ChemWiki - User contributions [en]

Y2T301339518

2019-05-24T16:04:18Z

Ylc17: /* MO discussion of [Mn(CO)6]+ */

==BH3==

The optimisation finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm. Due to the unstable nature of the N-I bond, it is difficult to find literature regarding empirical evidence for the bond length.

=Metal Carbonyls =

Carbon monoxide, while toxic, has much use within the field of transition metal complex as a π acceptor ligand, especially for manipulating the Δ value within a complex. As well as that, they have shown much use for measuring the trans effects from other ligands. Here, calculations were made to understand the effects of changing the metal centre in hexacarbonyl complexes.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.

</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

<jmol><jmolApplet>
<title>[V(CO)6]-</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518VFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

<jmol><jmolApplet>
<title>[Cr(CO)6]</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518CRFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

<jmol><jmolApplet>
<title>[Mn(CO)6]+</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518MnFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===MO discussion of [Mn(CO)6]+ ===

{| class="wikitable"
|+
|-
|[[File:01339518BMO1corrected.png|thumb|600px|center| This orbital is bonding overall. The dxz-π* interactions are very strongly bonding considering there are 4 regions of bonding occurring. The only significant antibonding interaction that occurs is within the π* orbitals.]]
|[[File:01339518BMOreal.png|thumb|300px|center|The calculated bonding orbital. (E = -0.47693 eV)]][[File:01339518BMOreal2real.PNG|thumb|300px|center|]]
|-
|[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall. Note that this is more antibonding than the one below (E = -0.22289 eV).]]
|[[File:01339518ABMOreal.png|thumb|300px|center| The calculated antibonding orbital.]][[File:01339518BMO2real2.png|thumb|300px|center|]]
|-
|[[File:01339518ABMO2annotated2.PNG|thumb|600px|center| This orbital is antibonding overall.It's worth noting the lack of presence from the metal d orbitals. This orbital is lower in energy than the other, due to the lack of the d orbital which contributes another antibonding interaction which increases the energy. Instead, the bonding ring formed by the π* orbitals is left uninterrupted (E = -0.23075 eV)]]
|[[File:01339518ABMO2real.png|thumb|600px|center| The calculated antibonding orbital.]]
|}

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten thus leading to an increase in bond strength, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row which is what we expect. However, for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations. This has been attributed to the inadequacy of the method used for the calculations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T16:03:46Z

Ylc17: /* MO discussion of [Mn(CO)6]+ */

==BH3==

The optimisation finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm. Due to the unstable nature of the N-I bond, it is difficult to find literature regarding empirical evidence for the bond length.

=Metal Carbonyls =

Carbon monoxide, while toxic, has much use within the field of transition metal complex as a π acceptor ligand, especially for manipulating the Δ value within a complex. As well as that, they have shown much use for measuring the trans effects from other ligands. Here, calculations were made to understand the effects of changing the metal centre in hexacarbonyl complexes.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.

</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

<jmol><jmolApplet>
<title>[V(CO)6]-</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518VFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

<jmol><jmolApplet>
<title>[Cr(CO)6]</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518CRFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

<jmol><jmolApplet>
<title>[Mn(CO)6]+</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518MnFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===MO discussion of [Mn(CO)6]+ ===

{| class="wikitable"
|+
|-
|[[File:01339518BMO1corrected.png|thumb|600px|center| This orbital is bonding overall. The dxz-π* interactions are very strongly bonding considering there are 4 regions of bonding occurring. The only significant antibonding interaction that occurs is within the π* orbitals.]]
|[[File:01339518BMOreal.png|thumb|300px|center|The calculated bonding orbital. (E = -0.47693 eV)]][[File:01339518BMOreal2real.PNG|thumb|300px|center|]]
|-
|[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall. Note that this is more antibonding than the one below (E = -0.22289 eV).]]
|[[File:01339518ABMOreal.png|thumb|300px|center| The calculated antibonding orbital.]][[File:01339518BMO2real2.png|thumb|300px|center|]]
|-
|[[File:01339518ABMO2annotated2.PNG|thumb|600px|center| This orbital is antibonding overall.It's worth noting the lack of presence from the metal d orbitals. This orbital is lower in energy than the other, due to the lack of the d orbital which contributes another antibonding interaction which increases the energy. Instead, the bonding ring formed by the π* orbitals is left uninterrupted (E = -0.23075 eV)]]
|[[File:01339518ABMOreal.PNG|thumb|600px|center| The calculated antibonding orbital.]]
|}

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten thus leading to an increase in bond strength, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row which is what we expect. However, for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations. This has been attributed to the inadequacy of the method used for the calculations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T16:03:11Z

Ylc17: /* MO discussion of [Mn(CO)6]+ */

==BH3==

The optimisation finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm. Due to the unstable nature of the N-I bond, it is difficult to find literature regarding empirical evidence for the bond length.

=Metal Carbonyls =

Carbon monoxide, while toxic, has much use within the field of transition metal complex as a π acceptor ligand, especially for manipulating the Δ value within a complex. As well as that, they have shown much use for measuring the trans effects from other ligands. Here, calculations were made to understand the effects of changing the metal centre in hexacarbonyl complexes.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.

</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

<jmol><jmolApplet>
<title>[V(CO)6]-</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518VFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

<jmol><jmolApplet>
<title>[Cr(CO)6]</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518CRFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

<jmol><jmolApplet>
<title>[Mn(CO)6]+</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518MnFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===MO discussion of [Mn(CO)6]+ ===

{| class="wikitable"
|+
|-
|[[File:01339518BMO1corrected.png|thumb|600px|center| This orbital is bonding overall. The dxz-π* interactions are very strongly bonding considering there are 4 regions of bonding occurring. The only significant antibonding interaction that occurs is within the π* orbitals.]]
|[[File:01339518BMOreal.png|thumb|300px|center|The calculated bonding orbital. (E = -0.47693 eV)]][[File:01339518BMOreal2real.PNG|thumb|300px|center|]]
|-
|[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall. Note that this is more antibonding than the one below (E = -0.22289 eV).]]
|[[File:01339518ABMOreal.png|thumb|300px|center| The calculated antibonding orbital.]][[File:01339518BMO2real2.png|thumb|300px|center|]]
|-
|[[File:01339518ABMO2annotated2.PNG|thumb|600px|center| This orbital is antibonding overall.It's worth noting the lack of presence from the metal d orbitals. This orbital is lower in energy than the other, due to the lack of the d orbital which contributes another antibonding interaction which increases the energy. Instead, the bonding ring formed by the π* orbitals is left uninterrupted (E = -0.23075 eV)]]
|[[File:01339518ABMO2real.PNG|thumb|600px|center| The calculated antibonding orbital.]]
|}

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten thus leading to an increase in bond strength, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row which is what we expect. However, for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations. This has been attributed to the inadequacy of the method used for the calculations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T16:02:50Z

Ylc17: /* MO discussion of [Mn(CO)6]+ */

==BH3==

The optimisation finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm. Due to the unstable nature of the N-I bond, it is difficult to find literature regarding empirical evidence for the bond length.

=Metal Carbonyls =

Carbon monoxide, while toxic, has much use within the field of transition metal complex as a π acceptor ligand, especially for manipulating the Δ value within a complex. As well as that, they have shown much use for measuring the trans effects from other ligands. Here, calculations were made to understand the effects of changing the metal centre in hexacarbonyl complexes.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.

</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

<jmol><jmolApplet>
<title>[V(CO)6]-</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518VFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

<jmol><jmolApplet>
<title>[Cr(CO)6]</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518CRFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

<jmol><jmolApplet>
<title>[Mn(CO)6]+</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518MnFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===MO discussion of [Mn(CO)6]+ ===

{| class="wikitable"
|+
|-
|[[File:01339518BMO1corrected.png|thumb|600px|center| This orbital is bonding overall. The dxz-π* interactions are very strongly bonding considering there are 4 regions of bonding occurring. The only significant antibonding interaction that occurs is within the π* orbitals.]]
|[[File:01339518BMOreal.png|thumb|300px|center|The calculated bonding orbital. (E = -0.47693 eV)]][[File:01339518BMOreal2real.PNG|thumb|300px|center|]]
|-
|[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall. Note that this is more antibonding than the one below (E = -0.22289 eV).]]
|[[File:01339518ABMOreal.png|thumb|300px|center| The calculated antibonding orbital.]][[File:01339518BMO2real2.png|thumb|300px|center|]]
|-
|[[File:01339518ABMO2.png|thumb|600px|center| This orbital is antibonding overall.It's worth noting the lack of presence from the metal d orbitals. This orbital is lower in energy than the other, due to the lack of the d orbital which contributes another antibonding interaction which increases the energy. Instead, the bonding ring formed by the π* orbitals is left uninterrupted (E = -0.23075 eV)]]
|[[File:01339518ABMO2annotated2.PNG|thumb|600px|center| The calculated antibonding orbital.]]
|}

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten thus leading to an increase in bond strength, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row which is what we expect. However, for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations. This has been attributed to the inadequacy of the method used for the calculations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

File:01339518ABMO2annotated2.PNG

2019-05-24T16:02:37Z

Ylc17:

Y2T301339518

2019-05-24T15:43:19Z

Ylc17: /* MO discussion of [Mn(CO)6]+ */

==BH3==

The optimisation finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm. Due to the unstable nature of the N-I bond, it is difficult to find literature regarding empirical evidence for the bond length.

=Metal Carbonyls =

Carbon monoxide, while toxic, has much use within the field of transition metal complex as a π acceptor ligand, especially for manipulating the Δ value within a complex. As well as that, they have shown much use for measuring the trans effects from other ligands. Here, calculations were made to understand the effects of changing the metal centre in hexacarbonyl complexes.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.

</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

<jmol><jmolApplet>
<title>[V(CO)6]-</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518VFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

<jmol><jmolApplet>
<title>[Cr(CO)6]</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518CRFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

<jmol><jmolApplet>
<title>[Mn(CO)6]+</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518MnFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===MO discussion of [Mn(CO)6]+ ===

{| class="wikitable"
|+
|-
|[[File:01339518BMO1corrected.png|thumb|600px|center| This orbital is bonding overall. The dxz-π* interactions are very strongly bonding considering there are 4 regions of bonding occurring. The only significant antibonding interaction that occurs is within the π* orbitals.]]
|[[File:01339518BMOreal.png|thumb|300px|center|The calculated bonding orbital. (E = -0.47693 eV)]][[File:01339518BMOreal2real.PNG|thumb|300px|center|]]
|-
|[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall. Note that this is more antibonding than the one below (E = -0.22289 eV).]]
|[[File:01339518ABMOreal.png|thumb|300px|center| The calculated antibonding orbital.]][[File:01339518BMO2real2.png|thumb|300px|center|]]
|-
|[[File:01339518ABMO2.png|thumb|600px|center| This orbital is antibonding overall.It's worth noting the lack of presence from the metal d orbitals. This orbital is lower in energy than the other, due to the lack of the d orbital which contributes another antibonding interaction which increases the energy. Instead, the bonding ring formed by the π* orbitals is left uninterrupted (E = -0.23075 eV)]]
|[[File:01339518ABMO2real.png|thumb|600px|center| The calculated antibonding orbital.]]
|}

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten thus leading to an increase in bond strength, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row which is what we expect. However, for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations. This has been attributed to the inadequacy of the method used for the calculations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

File:01339518BMOreal2real.PNG

2019-05-24T15:42:51Z

Ylc17:

Y2T301339518

2019-05-24T15:40:50Z

Ylc17: /* MO discussion of [Mn(CO)6]+ */

==BH3==

The optimisation finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm. Due to the unstable nature of the N-I bond, it is difficult to find literature regarding empirical evidence for the bond length.

