. Thus, as you move from period 2 (N) to period 3 (P), the length of the bond increases and is in turn the overall size of each ion. There is slight variance in the length of a C-H bond in each complex, however no pattern is immediately discernible (it increases in the order S > P > N) - it is thought this is just some random error in the calculation.

Whilst there is an increase in bond length, there is no change in orientation of the bonds, thus the symmetry of TD is maintained in both the phosphorous and nitrogen molecules. As a result of this, the bond angle is the same for these two complexes. No other arrangement of the ligands is sterically possible, so ensuring that this symmetry label cannot be changed, and therefore the bond angle also cannot change. The bond angle is different for sulphur, as a result of the change of symmetry to C3v, it is not known if the change in metal centre contributes to this change - further investigation would be required.

Of note, the bond length does not appear to change going across the period. There is actually a small increase of 0.01Å if the bond length is reported accurate to 0.001Å, however it is not known if this is just an inherent error in the calculation or not. In any event, it is expected that there is a slight decrease in the bond length as you move towards the right of a period, as the increased nuclear charge better shields the electrons and thus shortens the bond length, but this is not observed here. This may be a result of this complex containing one less ligand, with the arrangement instead taken (along with the lone pair) resulting in some interactions (steric or electronic repulsion) which causes the carbon and metal atoms to move apart from each other. This theory is supported by the large deviation from bond length for the sulphur complex, indicating some feature about the arrangement it has taken is causing the bond length to be artificially lengthened.

Otherwise no strange observations are seen with the structures, with all methyl groups taking the expected tetrahedral structure, and either tetrahedral or C3v structures for the central atom as expected by the number of ligands which are present.

= Molecular orbitals and NBO charges of methyl-ligand complexes =
All three complexes discussed previously have been subject to a full NBO and MO analysis via an energy calculation with the <code>pop=(full,nbo)</code> keyword, retaining any previously used keywords as appropriate. Calculations were performed on the laptop due to load on the HPC, except for the sulphur complex as the calculation took too long on the laptop.

Log files are available as follows:

* '''[N(CH3)4]+''': [[media:Pk_log_nch34_egy.log]]
* '''[P(CH3)4]+''': [[media:Pk_log_pch34_egy.log]]
* '''[S(CH3)3]+''': {{DOI|10042/26274}}
== Calculation output ==

''' [N(CH3)4]+ '''

<pre>
File Name NCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

''' [P(CH3)4]+ '''

<pre>
File Name PCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701105 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 20.0 seconds.
</pre>

''' [S(CH3)3]+ '''

<pre>File Name sch33_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 0 minutes 57.7 seconds.
</pre>

== Sample MOs for [N(CH3)4]+ ==
A variety of 5 molecular orbitals have been calculated and shown below. Only occupied non-core MOs from the totally bonding to totally antibonding are shown.

{| class="wikitable" border="1"
|+ Totally bonding towards the top
! MO number !! Energy (hartree) !! Picture !! Degeneracy !! Notes
|-
| 6 || -1.19645 || [[Image:Pk-n-mo0.png|200px]] || Singly degenerate || This MO exhibits a great degree of strong bonding interactions across the entire molecule up to the protons, the orbitals of which do not appear to be part of this MO. This is seen by the huge red surface containing almost the entirety of the molecule. As a result of the huge amount of delocalisation seen in the MO, there is a lot of through space interactions between adjacent carbon groups, as seen by how the MO forms a 'cage' around the entire molecule - the empty space between two carbon atoms is part of this red object. As there are no other molecular orbitals other than this huge one, there is no concept of a node in this MO diagram.
|-
| 10 || -0.80745 || [[Image:Pk-n-mo1.png|200px]] || Singly degenerate || This is the first MO in this series of 5 to contain a slight degree of antibonding character, as seen by the fact each ligand is in its own (+) phase orbital, whereas the central metal is in a (-) phase one. This leads to a minor degree of antibonding character, and also a node in the centre of the M-C bond where the two MOs end. Through space interactions are present in each ligand MO, with all the protons and the central carbon existing within the boundaries of the MO, and hence there are through-space interactions between the protons. MOs of the same phase interact weakly with each other due to the large distance between each green orbital (seen in the picture), however the interaction between the (+) and (-) orbitals is quite strong as the nodal area is very small in size - the orbitals are nearly touching. The level of delocalisation is reduced, with delocalisation only occurring across each ligand group - the ligands themselves are not delocalised onto one unit.
|-
| 14 || -0.62248 || [[Image:Pk-n-mo2.png|200px]] || Doubly degenerate || For this MO, nodes exist on every carbon atom, as each MO covers two halves of a carbon atom, two protons, and nothing else. This does lead to delocalisationa cross the protons and carbon atoms, however this also does result in strong antibonding interactions at each carbon as the (+) and (-) MOs become quite close. Some protons, and the metal centre are not covered at all by this MO, however from what is delocalised, there is a significant amount of through space interactions between protons on differing methyl ligands - this is of note as the ligand protons are quite a distance away. There may be some weak bonding interactions between orbitals of the same phase, however they are quite a distance away (separated by the metal centre) so this is expected to be quite weak.
|-
| 17 || -0.58035 || [[Image:Pk-n-mo3.png|200px]] || Triply degenerate || This one again has a node on each carbon, however it differs in that each orbital only covers a single proton and half a carbon. This results in there being no through-space interactions in this molecule. Additionally, there are many strong antibonding interactions as all the orbitals are quite close together, with the a (+) orbital being surrounded by a (-) orbital on every side. If there are any bonding interactions, these are going to be very weak.
|-
| 21 || -0.57934 || [[Image:Pk-n-mo4.png|200px]] || Triply degenerate || This MO is similar to the previous, but differs in that each orbital now consists of two protons, so there are no protons which aren't enclosed in an orbital. Again, there are nodes in each carbon, but also a node in the metal center, with orbitals now also covering the metal center. This results in there being strong antibonding interactions over almost the entire molecule, with (+) interacting with (-) almost over the entire surface of every orbital. Through-space interactions are now back with there being two protons in each orbital, making it possible for these to interact, and there is also the potential for protons and metal center to interact as well. This orbital is only slightly higher energy than the previous one, and this is solely because of the increased degree of antibonding interactions present.
|}

