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Introduction

Computational chemistry is a powerful technique to analyse compounds. This is of particular use when these compounds are toxic, expensive or impractical to test manually using standard laboratory techniques. Recently, with advances in computing power and better models, computational chemistry has come to the fore as a tool to design better catalysts, and to analyse a wide range of ionic liquids which would be impractical to synthesis in their entirety, allowing their properties and reactivity to be analysed from the comfort of the researchers desk.

Part 1

A range of simple molecules are built, optimised and analysed using Guassview 09.

Borane Optimisation

Initial Optimisation

BH3
Optimised
File Type .log
Log File File:BH3 OPT2 log OB.LOG
Calculation Type FOPT
Calculation Method B3YLP
Basis Set 3-21G
Final Energy -26.46 a.u.
Gradient 0.00020672 a.u.
Dipole Moment 0.00 Debye
Point Group D3H
CPU Time 7.0 seconds
B-H Bond Length 1.19 a.u.
H-B-H Bond Angle 120.0


Initially BH3 was drawn in with a trigonal planar geometry with 1.5Å B-H bond lengths. It was then optimised using a B3LYP method with a 3-21G basis set. Although this basis set has a very low accuracy, because of the small number of atoms and high level of symmetry (D3h) in borane, the basis set is sufficient.

The optimisation converged successfully as shown below. 

Item               Value     Threshold  Converged?
 Maximum Force            0.000413     0.000450     YES
 RMS     Force            0.000271     0.000300     YES
 Maximum Displacement     0.001610     0.001800     YES
 RMS     Displacement     0.001054     0.001200     YES
 Predicted change in Energy=-1.071764D-06
 Optimization completed.
    -- Stationary point found.


Optimisation Procedure

Some Gumph about how it optiises by changing the schrodinger equation and iterates values.

6-31G(d,p) Optimisation

Using the geometry optimised above, the more accurate basis set 6-31G(d,p) was used to further refine the optimisation of BH3

BH3 6-31G(d,p)
Optimised
File Type .log
Log File File:BH3 OPT 631 G OB.LOG
Calculation Type FOPT
Calculation Method RB3YLP
Basis Set 6-31G(d,p)
Final Energy -26.62 a.u.
Gradient 0.00000235 a.u.
Dipole Moment 0.00 Debye
Point Group D3H
CPU Time 8.0 seconds
B-H Bond Length 1.19 a.u.
H-B-H Bond Angle 120.0

The optimisation converged successfully. 

Item               Value     Threshold  Converged?
 Maximum Force            0.000005     0.000450     YES
 RMS     Force            0.000003     0.000300     YES
 Maximum Displacement     0.000019     0.001800     YES
 RMS     Displacement     0.000012     0.001200     YES
 Predicted change in Energy=-1.304276D-10
 Optimization completed.
    -- Stationary point found.

Comparison

These two results cannot be directly compared as they use different basis sets for the calculations, however both of the bond angles and lengths agree with literature values[1]

TlBr3

TlBr3
Optimised
File Type .log
Log File File:Log 69185.log
D-Space DOI:10042/22681
Calculation Type FOPT
Calculation Method RB3YLP
Basis Set LANL2DZ
Final Energy -91.22 a.u.
Gradient 0.00000090 a.u.
Dipole Moment 0.00 Debye
Point Group D3H
CPU Time 28.3 seconds
Tl-Br Bond Length 2.65 a.u.
Br-Tl-Br Bond Angle 120.0


TlBr3 was constructed using Gaussview, and its symmetry restricted to D3h (with a tolerance of 0.0001). A medium level basis set was used for the optimisation, that uses pseudo potentials with heavier elements. With over 186 electrons, TlBr3 displays relativistic effects which the standard Schrodinger equation doesn't recover. The idea is that there is little (to none) overlap between the core electrons and the valence electrons. These core electrons are not involved in bonding and the normal Coulombic term that would represent them in the Schrodinger equation is modified. This has the benefit of drastically reducing the number of electrons involved in calculations; hence a smaller basis set is needed.

The molecule successfully converged. 

Item               Value     Threshold  Converged?
 Maximum Force            0.000002     0.000450     YES
 RMS     Force            0.000001     0.000300     YES
 Maximum Displacement     0.000022     0.001800     YES
 RMS     Displacement     0.000014     0.001200     YES
 Predicted change in Energy=-6.084002D-11
 Optimization completed.
    -- Stationary point found.

BBr3

BBr3
File Type .log
Log File File:Log 69204.log
D-Space DOI:10042/22680
Calculation Type FOPT
Calculation Method RB3YLP
Basis Set Gen
Final Energy -64.44 a.u.
Gradient 0.00000382 a.u.
Dipole Moment 0.00 Debye
Point Group D3H
CPU Time 16.4 seconds
Tl-Br Bond Length 1.93 a.u.
Br-Tl-Br Bond Angle 120.0


BBr3, as it combines light and heavier elements needs a combination of pseudo potentials and basis sets. The BH3 optimised using the 6-31G(d,p)basis set was used as a starting point to construct the BBr3 molecule.

The molecule successfully converged. 


Item               Value     Threshold  Converged?
 Maximum Force            0.000008     0.000450     YES
 RMS     Force            0.000005     0.000300     YES
 Maximum Displacement     0.000036     0.001800     YES
 RMS     Displacement     0.000023     0.001200     YES
 Predicted change in Energy=-4.026780D-10
 Optimization completed.
    -- Stationary point found.