=Metal Carbonyls =

Carbon monoxide, while toxic, has much use within the field of transition metal complex as a π acceptor ligand, especially for manipulating the Δ value within a complex. As well as that, they have shown much use for measuring the trans effects from other ligands. Here, calculations were made to understand the effects of changing the metal centre in hexacarbonyl complexes.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.

</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

<jmol><jmolApplet>
<title>[V(CO)6]-</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518VFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

<jmol><jmolApplet>
<title>[Cr(CO)6]</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518CRFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

<jmol><jmolApplet>
<title>[Mn(CO)6]+</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518MnFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===MO discussion of [Mn(CO)6]+ ===

{| class="wikitable"
|+
|-
|[[File:01339518BMO1corrected.png|thumb|600px|center| This orbital is bonding overall. The dxz-π* interactions are very strongly bonding considering there are 4 regions of bonding occurring. The only significant antibonding interaction that occurs is within the π* orbitals.]]
|[[File:01339518BMOreal.png|thumb|300px|center|The calculated bonding orbital. (E = -0.47693 eV)]]
|-
|[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall. Note that this is more antibonding than the one below (E = -0.22289 eV).]]
|[[File:01339518ABMOreal.png|thumb|300px|center| The calculated antibonding orbital.]][[File:01339518BMO2real2.png|thumb|300px|center|The calculated bonding orbital. (E = -0.47693 eV)]]
|-
|[[File:01339518ABMO2.png|thumb|600px|center| This orbital is antibonding overall.It's worth noting the lack of presence from the metal d orbitals. This orbital is lower in energy than the other, due to the lack of the d orbital which contributes another antibonding interaction which increases the energy. Instead, the bonding ring formed by the π* orbitals is left uninterrupted (E = -0.23075 eV)]]
|[[File:01339518ABMO2real.png|thumb|600px|center| The calculated antibonding orbital.]]
|}

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten thus leading to an increase in bond strength, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row which is what we expect. However, for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations. This has been attributed to the inadequacy of the method used for the calculations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T15:40:31Z

Ylc17: /* MO discussion of [Mn(CO)6]+ */

==BH3==

The optimisation finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm. Due to the unstable nature of the N-I bond, it is difficult to find literature regarding empirical evidence for the bond length.

=Metal Carbonyls =

Carbon monoxide, while toxic, has much use within the field of transition metal complex as a π acceptor ligand, especially for manipulating the Δ value within a complex. As well as that, they have shown much use for measuring the trans effects from other ligands. Here, calculations were made to understand the effects of changing the metal centre in hexacarbonyl complexes.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.

</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

<jmol><jmolApplet>
<title>[V(CO)6]-</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518VFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

<jmol><jmolApplet>
<title>[Cr(CO)6]</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518CRFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

<jmol><jmolApplet>
<title>[Mn(CO)6]+</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518MnFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===MO discussion of [Mn(CO)6]+ ===

{| class="wikitable"
|+
|-
|[[File:01339518BMO1corrected.png|thumb|600px|center| This orbital is bonding overall. The dxz-π* interactions are very strongly bonding considering there are 4 regions of bonding occurring. The only significant antibonding interaction that occurs is within the π* orbitals.]]
|[[File:01339518BMOreal.png|thumb|300px|center|The calculated bonding orbital. (E = -0.47693 eV)]]
|-
|[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall. Note that this is more antibonding than the one below (E = -0.22289 eV).]]
|[[File:01339518ABMOreal.png|thumb|600px|center| The calculated antibonding orbital.]][[File:01339518BMO2real2.png|thumb|300px|center|The calculated bonding orbital. (E = -0.47693 eV)]]
|-
|[[File:01339518ABMO2.png|thumb|600px|center| This orbital is antibonding overall.It's worth noting the lack of presence from the metal d orbitals. This orbital is lower in energy than the other, due to the lack of the d orbital which contributes another antibonding interaction which increases the energy. Instead, the bonding ring formed by the π* orbitals is left uninterrupted (E = -0.23075 eV)]]
|[[File:01339518ABMO2real.png|thumb|600px|center| The calculated antibonding orbital.]]
|}

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten thus leading to an increase in bond strength, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row which is what we expect. However, for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations. This has been attributed to the inadequacy of the method used for the calculations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T15:39:59Z

Ylc17: /* MO discussion of [Mn(CO)6]+ */

==BH3==

The optimisation finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm. Due to the unstable nature of the N-I bond, it is difficult to find literature regarding empirical evidence for the bond length.

=Metal Carbonyls =

Carbon monoxide, while toxic, has much use within the field of transition metal complex as a π acceptor ligand, especially for manipulating the Δ value within a complex. As well as that, they have shown much use for measuring the trans effects from other ligands. Here, calculations were made to understand the effects of changing the metal centre in hexacarbonyl complexes.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.

</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

<jmol><jmolApplet>
<title>[V(CO)6]-</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518VFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

<jmol><jmolApplet>
<title>[Cr(CO)6]</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518CRFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

<jmol><jmolApplet>
<title>[Mn(CO)6]+</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518MnFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===MO discussion of [Mn(CO)6]+ ===

{| class="wikitable"
|+
|-
|[[File:01339518BMO1corrected.png|thumb|600px|center| This orbital is bonding overall. The dxz-π* interactions are very strongly bonding considering there are 4 regions of bonding occurring. The only significant antibonding interaction that occurs is within the π* orbitals.]]
|[[File:01339518BMOreal.png|thumb|300px|center|The calculated bonding orbital. (E = -0.47693 eV)]][[File:01339518BMO2real2.png|thumb|300px|center|The calculated bonding orbital. (E = -0.47693 eV)]]
|-
|[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall. Note that this is more antibonding than the one below (E = -0.22289 eV).]]
|[[File:01339518ABMOreal.png|thumb|600px|center| The calculated antibonding orbital.]]
|-
|[[File:01339518ABMO2.png|thumb|600px|center| This orbital is antibonding overall.It's worth noting the lack of presence from the metal d orbitals. This orbital is lower in energy than the other, due to the lack of the d orbital which contributes another antibonding interaction which increases the energy. Instead, the bonding ring formed by the π* orbitals is left uninterrupted (E = -0.23075 eV)]]
|[[File:01339518ABMO2real.png|thumb|600px|center| The calculated antibonding orbital.]]
|}

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten thus leading to an increase in bond strength, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row which is what we expect. However, for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations. This has been attributed to the inadequacy of the method used for the calculations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T15:39:40Z

Ylc17: /* MO discussion of [Mn(CO)6]+ */

==BH3==

The optimisation finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm. Due to the unstable nature of the N-I bond, it is difficult to find literature regarding empirical evidence for the bond length.

=Metal Carbonyls =

Carbon monoxide, while toxic, has much use within the field of transition metal complex as a π acceptor ligand, especially for manipulating the Δ value within a complex. As well as that, they have shown much use for measuring the trans effects from other ligands. Here, calculations were made to understand the effects of changing the metal centre in hexacarbonyl complexes.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.

</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

<jmol><jmolApplet>
<title>[V(CO)6]-</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518VFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

<jmol><jmolApplet>
<title>[Cr(CO)6]</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518CRFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

<jmol><jmolApplet>
<title>[Mn(CO)6]+</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518MnFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===MO discussion of [Mn(CO)6]+ ===

{| class="wikitable"
|+
|-
|[[File:01339518BMO1corrected.png|thumb|600px|center| This orbital is bonding overall. The dxz-π* interactions are very strongly bonding considering there are 4 regions of bonding occurring. The only significant antibonding interaction that occurs is within the π* orbitals.]]
|[[File:01339518BMOreal.png|thumb|400px|center|The calculated bonding orbital. (E = -0.47693 eV)]][[File:01339518BMO2real2.png|thumb|400px|right|The calculated bonding orbital. (E = -0.47693 eV)]]
|-
|[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall. Note that this is more antibonding than the one below (E = -0.22289 eV).]]
|[[File:01339518ABMOreal.png|thumb|600px|center| The calculated antibonding orbital.]]
|-
|[[File:01339518ABMO2.png|thumb|600px|center| This orbital is antibonding overall.It's worth noting the lack of presence from the metal d orbitals. This orbital is lower in energy than the other, due to the lack of the d orbital which contributes another antibonding interaction which increases the energy. Instead, the bonding ring formed by the π* orbitals is left uninterrupted (E = -0.23075 eV)]]
|[[File:01339518ABMO2real.png|thumb|600px|center| The calculated antibonding orbital.]]
|}

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten thus leading to an increase in bond strength, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row which is what we expect. However, for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations. This has been attributed to the inadequacy of the method used for the calculations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

File:01339518BMO2real2.png

2019-05-24T15:38:55Z

Ylc17:

Y2T301339518

2019-05-24T15:38:26Z

Ylc17: /* MO discussion of [Mn(CO)6]+ */

==BH3==

The optimisation finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm. Due to the unstable nature of the N-I bond, it is difficult to find literature regarding empirical evidence for the bond length.

=Metal Carbonyls =

Carbon monoxide, while toxic, has much use within the field of transition metal complex as a π acceptor ligand, especially for manipulating the Δ value within a complex. As well as that, they have shown much use for measuring the trans effects from other ligands. Here, calculations were made to understand the effects of changing the metal centre in hexacarbonyl complexes.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.

</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

<jmol><jmolApplet>
<title>[V(CO)6]-</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518VFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

<jmol><jmolApplet>
<title>[Cr(CO)6]</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518CRFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

<jmol><jmolApplet>
<title>[Mn(CO)6]+</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518MnFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===MO discussion of [Mn(CO)6]+ ===

{| class="wikitable"
|+
|-
|[[File:01339518BMO1corrected.png|thumb|600px|center| This orbital is bonding overall. The dxz-π* interactions are very strongly bonding considering there are 4 regions of bonding occurring. The only significant antibonding interaction that occurs is within the π* orbitals.]]
|[[File:01339518BMOreal.png|thumb|600px|center|The calculated bonding orbital. (E = -0.47693 eV)]]
|-
|[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall. Note that this is more antibonding than the one below (E = -0.22289 eV).]]
|[[File:01339518ABMOreal.png|thumb|600px|center| The calculated antibonding orbital.]]
|-
|[[File:01339518ABMO2.png|thumb|600px|center| This orbital is antibonding overall.It's worth noting the lack of presence from the metal d orbitals. This orbital is lower in energy than the other, due to the lack of the d orbital which contributes another antibonding interaction which increases the energy. Instead, the bonding ring formed by the π* orbitals is left uninterrupted (E = -0.23075 eV)]]
|[[File:01339518ABMO2real.png|thumb|600px|center| The calculated antibonding orbital.]]
|}

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten thus leading to an increase in bond strength, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row which is what we expect. However, for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations. This has been attributed to the inadequacy of the method used for the calculations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

File:01339518BMO1corrected.png

2019-05-24T15:38:18Z

Ylc17:

Y2T301339518

2019-05-24T15:26:59Z

Ylc17: /* [Mn(CO)6]+ */

==BH3==

The optimisation finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm. Due to the unstable nature of the N-I bond, it is difficult to find literature regarding empirical evidence for the bond length.