== NBO charge distributions ==

NBO charge distributions were calculated from the checkpoint file for a range of -1.750 to 1.750 as this ensured the range of charges for all 3 complexes could be accommodated on the same scale. The charges are as follows:

{| class="wikitable" border="1"
! Complex !! Metal charge (e) !! Carbon charge (e) !! Proton charge (e)
|-
| [P(NH3)4]+ || 1.667 || -1.060 || 0.298
|-
| [N(NH3)4]+ || 0.917 || -0.846 || 0.297
|-
| [S(NH3)3]+ || -0.295 || -0.483 || 0.269
|}

<gallery>
File:Pk-nbo-n.png|Nitrogen complex
File:Pk-nbo-p.png|Phosphorous complex
File:Pk-nbo-s.png|Sulphur complex
</gallery>

There appears to be a slight trend of the metal centre charge with electronegativity, with the charge much lower as it becomes more electronegative (and hence drawing a greater share of electrons to it). This in turn makes the carbon more positive as electron density is removed from it. The protons remain rather positively charged and do not appear to be greatly affected by the metal centre, but this is likely because they are too far away for the inductive effect to occur.

Interestingly, nitrogen is more eletronegative than sulphur, yet sulphur has a greater negative charge. The reduced degree of polarisation in the bond for the nitrogen complex also suggests why the bond length for the nitrogen complex is shorter compared to the sulphur. The reason for this increased amount of negative charge is due to the lone pair present on sulphur (hence the configuration it takes according to the Jmol clip above), and so there is simply more negative charge present on the sulphur.

Thus, for the general complex [NR4]+, the positive charge located on the nitrogen in the picture is indeed located on the nitrogen, however it is somewhat delocalised over the protons too. As the nitrogen contains the greatest degree of positive charge, though, the + sign is conventionally placed here as it gives the indication as to where most of the charge is.

Analysis of the log files show the exact NBO contributions to the bond:

'''[P(NH3)3]+'''
<pre>
1. (1.98031) BD ( 1) P 1 - C 2
( 40.43%) 0.6358* P 1 s( 25.00%)p 2.97( 74.15%)d 0.03( 0.85%)
0.0000 0.0001 0.5000 -0.0008 0.0000
0.0000 -0.4030 0.0006 0.0000 -0.4429
0.0006 0.0000 0.6188 -0.0009 0.0385
-0.0538 -0.0591 -0.0036 0.0254
( 59.57%) 0.7718* C 2 s( 25.24%)p 2.96( 74.67%)d 0.00( 0.08%)
0.0002 0.5021 0.0171 -0.0020 0.4044
-0.0074 0.4444 -0.0081 -0.6209 0.0114
0.0121 -0.0169 -0.0186 -0.0011 0.0080
</pre>

This shows almost equal contribution from each atom to the bond, with each atom assuming a sp3 arrangement as is expected by the TD symmetry. Carbon is sp3 as expected due to its saturation. As the carbon is slightly more negatively charged according to the charge distributions, the marginal increase in contribution from the carbon vs the phosphorous agrees with the charge distribution seen.

'''[N(NH3)3]+'''
<pre>
4. (1.98452) BD ( 1) C 1 - N 13
( 33.65%) 0.5801* C 1 s( 20.77%)p 3.81( 79.06%)d 0.01( 0.16%)
0.0003 0.4552 -0.0237 0.0026 -0.5129
-0.0218 -0.5129 -0.0218 -0.5129 -0.0218
0.0234 0.0234 0.0234 0.0000 0.0000
( 66.35%) 0.8146* N 13 s( 25.00%)p 3.00( 74.97%)d 0.00( 0.03%)
0.0000 0.5000 -0.0007 0.0000 0.4999
-0.0001 0.4999 -0.0001 0.4999 -0.0001
0.0103 0.0103 0.0103 0.0000 0.0000
</pre>

A similar argument can be made here. The large contribution from the nitrogen is surprising, but considering the smaller bond length for this complex based on the metal, an increased contribution from the nitrogen is not unreasonable. However this does disagree somewhat with the charge distribution which shows there is a much larger electron density on the carbon. It is thus thought that since it is possible to reach orbitals closer to the core on nitrogen rather than phosphorous, it makes nitrogen able to donate a greater share of electrons, and so polarises the bond towards it as a result of its electronegativity.

'''[S(NH3)3]+'''
<pre>
4. (1.98631) BD ( 1) C 1 - S 13
( 48.67%) 0.6976* C 1 s( 19.71%)p 4.07( 80.16%)d 0.01( 0.14%)
-0.0003 -0.4437 -0.0140 0.0033 0.7546
-0.0059 0.3161 -0.0025 0.3634 0.0098
-0.0189 -0.0222 -0.0093 -0.0186 0.0096
( 51.33%) 0.7165* S 13 s( 16.95%)p 4.86( 82.42%)d 0.04( 0.63%)
0.0000 -0.0001 -0.4117 0.0075 -0.0012
0.0000 -0.7489 0.0330 0.0000 -0.3137
0.0138 0.0000 -0.4037 -0.0260 -0.0353
-0.0572 -0.0240 -0.0347 0.0051
</pre>

Finally, for the sulphur, the bond is an almost equal contribution from each atom in the bond. The charges of the S and C atoms according to the charge distribution are both similar and negative, suggesting little polarisation in this bond, and so the balance seen here is to be expected.

= Ligand influences on nitrogen metal centre complexes =
To investigate how changes to the ligands affects the cation, two variants on the nitrogen complex analysed previously have been used. One has one of the protons on a methyl ligand replaced with CH2OH, the other has the proton replaced with CH2CN. Each complex is then optimised and subject to a frequency analysis so as to allow for investigation of its structure. A MO and NBO calculation is then subsequently run to analyse how the change in ligand affects the ions electronic behaviour.