Comparing and Contrasting BH3 BBr3 and TlBr3

Analyzing Bond Lengths
Molecule Bond Distance (a.u.)
BH3 1.19
BBr3 1.93
TlBr3 2.65

As the molecules get heavier and bigger, the bonds get longer. This pattern is observed throughout chemistry and is because further down a group the atoms are, the more higher their nuclear charge and the higher the number of electrons. these electrons, due to several factors including shielding, electrostatic repulsion, and the Pauli exclusion principle. H and Br are similar in that they both require one electron to 'fill' their molecular orbitals and so they have a full valence orbitals and are at their msot stable. How they differ however is that the hydrogen bonds are purely s in character, due to the nature of the hydrogen atom and only having one electron. The bonds with the Br atom, by contrast will have some p character due to the position of Br in the periodic table; it requires a p electron. The valence atomic orbitals in Br are a lot more diffuse than the s orbital in H due to the larger size of the atom. Br is also a lot heavier than H, and this will, coupled with the large increase in size will drastically effect the nature of bonds made. Within Guassview, a bond is determined by physical, through space distance. While for most molecules this gross approximation is sufficient, in some circumstances it does not represent the tru nature of the interactions between the molecules. A chemical bond is a strong electrostatic attraction between two or more molecules, with a high electron density between the two nuclei which binds them together.

Frequency Analysis

With knowledge gleaned from a frequency analysis, an IR spectra can be computed, predicting what stretches will occur and at what energies.

BH3

The previously optimised (using the 6-31G(d,p) basis set) BH3 molecule was analysed using Guassian.

BH3
Optimised
File Type .log
Log File File:OHB BH3 FREQ.LOG
Calculation Type FREQ
Calculation Method RB3YLP
Basis Set 6-31G(d,p)
Final Energy -26.62 a.u.
Gradient 0.00000237 a.u.
Dipole Moment 0.00 Debye
Point Group D3H
CPU Time 7.0 seconds
B-H Bond Length 1.19 a.u.
H-B-H Bond Angle 120.0 
Item               Value     Threshold  Converged?
 Maximum Force            0.000005     0.000450     YES
 RMS     Force            0.000002     0.000300     YES
 Maximum Displacement     0.000019     0.001800     YES
 RMS     Displacement     0.000009     0.001200     YES
 Predicted change in Energy=-1.323374D-10
 Optimization completed.
    -- Stationary point found.

Low frequencies ---   -0.9033   -0.7343   -0.0054    6.7375   12.2491   12.2824
 Low frequencies --- 1163.0003 1213.1853 1213.1880
Vibrations of BH3
Number Form of Vibration Description Frequency Intensity Symmetry D3H
1
Vibration
 Wag - All Hydrogens remain in plane and move together perpendicular to it, B moves in opposite direction 1163.00 92.54 A2"
2
Vibration
 Two hydrogens scissoring, other H and Boron moving away 1213.19 14.06 E'
3
Vibration
 Two hydrogens scissoring, third hydrogen moving laterally, boron counteracting motion. All in the same plane. 1213.19 14.06 E'
4
Vibration
 All three hydrogens symmetrically stretching 2582.26 0.00 A1'
5
Vibration
 Two hydrogens asymetrically stretching 2715.43 126.33 E'
6
Vibration
 Two hydrogens symmetrically stretching with each other, asymetrically with the third 2715.43 126.33 E'


While there are six vibrational modes, (see table, 'above') there are only three vibrations shown on the computed IR spectrum. This is for two reasons. Firstly, one of the vibrations has an intensity of 0, so does not show up on the spectrum as it is the same as the baseline. Secondly, there are two sets of two vibrations that occur at the same frequency and so the four vibrations, (modes 1 & 2 and modes 3 & 4) only show up as two vibrations.

TlBr3

The previously optimised TlBr3 molecule was analysed.

TlBr3
Optimised
File Type .log
Log File File:Ohb tlbr3 freq.log
D-Space DOI:10042/22683
Calculation Type Freq
Calculation Method RB3YLP
Basis Set LANL2DZ
Final Energy -91.22 a.u.
Gradient 0.00000088 a.u.
Dipole Moment 0.00 Debye
Point Group D3H
CPU Time 28.5 seconds
Tl-Br Bond Length 2.65 a.u.
Br-Tl-Br Bond Angle 120.0 


Item               Value     Threshold  Converged?
 Maximum Force            0.000002     0.000450     YES
 RMS     Force            0.000001     0.000300     YES
 Maximum Displacement     0.000022     0.001800     YES
 RMS     Displacement     0.000011     0.001200     YES
 Predicted change in Energy=-5.660901D-11
 Optimization completed.
    -- Stationary point found.

Low frequencies ---   -3.4213   -0.0026   -0.0004    0.0015    3.9367    3.9367
 Low frequencies ---   46.4289   46.4292   52.1449
Vibrations of TlBr3
Number Form of Vibration Description Frequency (cm-1) Intensity Symmetry D3H
1
Vibration
 Two Br scissoring, other Br and Boron moving away 46.43 3.69 E'
2
Vibration
 Rocking in plane. 46.43 3.69 E'
3
Vibration
 Wag - All Br remain in plane and move together perpendicular to it, Tl moves in opposite direction 52.14 3.69 A2"
4
Vibration
 All three Br symmetrically stretching 165.27 0.00 A1'
5
Vibration
 Two Br asymetrically stretching 210.69 126.33 E'
6
Vibration
 Two Br symmetrically stretching with each other, asymetrically with the third 210.69 126.33 E'


While there are six vibrational modes, (see table) there are only three vibrations shown on the computed IR spectrum. One of the vibrations has an intensity of 0, so does not show up on the spectrum as it is the same as the baseline. It has an intensity of 0 as it is a symmetrical stretch and does not change the dipole, it is therefore IR inactive.