=Metal Carbonyls =

Carbon monoxide, while toxic, has much use within the field of transition metal complex as a π acceptor ligand, especially for manipulating the Δ value within a complex. As well as that, they have shown much use for measuring the trans effects from other ligands. Here, calculations were made to understand the effects of changing the metal centre in hexacarbonyl complexes.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.

</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

<jmol><jmolApplet>
<title>[V(CO)6]-</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518VFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

<jmol><jmolApplet>
<title>[Cr(CO)6]</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518CRFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

<jmol><jmolApplet>
<title>[Mn(CO)6]+</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518MnFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

===MO discussion of [Mn(CO)6]+ ===

{| class="wikitable"
|+
|-
|[[File:01339518BMO1.png|thumb|600px|center| This orbital is bonding overall. The dxz-π* interactions are very strongly bonding considering there are 4 regions of bonding occurring. The only significant antibonding interaction that occurs is within the π* orbitals.]]
|[[File:01339518BMOreal.png|thumb|600px|center|The calculated bonding orbital. (E = -0.47693 eV)]]
|-
|[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall. Note that this is more antibonding than the one below (E = -0.22289 eV).]]
|[[File:01339518ABMOreal.png|thumb|600px|center| The calculated antibonding orbital.]]
|-
|[[File:01339518ABMO2.png|thumb|600px|center| This orbital is antibonding overall.It's worth noting the lack of presence from the metal d orbitals. This orbital is lower in energy than the other, due to the lack of the d orbital which contributes another antibonding interaction which increases the energy. Instead, the bonding ring formed by the π* orbitals is left uninterrupted (E = -0.23075 eV)]]
|[[File:01339518ABMO2real.png|thumb|600px|center| The calculated antibonding orbital.]]
|}

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten thus leading to an increase in bond strength, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row which is what we expect. However, for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations. This has been attributed to the inadequacy of the method used for the calculations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T15:26:00Z

Ylc17: /* Frequency Analysis */

==BH3==

The optimisation finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm. Due to the unstable nature of the N-I bond, it is difficult to find literature regarding empirical evidence for the bond length.

=Metal Carbonyls =

Carbon monoxide, while toxic, has much use within the field of transition metal complex as a π acceptor ligand, especially for manipulating the Δ value within a complex. As well as that, they have shown much use for measuring the trans effects from other ligands. Here, calculations were made to understand the effects of changing the metal centre in hexacarbonyl complexes.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.

</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

<jmol><jmolApplet>
<title>[V(CO)6]-</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518VFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

<jmol><jmolApplet>
<title>[Cr(CO)6]</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518CRFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

{| class="wikitable"
|+
|-
|[[File:01339518BMO1.png|thumb|600px|center| This orbital is bonding overall. The dxz-π* interactions are very strongly bonding considering there are 4 regions of bonding occurring. The only significant antibonding interaction that occurs is within the π* orbitals.]]
|[[File:01339518BMOreal.png|thumb|600px|center|The calculated bonding orbital. (E = -0.47693 eV)]]
|-
|[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall. Note that this is more antibonding than the one below (E = -0.22289 eV).]]
|[[File:01339518ABMOreal.png|thumb|600px|center| The calculated antibonding orbital.]]
|-
|[[File:01339518ABMO2.png|thumb|600px|center| This orbital is antibonding overall.It's worth noting the lack of presence from the metal d orbitals. This orbital is lower in energy than the other, due to the lack of the d orbital which contributes another antibonding interaction which increases the energy. Instead, the bonding ring formed by the π* orbitals is left uninterrupted (E = -0.23075 eV)]]
|[[File:01339518ABMO2real.png|thumb|600px|center| The calculated antibonding orbital.]]
|}

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten thus leading to an increase in bond strength, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row which is what we expect. However, for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations. This has been attributed to the inadequacy of the method used for the calculations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T15:24:59Z

Ylc17: /* [Cr(CO)6] */

==BH3==

The optimisation finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm. Due to the unstable nature of the N-I bond, it is difficult to find literature regarding empirical evidence for the bond length.

=Metal Carbonyls =

Carbon monoxide, while toxic, has much use within the field of transition metal complex as a π acceptor ligand, especially for manipulating the Δ value within a complex. As well as that, they have shown much use for measuring the trans effects from other ligands. Here, calculations were made to understand the effects of changing the metal centre in hexacarbonyl complexes.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.

</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

<jmol><jmolApplet>
<title>[V(CO)6]-</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518VFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

{| class="wikitable"
|+
|-
|[[File:01339518BMO1.png|thumb|600px|center| This orbital is bonding overall. The dxz-π* interactions are very strongly bonding considering there are 4 regions of bonding occurring. The only significant antibonding interaction that occurs is within the π* orbitals.]]
|[[File:01339518BMOreal.png|thumb|600px|center|The calculated bonding orbital. (E = -0.47693 eV)]]
|-
|[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall. Note that this is more antibonding than the one below (E = -0.22289 eV).]]
|[[File:01339518ABMOreal.png|thumb|600px|center| The calculated antibonding orbital.]]
|-
|[[File:01339518ABMO2.png|thumb|600px|center| This orbital is antibonding overall.It's worth noting the lack of presence from the metal d orbitals. This orbital is lower in energy than the other, due to the lack of the d orbital which contributes another antibonding interaction which increases the energy. Instead, the bonding ring formed by the π* orbitals is left uninterrupted (E = -0.23075 eV)]]
|[[File:01339518ABMO2real.png|thumb|600px|center| The calculated antibonding orbital.]]
|}

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten thus leading to an increase in bond strength, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row which is what we expect. However, for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations. This has been attributed to the inadequacy of the method used for the calculations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T15:24:11Z

Ylc17: /* [V(CO)6]- */

==BH3==

The optimisation finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm. Due to the unstable nature of the N-I bond, it is difficult to find literature regarding empirical evidence for the bond length.

=Metal Carbonyls =

Carbon monoxide, while toxic, has much use within the field of transition metal complex as a π acceptor ligand, especially for manipulating the Δ value within a complex. As well as that, they have shown much use for measuring the trans effects from other ligands. Here, calculations were made to understand the effects of changing the metal centre in hexacarbonyl complexes.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.

</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

<jmol><jmolApplet>
<title>[V(CO)6]-</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518VFREQ.log</uploadedFileContents>
</jmolApplet></jmol>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

{| class="wikitable"
|+
|-
|[[File:01339518BMO1.png|thumb|600px|center| This orbital is bonding overall. The dxz-π* interactions are very strongly bonding considering there are 4 regions of bonding occurring. The only significant antibonding interaction that occurs is within the π* orbitals.]]
|[[File:01339518BMOreal.png|thumb|600px|center|The calculated bonding orbital. (E = -0.47693 eV)]]
|-
|[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall. Note that this is more antibonding than the one below (E = -0.22289 eV).]]
|[[File:01339518ABMOreal.png|thumb|600px|center| The calculated antibonding orbital.]]
|-
|[[File:01339518ABMO2.png|thumb|600px|center| This orbital is antibonding overall.It's worth noting the lack of presence from the metal d orbitals. This orbital is lower in energy than the other, due to the lack of the d orbital which contributes another antibonding interaction which increases the energy. Instead, the bonding ring formed by the π* orbitals is left uninterrupted (E = -0.23075 eV)]]
|[[File:01339518ABMO2real.png|thumb|600px|center| The calculated antibonding orbital.]]
|}

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten thus leading to an increase in bond strength, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row which is what we expect. However, for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations. This has been attributed to the inadequacy of the method used for the calculations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T15:23:02Z

Ylc17: /* Optimisation of the anion */

==BH3==

The optimisation finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm. Due to the unstable nature of the N-I bond, it is difficult to find literature regarding empirical evidence for the bond length.

=Metal Carbonyls =

Carbon monoxide, while toxic, has much use within the field of transition metal complex as a π acceptor ligand, especially for manipulating the Δ value within a complex. As well as that, they have shown much use for measuring the trans effects from other ligands. Here, calculations were made to understand the effects of changing the metal centre in hexacarbonyl complexes.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.

</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

{| class="wikitable"
|+
|-
|[[File:01339518BMO1.png|thumb|600px|center| This orbital is bonding overall. The dxz-π* interactions are very strongly bonding considering there are 4 regions of bonding occurring. The only significant antibonding interaction that occurs is within the π* orbitals.]]
|[[File:01339518BMOreal.png|thumb|600px|center|The calculated bonding orbital. (E = -0.47693 eV)]]
|-
|[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall. Note that this is more antibonding than the one below (E = -0.22289 eV).]]
|[[File:01339518ABMOreal.png|thumb|600px|center| The calculated antibonding orbital.]]
|-
|[[File:01339518ABMO2.png|thumb|600px|center| This orbital is antibonding overall.It's worth noting the lack of presence from the metal d orbitals. This orbital is lower in energy than the other, due to the lack of the d orbital which contributes another antibonding interaction which increases the energy. Instead, the bonding ring formed by the π* orbitals is left uninterrupted (E = -0.23075 eV)]]
|[[File:01339518ABMO2real.png|thumb|600px|center| The calculated antibonding orbital.]]
|}

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten thus leading to an increase in bond strength, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row which is what we expect. However, for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations. This has been attributed to the inadequacy of the method used for the calculations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T15:13:02Z

Ylc17: /* BH3 */

==BH3==

The optimisation finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm. Due to the unstable nature of the N-I bond, it is difficult to find literature regarding empirical evidence for the bond length.

=Metal Carbonyls =

Carbon monoxide, while toxic, has much use within the field of transition metal complex as a π acceptor ligand, especially for manipulating the Δ value within a complex. As well as that, they have shown much use for measuring the trans effects from other ligands. Here, calculations were made to understand the effects of changing the metal centre in hexacarbonyl complexes.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9538 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9538 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9538 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9538 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9538 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9538 -DE/DX = -0.0001 !
! R7 R(2,12) 1.166 -DE/DX = 0.0 !
! R8 R(3,9) 1.166 -DE/DX = 0.0 !
! R9 R(4,8) 1.166 -DE/DX = 0.0 !
! R10 R(5,11) 1.166 -DE/DX = 0.0 !
! R11 R(6,10) 1.166 -DE/DX = 0.0 !
! R12 R(7,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,7,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,12,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,9,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,9,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,13,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,7,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,12,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,9,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,9,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,13,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,7,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,6) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,7,5) 90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

{| class="wikitable"
|+
|-
|[[File:01339518BMO1.png|thumb|600px|center| This orbital is bonding overall. The dxz-π* interactions are very strongly bonding considering there are 4 regions of bonding occurring. The only significant antibonding interaction that occurs is within the π* orbitals.]]
|[[File:01339518BMOreal.png|thumb|600px|center|The calculated bonding orbital. (E = -0.47693 eV)]]
|-
|[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall. Note that this is more antibonding than the one below (E = -0.22289 eV).]]
|[[File:01339518ABMOreal.png|thumb|600px|center| The calculated antibonding orbital.]]
|-
|[[File:01339518ABMO2.png|thumb|600px|center| This orbital is antibonding overall.It's worth noting the lack of presence from the metal d orbitals. This orbital is lower in energy than the other, due to the lack of the d orbital which contributes another antibonding interaction which increases the energy. Instead, the bonding ring formed by the π* orbitals is left uninterrupted (E = -0.23075 eV)]]
|[[File:01339518ABMO2real.png|thumb|600px|center| The calculated antibonding orbital.]]
|}

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten thus leading to an increase in bond strength, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row which is what we expect. However, for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations. This has been attributed to the inadequacy of the method used for the calculations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T14:57:08Z

Ylc17: /* MO discussion of [Mn(CO)6]+ */

==BH3==

Gradient should be less than 0.001
Significant figures = 5 decimal places.
Do not compare energies with different methods/basis sets 

Purpose of optimisation - to find the equilibrium position at the bottom of a Morse potential for a given bond. This finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm. Due to the unstable nature of the N-I bond, it is difficult to find literature regarding empirical evidence for the bond length.