== Optimisations ==
Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26206}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26207}}

=== Summary output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
File Name nch33ch2oh_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000102 a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 1 hours 22 minutes 37.5 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
File Name nch33ch2cn_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000045 a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 50 minutes 39.5 seconds.
</pre>

=== Convergence output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000034 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-5.591936D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000011 0.000040 YES
Predicted change in Energy=-2.269581D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==

Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26290}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26291}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000106 a.u.
Imaginary Freq 0
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 26 minutes 10.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000102 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-5.078379D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000059 a.u.
Imaginary Freq 0
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 29 minutes 19.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-6.144746D-12
Optimization completed.
-- Stationary point found.
</pre>

=== Vibrational modes ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2oh_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

'''[N(CH3)3(CH2CN)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2cn_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== MO and NBO calculations ==
<code>pop=(nbo,full)</code> energy calculations were then performed on the complexes to generate MOs and NBO charge diagrams, just as has been done previously. All calculations were performed on the HPC and log files are available as follows:

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26294}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26295}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 59.3 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 25.0 seconds.
</pre>

=== Sample MOs ===

{| class="wikitable" border="1"
! !! [N(CH3)3(CH2OH)]+ !!
[N(CH3)3(CH2CN)]+
|-
| HOMO || cell
|-
| LUMO || cell
|-
| HOMO Energy ||
|-
| LUMO Energy ||
|}

=== NBO energy distributions ===

=== Discussion ===

== Ligand influence on structure ==

== Ligand influence on charge distribution ==

== Ligand influence on molecular orbitals ==

= References =
<references />

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T12:18:46Z

Pk1811: /* Summary outputs */

<div style="font-size: 40px;"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px;"><center>Ionic liquids: Designer solvents</center></div>
 
= Introduction =
The aim of this project is to explore the physical nature of ionic liquids, which have application in designing solvents through customisation of the nature of the cation and anion<ref name="abs">M. Freemantle. ''Chem. Eng. News'', 1998, '''76''', 32–37</ref>. In this work, a variety of cations have been investigated to identify what trends are present in the variation in central atom and its ligands.

= Structures of methyl-ligand complexes =
== Optimisations ==
A number of cations have been optimised using Gaussian 09 D.01, namely [N(CH3)4]+, [P(CH3)4]+ and [F(CH3)3]+. All these complexes have been optimised to a DFT B3LYP 6-31G(d,p) level with the <code>int=ultrafine scf=conver=9</code> keywords and tight convergence - this is as a consequence of behaviour seen in previous work<ref name="labintro">P. Kent, unpublished work ([[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|lab intro]])</ref> where low frequencies did not exist within a tight range unless these keywords were specified. All calculations were run on the supplied laptop due to a significant queue of jobs on the HPC (except for [S(CH3)3]+ as it took a very long time), and the log files are available here:

* [N(CH3)4]+: [[media:Pk_log_nch34_opt.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_opt.log]]
* [S(CH3)3]+: The first attempt did not converge: {{DOI|10042/26201}}. A partially optimised structure was resubmitted as a second attempt: {{DOI|10042/26205}}. This also did not converge so a final optimisation was run on this partially optimised structure with the <code>nosymm</code> keyword. This converged: {{DOI|10042/26214}}.

Once done, convergence was verified via inspection of the log file.

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name nch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000090 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 1 minutes 27.0 seconds.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name pch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701126 a.u.
RMS Gradient Norm 0.00000675 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 24 minutes 21.0 seconds.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_opt3
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000101 a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 52.2 seconds.
</pre>

=== Convergence outputs ===

''' [N(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000014 0.000060 YES
RMS Displacement 0.000005 0.000040 YES
Predicted change in Energy=-1.010077D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000015 YES
RMS Force 0.000005 0.000010 YES
Maximum Displacement 0.000026 0.000060 YES
RMS Displacement 0.000009 0.000040 YES
Predicted change in Energy=-1.723206D-06
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''

Initial failed optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000015 NO
RMS Force 0.000006 0.000010 YES
Maximum Displacement 0.002915 0.000060 NO
RMS Displacement 0.000869 0.000040 NO
Predicted change in Energy=-5.685776D-09
Optimization stopped.
-- Number of steps exceeded, NStep= 61
-- Flag reset to prevent archiving.
</pre>

During this failed optimisation, it appears the molecule just spent a large amount of time rotating around the C3 axis through the sulphur.

The final optimisation yielded:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000049 0.000060 YES
RMS Displacement 0.000018 0.000040 YES
Predicted change in Energy=-6.520157D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==
Following this, frequency analysis was conducted with the same keywords and calculation level to ensure a minima has been found. This is ensured by checking there are no negative vibrations in the molecule. Calculations were again run on the laptop, and the log files, summaries, and frequencies are listed below. Actual animations of the modes have not been exported, however a Jmol of the log file is available and the modes can be seen by right clicking and choosing '''model -> the mode you want to see'''. This time, a range of
-30 to +30 cm-1 has been accepted for the low frequencies as molecules investigated are quite complex, and a relatively simple basis set has been used. Optimising to 6-311G(d,p) would likely bring the frequencies within the range used previously however this would be at the expense of much longer computation times.

* [N(CH3)4]+: [[media:Pk_log_nch34_freq.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_freq.log]]
* [S(CH3)3]+: {{DOI|10042/26273}}

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name NCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000085 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 3 minutes 17.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000009 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.014288D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name PCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701149 a.u.
RMS Gradient Norm 0.00000668 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 12 minutes 11.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001774 0.001800 YES
RMS Displacement 0.000659 0.001200 YES
Predicted change in Energy=-3.008780D-08
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000104 a.u.
Imaginary Freq 0
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 9 minutes 6.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000093 0.001800 YES
RMS Displacement 0.000033 0.001200 YES
Predicted change in Energy=-7.179584D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Vibration modes ===

''' [N(CH3)4]+ '''
<pre>
Low frequencies --- 0.0007 0.0011 0.0013 21.5288 21.5288 21.5288
Low frequencies --- 188.5488 292.6546 292.6546
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [P(CH3)4]+ '''
<pre>
Low frequencies --- -15.1139 -0.0002 0.0012 0.0012 5.8940 14.7736
Low frequencies --- 156.2222 191.5376 191.9513
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_pch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [S(CH3)3]+ '''
<pre>
Low frequencies --- -8.5871 0.0029 0.0049 0.0051 5.7111 9.1755
Low frequencies --- 162.4159 200.3446 200.5391
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_sch33_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== Conclusions on molecular structure ==
Investigation of structures is focused on the central atom as this is the only point at which variance should occur. The length of the M-C bonds and the angle between C-M-C on each complex is reported below:

{| class="wikitable" border="1"
! Complex !! M-C Length (Å) !! Angle (°) !! M-C length (lit<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref>) (Å)
|-
| [P(CH3)4]+ || 1.82 || 109.5 || 1.84
|-
| [N(CH3)4]+ || 1.51 || 109.5 || 1.46
|-
| [S(CH3)3]+ || 1.82 || 102.7 || 1.79
|}

''Literature bond lengths are found by adding the covalent radii for the atoms.''