Secondly, there are two sets of two vibrations that are degenerate, so the four vibrations, (modes 1 & 2 and modes 3 & 4) only show up as two vibrations.


Comparison of Frequencies and Analysis

Vibrations of TlBr3
Symmetry TlBr3 Frequency (cm-1) BH3 Frequency (cm-1)
E' 46.43 1213.19
E' 46.43 1213.19
A2" 52.14 1163.00
A1' 165.27 2582.26
E' 210.69 2715.43
E' 210.69 2715.43

There is a large difference in the frequencies between TlBr3 and BH3, over an order of magnitude difference. This can be explained by the effect of the reduced mass on the effect of vibrational frequencies. Using the approximation of Hooke's law to model the vibrational modes, where

ν¯=12πcfμ

Thus the magnitude of the vibrational modes is inversely proportional to the square root of μ.

μ=m1m2m1+m2,

and so μ for BH3 is 0.92, whereas for TlBr3 it is 57, a much higher value. Another reason is that the B-H bond is a lot stronger than the Tl-Br bond. In BH3, the orbitals overlap significantly, producing a stronger bond, whereas in the TlBr3 analogue, because of the larger, more diffuse orbitals, the overlap is poorer, leading to a weaker bond. Both spectra display three peaks, two of these are the result of the summation of two degenerate vibrational modes. In both spectra the A2' and E' modes lie close together and at a higher energy, the A1' and E' modes lie close together. the large E gap between the two groups of modes, which is present in both molecules is due to the different amount of energy required to bend or stretch a molecule. Bending requires significantly lower energy to occur and as such all of the bending modes occur at lower frequencies. The ordering of the modes is however switched between the two molecules, as highlighted by the diagram. It is switched due to the different masses of the elements involved; as Br is a lot more massive than H, it requires more energy to perform the out of plane bending required of the A2' mode. The same logic can be applied as to why the A1' mode is lower than the E' modes for the BH3 molecule; due to the relative lightness of the hydrogen atom it requires very little energy to move it out of the plane of the atom, and hence happens at a lower frequency.

The same method and basis set must be used for both the optimisation and frequency calculations because the method used and quality of the basis set used directly effect the molecules final energy. If different methods and basis sets are used it is like comparing apples and oranges; different methods and quality of starting assumptions have been used and so will generate a different result; the end products are not comparable.

The "low frequencies" in the frequency calculation represent the molecules centre of mass. If a non linear molecule has 3N-6 normal vibrational modes [2] the low frequencies represent the -6 of the number of modes.

Mo Analysis

BH3

The previously optimised (#6-31G(d,p) Optimisation) BH3 molecule had it's MOs calculated.


BH3
Vibration
File Type .fch
Log File File:Bh3 opt 631 g OB.chk
Calculation Type SP
Calculation Method RB3YLP
Basis Set 6-31G(D,P)
Final Energy -26.62 a.u.
Gradient 0.00000000 a.u.
Dipole Moment 0.00 Debye
Point Group
CPU Time 8.0 seconds
B-H Bond Length 1.19 a.u.
H-B-H Bond Angle 120.0


The calculated and qualitated MO diagrams show very similar if not exactly the same result. The Calculated MO's are more spread out, highlighting the more diffuse nature, however the differences are small; this shows the power of qualitative MO theory and how well it relates to high power comptational methods.

NBO analysis

NH3 was optimised using the 6-31G(d,p) basis set. It is appropriate to skip the initial optimisation that was performed for BH3 as NH3 is a smaller molecule. Frequency analysis was also carried out to ensure a minimum was obtained.

NH3
Molecule
Vibration
File Type .log .log .log
Log File File:OhbNH3OPT.LOG File:OHBNH3FREQ.LOG File:OHBNH3NBO.LOG
Calculation Type FOPT FREQ SP
Calculation Method RB3YLP RB3YLP RB3YLP
Basis Set 6-31G(d,p) 6-31G(d,p) 6-31G(d,p)
Final Energy -56.56 a.u. -56.56 a.u. -56.56 a.u.
Gradient 0.00000289 a.u. 0.00000281 a.u. -
Dipole Moment 1.8464 Debye 1.8464 Debye 1.8464 Debye
Point Group C3V C3 C3V
CPU Time 13.0 seconds 8.0 seconds 3.0 seconds

The outputs are summarised below

Optimisation
          Item               Value     Threshold  Converged?
 Maximum Force            0.000005     0.000450     YES
 RMS     Force            0.000003     0.000300     YES
 Maximum Displacement     0.000010     0.001800     YES
 RMS     Displacement     0.000007     0.001200     YES
 Predicted change in Energy=-7.830780D-11
 Optimization completed.
Frequency analysis
Low frequencies ---  -11.6313  -11.5960   -0.0028    0.0243    0.1402   25.5608
 Low frequencies --- 1089.6620 1694.1733 1694.1736