=Metal Carbonyls =

Carbon monoxide, while toxic, has much use within the field of transition metal complex as a π acceptor ligand, especially for manipulating the Δ value within a complex. As well as that, they have shown much use for measuring the trans effects from other ligands. Here, calculations were made to understand the effects of changing the metal centre in hexacarbonyl complexes.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9538 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9538 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9538 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9538 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9538 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9538 -DE/DX = -0.0001 !
! R7 R(2,12) 1.166 -DE/DX = 0.0 !
! R8 R(3,9) 1.166 -DE/DX = 0.0 !
! R9 R(4,8) 1.166 -DE/DX = 0.0 !
! R10 R(5,11) 1.166 -DE/DX = 0.0 !
! R11 R(6,10) 1.166 -DE/DX = 0.0 !
! R12 R(7,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,7,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,12,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,9,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,9,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,13,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,7,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,12,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,9,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,9,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,13,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,7,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,6) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,7,5) 90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

{| class="wikitable"
|+
|-
|[[File:01339518BMO1.png|thumb|600px|center| This orbital is bonding overall. The dxz-π* interactions are very strongly bonding considering there are 4 regions of bonding occurring. The only significant antibonding interaction that occurs is within the π* orbitals.]]
|[[File:01339518BMOreal.png|thumb|600px|center|The calculated bonding orbital. (E = -0.47693 eV)]]
|-
|[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall. Note that this is more antibonding than the one below (E = -0.22289 eV).]]
|[[File:01339518ABMOreal.png|thumb|600px|center| The calculated antibonding orbital.]]
|-
|[[File:01339518ABMO2.png|thumb|600px|center| This orbital is antibonding overall.It's worth noting the lack of presence from the metal d orbitals. This orbital is lower in energy than the other, due to the lack of the d orbital which contributes another antibonding interaction which increases the energy. Instead, the bonding ring formed by the π* orbitals is left uninterrupted (E = -0.23075 eV)]]
|[[File:01339518ABMO2real.png|thumb|600px|center| The calculated antibonding orbital.]]
|}

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten thus leading to an increase in bond strength, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row which is what we expect. However, for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations. This has been attributed to the inadequacy of the method used for the calculations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T14:55:02Z

Ylc17: /* Metal Carbonyls */

==BH3==

Gradient should be less than 0.001
Significant figures = 5 decimal places.
Do not compare energies with different methods/basis sets 

Purpose of optimisation - to find the equilibrium position at the bottom of a Morse potential for a given bond. This finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm. Due to the unstable nature of the N-I bond, it is difficult to find literature regarding empirical evidence for the bond length.

=Metal Carbonyls =

Carbon monoxide, while toxic, has much use within the field of transition metal complex as a π acceptor ligand, especially for manipulating the Δ value within a complex. As well as that, they have shown much use for measuring the trans effects from other ligands. Here, calculations were made to understand the effects of changing the metal centre in hexacarbonyl complexes.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9538 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9538 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9538 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9538 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9538 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9538 -DE/DX = -0.0001 !
! R7 R(2,12) 1.166 -DE/DX = 0.0 !
! R8 R(3,9) 1.166 -DE/DX = 0.0 !
! R9 R(4,8) 1.166 -DE/DX = 0.0 !
! R10 R(5,11) 1.166 -DE/DX = 0.0 !
! R11 R(6,10) 1.166 -DE/DX = 0.0 !
! R12 R(7,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,7,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,12,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,9,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,9,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,13,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,7,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,12,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,9,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,9,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,13,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,7,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,6) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,7,5) 90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

[[File:01339518BMO1.png|thumb|600px|center| This orbital is bonding overall. The dxz-π* interactions are very strongly bonding considering there are 4 regions of bonding occurring. The only significant antibonding interaction that occurs is within the π* orbitals.]]
[[File:01339518BMOreal.png|thumb|600px|center|The calculated bonding orbital. (E = -0.47693 eV)]]

[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall. Note that this is more antibonding than the one below (E = -0.22289 eV).]]
[[File:01339518ABMOreal.png|thumb|600px|center| The calculated antibonding orbital.]]

[[File:01339518ABMO2.png|thumb|600px|center| This orbital is antibonding overall.It's worth noting the lack of presence from the metal d orbitals. This orbital is lower in energy than the other, due to the lack of the d orbital which contributes another antibonding interaction which increases the energy. Instead, the bonding ring formed by the π* orbitals is left uninterrupted (E = -0.23075 eV)]]
[[File:01339518ABMO2real.png|thumb|600px|center| The calculated antibonding orbital.]]

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten thus leading to an increase in bond strength, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row which is what we expect. However, for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations. This has been attributed to the inadequacy of the method used for the calculations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T14:46:37Z

Ylc17: /* Frequency calculation */

==BH3==

Gradient should be less than 0.001
Significant figures = 5 decimal places.
Do not compare energies with different methods/basis sets 

Purpose of optimisation - to find the equilibrium position at the bottom of a Morse potential for a given bond. This finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm. Due to the unstable nature of the N-I bond, it is difficult to find literature regarding empirical evidence for the bond length.

=Metal Carbonyls =

Significance of carbon monoxide as a ligand especially with use towards IR as a show of it's bond strength in regards to the change in charge.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9538 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9538 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9538 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9538 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9538 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9538 -DE/DX = -0.0001 !
! R7 R(2,12) 1.166 -DE/DX = 0.0 !
! R8 R(3,9) 1.166 -DE/DX = 0.0 !
! R9 R(4,8) 1.166 -DE/DX = 0.0 !
! R10 R(5,11) 1.166 -DE/DX = 0.0 !
! R11 R(6,10) 1.166 -DE/DX = 0.0 !
! R12 R(7,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,7,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,12,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,9,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,9,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,13,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,7,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,12,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,9,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,9,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,13,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,7,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,6) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,7,5) 90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

[[File:01339518BMO1.png|thumb|600px|center| This orbital is bonding overall. The dxz-π* interactions are very strongly bonding considering there are 4 regions of bonding occurring. The only significant antibonding interaction that occurs is within the π* orbitals.]]
[[File:01339518BMOreal.png|thumb|600px|center|The calculated bonding orbital. (E = -0.47693 eV)]]

[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall. Note that this is more antibonding than the one below (E = -0.22289 eV).]]
[[File:01339518ABMOreal.png|thumb|600px|center| The calculated antibonding orbital.]]

[[File:01339518ABMO2.png|thumb|600px|center| This orbital is antibonding overall.It's worth noting the lack of presence from the metal d orbitals. This orbital is lower in energy than the other, due to the lack of the d orbital which contributes another antibonding interaction which increases the energy. Instead, the bonding ring formed by the π* orbitals is left uninterrupted (E = -0.23075 eV)]]
[[File:01339518ABMO2real.png|thumb|600px|center| The calculated antibonding orbital.]]

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten thus leading to an increase in bond strength, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row which is what we expect. However, for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations. This has been attributed to the inadequacy of the method used for the calculations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T14:41:15Z

Ylc17: /* The trends */

==BH3==

Gradient should be less than 0.001
Significant figures = 5 decimal places.
Do not compare energies with different methods/basis sets 

Purpose of optimisation - to find the equilibrium position at the bottom of a Morse potential for a given bond. This finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm.

=Metal Carbonyls =

Significance of carbon monoxide as a ligand especially with use towards IR as a show of it's bond strength in regards to the change in charge.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9538 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9538 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9538 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9538 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9538 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9538 -DE/DX = -0.0001 !
! R7 R(2,12) 1.166 -DE/DX = 0.0 !
! R8 R(3,9) 1.166 -DE/DX = 0.0 !
! R9 R(4,8) 1.166 -DE/DX = 0.0 !
! R10 R(5,11) 1.166 -DE/DX = 0.0 !
! R11 R(6,10) 1.166 -DE/DX = 0.0 !
! R12 R(7,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,7,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,12,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,9,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,9,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,13,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,7,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,12,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,9,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,9,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,13,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,7,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,6) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,7,5) 90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

[[File:01339518BMO1.png|thumb|600px|center| This orbital is bonding overall. The dxz-π* interactions are very strongly bonding considering there are 4 regions of bonding occurring. The only significant antibonding interaction that occurs is within the π* orbitals.]]
[[File:01339518BMOreal.png|thumb|600px|center|The calculated bonding orbital. (E = -0.47693 eV)]]

[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall. Note that this is more antibonding than the one below (E = -0.22289 eV).]]
[[File:01339518ABMOreal.png|thumb|600px|center| The calculated antibonding orbital.]]

[[File:01339518ABMO2.png|thumb|600px|center| This orbital is antibonding overall.It's worth noting the lack of presence from the metal d orbitals. This orbital is lower in energy than the other, due to the lack of the d orbital which contributes another antibonding interaction which increases the energy. Instead, the bonding ring formed by the π* orbitals is left uninterrupted (E = -0.23075 eV)]]
[[File:01339518ABMO2real.png|thumb|600px|center| The calculated antibonding orbital.]]

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten thus leading to an increase in bond strength, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row which is what we expect. However, for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations. This has been attributed to the inadequacy of the method used for the calculations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T14:40:00Z

Ylc17: /* The trends */

==BH3==

Gradient should be less than 0.001
Significant figures = 5 decimal places.
Do not compare energies with different methods/basis sets 

Purpose of optimisation - to find the equilibrium position at the bottom of a Morse potential for a given bond. This finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm.

=Metal Carbonyls =

Significance of carbon monoxide as a ligand especially with use towards IR as a show of it's bond strength in regards to the change in charge.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9538 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9538 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9538 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9538 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9538 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9538 -DE/DX = -0.0001 !
! R7 R(2,12) 1.166 -DE/DX = 0.0 !
! R8 R(3,9) 1.166 -DE/DX = 0.0 !
! R9 R(4,8) 1.166 -DE/DX = 0.0 !
! R10 R(5,11) 1.166 -DE/DX = 0.0 !
! R11 R(6,10) 1.166 -DE/DX = 0.0 !
! R12 R(7,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,7,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,12,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,9,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,9,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,13,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,7,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,12,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,9,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,9,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,13,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,7,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,6) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,7,5) 90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

[[File:01339518BMO1.png|thumb|600px|center| This orbital is bonding overall. The dxz-π* interactions are very strongly bonding considering there are 4 regions of bonding occurring. The only significant antibonding interaction that occurs is within the π* orbitals.]]
[[File:01339518BMOreal.png|thumb|600px|center|The calculated bonding orbital. (E = -0.47693 eV)]]

[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall. Note that this is more antibonding than the one below (E = -0.22289 eV).]]
[[File:01339518ABMOreal.png|thumb|600px|center| The calculated antibonding orbital.]]