Two key trends are:
* As you go down a group, the bond length decreases
* As you go across a group (so losing a ligand), the bond angle is reduced)

The first trend is straightforward to explain, as bond lengths increase down the group. This is in tandem with the increase in atomic radius down the group as orbitals in a greater shell begin to be filled. Thus, as you move from period 2 (N) to period 3 (P), the length of the bond increases and is in turn the overall size of each ion. There is slight variance in the length of a C-H bond in each complex, however no pattern is immediately discernible (it increases in the order S > P > N) - it is thought this is just some random error in the calculation.

Whilst there is an increase in bond length, there is no change in orientation of the bonds, thus the symmetry of TD is maintained in both the phosphorous and nitrogen molecules. As a result of this, the bond angle is the same for these two complexes. No other arrangement of the ligands is sterically possible, so ensuring that this symmetry label cannot be changed, and therefore the bond angle also cannot change. The bond angle is different for sulphur, as a result of the change of symmetry to C3v, it is not known if the change in metal centre contributes to this change - further investigation would be required.

Of note, the bond length does not appear to change going across the period. There is actually a small increase of 0.01Å if the bond length is reported accurate to 0.001Å, however it is not known if this is just an inherent error in the calculation or not. In any event, it is expected that there is a slight decrease in the bond length as you move towards the right of a period, as the increased nuclear charge better shields the electrons and thus shortens the bond length, but this is not observed here. This may be a result of this complex containing one less ligand, with the arrangement instead taken (along with the lone pair) resulting in some interactions (steric or electronic repulsion) which causes the carbon and metal atoms to move apart from each other. This theory is supported by the large deviation from bond length for the sulphur complex, indicating some feature about the arrangement it has taken is causing the bond length to be artificially lengthened.

Otherwise no strange observations are seen with the structures, with all methyl groups taking the expected tetrahedral structure, and either tetrahedral or C3v structures for the central atom as expected by the number of ligands which are present.

= Molecular orbitals and NBO charges of methyl-ligand complexes =
All three complexes discussed previously have been subject to a full NBO and MO analysis via an energy calculation with the <code>pop=(full,nbo)</code> keyword, retaining any previously used keywords as appropriate. Calculations were performed on the laptop due to load on the HPC, except for the sulphur complex as the calculation took too long on the laptop.

Log files are available as follows:

* '''[N(CH3)4]+''': [[media:Pk_log_nch34_egy.log]]
* '''[P(CH3)4]+''': [[media:Pk_log_pch34_egy.log]]
* '''[S(CH3)3]+''': {{DOI|10042/26274}}
== Calculation output ==

''' [N(CH3)4]+ '''

<pre>
File Name NCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

''' [P(CH3)4]+ '''

<pre>
File Name PCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701105 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 20.0 seconds.
</pre>

''' [S(CH3)3]+ '''

<pre>File Name sch33_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 0 minutes 57.7 seconds.
</pre>

== Sample MOs for [N(CH3)4]+ ==
A variety of 5 molecular orbitals have been calculated and shown below. Only occupied non-core MOs from the totally bonding to totally antibonding are shown.

{| class="wikitable" border="1"
|+ Totally bonding towards the top
! MO number !! Energy (hartree) !! Picture !! Degeneracy !! Notes
|-
| 6 || -1.19645 || [[Image:Pk-n-mo0.png|200px]] || Singly degenerate || This MO exhibits a great degree of strong bonding interactions across the entire molecule up to the protons, the orbitals of which do not appear to be part of this MO. This is seen by the huge red surface containing almost the entirety of the molecule. As a result of the huge amount of delocalisation seen in the MO, there is a lot of through space interactions between adjacent carbon groups, as seen by how the MO forms a 'cage' around the entire molecule - the empty space between two carbon atoms is part of this red object. As there are no other molecular orbitals other than this huge one, there is no concept of a node in this MO diagram.
|-
| 10 || -0.80745 || [[Image:Pk-n-mo1.png|200px]] || Singly degenerate || This is the first MO in this series of 5 to contain a slight degree of antibonding character, as seen by the fact each ligand is in its own (+) phase orbital, whereas the central metal is in a (-) phase one. This leads to a minor degree of antibonding character, and also a node in the centre of the M-C bond where the two MOs end. Through space interactions are present in each ligand MO, with all the protons and the central carbon existing within the boundaries of the MO, and hence there are through-space interactions between the protons. MOs of the same phase interact weakly with each other due to the large distance between each green orbital (seen in the picture), however the interaction between the (+) and (-) orbitals is quite strong as the nodal area is very small in size - the orbitals are nearly touching. The level of delocalisation is reduced, with delocalisation only occurring across each ligand group - the ligands themselves are not delocalised onto one unit.
|-
| 14 || -0.62248 || [[Image:Pk-n-mo2.png|200px]] || Doubly degenerate || For this MO, nodes exist on every carbon atom, as each MO covers two halves of a carbon atom, two protons, and nothing else. This does lead to delocalisationa cross the protons and carbon atoms, however this also does result in strong antibonding interactions at each carbon as the (+) and (-) MOs become quite close. Some protons, and the metal centre are not covered at all by this MO, however from what is delocalised, there is a significant amount of through space interactions between protons on differing methyl ligands - this is of note as the ligand protons are quite a distance away. There may be some weak bonding interactions between orbitals of the same phase, however they are quite a distance away (separated by the metal centre) so this is expected to be quite weak.
|-
| 17 || -0.58035 || [[Image:Pk-n-mo3.png|200px]] || Triply degenerate || This one again has a node on each carbon, however it differs in that each orbital only covers a single proton and half a carbon. This results in there being no through-space interactions in this molecule. Additionally, there are many strong antibonding interactions as all the orbitals are quite close together, with the a (+) orbital being surrounded by a (-) orbital on every side. If there are any bonding interactions, these are going to be very weak.
|-
| 21 || -0.57934 || [[Image:Pk-n-mo4.png|200px]] || Triply degenerate || This MO is similar to the previous, but differs in that each orbital now consists of two protons, so there are no protons which aren't enclosed in an orbital. Again, there are nodes in each carbon, but also a node in the metal center, with orbitals now also covering the metal center. This results in there being strong antibonding interactions over almost the entire molecule, with (+) interacting with (-) almost over the entire surface of every orbital. Through-space interactions are now back with there being two protons in each orbital, making it possible for these to interact, and there is also the potential for protons and metal center to interact as well. This orbital is only slightly higher energy than the previous one, and this is solely because of the increased degree of antibonding interactions present.
|}