         Item               Value     Threshold  Converged?
 Maximum Force            0.000005     0.000450     YES
 RMS     Force            0.000003     0.000300     YES
 Maximum Displacement     0.000011     0.001800     YES
 RMS     Displacement     0.000006     0.001200     YES
 Predicted change in Energy=-8.408692D-11

NBO Analysis

colour range from -1 to +1
(Occupancy)   Bond orbital/ Coefficients/ Hybrids
 ---------------------------------------------------------------------------------
     1. (1.99909) BD ( 1) N   1 - H   2  
                ( 68.83%)   0.8297* N   1 s( 24.87%)p 3.02( 75.05%)d 0.00(  0.09%)
                                            0.0001  0.4986  0.0059  0.0000  0.0000
                                            0.0000  0.8155  0.0277 -0.2909  0.0052
                                            0.0000  0.0000 -0.0281 -0.0087  0.0013
                ( 31.17%)   0.5583* H   2 s( 99.91%)p 0.00(  0.09%)
                                            0.9996  0.0000  0.0000 -0.0289  0.0072
     2. (1.99909) BD ( 1) N   1 - H   3  
                ( 68.83%)   0.8297* N   1 s( 24.87%)p 3.02( 75.05%)d 0.00(  0.09%)
                                            0.0001  0.4986  0.0059  0.0000 -0.7062
                                           -0.0240 -0.4077 -0.0138 -0.2909  0.0052
                                            0.0076  0.0243  0.0140  0.0044  0.0013
                ( 31.17%)   0.5583* H   3 s( 99.91%)p 0.00(  0.09%)
                                            0.9996  0.0000  0.0250  0.0145  0.0072
     3. (1.99909) BD ( 1) N   1 - H   4  
                ( 68.83%)   0.8297* N   1 s( 24.87%)p 3.02( 75.05%)d 0.00(  0.09%)
                                            0.0001  0.4986  0.0059  0.0000  0.7062
                                            0.0240 -0.4077 -0.0138 -0.2909  0.0052
                                           -0.0076 -0.0243  0.0140  0.0044  0.0013
                ( 31.17%)   0.5583* H   4 s( 99.91%)p 0.00(  0.09%)
                                            0.9996  0.0000 -0.0250  0.0145  0.0072
     4. (1.99982) CR ( 1) N   1           s(100.00%)
                                            1.0000 -0.0002  0.0000  0.0000  0.0000
                                            0.0000  0.0000  0.0000  0.0000  0.0000
                                            0.0000  0.0000  0.0000  0.0000  0.0000
     5. (1.99721) LP ( 1) N   1           s( 25.38%)p 2.94( 74.53%)d 0.00(  0.10%)
                                            0.0001  0.5036 -0.0120  0.0000  0.0000
                                            0.0000  0.0000  0.0000  0.8618 -0.0505
                                            0.0000  0.0000  0.0000  0.0000 -0.0310

Natural Bond Orbitals (Summary):

                                                            Principal Delocalizations
           NBO                        Occupancy    Energy   (geminal,vicinal,remote)
 ====================================================================================
 Molecular unit  1  (H3N)
     1. BD (   1) N   1 - H   2          1.99909    -0.60417   
     2. BD (   1) N   1 - H   3          1.99909    -0.60417   
     3. BD (   1) N   1 - H   4          1.99909    -0.60417   
     4. CR (   1) N   1                  1.99982   -14.16767   
     5. LP (   1) N   1                  1.99721    -0.31755  16(v),20(v),24(v),17(v)
                                                    21(v),25(v)

The natural bond order analysis shows where the electrons are situated and how the bonding occurs within the molecule. The information above shows that the three N-H bonds are equal in energy, and the lone pair has a high energy and all are occupied by two electrons; ie the bonds are 2c-2e bonds. It also hiughlight that the nitrogen bonds are sp3 hybridised as each one has a 24.87% S character and a 75.05% p character.

NH3BH3

A molecule of NH3BH3 was optimised to the 6-31G(d,p) level using the B3YLP method.

NH3
Molecule
Vibration
File Type .log .log .log
Log File File:OHBNB1.LOG File:OHBNB2.LOG File:OHBNB3.LOG
Calculation Type FOPT FOPT FREQ
Calculation Method RB3YLP RB3YLP RB3YLP
Basis Set 3-21G 6-31G(d,p) 6-31G(d,p)
Final Energy -82.7666 a.u. -83.2247 a.u. -83.2247 a.u.
Gradient 0.00003006 a.u. 0.00005659 a.u. 0.00005643 a.u.
Dipole Moment 5.8431 Debye 5.5623 Debye 5.5623 Debye
Point Group C1 C1 C1
CPU Time 29.0 seconds 30.0 seconds 38.0 seconds

3-21G Optimisation

        Item               Value     Threshold  Converged?
 Maximum Force            0.000094     0.000450     YES
 RMS     Force            0.000030     0.000300     YES
 Maximum Displacement     0.000419     0.001800     YES
 RMS     Displacement     0.000178     0.001200     YES
 Predicted change in Energy=-5.742842D-08
 Optimization completed.
    -- Stationary point found.

6-31G(d,p) Optimisation

        Item               Value     Threshold  Converged?
 Maximum Force            0.000133     0.000450     YES
 RMS     Force            0.000037     0.000300     YES
 Maximum Displacement     0.001280     0.001800     YES
 RMS     Displacement     0.000567     0.001200     YES
 Predicted change in Energy=-1.199663D-07
 Optimization completed.
    -- Stationary point found.