[[File:01339518ABMO2.png|thumb|600px|center| This orbital is antibonding overall.It's worth noting the lack of presence from the metal d orbitals. This orbital is lower in energy than the other, due to the lack of the d orbital which contributes another antibonding interaction which increases the energy. Instead, the bonding ring formed by the π* orbitals is left uninterrupted (E = -0.23075 eV)]]
[[File:01339518ABMO2real.png|thumb|600px|center| The calculated antibonding orbital.]]

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row, however for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations. This has been attributed to the inadequacy of the method used for the calculations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T14:38:56Z

Ylc17: /* MO discussion of [Mn(CO)6]+ */

==BH3==

Gradient should be less than 0.001
Significant figures = 5 decimal places.
Do not compare energies with different methods/basis sets 

Purpose of optimisation - to find the equilibrium position at the bottom of a Morse potential for a given bond. This finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm.

=Metal Carbonyls =

Significance of carbon monoxide as a ligand especially with use towards IR as a show of it's bond strength in regards to the change in charge.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9538 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9538 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9538 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9538 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9538 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9538 -DE/DX = -0.0001 !
! R7 R(2,12) 1.166 -DE/DX = 0.0 !
! R8 R(3,9) 1.166 -DE/DX = 0.0 !
! R9 R(4,8) 1.166 -DE/DX = 0.0 !
! R10 R(5,11) 1.166 -DE/DX = 0.0 !
! R11 R(6,10) 1.166 -DE/DX = 0.0 !
! R12 R(7,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,7,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,12,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,9,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,9,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,13,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,7,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,12,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,9,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,9,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,13,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,7,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,6) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,7,5) 90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

[[File:01339518BMO1.png|thumb|600px|center| This orbital is bonding overall. The dxz-π* interactions are very strongly bonding considering there are 4 regions of bonding occurring. The only significant antibonding interaction that occurs is within the π* orbitals.]]
[[File:01339518BMOreal.png|thumb|600px|center|The calculated bonding orbital. (E = -0.47693 eV)]]

[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall. Note that this is more antibonding than the one below (E = -0.22289 eV).]]
[[File:01339518ABMOreal.png|thumb|600px|center| The calculated antibonding orbital.]]

[[File:01339518ABMO2.png|thumb|600px|center| This orbital is antibonding overall.It's worth noting the lack of presence from the metal d orbitals. This orbital is lower in energy than the other, due to the lack of the d orbital which contributes another antibonding interaction which increases the energy. Instead, the bonding ring formed by the π* orbitals is left uninterrupted (E = -0.23075 eV)]]
[[File:01339518ABMO2real.png|thumb|600px|center| The calculated antibonding orbital.]]

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row, however for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T14:25:13Z

Ylc17: /* MO discussion of [Mn(CO)6]+ */

==BH3==

Gradient should be less than 0.001
Significant figures = 5 decimal places.
Do not compare energies with different methods/basis sets 

Purpose of optimisation - to find the equilibrium position at the bottom of a Morse potential for a given bond. This finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm.

=Metal Carbonyls =

Significance of carbon monoxide as a ligand especially with use towards IR as a show of it's bond strength in regards to the change in charge.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9538 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9538 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9538 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9538 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9538 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9538 -DE/DX = -0.0001 !
! R7 R(2,12) 1.166 -DE/DX = 0.0 !
! R8 R(3,9) 1.166 -DE/DX = 0.0 !
! R9 R(4,8) 1.166 -DE/DX = 0.0 !
! R10 R(5,11) 1.166 -DE/DX = 0.0 !
! R11 R(6,10) 1.166 -DE/DX = 0.0 !
! R12 R(7,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,7,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,12,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,9,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,9,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,13,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,7,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,12,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,9,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,9,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,13,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,7,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,6) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,7,5) 90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

[[File:01339518BMO1.png|thumb|600px|center| This orbital is bonding overall. ]]
[[File:01339518BMOreal.png|thumb|600px|center|The calculated bonding orbital. ]]

[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall. Note that this is more antibonding than the one below (E = -0.22289 eV)]]
[[File:01339518ABMOreal.png|thumb|600px|center| The calculated antibonding orbital.]]

[[File:01339518ABMO2.png|thumb|600px|center| This orbital is antibonding overall. (E = -0.23075 eV)]]
[[File:01339518ABMO2real.png|thumb|600px|center| The calculated antibonding orbital.]]

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row, however for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

File:01339518ABMO2real.png

2019-05-24T14:25:02Z

Ylc17:

File:01339518ABMO2.png

2019-05-24T14:24:17Z

Ylc17:

Y2T301339518

2019-05-24T13:40:14Z

Ylc17: /* MO discussion of [Mn(CO)6]+ */

==BH3==

Gradient should be less than 0.001
Significant figures = 5 decimal places.
Do not compare energies with different methods/basis sets 

Purpose of optimisation - to find the equilibrium position at the bottom of a Morse potential for a given bond. This finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm.

=Metal Carbonyls =

Significance of carbon monoxide as a ligand especially with use towards IR as a show of it's bond strength in regards to the change in charge.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9538 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9538 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9538 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9538 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9538 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9538 -DE/DX = -0.0001 !
! R7 R(2,12) 1.166 -DE/DX = 0.0 !
! R8 R(3,9) 1.166 -DE/DX = 0.0 !
! R9 R(4,8) 1.166 -DE/DX = 0.0 !
! R10 R(5,11) 1.166 -DE/DX = 0.0 !
! R11 R(6,10) 1.166 -DE/DX = 0.0 !
! R12 R(7,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,7,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,12,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,9,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,9,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,13,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,7,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,12,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,9,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,9,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,13,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,7,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,6) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,7,5) 90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

[[File:01339518BMO1.png|thumb|600px|center| This orbital is bonding overall. ]]
[[File:01339518BMOreal.png|thumb|600px|center|The calculated bonding orbital. ]]

[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall]]
[[File:01339518ABMOreal.png|thumb|600px|center| The calculated antibonding orbital. ]]

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row, however for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

File:01339518BMOreal.png

2019-05-24T13:38:59Z

Ylc17:

Y2T301339518

2019-05-24T13:37:08Z

Ylc17: /* MO discussion of [Mn(CO)6]+ */

==BH3==

Gradient should be less than 0.001
Significant figures = 5 decimal places.
Do not compare energies with different methods/basis sets 

Purpose of optimisation - to find the equilibrium position at the bottom of a Morse potential for a given bond. This finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm.

=Metal Carbonyls =

Significance of carbon monoxide as a ligand especially with use towards IR as a show of it's bond strength in regards to the change in charge.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9538 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9538 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9538 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9538 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9538 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9538 -DE/DX = -0.0001 !
! R7 R(2,12) 1.166 -DE/DX = 0.0 !
! R8 R(3,9) 1.166 -DE/DX = 0.0 !
! R9 R(4,8) 1.166 -DE/DX = 0.0 !
! R10 R(5,11) 1.166 -DE/DX = 0.0 !
! R11 R(6,10) 1.166 -DE/DX = 0.0 !
! R12 R(7,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,7,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,12,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,9,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,9,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,13,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,7,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,12,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,9,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,9,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,13,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,7,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,6) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,7,5) 90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

[[File:01339518BMO1.png|thumb|600px|center| This orbital is bonding overall. ]]
[[File:|thumb|600px|| ]]

[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall]]
[[File:01339518ABMOreal.png|thumb|600px|| ]]

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row, however for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

File:01339518ABMOreal.png

2019-05-24T13:36:50Z

Ylc17:

Y2T301339518

2019-05-24T13:35:31Z

Ylc17: /* MO discussion of [Mn(CO)6]+ */

==BH3==

Gradient should be less than 0.001
Significant figures = 5 decimal places.
Do not compare energies with different methods/basis sets 

Purpose of optimisation - to find the equilibrium position at the bottom of a Morse potential for a given bond. This finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm.

=Metal Carbonyls =

Significance of carbon monoxide as a ligand especially with use towards IR as a show of it's bond strength in regards to the change in charge.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9538 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9538 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9538 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9538 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9538 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9538 -DE/DX = -0.0001 !
! R7 R(2,12) 1.166 -DE/DX = 0.0 !
! R8 R(3,9) 1.166 -DE/DX = 0.0 !
! R9 R(4,8) 1.166 -DE/DX = 0.0 !
! R10 R(5,11) 1.166 -DE/DX = 0.0 !
! R11 R(6,10) 1.166 -DE/DX = 0.0 !
! R12 R(7,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,7,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,12,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,9,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,9,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,13,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,7,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,12,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,9,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,9,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,13,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,7,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,6) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,7,5) 90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

[[File:01339518BMO1.png|thumb|600px|center| This orbital is bonding overall. ]]
[[File:|thumb|600px|| ]]

[[File:01339518ABMO1.png|thumb|600px|center| This orbital is antibonding overall]]
[[File:|thumb|600px|| ]]

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row, however for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T13:21:33Z

Ylc17: /* MO discussion of [Mn(CO)6]+ */

==BH3==

Gradient should be less than 0.001
Significant figures = 5 decimal places.
Do not compare energies with different methods/basis sets 

Purpose of optimisation - to find the equilibrium position at the bottom of a Morse potential for a given bond. This finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm.

=Metal Carbonyls =

Significance of carbon monoxide as a ligand especially with use towards IR as a show of it's bond strength in regards to the change in charge.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9538 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9538 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9538 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9538 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9538 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9538 -DE/DX = -0.0001 !
! R7 R(2,12) 1.166 -DE/DX = 0.0 !
! R8 R(3,9) 1.166 -DE/DX = 0.0 !
! R9 R(4,8) 1.166 -DE/DX = 0.0 !
! R10 R(5,11) 1.166 -DE/DX = 0.0 !
! R11 R(6,10) 1.166 -DE/DX = 0.0 !
! R12 R(7,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,7,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,12,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,9,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,9,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,13,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,7,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,12,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,9,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,9,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,13,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,7,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,6) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,7,5) 90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

[[Fileː01339518BMO1.png|thumb|600px|centre| This MO is bonding overall, wit ]]

Antibonding orbitals

[[File:01339518ABMO1.pngg|thumb|400px|center| The initial optimisation details of BH3]]

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row, however for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T13:20:36Z

Ylc17: /* MO discussion of [Mn(CO)6]+ */

==BH3==

Gradient should be less than 0.001
Significant figures = 5 decimal places.
Do not compare energies with different methods/basis sets 

Purpose of optimisation - to find the equilibrium position at the bottom of a Morse potential for a given bond. This finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm.

=Metal Carbonyls =

Significance of carbon monoxide as a ligand especially with use towards IR as a show of it's bond strength in regards to the change in charge.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9538 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9538 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9538 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9538 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9538 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9538 -DE/DX = -0.0001 !
! R7 R(2,12) 1.166 -DE/DX = 0.0 !
! R8 R(3,9) 1.166 -DE/DX = 0.0 !
! R9 R(4,8) 1.166 -DE/DX = 0.0 !
! R10 R(5,11) 1.166 -DE/DX = 0.0 !
! R11 R(6,10) 1.166 -DE/DX = 0.0 !
! R12 R(7,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,7,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,12,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,9,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,9,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,13,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,7,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,12,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,9,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,9,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,13,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,7,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,6) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,7,5) 90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

[[Fileː01339518BMO1.png|thumb|600px|centre| This MO is bonding overall, wit ]]

Antibonding orbitals

[[Fileː01339518ABMO1.png|thumb|600px|centre| ]]
[[Fileː01339518BMO1.png||600px|centre| ]]

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row, however for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T13:20:25Z

Ylc17: /* MO discussion of [Mn(CO)6]+ */

==BH3==

Gradient should be less than 0.001
Significant figures = 5 decimal places.
Do not compare energies with different methods/basis sets 

Purpose of optimisation - to find the equilibrium position at the bottom of a Morse potential for a given bond. This finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm.