== NBO charge distributions ==

NBO charge distributions were calculated from the checkpoint file for a range of -1.750 to 1.750 as this ensured the range of charges for all 3 complexes could be accommodated on the same scale. The charges are as follows:

{| class="wikitable" border="1"
! Complex !! Metal charge (e) !! Carbon charge (e) !! Proton charge (e)
|-
| P || 1.667 || -1.060 || 0.298
|-
| N || 0.917 || -0.846 || 0.297
|-
| S || -0.295 || -0.483 || 0.269
|}

<gallery>
File:Pk-nbo-n.png|Nitrogen complex
File:Pk-nbo-p.png|Phosphorous complex
File:Pk-nbo-s.png|Sulphur complex
</gallery>

There appears to be a slight trend of the metal centre charge with electronegativity, with the charge much lower as it becomes more electronegative (and hence drawing a greater share of electrons to it). This in turn makes the carbon more positive as electron density is removed from it. The protons remain rather positively charged and do not appear to be greatly affected by the metal centre, but this is likely because they are too far away for the inductive effect to occur.

Interestingly, nitrogen is more eletronegative than sulphur, yet sulphur has a greater negative charge. The reduced degree of polarisation in the bond for the nitrogen complex also suggests why the bond length for the nitrogen complex is shorter compared to the sulphur. The reason for this increased amount of negative charge is due to the lone pair present on sulphur (hence the configuration it takes according to the Jmol clip above), and so there is simply more negative charge present on the sulphur.

Thus, for the general complex [NR4]+, the positive charge located on the nitrogen in the picture is indeed located on the nitrogen, however it is somewhat delocalised over the protons too. As the nitrogen contains the greatest degree of positive charge, though, the + sign is conventionally placed here as it gives the indication as to where most of the charge is.

= Ligand influences on nitrogen metal centre complexes =
To investigate how changes to the ligands affects the cation, two variants on the nitrogen complex analysed previously have been used. One has one of the protons on a methyl ligand replaced with CH2OH, the other has the proton replaced with CH2CN. Each complex is then optimised and subject to a frequency analysis so as to allow for investigation of its structure. A MO and NBO calculation is then subsequently run to analyse how the change in ligand affects the ions electronic behaviour.

== Optimisations ==
Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26206}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26207}}

=== Summary output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
File Name nch33ch2oh_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000102 a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 1 hours 22 minutes 37.5 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
File Name nch33ch2cn_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000045 a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 50 minutes 39.5 seconds.
</pre>

=== Convergence output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000034 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-5.591936D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000011 0.000040 YES
Predicted change in Energy=-2.269581D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==

Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26290}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26291}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000106 a.u.
Imaginary Freq 0
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 26 minutes 10.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000102 0.001800 YES
RMS Displacement 0.000029 0.001200 YES
Predicted change in Energy=-5.078379D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000059 a.u.
Imaginary Freq 0
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 29 minutes 19.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000065 0.001800 YES
RMS Displacement 0.000019 0.001200 YES
Predicted change in Energy=-6.144746D-12
Optimization completed.
-- Stationary point found.
</pre>

=== Vibrational modes ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2oh_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

'''[N(CH3)3(CH2CN)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2cn_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== MO and NBO calculations ==
<code>pop=(nbo,full)</code> energy calculations were then performed on the complexes to generate MOs and NBO charge diagrams, just as has been done previously. All calculations were performed on the HPC and log files are available as follows:

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26294}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26295}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 59.3 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 25.0 seconds.
</pre>

=== Sample MOs ===

{| class="wikitable" border="1"
! !! [N(CH3)3(CH2OH)]+ !!
[N(CH3)3(CH2CN)]+
|-
| HOMO || cell
|-
| LUMO || cell
|-
| HOMO Energy ||
|-
| LUMO Energy ||
|}

=== NBO energy distributions ===

=== Discussion ===

== Ligand influence on structure ==

== Ligand influence on charge distribution ==

== Ligand influence on molecular orbitals ==

= References =
<references />

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T12:16:13Z

Pk1811: /* Summary outputs */

<div style="font-size: 40px;"><center>Philip Kent: Inorganic Computational Lab</center></div>
 
<div style="font-size: 30px;"><center>Ionic liquids: Designer solvents</center></div>
 
= Introduction =
The aim of this project is to explore the physical nature of ionic liquids, which have application in designing solvents through customisation of the nature of the cation and anion<ref name="abs">M. Freemantle. ''Chem. Eng. News'', 1998, '''76''', 32–37</ref>. In this work, a variety of cations have been investigated to identify what trends are present in the variation in central atom and its ligands.

= Structures of methyl-ligand complexes =
== Optimisations ==
A number of cations have been optimised using Gaussian 09 D.01, namely [N(CH3)4]+, [P(CH3)4]+ and [F(CH3)3]+. All these complexes have been optimised to a DFT B3LYP 6-31G(d,p) level with the <code>int=ultrafine scf=conver=9</code> keywords and tight convergence - this is as a consequence of behaviour seen in previous work<ref name="labintro">P. Kent, unpublished work ([[Mod:de403e6c-ea35-4dd5-aec1-fd7e3c51f158|lab intro]])</ref> where low frequencies did not exist within a tight range unless these keywords were specified. All calculations were run on the supplied laptop due to a significant queue of jobs on the HPC (except for [S(CH3)3]+ as it took a very long time), and the log files are available here:

* [N(CH3)4]+: [[media:Pk_log_nch34_opt.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_opt.log]]
* [S(CH3)3]+: The first attempt did not converge: {{DOI|10042/26201}}. A partially optimised structure was resubmitted as a second attempt: {{DOI|10042/26205}}. This also did not converge so a final optimisation was run on this partially optimised structure with the <code>nosymm</code> keyword. This converged: {{DOI|10042/26214}}.

Once done, convergence was verified via inspection of the log file.