Frequency

       Low frequencies ---   -0.0013   -0.0010    0.0010    9.3030   12.2326   19.6429
 Low frequencies ---  263.2969  631.3087  637.9206

Item               Value     Threshold  Converged?
 Maximum Force            0.000254     0.000450     YES
 RMS     Force            0.000056     0.000300     YES
 Maximum Displacement     0.001417     0.001800     YES
 RMS     Displacement     0.000712     0.001200     YES
 Predicted change in Energy=-2.159749D-07
 Optimization completed.
    -- Stationary point found.

Comparison of reaction energies

Species Energy (a.u.)
NH3 -56.5578
BH3 -26.6153
BH3NH3 -83.2247 a.u.

The difference in energy between the two reactants and the Lewis acid-base adduct is 135.4758kJ/mol

Part 2 - Ionic Liquids

Ionic liquids are molten ionic salts which are liquids at room temperature. They have some quite novel properties, and are being researched for use in liquid flow supercapacitors [3]

Comparison of cations

[N(CH3)4 ]+

[N(CH3)4 ]+
Molecule
Vibration
File Type .log .log .log .fch
Log File File:OhbN1 321log 69500.log File:OhbN2 631log 69503.log File:OhbN3 FREQlog 69513.log File:OhbN4 MOlog 69525.log
D-Space DOI:10042/22661 DOI:10042/22662 DOI:10042/22663 DOI:10042/22664
Calculation Type FOPT FOPT FREQ SP
Calculation Method RB3YLP RB3YLP RB3YLP RB3YLP
Basis Set 3-21 6-31G(d,p) 6-31G(d,p) 6-31G(d,p)
Final Energy -213.0164 a.u. -214.1813 a.u. -214.1813 a.u. -214.1813 a.u.
Gradient 0.00000763 a.u. 0.00006797 a.u. 0.00006800 a.u. - a.u.
Dipole Moment 22.2224 Debye 22.2224 Debye 22.2224 Debye 0.0005 Debye
Point Group C1 C1 C1 C1
CPU Time 1 minute 12.8 seconds 2 minutes 28.8 seconds 6 minutes 36.5 seconds 58.3 seconds

The outputs are summarised below [N(CH3)4 ]+

3-21 Basis Set Optimisation

     Item               Value     Threshold  Converged?
 Maximum Force            0.000031     0.000450     YES
 RMS     Force            0.000005     0.000300     YES
 Maximum Displacement     0.000641     0.001800     YES
 RMS     Displacement     0.000206     0.001200     YES
 Predicted change in Energy=-7.454775D-09
 Optimization completed.
    -- Stationary point found.

6-31G(d,p)Basis Set Optimisation

 Item               Value     Threshold  Converged?
 Maximum Force            0.000129     0.000450     YES
 RMS     Force            0.000049     0.000300     YES
 Maximum Displacement     0.000809     0.001800     YES
 RMS     Displacement     0.000302     0.001200     YES
 Predicted change in Energy=-2.842702D-07
 Optimization completed.
    -- Stationary point found.

6-31G(d,p)Basis Set Frequency Calculation

Full mass-weighted force constant matrix:
 Low frequencies ---  -19.2061  -12.7564   -8.2164   -0.0007   -0.0001    0.0007
 Low frequencies ---  174.6301  275.6794  282.5852

Item               Value     Threshold  Converged?
 Maximum Force            0.000132     0.000450     YES
 RMS     Force            0.000068     0.000300     YES
 Maximum Displacement     0.000603     0.001800     YES
 RMS     Displacement     0.000305     0.001200     YES
 Predicted change in Energy=-2.759911D-07
 Optimization completed.
    -- Stationary point found.


MO Energy (a.u.) Explanation
MO 6 - Strongly Bonding -1.19647 All the atomic orbitals are in phase and highlighy overlapping. There are no nodes or nodal planes and although delocalised the MO exists entirely within the structure of the molecule, where bonds would be expected. All of constituent orbitals are also of a similar size so good overlap could be expected.
MO 10 - Weakly Bonding -0.80750 Nitrogen bonding to Carbon atoms weakly, however experiencing repulsion with the 4 external methyl groups which are strongly bound together, with good overlap within the methyl group, indicating strong C-H bonds, and reasonable overlap with the other three orbitals, although this MO is more delocalised than MO6, above, which also helps contribute to its overall lack of bonding character.
MO 14 - Nonbonding -0.62253 Two nodal planes bisect this MO, and there is very little electron density within the C-N bonds. Neighbouring methyl groups interact with each other creating two 'discs' seperated by an out of phase ring. The N atom is not involved.
MO 17 - Weakly Antibonding -0.58040 Three major sets of opposing lobes and one minor set all centrered on the external C-H bonds create an antibonding orbital
MO22 - Highly antibonding 2.75322 Each atom has an in phase and out of phase lobe, which are connected loosely to others and intertwined with lobes of the opposite phase. Close proximity and regular changes of phase create a highly antibonding and energetically unfavourable MO