=Metal Carbonyls =

Significance of carbon monoxide as a ligand especially with use towards IR as a show of it's bond strength in regards to the change in charge.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9538 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9538 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9538 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9538 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9538 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9538 -DE/DX = -0.0001 !
! R7 R(2,12) 1.166 -DE/DX = 0.0 !
! R8 R(3,9) 1.166 -DE/DX = 0.0 !
! R9 R(4,8) 1.166 -DE/DX = 0.0 !
! R10 R(5,11) 1.166 -DE/DX = 0.0 !
! R11 R(6,10) 1.166 -DE/DX = 0.0 !
! R12 R(7,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,7,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,12,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,9,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,9,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,13,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,7,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,12,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,9,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,9,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,13,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,7,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,6) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,7,5) 90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

[[Fileː01339518BMO1.png|thumb|600px|centre| This MO is bonding overall, wit ]]

Antibonding orbitals

[[Fileː01339518ABMO1.png|thumb|600px|centre| ]]

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row, however for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T13:16:11Z

Ylc17: /* MO discussion of [Mn(CO)6]+ */

==BH3==

Gradient should be less than 0.001
Significant figures = 5 decimal places.
Do not compare energies with different methods/basis sets 

Purpose of optimisation - to find the equilibrium position at the bottom of a Morse potential for a given bond. This finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm.

=Metal Carbonyls =

Significance of carbon monoxide as a ligand especially with use towards IR as a show of it's bond strength in regards to the change in charge.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9538 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9538 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9538 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9538 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9538 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9538 -DE/DX = -0.0001 !
! R7 R(2,12) 1.166 -DE/DX = 0.0 !
! R8 R(3,9) 1.166 -DE/DX = 0.0 !
! R9 R(4,8) 1.166 -DE/DX = 0.0 !
! R10 R(5,11) 1.166 -DE/DX = 0.0 !
! R11 R(6,10) 1.166 -DE/DX = 0.0 !
! R12 R(7,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,7,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,12,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,9,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,9,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,13,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,7,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,12,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,9,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,9,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,13,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,7,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,6) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,7,5) 90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

Bonding orbitals
01339518BMO1.png

Antibonding orbitals
01339518ABMO1.png

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row, however for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

File:01339518BMO1.png

2019-05-24T13:15:22Z

Ylc17:

File:01339518ABMO1.png

2019-05-24T13:14:49Z

Ylc17:

Y2T301339518

2019-05-24T12:48:11Z

Ylc17: /* The trends */

==BH3==

Gradient should be less than 0.001
Significant figures = 5 decimal places.
Do not compare energies with different methods/basis sets 

Purpose of optimisation - to find the equilibrium position at the bottom of a Morse potential for a given bond. This finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm.

=Metal Carbonyls =

Significance of carbon monoxide as a ligand especially with use towards IR as a show of it's bond strength in regards to the change in charge.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9538 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9538 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9538 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9538 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9538 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9538 -DE/DX = -0.0001 !
! R7 R(2,12) 1.166 -DE/DX = 0.0 !
! R8 R(3,9) 1.166 -DE/DX = 0.0 !
! R9 R(4,8) 1.166 -DE/DX = 0.0 !
! R10 R(5,11) 1.166 -DE/DX = 0.0 !
! R11 R(6,10) 1.166 -DE/DX = 0.0 !
! R12 R(7,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,7,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,12,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,9,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,9,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,13,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,7,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,12,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,9,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,9,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,13,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,7,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,6) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,7,5) 90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

Bonding orbitals

Antibonding orbitals

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

While going across the row would cause the bond lengths to shorten, the trends for the strengths of the bonds seen from IR is different.
For the C-O bond stretch, there is an increase as you go along the row, however for the M-C bond stretch, there is a decrease in bond strength. This is at odds with the shortening bond lengths calculated in the optimisations.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T12:34:45Z

Ylc17: /* The trends */

==BH3==

Gradient should be less than 0.001
Significant figures = 5 decimal places.
Do not compare energies with different methods/basis sets 

Purpose of optimisation - to find the equilibrium position at the bottom of a Morse potential for a given bond. This finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm.

=Metal Carbonyls =

Significance of carbon monoxide as a ligand especially with use towards IR as a show of it's bond strength in regards to the change in charge.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9538 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9538 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9538 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9538 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9538 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9538 -DE/DX = -0.0001 !
! R7 R(2,12) 1.166 -DE/DX = 0.0 !
! R8 R(3,9) 1.166 -DE/DX = 0.0 !
! R9 R(4,8) 1.166 -DE/DX = 0.0 !
! R10 R(5,11) 1.166 -DE/DX = 0.0 !
! R11 R(6,10) 1.166 -DE/DX = 0.0 !
! R12 R(7,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,7,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,12,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,9,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,9,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,13,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,7,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,12,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,9,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,9,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,13,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,7,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,6) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,7,5) 90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

Bonding orbitals

Antibonding orbitals

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is weaker. This would be seen in the decreased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only 12 are IR active. Of those 12, there is triple degeneracy across all of them resulting in 4 peaks.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

With considerations towards only the vibrations, if the C-O wavenumber is higher, this would suggest that there is lower back-bonding in comparison to the other complexes. This is also reflected in the weaker M-C bond. However, this is at odds with the computed optimum bond lengths.

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T12:24:40Z

Ylc17: /* The trends */

==BH3==

Gradient should be less than 0.001
Significant figures = 5 decimal places.
Do not compare energies with different methods/basis sets 

Purpose of optimisation - to find the equilibrium position at the bottom of a Morse potential for a given bond. This finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm.

=Metal Carbonyls =

Significance of carbon monoxide as a ligand especially with use towards IR as a show of it's bond strength in regards to the change in charge.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9538 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9538 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9538 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9538 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9538 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9538 -DE/DX = -0.0001 !
! R7 R(2,12) 1.166 -DE/DX = 0.0 !
! R8 R(3,9) 1.166 -DE/DX = 0.0 !
! R9 R(4,8) 1.166 -DE/DX = 0.0 !
! R10 R(5,11) 1.166 -DE/DX = 0.0 !
! R11 R(6,10) 1.166 -DE/DX = 0.0 !
! R12 R(7,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,7,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,12,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,9,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,9,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,13,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,7,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,12,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,9,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,9,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,13,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,7,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,6) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,7,5) 90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

Bonding orbitals

Antibonding orbitals

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is higher. This would be seen in the increased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only Something are IR active. Of those that are IR active, there are Something degenerate modes.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1 || M-C Stretch / cm-1
|-
|[V(CO)6]-
|1968
|457
|-
|[Cr(CO)6]
|2086
|429
|-
|[Mn(CO)6]+
|2198
|389
|-
|}

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T12:20:33Z

Ylc17: /* The trends */

==BH3==

Gradient should be less than 0.001
Significant figures = 5 decimal places.
Do not compare energies with different methods/basis sets 

Purpose of optimisation - to find the equilibrium position at the bottom of a Morse potential for a given bond. This finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm.

=Metal Carbonyls =

Significance of carbon monoxide as a ligand especially with use towards IR as a show of it's bond strength in regards to the change in charge.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9538 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9538 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9538 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9538 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9538 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9538 -DE/DX = -0.0001 !
! R7 R(2,12) 1.166 -DE/DX = 0.0 !
! R8 R(3,9) 1.166 -DE/DX = 0.0 !
! R9 R(4,8) 1.166 -DE/DX = 0.0 !
! R10 R(5,11) 1.166 -DE/DX = 0.0 !
! R11 R(6,10) 1.166 -DE/DX = 0.0 !
! R12 R(7,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,7,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,12,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,9,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,9,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,13,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,7,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,12,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,9,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,9,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,13,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,7,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,6) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,7,5) 90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

Bonding orbitals

Antibonding orbitals

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is higher. This would be seen in the increased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only Something are IR active. Of those that are IR active, there are Something degenerate modes.

{| class="wikitable"
|+
|-
| Species || C-O Stretch / cm-1
|-
|[V(CO)6]-
|1968
|-
|[Cr(CO)6]
|2086
|-
|[Mn(CO)6]+
|2198
|-
|}

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T12:09:12Z

Ylc17: /* References */

==BH3==

Gradient should be less than 0.001
Significant figures = 5 decimal places.
Do not compare energies with different methods/basis sets 

Purpose of optimisation - to find the equilibrium position at the bottom of a Morse potential for a given bond. This finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm.

=Metal Carbonyls =

Significance of carbon monoxide as a ligand especially with use towards IR as a show of it's bond strength in regards to the change in charge.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9538 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9538 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9538 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9538 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9538 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9538 -DE/DX = -0.0001 !
! R7 R(2,12) 1.166 -DE/DX = 0.0 !
! R8 R(3,9) 1.166 -DE/DX = 0.0 !
! R9 R(4,8) 1.166 -DE/DX = 0.0 !
! R10 R(5,11) 1.166 -DE/DX = 0.0 !
! R11 R(6,10) 1.166 -DE/DX = 0.0 !
! R12 R(7,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,7,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,12,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,9,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,9,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,13,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,7,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,12,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,9,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,9,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,13,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,7,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,6) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,7,5) 90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

Bonding orbitals

Antibonding orbitals

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is higher. This would be seen in the increased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only Something are IR active. Of those that are IR active, there are Something degenerate modes.

{| class="wikitable"
|+
|-
| Species || Stretch 1 / cm-1 ||Stretch 2 / cm-1 || Stretch 3 / cm-1
|-
|
|
|
|
|-
|
|
|
|
|-
|
|
|
|
|-
|}

== References ==

<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T12:08:40Z

Ylc17: /* References */

==BH3==

Gradient should be less than 0.001
Significant figures = 5 decimal places.
Do not compare energies with different methods/basis sets 

Purpose of optimisation - to find the equilibrium position at the bottom of a Morse potential for a given bond. This finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm.

=Metal Carbonyls =

Significance of carbon monoxide as a ligand especially with use towards IR as a show of it's bond strength in regards to the change in charge.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9538 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9538 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9538 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9538 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9538 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9538 -DE/DX = -0.0001 !
! R7 R(2,12) 1.166 -DE/DX = 0.0 !
! R8 R(3,9) 1.166 -DE/DX = 0.0 !
! R9 R(4,8) 1.166 -DE/DX = 0.0 !
! R10 R(5,11) 1.166 -DE/DX = 0.0 !
! R11 R(6,10) 1.166 -DE/DX = 0.0 !
! R12 R(7,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,7,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,12,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,9,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,9,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,13,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,7,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,12,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,9,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,9,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,13,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,7,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,6) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,7,5) 90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

Bonding orbitals

Antibonding orbitals

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is higher. This would be seen in the increased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only Something are IR active. Of those that are IR active, there are Something degenerate modes.