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name nch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000090 a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 1 minutes 27.0 seconds.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name pch34_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701126 a.u.
RMS Gradient Norm 0.00000675 a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 24 minutes 21.0 seconds.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_opt3
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000101 a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 52.2 seconds.
</pre>

=== Convergence outputs ===

''' [N(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000014 0.000060 YES
RMS Displacement 0.000005 0.000040 YES
Predicted change in Energy=-1.010077D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000014 0.000015 YES
RMS Force 0.000005 0.000010 YES
Maximum Displacement 0.000026 0.000060 YES
RMS Displacement 0.000009 0.000040 YES
Predicted change in Energy=-1.723206D-06
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''

Initial failed optimisation:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000015 NO
RMS Force 0.000006 0.000010 YES
Maximum Displacement 0.002915 0.000060 NO
RMS Displacement 0.000869 0.000040 NO
Predicted change in Energy=-5.685776D-09
Optimization stopped.
-- Number of steps exceeded, NStep= 61
-- Flag reset to prevent archiving.
</pre>

During this failed optimisation, it appears the molecule just spent a large amount of time rotating around the C3 axis through the sulphur.

The final optimisation yielded:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000049 0.000060 YES
RMS Displacement 0.000018 0.000040 YES
Predicted change in Energy=-6.520157D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==
Following this, frequency analysis was conducted with the same keywords and calculation level to ensure a minima has been found. This is ensured by checking there are no negative vibrations in the molecule. Calculations were again run on the laptop, and the log files, summaries, and frequencies are listed below. Actual animations of the modes have not been exported, however a Jmol of the log file is available and the modes can be seen by right clicking and choosing '''model -> the mode you want to see'''. This time, a range of
-30 to +30 cm-1 has been accepted for the low frequencies as molecules investigated are quite complex, and a relatively simple basis set has been used. Optimising to 6-311G(d,p) would likely bring the frequencies within the range used previously however this would be at the expense of much longer computation times.

* [N(CH3)4]+: [[media:Pk_log_nch34_freq.log]]
* [P(CH3)4]+: [[media:Pk_log_pch34_freq.log]]
* [S(CH3)3]+: {{DOI|10042/26273}}

=== Summary outputs ===

''' [N(CH3)4]+ '''
<pre>
File Name NCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm 0.00000085 a.u.
Imaginary Freq 0
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 3 minutes 17.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000009 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
Predicted change in Energy=-1.014288D-10
Optimization completed.
-- Stationary point found.
</pre>

''' [P(CH3)4]+ '''
<pre>
File Name PCH34_FREQ
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701149 a.u.
RMS Gradient Norm 0.00000668 a.u.
Imaginary Freq 0
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 12 minutes 11.0 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001774 0.001800 YES
RMS Displacement 0.000659 0.001200 YES
Predicted change in Energy=-3.008780D-08
Optimization completed.
-- Stationary point found.
</pre>

''' [S(CH3)3]+ '''
<pre>
File Name sch33_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm 0.00000104 a.u.
Imaginary Freq 0
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 9 minutes 6.7 seconds.
</pre>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000093 0.001800 YES
RMS Displacement 0.000033 0.001200 YES
Predicted change in Energy=-7.179584D-11
Optimization completed.
-- Stationary point found.
</pre>

=== Vibration modes ===

''' [N(CH3)4]+ '''
<pre>
Low frequencies --- 0.0007 0.0011 0.0013 21.5288 21.5288 21.5288
Low frequencies --- 188.5488 292.6546 292.6546
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [P(CH3)4]+ '''
<pre>
Low frequencies --- -15.1139 -0.0002 0.0012 0.0012 5.8940 14.7736
Low frequencies --- 156.2222 191.5376 191.9513
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_pch34_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

''' [S(CH3)3]+ '''
<pre>
Low frequencies --- -8.5871 0.0029 0.0049 0.0051 5.7111 9.1755
Low frequencies --- 162.4159 200.3446 200.5391
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_sch33_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== Conclusions on molecular structure ==
Investigation of structures is focused on the central atom as this is the only point at which variance should occur. The length of the M-C bonds and the angle between C-M-C on each complex is reported below:

{| class="wikitable" border="1"
! Complex !! M-C Length (Å) !! Angle (°) !! M-C length (lit<ref name="crc">''CRC Handbook of Chemistry and Physics'', ed. W. M. Haynes and D. R. Lide, CRC Press, Boca Raton, 93rd edn., 2012</ref>) (Å)
|-
| [P(CH3)4]+ || 1.82 || 109.5 || 1.84
|-
| [N(CH3)4]+ || 1.51 || 109.5 || 1.46
|-
| [S(CH3)3]+ || 1.82 || 102.7 || 1.79
|}

''Literature bond lengths are found by adding the covalent radii for the atoms.''

Two key trends are:
* As you go down a group, the bond length decreases
* As you go across a group (so losing a ligand), the bond angle is reduced)

The first trend is straightforward to explain, as bond lengths increase down the group. This is in tandem with the increase in atomic radius down the group as orbitals in a greater shell begin to be filled. Thus, as you move from period 2 (N) to period 3 (P), the length of the bond increases and is in turn the overall size of each ion. There is slight variance in the length of a C-H bond in each complex, however no pattern is immediately discernible (it increases in the order S > P > N) - it is thought this is just some random error in the calculation.

Whilst there is an increase in bond length, there is no change in orientation of the bonds, thus the symmetry of TD is maintained in both the phosphorous and nitrogen molecules. As a result of this, the bond angle is the same for these two complexes. No other arrangement of the ligands is sterically possible, so ensuring that this symmetry label cannot be changed, and therefore the bond angle also cannot change. The bond angle is different for sulphur, as a result of the change of symmetry to C3v, it is not known if the change in metal centre contributes to this change - further investigation would be required.

Of note, the bond length does not appear to change going across the period. There is actually a small increase of 0.01Å if the bond length is reported accurate to 0.001Å, however it is not known if this is just an inherent error in the calculation or not. In any event, it is expected that there is a slight decrease in the bond length as you move towards the right of a period, as the increased nuclear charge better shields the electrons and thus shortens the bond length, but this is not observed here. This may be a result of this complex containing one less ligand, with the arrangement instead taken (along with the lone pair) resulting in some interactions (steric or electronic repulsion) which causes the carbon and metal atoms to move apart from each other. This theory is supported by the large deviation from bond length for the sulphur complex, indicating some feature about the arrangement it has taken is causing the bond length to be artificially lengthened.