[P(CH3)4 ]+

[P(CH3)4 ]+
Molecule
Vibration
File Type .log .log .log .log
Log File File:OHBP1 321log 69501.log File:OHBP2 631log 69504.log File:OHBP3freq2ultrafine log 69624.log File:OHBP4 MOlog 69527.log
D-Space DOI:10042/22667 DOI:10042/22668 DOI:10042/22669 DOI:10042/22670
Calculation Type FOPT FOPT FREQ SP
Calculation Method RB3YLP RB3YLP RB3YLP RB3YLP
Basis Set 3-21 6-31G(d,p) 6-31G(d,p) 6-31G(d,p)
Final Energy -498.2055 a.u. -500.8270 a.u. -500.8270 a.u. -500.8270 a.u.
Gradient 0.00002920 a.u. 0.00001371 a.u. 0.00000071 a.u. - a.u.
Dipole Moment 22.2188 Debye 22.2177 Debye 22.2223 Debye 0.0022 Debye
Point Group C1 C1 C1 C1
CPU Time 1 minute 51.2 seconds 3 minutes 20.0 seconds 18 minutes 24.9 seconds 56.0 seconds

The outputs are summarised below [N(CH3)4 ]+

3-21 Basis Set Optimisation

    Item               Value     Threshold  Converged?
 Maximum Force            0.000114     0.000450     YES
 RMS     Force            0.000027     0.000300     YES
 Maximum Displacement     0.000685     0.001800     YES
 RMS     Displacement     0.000236     0.001200     YES
 Predicted change in Energy=-1.277134D-07
 Optimization completed.
    -- Stationary point found.

6-31G(d,p)Basis Set Optimisation

 Item               Value     Threshold  Converged?
 Maximum Force            0.000051     0.000450     YES
 RMS     Force            0.000016     0.000300     YES
 Maximum Displacement     0.000987     0.001800     YES
 RMS     Displacement     0.000310     0.001200     YES
 Predicted change in Energy=-5.307280D-08
 Optimization completed.
    -- Stationary point found.

6-31G(d,p)Basis Set Frequency Calculation

Full mass-weighted force constant matrix:
 Low frequencies ---   -2.6330    0.0021    0.0028    0.0030    5.1381    7.5743
 Low frequencies ---  156.4446  192.0398  192.2775

Item               Value     Threshold  Converged?
 Maximum Force            0.000001     0.000015     YES
 RMS     Force            0.000000     0.000010     YES
 Maximum Displacement     0.000098     0.000060     NO 
 RMS     Displacement     0.000032     0.000040     YES
 Predicted change in Energy=-8.257063D-11

Although the above highlights that this calculation did not converge to the tight tolerences set for the maximum displacement, this calculation continued to be used. The value, while larger than the threshold set, is still over an order of magnitude smaller that the normal threshold value. The low frequencies are also very close to 0,which is also indicative that the calculation has run correctly, and so the result can be relied on to the degree of accuracy required.

[S(CH3)3]+

[S(CH3)3 ]+
Molecule
Vibration
File Type .log .log .log .log
Log File File:OhbS1log 69541.log File:OHBS2log 69556.log File:S3FREQlog 69561.log File:S4MOlog 69564.log
D-Space DOI:10042/22678 DOI:10042/22679 DOI:10042/22844 DOI:10042/22843
Calculation Type FOPT FOPT FREQ SP
Calculation Method RB3YLP RB3YLP RB3YLP RB3YLP
Basis Set 3-21 6-31G(d,p) 6-31G(d,p) 6-31G(d,p)
Final Energy -515.0523 a.u. -517.6833 a.u. -517.6833 a.u. XXX a.u.
Gradient 0.00004889 a.u. 0.00002584 a.u. 0.00002542 a.u. 0.00000XXX a.u.
Dipole Moment 1.2886 Debye 0.9652 Debye 0.9652 Debye xxx Debye
CPU Time 2 minuteS 0.0 seconds 3 minutes 59.4 seconds 3 minutes 37.9 seconds XX seconds


3-21 Basis Set Optimisation

     Item               Value     Threshold  Converged?
 Maximum Force            0.000159     0.000450     YES
 RMS     Force            0.000044     0.000300     YES
 Maximum Displacement     0.001697     0.001800     YES
 RMS     Displacement     0.000572     0.001200     YES
 Predicted change in Energy=-2.884895D-07
 Optimization completed.
    -- Stationary point found.

6-31G(d,p)Basis Set Optimisation

 Item               Value     Threshold  Converged?
 Maximum Force            0.000053     0.000450     YES
 RMS     Force            0.000023     0.000300     YES
 Maximum Displacement     0.001368     0.001800     YES
 RMS     Displacement     0.000420     0.001200     YES
 Predicted change in Energy=-6.993418D-08
 Optimization completed.
    -- Stationary point found.

6-31G(d,p)Basis Set Frequency Calculation

Full mass-weighted force constant matrix:
 Low frequencies ---  -23.9260  -14.4954   -0.0038   -0.0031   -0.0025   10.3677
 Low frequencies ---  161.5670  195.2390  207.2525

The values for the frequencies are a little higher than is ideal. However, because the basis set is too small for sulphur to be calculated accurately, the reasonably large values of -23.9260 and -14.4954 are acceptable. These frequencies represent the movement of the centre of mass; translations and rotations.