{| class="wikitable"
|+
|-
| Species || Stretch 1 / cm-1 ||Stretch 2 / cm-1 || Stretch 3 / cm-1
|-
|
|
|
|
|-
|
|
|
|
|-
|
|
|
|
|-
|}

== References ==
[[File:Oana.lemon.png|thumb|400px|centre| A lemon. ]]
<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

Y2T301339518

2019-05-24T12:08:20Z

Ylc17: /* References */

==BH3==

Gradient should be less than 0.001
Significant figures = 5 decimal places.
Do not compare energies with different methods/basis sets 

Purpose of optimisation - to find the equilibrium position at the bottom of a Morse potential for a given bond. This finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm.

=Metal Carbonyls =

Significance of carbon monoxide as a ligand especially with use towards IR as a show of it's bond strength in regards to the change in charge.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9538 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9538 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9538 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9538 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9538 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9538 -DE/DX = -0.0001 !
! R7 R(2,12) 1.166 -DE/DX = 0.0 !
! R8 R(3,9) 1.166 -DE/DX = 0.0 !
! R9 R(4,8) 1.166 -DE/DX = 0.0 !
! R10 R(5,11) 1.166 -DE/DX = 0.0 !
! R11 R(6,10) 1.166 -DE/DX = 0.0 !
! R12 R(7,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,7,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,12,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,9,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,9,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,13,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,7,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,12,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,9,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,9,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,13,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,7,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,6) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,7,5) 90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

Bonding orbitals

Antibonding orbitals

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is higher. This would be seen in the increased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only Something are IR active. Of those that are IR active, there are Something degenerate modes.

{| class="wikitable"
|+
|-
| Species || Stretch 1 / cm-1 ||Stretch 2 / cm-1 || Stretch 3 / cm-1
|-
|
|
|
|
|-
|
|
|
|
|-
|
|
|
|
|-
|}

== References ==
<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

[[File:Oana.lemon.png|thumb|400px|centre| A lemon. ]]

File:Oana.lemon.png

2019-05-24T12:08:12Z

Ylc17:

Y2T301339518

2019-05-24T11:32:00Z

Ylc17: /* Frequency Analysis */

==BH3==

Gradient should be less than 0.001
Significant figures = 5 decimal places.
Do not compare energies with different methods/basis sets 

Purpose of optimisation - to find the equilibrium position at the bottom of a Morse potential for a given bond. This finds the ground state of a given molecule. Mathematically, it’s the point at which <math>\frac {\partial V}{\partial r} = 0 </math>, where V is the potential energy and r is the separation distance between a given set of atoms bound to each other.

===Optimisation of BH3 via 3-21G ===
[[File:01339518BH3321G.png|thumb|400px|| The initial optimisation details of BH3]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000090 0.000450 YES
RMS Force 0.000059 0.000300 YES
Maximum Displacement 0.000350 0.001800 YES
RMS Displacement 0.000229 0.001200 YES
Predicted change in Energy=-4.546985D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1945 -DE/DX = -0.0001 !
! R2 R(1,3) 1.1945 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1945 -DE/DX = -0.0001 !
! 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 optimisation file is linked [[Media:01339518BH3321G.log| here]]

===Optimisation of BH3 via 6-31G ===
[[File:01339518BH3631G.png|thumb|400px|| The final optimisation details of BH3]]
The 6-31G(d,p) basis set is regarded as more accurate, and it returns a more stable energy for BH3.
<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000017 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.021830D-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 optimisation file is linked [[Media:01339518BH3631G.log| here]]

===IR activity of BH3===
<pre>
Low frequencies --- -11.7009 -11.6930 -6.5683 -0.0008 0.0280 0.4286
Low frequencies --- 1162.9745 1213.1389 1213.1392
Diagonal vibrational polarizability:
0.7179797 0.7179479 1.8418514
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
A2" E' E'
Frequencies -- 1162.9745 1213.1389 1213.1392
Red. masses -- 1.2531 1.1072 1.1072
Frc consts -- 0.9986 0.9600 0.9600
IR Inten -- 92.5682 14.0550 14.0544
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.16 -0.10 0.00 0.00 0.00 0.10 0.00
2 1 0.00 0.00 -0.57 0.81 0.00 0.00 0.00 0.08 0.00
3 1 0.00 0.00 -0.57 0.14 0.39 0.00 -0.39 -0.59 0.00
4 1 0.00 0.00 -0.57 0.14 -0.39 0.00 0.39 -0.59 0.00
4 5 6
A1' E' E'
Frequencies -- 2582.5816 2715.7183 2715.7192
Red. masses -- 1.0078 1.1273 1.1273
Frc consts -- 3.9604 4.8987 4.8987
IR Inten -- 0.0000 126.3320 126.3260
Atom AN X Y Z X Y Z X Y Z
1 5 0.00 0.00 0.00 0.11 0.00 0.00 0.00 0.11 0.00
2 1 0.00 0.58 0.00 0.02 0.00 0.00 0.00 -0.81 0.00
3 1 0.50 -0.29 0.00 -0.60 0.36 0.00 0.36 -0.19 0.00
4 1 -0.50 -0.29 0.00 -0.60 -0.36 0.00 -0.36 -0.19 0.00
</pre>

The frequency file is linked [[Media:01339518BH3Freq.log| here]]

<jmol><jmolApplet>
<title>BH3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518BH3Freq.log</uploadedFileContents>
</jmolApplet></jmol>

For BH3, as it's a non-linear molecule, the number of vibrational modes it has is <math>3N-6</math>, where <math>N</math> is the number of atoms (4). Therefore, it has 6 vibrational modes. This does not consider the degeneracy of the vibrational modes, or whether the vibrational mode has a change in dipole moment. In the IR spectrum below, only 3 peaks which can be seen. One of the vibrational modes has no change in dipole moment, therefore it is not IR active. For the other 2 peaks, they're each composed of 2 modes which are degenerate in energy, so they overlap each other and cannot be distinguished.

[[File:01339518IRBH3.png|thumb|800px|centre| The computed IR spectrum from the 6-31G(d,p) frequency calculation above.]]

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry label || IR active || Type
|-
|1162.97
|816.53
|A2"
|Yes
|sp2 out of plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|1213.14
|118.85
|E'
|Yes
|sp2 in plane bend
|-
|2715.72
|477.21
|E'
|Yes
|sp2 asymmetric stretch
|-
|2715.72
|477.19
|E'
|Yes
|sp2 asymmetric stretch
|-
|}

===BH3 MO diagram===
[[File:01339518BH3MO.png|thumb|600px|center| The MO diagram of BH3. The linear combination atomic orbitals (LCAOs) and the molecular orbitals (MOs) are drawn in black and white. The computed MOs are shown in red and green. Note the similarity in shape.]]

The use of a qualitative MO diagram (shown in Fig), gives a good representation of the shape of the orbitals and a moderate idea of the relative energy ordering of the orbital. The relative energy ordering is subjective and for any order to be confirmed, calculations are required. However, for the geometry of the orbitals, a qualitative MO diagram is adequate. The main features of each MO are still present in both the LCAO's and the computed MO's, such as the presence of nodes in the anti-bonding MOs (ABMOs) and the density of the MO's around given atoms.

==NH3==
[[File:01339518NH3631G.png|thumb|400px|| The optimisation details of NH3]]
===Optimisation of NH3===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844182D-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>

The optimisation file is [[Media:01339518NH3opt.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3opt.log</uploadedFileContents>
</jmolApplet></jmol>

==Ammonia-Borane==

[[File:01339518NH3BH3.png|thumb|400px|| The optimisation details of NH3-BH3]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000766 0.001800 YES
RMS Displacement 0.000177 0.001200 YES
Predicted change in Energy=-1.143978D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.2097 -DE/DX = 0.0 !
! R2 R(1,3) 1.2097 -DE/DX = 0.0 !
! R3 R(1,4) 1.2097 -DE/DX = 0.0 !
! R4 R(1,5) 1.6686 -DE/DX = -0.0001 !
! R5 R(5,6) 1.0185 -DE/DX = 0.0 !
! R6 R(5,7) 1.0185 -DE/DX = 0.0 !
! R7 R(5,8) 1.0185 -DE/DX = 0.0 !
! A1 A(2,1,3) 113.9013 -DE/DX = 0.0 !
! A2 A(2,1,4) 113.9013 -DE/DX = 0.0 !
! A3 A(2,1,5) 104.563 -DE/DX = 0.0001 !
! A4 A(3,1,4) 113.9013 -DE/DX = 0.0 !
! A5 A(3,1,5) 104.563 -DE/DX = 0.0001 !
! A6 A(4,1,5) 104.563 -DE/DX = 0.0001 !
! A7 A(1,5,6) 111.0363 -DE/DX = 0.0 !
! A8 A(1,5,7) 111.0363 -DE/DX = 0.0 !
! A9 A(1,5,8) 111.0363 -DE/DX = 0.0 !
! A10 A(6,5,7) 107.8618 -DE/DX = 0.0 !
! A11 A(6,5,8) 107.8618 -DE/DX = 0.0 !
! A12 A(7,5,8) 107.8618 -DE/DX = 0.0 !
! D1 D(2,1,5,6) -60.0 -DE/DX = 0.0 !
! D2 D(2,1,5,7) 180.0 -DE/DX = 0.0 !
! D3 D(2,1,5,8) 60.0 -DE/DX = 0.0 !
! D4 D(3,1,5,6) 180.0 -DE/DX = 0.0 !
! D5 D(3,1,5,7) 60.0 -DE/DX = 0.0 !
! D6 D(3,1,5,8) -60.0 -DE/DX = 0.0 !
! D7 D(4,1,5,6) 60.0 -DE/DX = 0.0 !
! D8 D(4,1,5,7) -60.0 -DE/DX = 0.0 !
! D9 D(4,1,5,8) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NH3BH3log.log|here]]

<jmol><jmolApplet>
<title>NI3 optimised via 6-31G</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NH3BH3log.log</uploadedFileContents>
</jmolApplet></jmol>

With considerations for the energy of BH3 (-26.61532364 a.u), NH3 (-56.55776873 a.u) and H3B-NH3 (-83.22468887 a.u), the difference in energy between the 2 molecules and the single molecule is -0.0515965 a.u. For more contextual units, that's 135.5 kJmol-1. This corresponds to the energy of the B-N bond. A C-C bond is 346 kJmol-1 <ref name = 'Atkins'/>, which is moderate. A B-N bond in comparison is much weaker.