Otherwise no strange observations are seen with the structures, with all methyl groups taking the expected tetrahedral structure, and either tetrahedral or C3v structures for the central atom as expected by the number of ligands which are present.

= Molecular orbitals and NBO charges of methyl-ligand complexes =
All three complexes discussed previously have been subject to a full NBO and MO analysis via an energy calculation with the <code>pop=(full,nbo)</code> keyword, retaining any previously used keywords as appropriate. Calculations were performed on the laptop due to load on the HPC, except for the sulphur complex as the calculation took too long on the laptop.

Log files are available as follows:

* '''[N(CH3)4]+''': [[media:Pk_log_nch34_egy.log]]
* '''[P(CH3)4]+''': [[media:Pk_log_pch34_egy.log]]
* '''[S(CH3)3]+''': {{DOI|10042/26274}}
== Calculation output ==

''' [N(CH3)4]+ '''

<pre>
File Name NCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -214.18128421 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0000 Debye
Point Group TD
Job cpu time: 0 days 0 hours 0 minutes 19.0 seconds.
</pre>

''' [P(CH3)4]+ '''

<pre>
File Name PCH34_EGY
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -500.82701105 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.0001 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 20.0 seconds.
</pre>

''' [S(CH3)3]+ '''

<pre>File Name sch33_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -517.68327460 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 0.9651 Debye
Point Group C1
Job cpu time: 0 days 0 hours 0 minutes 57.7 seconds.
</pre>

== Sample MOs for [N(CH3)4]+ ==
A variety of 5 molecular orbitals have been calculated and shown below. Only occupied non-core MOs from the totally bonding to totally antibonding are shown.

{| class="wikitable" border="1"
|+ Totally bonding towards the top
! MO number !! Energy (hartree) !! Picture !! Degeneracy !! Notes
|-
| 6 || -1.19645 || [[Image:Pk-n-mo0.png|200px]] || Singly degenerate || This MO exhibits a great degree of strong bonding interactions across the entire molecule up to the protons, the orbitals of which do not appear to be part of this MO. This is seen by the huge red surface containing almost the entirety of the molecule. As a result of the huge amount of delocalisation seen in the MO, there is a lot of through space interactions between adjacent carbon groups, as seen by how the MO forms a 'cage' around the entire molecule - the empty space between two carbon atoms is part of this red object. As there are no other molecular orbitals other than this huge one, there is no concept of a node in this MO diagram.
|-
| 10 || -0.80745 || [[Image:Pk-n-mo1.png|200px]] || Singly degenerate || This is the first MO in this series of 5 to contain a slight degree of antibonding character, as seen by the fact each ligand is in its own (+) phase orbital, whereas the central metal is in a (-) phase one. This leads to a minor degree of antibonding character, and also a node in the centre of the M-C bond where the two MOs end. Through space interactions are present in each ligand MO, with all the protons and the central carbon existing within the boundaries of the MO, and hence there are through-space interactions between the protons. MOs of the same phase interact weakly with each other due to the large distance between each green orbital (seen in the picture), however the interaction between the (+) and (-) orbitals is quite strong as the nodal area is very small in size - the orbitals are nearly touching. The level of delocalisation is reduced, with delocalisation only occurring across each ligand group - the ligands themselves are not delocalised onto one unit.
|-
| 14 || -0.62248 || [[Image:Pk-n-mo2.png|200px]] || Doubly degenerate || For this MO, nodes exist on every carbon atom, as each MO covers two halves of a carbon atom, two protons, and nothing else. This does lead to delocalisationa cross the protons and carbon atoms, however this also does result in strong antibonding interactions at each carbon as the (+) and (-) MOs become quite close. Some protons, and the metal centre are not covered at all by this MO, however from what is delocalised, there is a significant amount of through space interactions between protons on differing methyl ligands - this is of note as the ligand protons are quite a distance away. There may be some weak bonding interactions between orbitals of the same phase, however they are quite a distance away (separated by the metal centre) so this is expected to be quite weak.
|-
| 17 || -0.58035 || [[Image:Pk-n-mo3.png|200px]] || Triply degenerate || This one again has a node on each carbon, however it differs in that each orbital only covers a single proton and half a carbon. This results in there being no through-space interactions in this molecule. Additionally, there are many strong antibonding interactions as all the orbitals are quite close together, with the a (+) orbital being surrounded by a (-) orbital on every side. If there are any bonding interactions, these are going to be very weak.
|-
| 21 || -0.57934 || [[Image:Pk-n-mo4.png|200px]] || Triply degenerate || This MO is similar to the previous, but differs in that each orbital now consists of two protons, so there are no protons which aren't enclosed in an orbital. Again, there are nodes in each carbon, but also a node in the metal center, with orbitals now also covering the metal center. This results in there being strong antibonding interactions over almost the entire molecule, with (+) interacting with (-) almost over the entire surface of every orbital. Through-space interactions are now back with there being two protons in each orbital, making it possible for these to interact, and there is also the potential for protons and metal center to interact as well. This orbital is only slightly higher energy than the previous one, and this is solely because of the increased degree of antibonding interactions present.
|}

== NBO charge distributions ==

NBO charge distributions were calculated from the checkpoint file for a range of -1.750 to 1.750 as this ensured the range of charges for all 3 complexes could be accommodated on the same scale. The charges are as follows:

{| class="wikitable" border="1"
! Complex !! Metal charge (e) !! Carbon charge (e) !! Proton charge (e)
|-
| P || 1.667 || -1.060 || 0.298
|-
| N || 0.917 || -0.846 || 0.297
|-
| S || -0.295 || -0.483 || 0.269
|}

<gallery>
File:Pk-nbo-n.png|Nitrogen complex
File:Pk-nbo-p.png|Phosphorous complex
File:Pk-nbo-s.png|Sulphur complex
</gallery>

There appears to be a slight trend of the metal centre charge with electronegativity, with the charge much lower as it becomes more electronegative (and hence drawing a greater share of electrons to it). This in turn makes the carbon more positive as electron density is removed from it. The protons remain rather positively charged and do not appear to be greatly affected by the metal centre, but this is likely because they are too far away for the inductive effect to occur.

Interestingly, nitrogen is more eletronegative than sulphur, yet sulphur has a greater negative charge. The reduced degree of polarisation in the bond for the nitrogen complex also suggests why the bond length for the nitrogen complex is shorter compared to the sulphur. The reason for this increased amount of negative charge is due to the lone pair present on sulphur (hence the configuration it takes according to the Jmol clip above), and so there is simply more negative charge present on the sulphur.

Thus, for the general complex [NR4]+, the positive charge located on the nitrogen in the picture is indeed located on the nitrogen, however it is somewhat delocalised over the protons too. As the nitrogen contains the greatest degree of positive charge, though, the + sign is conventionally placed here as it gives the indication as to where most of the charge is.

= Ligand influences on nitrogen metal centre complexes =
To investigate how changes to the ligands affects the cation, two variants on the nitrogen complex analysed previously have been used. One has one of the protons on a methyl ligand replaced with CH2OH, the other has the proton replaced with CH2CN. Each complex is then optimised and subject to a frequency analysis so as to allow for investigation of its structure. A MO and NBO calculation is then subsequently run to analyse how the change in ligand affects the ions electronic behaviour.

== Optimisations ==
Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26206}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26207}}

=== Summary output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
File Name nch33ch2oh_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000102 a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 1 hours 22 minutes 37.5 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
File Name nch33ch2cn_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000045 a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 50 minutes 39.5 seconds.
</pre>

=== Convergence output ===

'''[N(CH3)3(CH2OH)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000034 0.000060 YES
RMS Displacement 0.000008 0.000040 YES
Predicted change in Energy=-5.591936D-11
Optimization completed.
-- Stationary point found.
</pre>

'''[N(CH3)3(CH2CN)]+''':

<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000036 0.000060 YES
RMS Displacement 0.000011 0.000040 YES
Predicted change in Energy=-2.269581D-11
Optimization completed.
-- Stationary point found.
</pre>

== Frequency analysis ==

Optimisations were conducted to the 6-31G(d,p) level directly with the same keywords as used previously (but no <code>nosymm</code>). The log files are available below on Dspace after being optimised on the HPC.

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26290}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26291}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm 0.00000106 a.u.
Imaginary Freq 0
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 26 minutes 10.7 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_freq
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm 0.00000059 a.u.
Imaginary Freq 0
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 29 minutes 19.0 seconds.
</pre>

=== Vibrational modes ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2oh_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

'''[N(CH3)3(CH2CN)]+'''

<pre>
Low frequencies --- -8.4158 -5.0201 -1.2272 -0.0010 -0.0008 -0.0007
Low frequencies --- 131.1073 213.4620 255.7131
</pre>

''Right click and use the Model menu to see the available modes''

<jmol>
<jmolApplet>
<title>Vibration</title><color>white</color><size>400</size>
<script>vectors 4;vectors scale 5.0;color vectors red;vibration 10;</script>
<uploadedFileContents>Pk_log_nch33ch2cn_freq.log</uploadedFileContents>
</jmolApplet>
</jmol>

== MO and NBO calculations ==
<code>pop=(nbo,full)</code> energy calculations were then performed on the complexes to generate MOs and NBO charge diagrams, just as has been done previously. All calculations were performed on the HPC and log files are available as follows:

* '''[N(CH3)3(CH2OH)]+''': {{DOI|10042/26294}}
* '''[N(CH3)3(CH2CN)]+''': {{DOI|10042/26295}}

=== Summary outputs ===

'''[N(CH3)3(CH2OH)]+'''

<pre>
File Name nch33ch2oh_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -289.39470724 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 2.1358 Debye
Point Group C1
Job cpu time: 0 days 0 hours 1 minutes 59.3 seconds.
</pre>

'''[N(CH3)3(CH2CN)]+'''

<pre>
File Name nch33ch2cn_egy
File Type .log
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 1
Spin Singlet
E(RB3LYP) -306.39376383 a.u.
RMS Gradient Norm a.u.
Imaginary Freq
Dipole Moment 5.7642 Debye
Point Group C1
Job cpu time: 0 days 0 hours 2 minutes 25.0 seconds.
</pre>

=== Sample MOs ===

{| class="wikitable" border="1"
! !! [N(CH3)3(CH2OH)]+ !!
[N(CH3)3(CH2CN)]+
|-
| HOMO || cell
|-
| LUMO || cell
|-
| HOMO Energy ||
|-
| LUMO Energy ||
|}

=== NBO energy distributions ===

=== Discussion ===

== Ligand influence on structure ==

== Ligand influence on charge distribution ==

== Ligand influence on molecular orbitals ==

= References =
<references />

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T12:14:20Z

Pk1811: /* Sample MOs for [N(CH3)4]+ */

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T12:14:00Z

Pk1811: /* Sample MOs for [N(CH3)4]+ */

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T12:06:21Z

Pk1811: /* Sample MOs for [N(CH3)4]+ */

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T11:53:36Z

Pk1811: /* Conclusions on molecular structure */

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-22T10:44:56Z

Pk1811: /* Sample MOs for [N(CH3)4]+ */

File:Pk-n-mo4.png

2013-11-21T17:30:36Z

Pk1811:

File:Pk-n-mo3.png

2013-11-21T17:30:36Z

Pk1811:

File:Pk-n-mo2.png

2013-11-21T17:30:35Z

Pk1811:

File:Pk-n-mo1.png

2013-11-21T17:30:35Z

Pk1811:

File:Pk-n-mo0.png

2013-11-21T17:30:35Z

Pk1811:

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-21T17:29:47Z

Pk1811: /* Sample MOs for [N(CH3)4]+ */

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-21T17:20:36Z

Pk1811: /* NBO charge distributions */

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-21T17:15:36Z

Pk1811: /* Conclusions on molecular structure */

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-21T17:13:58Z

Pk1811: /* NBO charge distributions */

File:Pk-nbo-s.png

2013-11-21T17:01:50Z

Pk1811:

File:Pk-nbo-p.png

2013-11-21T17:01:49Z

Pk1811:

File:Pk-nbo-n.png

2013-11-21T17:01:49Z

Pk1811:

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-21T16:54:18Z

Pk1811: /* NBO charge distributions */

Rep:Mod:cbf5a234-49e7-4e4b-9d5d-85cf22add185

2013-11-21T16:07:28Z

Pk1811: /* NBO charge distributions */