Comparison of NBOs

Molecule [N(CH3)4 ]+ [P(CH3)4 ]+ [S(CH3)3 ]+
Vibration
Vibration
Vibration
Charge Distribution (+1.0 to -1.0)
Bonds C-H 63% from C (sp3 (26% s, 74%p), 37% from H (100% s) C-H 65% from C (sp3 (25% s, 75%p), 35% from H (100% s) C-H 65% from C (sp3 (26% s, 74%p), 35% from H (100% s)
C-N 34% from C (sp3 (20% s, 80%p)), 66% from N (sp3 (25% s, 75%p)) C-P 60% from C (sp3 (25% s, 75%p)), 40% from P (sp3 (25% s, 75%p)) C-S 59% from C (sp3 (20% s, 80%p)), 51% from P (sp3 (17% s, 82%p))

The CH bonds in all the molecules remain almost the same, however the bond between the C-E (where E= N,P,S)changes depending on the nature of E. The nitrogen contributes more to the C-E bond than the phosphorous does as the atomic orbitals on N are less diffuse and overlap better with the carbon. Both N and P are completely sp3 hybridised, as could be rationalised from the tetrahedral shapes. The S compound is a distorted tetrahedral, with a lone pair occupying one of the tetrahedral sites.

Molecule Atom Charge
[N(CH3)4 ]+ N -0.295
C -0.483
H 0.269
[P(CH3)4 ]+ P 0.726
C -0.511
H 0.193
[S(CH3)3 ]+ S 0.917
C -0.845
H 0.279-0.297

As is highlighted above, the distribution of charge changes depending on the nature of E. In the Phosphorous analogue, the positive charge is mostly centered on the phosphorous atom, whereas the in the N molecule, the positive charge is distributed around the methyl-hydrogens around the edge of the molecule, with a negative core. As nitrogen is more electronegative than phosphorous the atom holds onto its charge better; the phosphorous atom more readily gives up its electrons to the rest of the electron deficient structure. This also links to the population analyses above; because the N atom is more electronegative it is more able to donate more electrons into the 2c-2e C-E bond, whereas because phosphorous int he cation is more electron deficient than in the uncharged species, it is able to contribute less to the C-E bond. The population analysis shows that the with the sulphur compound, most of the positive charge is on the sulphur atom. Despite being of similar electronegativity to carbon, the sulphur atom has a lone pair and so is more easily able to lose an electron. In comparison to the simplified picture of NR4+, where the positive charge resides purely on the nitrogen. This picture arises from a lewis structure of the bonding, that the lone pair of the acts as a nucleophile and bonds to a methyl cation, forming a tetravalent N+ compound. This picture is not correct however, as shown by the NBO analysis. The positive charge is actually distributed equally among the hydrogens on the exterior of the molecule, leaving a negative, neucleophilic centre. This can be rationalised that as nitrogen very electronegative, it draws electrons towards it, leaving the exterior, which is further away, more positive.

Influence of Functional Groups

[N(CH3)3CH2CN]+

[N(CH3)3CH2CN]+
Molecule
Vibration
File Type .log .log .log .log
Log File File:OHBNCN1 321log 69612.log File:OHBNCN2 631log 69620.log File:OHBNCN3 FREQ2log 69647.log File:OHBNCN4 MOlog 69675.log
D-Space DOI:10042/22686 DOI:10042/22687 DOI:10042/22688 DOI:10042/22689
Calculation Type FOPT FOPT FREQ SP
Calculation Method RB3YLP RB3YLP RB3YLP RB3YLP
Basis Set 3-21 6-31G(d,p) 6-31G(d,p) 6-31G(d,p)
Final Energy -304.7232 a.u. -306.3938 a.u. -306.3938 a.u. -306.3938 a.u.
Gradient 0.00002973 a.u. 0.00001171 a.u. 0.00000027 a.u. - a.u.
Dipole Moment 24.5324 Debye 24.6488 Debye 24.6491 Debye 24.6488 Debye
Point Group C1 C1 C1 C1
CPU Time 3 minutes 31.1 seconds 9 minutes 10.8 seconds 24 minutes 22.0 seconds 1 minute 24.3 seconds


3-21 Basis Set Optimisation

     Item               Value     Threshold  Converged?
 Maximum Force            0.000092     0.000450     YES
 RMS     Force            0.000015     0.000300     YES
 Maximum Displacement     0.001099     0.001800     YES
 RMS     Displacement     0.000160     0.001200     YES
 Predicted change in Energy=-5.666743D-08
 Optimization completed.
    -- Stationary point found.

6-31G(d,p)Basis Set Optimisation

  Item               Value     Threshold  Converged?
 Maximum Force            0.000030     0.000450     YES
 RMS     Force            0.000007     0.000300     YES
 Maximum Displacement     0.001664     0.001800     YES
 RMS     Displacement     0.000353     0.001200     YES
 Predicted change in Energy=-1.729211D-08
 Optimization completed.

6-31G(d,p)Basis Set Frequency Calculation

 Low frequencies ---   -4.9042   -2.0431   -0.0010   -0.0009   -0.0009    5.0633
 Low frequencies ---   91.6470  153.9751  211.4258

 Item               Value     Threshold  Converged?
 Maximum Force            0.000030     0.000450     YES
 RMS     Force            0.000007     0.000300     YES
 Maximum Displacement     0.001664     0.001800     YES
 RMS     Displacement     0.000353     0.001200     YES
 Predicted change in Energy=-1.729211D-08
 Optimization completed.

[N(CH3)3CH2OH]+

[N(CH3)3CH2OH]+
Molecule
Vibration
File Type .log .log .log .log
Log File File:NOH1log 70296.log File:NOH2log 70298.log File:NOH3log 70302.log File:NOH4log 70305.log
D-Space DOI:10042/22855 DOI:10042/22856 DOI:10042/22857 DOI:10042/22859
Calculation Type FOPT FOPT FREQ SP
Calculation Method RB3YLP RB3YLP RB3YLP RB3YLP
Basis Set 3-21 6-31G(d,p) 6-31G(d,p) 6-31G(d,p)
Final Energy -287.8066 a.u. -289.3947 a.u. -289.3947 a.u. -289.3947 a.u.
Gradient 0.00000631 a.u. 0.00002696 a.u. 0.00000529 a.u. - a.u.
Dipole Moment 2.2674 Debye 2.1353 Debye 2.1353 Debye 2.1353 Debye
CPU Time 6 minutes 3.1 seconds 11 minutes 5.3 seconds 9 minutes 53.8 seconds 1 minutes 42.6 seconds


3-21 Basis Set Optimisation

     Item               Value     Threshold  Converged?
 Maximum Force            0.000090     0.000450     YES
 RMS     Force            0.000021     0.000300     YES
 Maximum Displacement     0.001386     0.001800     YES
 RMS     Displacement     0.000440     0.001200     YES
 Predicted change in Energy=-8.835078D-08
 Optimization completed.
    -- Stationary point found.

6-31G(d,p)Basis Set Optimisation

 Item               Value     Threshold  Converged?
 Maximum Force            0.000022     0.000450     YES
 RMS     Force            0.000005     0.000300     YES
 Maximum Displacement     0.001142     0.001800     YES
 RMS     Displacement     0.000261     0.001200     YES
 Predicted change in Energy=-1.010997D-08
 Optimization completed.

Comparison

Molecule [N(CH3)4]+ [N(CH3)3CH2OH]+ [N(CH3)33CH2CN]+
Vibration
Vibration
Vibration
Charge Distribution (+0.8 TO -0.8)
Bonds C-H 63% from C (sp3 (26% s, 74%p), 37% from H (100% s) C-H 63% from C (sp3 (26% s, 74%p), 36% from H (100% s) C-H 64% from C (sp3 (27% s, 73%p), 36% from H (100% s)
C-N 34% from C (sp3 (20% s, 80%p)), 66% from N (sp3 (25% s, 75%p)) C-N 34% from C (sp3 (21% s, 79%p)), 66% from N (sp3 (25% s, 75%p)) C-N 33% from C (sp3 (20% s, 80%p)), 67% from N (sp3 (25% s, 75%p))
HOMO
LUMO
HOMO E (a.u.) -0.57933 -0.48766 -0.50048
HOMO-LUMO GAP E (a.u.) -0.44631 -0.36308 -0.31863
Molecule Atom Charge
[N(CH3)4 ]+ N -0.295
C -0.483
H 0.269
[N(CH3)3CH2OH]+ N 0.726
C -0.511
(CH2)H 0.259-0.284
C(OH)HH 0.237
O -0.678
OH 0.493
[N(CH3)33CH2CN]+ N 0.411
C 0.194-0.208
(CH2)H 0.184-0.284
CCN -0.089
C(CN)HH 0.220
CCN 0.354
N -0.394

Comparison

The Homos and lumos are very different for the substituted compounds. With the unsubstituted compound, [N(CH3)4]+ the HOMO and LUMO are spread fairly evenly throughout the molecule, particularly the LUMO, which displays loose Td symmetry. However, when the molecule has different substituents on one of the methyl groups, the LUMO and HOMO change accordingly. With an OH substituent, the HOMO becomes a lot more compact. This can be expected as the oxygen donates electrons to the rest of the molecule. Coupled with the electronegativity of the N, the homo is mainly focused on these two molecules and the bridging carbon. The LUMO however is very diffuse, with the carbons and hetero atoms in phase and the hydrogens out of phase; which expands out from the structure of the molecule. The LUMO of the -CN substituted molecule follows a similar pattern, with the heteroatoms all being in phase and the hydrogens (plus half of the CN) and all the space in between is out of phase. However it is not as diffuse as the OH substituted molecule as CN is an electron withdrawing group. The HOMO of the -CN molecule is almost exclusively focused on the cyano group and bridging carbon. This can be rationalised as the CN withdraws electrons away from the rest of the molecule. With the addition of a functional group, the MOs tend to focus around the functional group due to the effect they have on the distribution of electrons within the molecule (either EWG for CN or EDG for O). The HOMOs for both molecules are focused ont he functional groups. The addition of a functional group has raised the energy of the HOMO in both cases here, and decreased the size of the HOMO-LUMO gap; this implies that both of these molecules are more reactive than their unfunctionalised analogue.

Conclusion

After initially optimising and analysing a small molecule, five different cations where optimised and analysed to determine how the charge is distributed amongst the constituent atoms. While qualitative MO theory was shown to have a high level of accuracy, this further analyses showed that some traditional pictures of the location of charges are inaccurate.

References

  1. ↑ M. Schuurman, W. Allen, H. Schaefer, Journal of Computational Chemistry, 2005, 26, 1106
  2. ↑ Landau LD and Lifshitz EM (1976) Mechanics, 3rd. ed., Pergamon Press. ISBN 0-08-021022-8 (hardcover) and ISBN 0-08-029141-4 (softcover)
  3. ↑ The Electrochemical Flow Capacitor: A New Concept for Rapid Energy Storage and Recovery, Volker Presser, Christopher R. Dennison, Jonathan Campos1, Kevin W. Knehr, Emin C. Kumbur2, Yury Gogotsi1, <DOI|10.1002/aenm.201100768>
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