==NI3==

===Optimisation===
[[File:01339518NI3GENOPT.png|thumb|400px|| The optimisation details of NI3. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000192 0.001800 YES
RMS Displacement 0.000126 0.001200 YES
Predicted change in Energy=-8.028147D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.1836 -DE/DX = 0.0 !
! R2 R(1,3) 2.1836 -DE/DX = 0.0 !
! R3 R(1,4) 2.1836 -DE/DX = 0.0 !
! A1 A(2,1,3) 110.8866 -DE/DX = 0.0 !
! A2 A(2,1,4) 110.8866 -DE/DX = 0.0 !
! A3 A(3,1,4) 110.8866 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 123.6452 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The optimisation file is [[Media:01339518NI3GENOPT.log|here]]

===Frequency calculation===
<pre>
Low frequencies --- -0.0576 -0.0292 -0.0031 1.9682 2.0035 2.2189
Low frequencies --- 101.3080 101.3087 148.3159
Diagonal vibrational polarizability:
12.4608723 12.4575690 1.3046911
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
1 2 3
E E A1
Frequencies -- 101.3080 101.3087 148.3159
Red. masses -- 115.8870 115.8871 104.7718
Frc consts -- 0.7008 0.7008 1.3579
IR Inten -- 1.0245 1.0246 0.8821
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.31 0.00 -0.31 0.00 0.00 0.00 0.00 -0.44
2 53 0.00 0.54 0.01 0.56 0.00 0.00 0.00 0.52 0.02
3 53 -0.47 -0.29 0.00 -0.26 0.47 -0.01 0.45 -0.26 0.02
4 53 0.47 -0.29 0.00 -0.26 -0.47 0.01 -0.45 -0.26 0.02
4 5 6
A1 E E
Frequencies -- 361.2374 468.9935 469.0019
Red. masses -- 14.8160 14.7159 14.7159
Frc consts -- 1.1391 1.9071 1.9072
IR Inten -- 1.0935 79.8887 79.8677
Atom AN X Y Z X Y Z X Y Z
1 7 0.00 0.00 1.00 1.00 0.00 0.00 0.00 1.00 0.00
2 53 0.00 0.03 -0.04 -0.01 0.00 0.00 0.00 -0.06 0.02
3 53 0.03 -0.02 -0.04 -0.05 0.02 0.02 0.02 -0.03 -0.01
4 53 -0.03 -0.02 -0.04 -0.05 -0.02 -0.02 -0.02 -0.03 -0.01
</pre>

The frequency file is [[Media:01339518NI3GENFreqlog.log|here]]

<jmol><jmolApplet>
<title>NI3 Nitrogen was optimised by 6-31G, whereas the iodine atoms were optimised via pseudo potential (LanL2DZ)</title>
<color>black</color>
<size>300</size>
<uploadedFileContents>01339518NI3GENFreqlog.log</uploadedFileContents>
</jmolApplet></jmol>

The optimised N-I bond distance is 0.218 nm.

=Metal Carbonyls =

Significance of carbon monoxide as a ligand especially with use towards IR as a show of it's bond strength in regards to the change in charge.

==[V(CO)6]-==
===Optimisation of the anion===
[[File:01339518VCO6Summary.png|thumb|400px|| The optimisation details of [V(CO)6]-. The method and basis set for the CO ligands was 6-31G(d,p), and for the metal centre, it was LanL2DZ. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000532 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.235706D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9538 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9538 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9538 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9538 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9538 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9538 -DE/DX = -0.0001 !
! R7 R(2,12) 1.166 -DE/DX = 0.0 !
! R8 R(3,9) 1.166 -DE/DX = 0.0 !
! R9 R(4,8) 1.166 -DE/DX = 0.0 !
! R10 R(5,11) 1.166 -DE/DX = 0.0 !
! R11 R(6,10) 1.166 -DE/DX = 0.0 !
! R12 R(7,13) 1.166 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,7,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,12,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,9,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,9,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,13,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,7,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,12,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,9,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,9,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,13,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,5,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,7,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,6) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,7,5) 90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518VLOG.log|here]]

===Frequency Analysis===

<pre>
Low frequencies --- -0.0012 -0.0011 -0.0010 5.5219 5.5220 5.5220
Low frequencies --- 50.4353 50.4353 50.4353
</pre>

The file is [[Media:01339518VFREQ.log|here]]

==[Cr(CO)6]==
===Optimisation of the complex ===
[[File:01339518CrSUM.png|thumb|400px|| The optimisation details of [Cr(CO)6]. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000109 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000703 0.001800 YES
RMS Displacement 0.000333 0.001200 YES
Predicted change in Energy=-2.360252D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9154 -DE/DX = -0.0001 !
! R2 R(1,3) 1.9154 -DE/DX = -0.0001 !
! R3 R(1,4) 1.9154 -DE/DX = -0.0001 !
! R4 R(1,5) 1.9154 -DE/DX = -0.0001 !
! R5 R(1,6) 1.9154 -DE/DX = -0.0001 !
! R6 R(1,7) 1.9154 -DE/DX = -0.0001 !
! R7 R(2,9) 1.1494 -DE/DX = 0.0 !
! R8 R(3,13) 1.1494 -DE/DX = 0.0 !
! R9 R(4,12) 1.1494 -DE/DX = 0.0 !
! R10 R(5,11) 1.1494 -DE/DX = 0.0 !
! R11 R(6,10) 1.1494 -DE/DX = 0.0 !
! R12 R(7,8) 1.1494 -DE/DX = 0.0 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,5) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A12 A(6,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,5,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,6,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(4,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,9,8,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,13,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,12,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,11,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,10,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,8,9,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,5,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,6,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(4,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,9,8,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,13,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,12,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,11,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,10,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,8,9,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) 90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,4) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,6) -90.0 -DE/DX = 0.0 !
! D5 D(3,1,5,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,5) 90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) -90.0 -DE/DX = 0.0 !
! D8 D(5,1,7,6) 90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518CRLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518CRFREQ.log|here]]

<pre>
Low frequencies --- 0.0009 0.0011 0.0012 5.2328 5.2329 5.2330
Low frequencies --- 65.2259 65.2260 65.2260
</pre>

==[Mn(CO)6]+==
===Optimisation of the cation ===
[[File:01339518MNSUM.png|thumb|400px|| The optimisation details of [Mn(CO)6]+. ]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000382 0.000450 YES
RMS Force 0.000132 0.000300 YES
Maximum Displacement 0.000237 0.001800 YES
RMS Displacement 0.000083 0.001200 YES
Predicted change in Energy=-3.146435D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.9079 -DE/DX = 0.0 !
! R2 R(1,3) 1.9079 -DE/DX = 0.0 !
! R3 R(1,4) 1.9079 -DE/DX = 0.0 !
! R4 R(1,5) 1.9079 -DE/DX = 0.0 !
! R5 R(1,6) 1.9079 -DE/DX = 0.0 !
! R6 R(1,7) 1.9079 -DE/DX = 0.0 !
! R7 R(2,11) 1.1359 -DE/DX = -0.0004 !
! R8 R(3,12) 1.1359 -DE/DX = -0.0004 !
! R9 R(4,8) 1.1359 -DE/DX = -0.0004 !
! R10 R(5,9) 1.1359 -DE/DX = -0.0004 !
! R11 R(6,13) 1.1359 -DE/DX = -0.0004 !
! R12 R(7,10) 1.1359 -DE/DX = -0.0004 !
! A1 A(2,1,3) 90.0 -DE/DX = 0.0 !
! A2 A(2,1,5) 90.0 -DE/DX = 0.0 !
! A3 A(2,1,6) 90.0 -DE/DX = 0.0 !
! A4 A(2,1,7) 90.0 -DE/DX = 0.0 !
! A5 A(3,1,4) 90.0 -DE/DX = 0.0 !
! A6 A(3,1,6) 90.0 -DE/DX = 0.0 !
! A7 A(3,1,7) 90.0 -DE/DX = 0.0 !
! A8 A(4,1,5) 90.0 -DE/DX = 0.0 !
! A9 A(4,1,6) 90.0 -DE/DX = 0.0 !
! A10 A(4,1,7) 90.0 -DE/DX = 0.0 !
! A11 A(5,1,6) 90.0 -DE/DX = 0.0 !
! A12 A(5,1,7) 90.0 -DE/DX = 0.0 !
! A13 L(2,1,4,3,-1) 180.0 -DE/DX = 0.0 !
! A14 L(3,1,5,2,-1) 180.0 -DE/DX = 0.0 !
! A15 L(6,1,7,2,-1) 180.0 -DE/DX = 0.0 !
! A16 L(1,2,11,9,-1) 180.0 -DE/DX = 0.0 !
! A17 L(1,3,12,8,-1) 180.0 -DE/DX = 0.0 !
! A18 L(1,4,8,9,-1) 180.0 -DE/DX = 0.0 !
! A19 L(1,5,9,8,-1) 180.0 -DE/DX = 0.0 !
! A20 L(1,6,13,8,-1) 180.0 -DE/DX = 0.0 !
! A21 L(1,7,10,8,-1) 180.0 -DE/DX = 0.0 !
! A22 L(2,1,4,3,-2) 180.0 -DE/DX = 0.0 !
! A23 L(3,1,5,2,-2) 180.0 -DE/DX = 0.0 !
! A24 L(6,1,7,2,-2) 180.0 -DE/DX = 0.0 !
! A25 L(1,2,11,9,-2) 180.0 -DE/DX = 0.0 !
! A26 L(1,3,12,8,-2) 180.0 -DE/DX = 0.0 !
! A27 L(1,4,8,9,-2) 180.0 -DE/DX = 0.0 !
! A28 L(1,5,9,8,-2) 180.0 -DE/DX = 0.0 !
! A29 L(1,6,13,8,-2) 180.0 -DE/DX = 0.0 !
! A30 L(1,7,10,8,-2) 180.0 -DE/DX = 0.0 !
! D1 D(2,1,6,3) 90.0 -DE/DX = 0.0 !
! D2 D(2,1,7,3) -90.0 -DE/DX = 0.0 !
! D3 D(2,1,6,5) -90.0 -DE/DX = 0.0 !
! D4 D(2,1,7,5) 90.0 -DE/DX = 0.0 !
! D5 D(3,1,6,4) 90.0 -DE/DX = 0.0 !
! D6 D(3,1,7,4) -90.0 -DE/DX = 0.0 !
! D7 D(4,1,6,5) 90.0 -DE/DX = 0.0 !
! D8 D(4,1,7,5) -90.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

The file is [[Media:01339518MNLOG.log|here]]

===Frequency Analysis===
The file is [[Media:01339518MnFREQ.log|here]]
<pre>
Low frequencies --- 0.0010 0.0012 0.0013 5.9353 5.9353 5.9353
Low frequencies --- 76.1371 76.1371 76.1371
</pre>

===MO discussion of [Mn(CO)6]+ ===

Bonding orbitals

Antibonding orbitals

==The trends ==
For the 3 transition metal complexes that have been optimised, they're each isoelectronic, they each have the same point group, and they have the same ligands. As you go along the row, the trend that would be expected is that the bonds between the metal and the carbon would decrease due to the increased effective nuclear charge on the transition metal. The trend is shown in the table below.

{| class="wikitable"
|+
|-
|Species || M-C length / pm || CO length / pm
|-
|[V(CO)6]-
|195.4
|116.6
|-
|[Cr(CO)6]
|191.5
|114.9
|-
|[Mn(CO)6]+
|190.8
|113.6
|}

As well as this, the increased bond length means that the strength of the bond is higher. This would be seen in the increased wavenumber of the vibrational modes that the complexes all experience. For all the complexes, they have 33 vibrational modes. Of these, only Something are IR active. Of those that are IR active, there are Something degenerate modes.

{| class="wikitable"
|+
|-
| Species || Stretch 1 / cm-1 ||Stretch 2 / cm-1 || Stretch 3 / cm-1
|-
|
|
|
|
|-
|
|
|
|
|-
|
|
|
|
|-
|}

== References ==
<references>
<ref name = "Atkins"> Atkins P, D Paula J. Physical Chemistry. 10th Editi. Oxford University Press; 2014. </ref>
<references/>

File:01339518MnFREQ.log

2019-05-24T11:31:09Z

Ylc17: