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EX3 section

BH3:B3LYP/3-21G

Optimisation log file here

geometry summary data convergence Jmol
Cs 
       Item               Value     Threshold  Converged?
 Maximum Force            0.000217     0.000450     YES
 RMS     Force            0.000105     0.000300     YES
 Maximum Displacement     0.000900     0.001800     YES
 RMS     Displacement     0.000441     0.001200     YES
optimised ammonia molecule

Optimisation log file here

geometry summary data convergence Jmol
D3h 
       Item               Value     Threshold  Converged?
 Maximum Force            0.000410     0.000450     YES
 RMS     Force            0.000268     0.000300     YES
 Maximum Displacement     0.001597     0.001800     YES
 RMS     Displacement     0.001046     0.001200     YES
optimised ammonia molecule

Optimisation log file here

geometry summary data convergence Jmol
C1 
       Item               Value     Threshold  Converged?
 Maximum Force            0.000228     0.000450     YES
 RMS     Force            0.000111     0.000300     YES
 Maximum Displacement     0.000854     0.001800     YES
 RMS     Displacement     0.000495     0.001200     YES
optimised ammonia molecule

BH3:B3LYP/6-31G(d,p)

A better Basis-set

Optimisation log file here

geometry summary data convergence Jmol
Cs 
       Item               Value     Threshold  Converged?
 Maximum Force            0.000203     0.000450     YES
 RMS     Force            0.000098     0.000300     YES
 Maximum Displacement     0.000738     0.001800     YES
 RMS     Displacement     0.000395     0.001200     YES
optimised BH3 molecule

Optimisation log file here

geometry summary data convergence Jmol
D3h 
       Item               Value     Threshold  Converged?
 Maximum Force            0.000434     0.000450     YES
 RMS     Force            0.000284     0.000300     YES
 Maximum Displacement     0.001702     0.001800     YES
 RMS     Displacement     0.001114     0.001200     YES
optimised BH3 molecule

Optimisation log file here

geometry summary data convergence Jmol
C1 
       Item               Value     Threshold  Converged?
 Maximum Force            0.000255     0.000450     YES
 RMS     Force            0.000133     0.000300     YES
 Maximum Displacement     0.000920     0.001800     YES
 RMS     Displacement     0.000598     0.001200     YES
optimised Bh3 molecule

GaBr3:B3LYP/LANL2DZ

optimisation file: DOI:10042/193794

summary data convergence Jmol 
         Item             Value     Threshold  Converged?
 Maximum Force            0.000000     0.000450     YES
 RMS     Force            0.000000     0.000300     YES
 Maximum Displacement     0.000003     0.001800     YES
 RMS     Displacement     0.000002     0.001200     YES
optimised GaBr3 molecule

BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)

optimisation file: DOI:10042/193796

summary data convergence Jmol 
        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     0.000024     0.001200     YES
optimised BBr3 molecule

Geometry Comparison

geometry data
BH3 BBr3 GaBr3
r(E-X) Å 1.19 1.93 2.35
θ(X-E-X) degrees(º) 120.0 120.0 120.0

Summary of the data: Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

Frequency Analysis

BH3:B3LYP/6-31G(d,p)

Frequency file: here

summary data low modes

Energy exactly the same as previous optimization 6-31G BH3 model. 

 Low frequencies ---   -7.0630   -7.0272   -0.0278   -0.0010    0.7100    6.6480
 Low frequencies --- 1163.0024 1213.1577 1213.1579

Vibrational spectrum for BH3

wavenumber Intensity IR active? type
1161 93 yes bend
1212 14 very slight bend
1212 14 very slight bend
2588 0 no stretch
2721 126 yes stretch
2721 126 yes stretch

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There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

GaBr3:B3LYP/LANL2DZ

Frequency file: DOI:10042/193819

summary data low modes

Energy exactly the same as previous optimization GaBr3 model. 

 Low frequencies ---   -1.4877   -0.0015   -0.0002    0.0096    0.6540    0.6540
 Low frequencies ---   76.3920   76.3924   99.6767

Vibrational spectrum for GaBr3

wavenumber Intensity IR active? type
76 3 very slight bend
76 3 very slight bend
100 9 very slight bend
197 0 no stretch
316 57 yes stretch
316 57 yes stretch

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Compare and Contrast:

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions:

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

Molecular Orbitals for BH3

MO file: DOI:10042/193820

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

NH3:B3LYP/6-31G(d,p)

Optimization log file here

geometry summary data convergence Jmol
C3v 
         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
optimised BH3 molecule

NH3:B3LYP/6-31G(d,p)

Frequency file: here

summary data low modes

Energy exactly the same as previous optimization 6-31G BH3 model. 

 Low frequencies ---   -0.0130   -0.0029   -0.0019    7.1032    8.1046    8.1049
 Low frequencies --- 1089.3834 1693.9368 1693.9368

Vibrational spectrum for NH3

wavenumber Intensity IR active? type
1089 145 yes bend
1694 14 slight bend
1694 14 slight bend
3461 1 no stretch
3590 0 No stretch
3590 0 No stretch

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NBO Analysis of NH3

NBO log file: here

charge range: from -1.0 to 1.0.

Association Energy for NH3BH3

NH3BH3:B3LYP/6-31G(d,p)

Optimization log file here

geometry summary data convergence Jmol
C3v 
         Item               Value     Threshold  Converged?
 Maximum Force            0.000122     0.000450     YES
 RMS     Force            0.000058     0.000300     YES
 Maximum Displacement     0.000531     0.001800     YES
 RMS     Displacement     0.000296     0.001200     YES
optimised BH3 molecule

NH3BH3:B3LYP/6-31G(d,p)

Frequency file: here

summary data low modes

Energy exactly the same as previous optimization 6-31G NH3BH3 model. 

Low frequencies ---   -5.4077   -0.3705   -0.0565    0.0002    0.9580    1.0693
Low frequencies ---  263.2907  632.9543  638.4541

Vibrational spectrum for NH3BH3

wavenumber (cm-1) Intensity IR active? type
263 0 no bend
633 14 slight strecth
638 4 very slight bend
638 4 very slight bend
1069 41 yes bend
1069 41 yes bend
1196 108 yes bend
1204 3 very slight bend
1204 3 very slight bend
1329 114 yes bend
1676 28 slight bend
1676 28 slight bend
2472 67 yes stretch
2532 231 yes stretch
2532 231 yes stretch
3464 3 very slight stretch
3581 28 slight stretch
3581 28 slight stretch

Association energy calculation

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

NBO Analysis of ethane and aminoborane

Ethane NBO log file: here

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: here

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

Ionic Liquid Project: Part 1

[N(CH3)4]+:B3LYP/6-31G(d,p)

Optimization of [N(CH3)4]+

Optimization log file here

geometry summary data convergence Jmol
TD 
         Item               Value     Threshold  Converged?
 Maximum Force            0.000018     0.000450     YES
 RMS     Force            0.000010     0.000300     YES
 Maximum Displacement     0.000231     0.001800     YES
 RMS     Displacement     0.000089     0.001200     YES
optimised BH3 molecule

Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)

Frequency file: here

summary data low modes 


Low frequencies ---   -0.0006   -0.0002    0.0007   21.4457   21.4458   21.4458
Low frequencies ---  188.5907  292.6934  292.6934

Vibrational spectrum for [N(CH3)4]+

wavenumber (cm-1) Intensity IR active? type
941 22 yes bend
941 22 yes bend
941 22 yes bend
1305 1 very slight bend
1305 1 very slight bend
1305 1 very slight bend
1456 5 slight bend
1456 5 slight bend
1456 5 slight bend
1532 53 yes bend
1532 53 yes bend
1532 53 yes bend

NBO Analysis of [N(CH3)4]+

NBO log file: here

charge range: from -0.483 to 0.483.

[P(CH3)4]+:B3LYP/6-31G(d,p)

Optimization of [P(CH3)4]+

Optimization log file here

geometry summary data convergence Jmol
TD 
         Item               Value     Threshold  Converged?
 Maximum Force            0.000116     0.000450     YES
 RMS     Force            0.000033     0.000300     YES
 Maximum Displacement     0.000809     0.001800     YES
 RMS     Displacement     0.000326     0.001200     YES
optimised BH3 molecule

Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)

Frequency file: here

summary data low modes 


Low frequencies ---   -0.0022   -0.0012    0.0022   24.7170   24.7170   24.7170
Low frequencies ---  160.1015  194.8298  194.8298

Vibrational spectrum for [P(CH3)4]+

wavenumber (cm-1) Intensity IR active? type
271 2 very slight bend
271 2 very slight bend
271 2 very slight bend
756 4 slight bend
756 4 slight bend
756 4 slight bend
1013 78 yes bend
1013 78 yes bend
1013 78 yes bend
1362 21 yes bend
1362 21 yes bend
1362 21 yes bend
1481 26 yes bend
1481 26 yes bend
1481 26 yes bend
3064 5 slight stretch
3064 5 slight stretch
3064 5 slight stretch
3159 4 slight stretch
3159 4 slight stretch
3159 4 slight stretch

NBO Analysis of [P(CH3)4]+

NBO log file: here

charge range: from -1.667 to 1.667.

[S(CH3)3]+:B3LYP/6-31G(d,p)

Optimization of [S(CH3)3]+

Optimization log file here

geometry summary data convergence Jmol
C3v 
         Item               Value     Threshold  Converged?
 Maximum Force            0.000027     0.000450     YES
 RMS     Force            0.000008     0.000300     YES
 Maximum Displacement     0.000235     0.001800     YES
 RMS     Displacement     0.000073     0.001200     YES
optimised BH3 molecule

Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)

Frequency file: here

summary data low modes 


Low frequencies ---   -7.9007   -7.6403   -7.6370    0.0019    0.0040    0.0093
 Low frequencies ---  161.9049  199.6302  199.6302

Vibrational spectrum for [S(CH3)3]+

wavenumber (cm-1) Intensity IR active? type
624 2 very slight bend
704 1 very slight bend
704 1 very slight bend
958 1 very slight bend
958 1 very slight bend
1071 11 yes bend
1071 11 yes bend
1076 12 yes bend
1408 2 very slight bend
1464 10 yes bend
1464 10 yes bend
1473 25 yes bend
1473 25 yes bend
1485 42 yes bend
3075 3 very slight stretch
3075 3 very slight stretch
3185 8 slight stretch
3185 8 slight stretch
3187 2 very slight stretch
3187 2 very slight stretch
3187 2 very slight stretch

NBO Analysis of [S(CH3)3]+

NBO log file: here

charge range: from -0.917 to 0.917.

Geometry Comparison of [X(CH3)y]+ molecules

geometry data
[N(CH3)4]+ [P(CH3)4]+ [S(CH3)3]+
r(X-C) Å 1.51 1.82 1.82
r(C-H) Å 1.09 1.09 1.09
θ(C-X-C) degrees(º) 109.5 109.5 102.7
θ(H-C-H) degrees(º) 110.0 109.0 109.4 ; 111.1
θ(X-C-H) degrees(º) 108.9 109.9 107.3 ; 110.6


The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.


MOs of [N(CH3)4]+

MO=6 : strong bonding


MO=7 : medium bonding

MO=11 : weak bonding

MO=15 : weak anti-bonding

MO=16 : strong anti-bonding

[X(CH3)y]+ Charge Distribution (NBO) Comparison

charge distribution data
[N(CH3)4]+ [P(CH3)4]+ [S(CH3)3]+
charge on X -0.295 1.667 0.917
charge on C -0.483 -1.060 -0.846
charge on H 0.269 0.298 0.297 ; 0.279

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison

Relative Contribution data
[N(CH3)4]+ [P(CH3)4]+ [S(CH3)3]+
Contribution from X 66% 40% 51%
Hybridisation of X orbital 25% s + 75% p 25% s + 74% p + 1% d 17% s + 82% p + 1% d
Contribution from C 34% 60% 49%
Hybridisation of C orbital 21% s + 79% p 25% s + 75% p 20% s + 80% p


The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

Validity of the traditional [N(R)4]+ description

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

Ionic Liquid Project: Part 2

[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)

Optimization of [N(CH3)3(CH2OH)]+

Optimization log file here

geometry summary data convergence Jmol
C1 
        Item               Value     Threshold  Converged?
 Maximum Force            0.000015     0.000450     YES
 RMS     Force            0.000004     0.000300     YES
 Maximum Displacement     0.000428     0.001800     YES
 RMS     Displacement     0.000112     0.001200     YES
optimised BH3 molecule

Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)

Frequency file: here

summary data low modes 


Low frequencies ---   -8.4390   -5.0098   -1.0369   -0.0005   -0.0004    0.0009
Low frequencies ---  131.1078  213.4644  255.7166

Vibrational spectrum for [N(CH3)3(CH2OH)]+

wavenumber (cm-1) Intensity IR active? type
131 5 slight bend
213 3 very slight bend
256 29 yes bend
267 1 very slight bend
342 51 yes bend
355 4 very slight bend
393 28 yes bend
434 4 very slight bend
449 4 very slight bend
552 2 very slight bend
736 22 yes bend
839 96 yes bend
931 22 yes bend
982 12 yes bend
1033 20 yes bend
1122 38 yes bend
1133 7 slight bend
1184 91 yes bend
1219 8 slight bend
1276 6 slight bend
1289 2 very slight bend
1330 19 yes bend
1397 17 yes bend
1433 3 very slight bend
1445 7 slight bend
1452 9 slight bend
1496 5 slight bend
1501 3 very slight bend
1504 1 very slight bend
1514 26 yes bend
1521 33 yes bend
1530 17 yes bend
1540 51 yes bend
3074 9 slight stretch
3085 2 very slight stretch
3088 2 very slight stretch
3095 1 very slight stretch
3147 4 very slight stretch
3184 1 very slight stretch
3189 1 very slight stretch
3825 105 yes stretch

NBO analysis for [N(CH3)3(CH2OH)]+

Population log file here

charge range -0.757 to 0.757

[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level

Optimization of [N(CH3)3(CH2CN)]+

Optimization log file here

geometry summary data convergence Jmol
Cs 
         Item               Value     Threshold  Converged?
 Maximum Force            0.000250     0.000450     YES
 RMS     Force            0.000057     0.000300     YES
 Maximum Displacement     0.001338     0.001800     YES
 RMS     Displacement     0.000490     0.001200     YES
optimised BH3 molecule

Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)

Frequency file: here

summary data low modes 


 Low frequencies ---   -3.6828    0.0004    0.0005    0.0011    2.7427    3.8837
 Low frequencies ---   91.8731  153.9653  212.1350

Vibrational spectrum for [N(CH3)3(CH2CN)]+

wavenumber (cm-1) Intensity IR active? type
92 6 slight bend
154 9 slight bend
328 1 very slight bend
436 1 very slight bend
571 2 very slight bend
895 28 yes bend
911 20 yes bend
963 14 yes bend
990 20 yes bend
1008 2 very slight bend
1140 1 very slight bend
1259 1 very slight bend
1333 3 very slight bend
1395 8 slight bend
1454 8 slight bend
1455 8 slight bend
1475 3 very slight bend
1495 3 very slight bend
1503 3 very slight bend
1519 34 yes bend
1521 47 yes bend
1532 61 yes bend
2385 8 slight stretch
3087 1 very slight stretch
3144 2 very slight stretch

NBO analysis for [N(CH3)3(CH2CN)]+

Population log file here

charge range -0.489 to 0.489

Charge distribution comparison

charge distribution data
[N(CH3)3(CH2OH)]+ [N(CH3)3(CH2CN)]+ [N(CH3)4]+
charge on N -0.313(central atom) -0.289(central atom), -0.186(CN) -0.295 (central atom)
charge on C -0.488, -0.489(CH3), 0.094(CH2OH) -0.489(CH3),-0.385 (the CH2 next to CN), 0.209((CN) -0.483 (CH3)
charge on O -0.757 N/A N/A
charge on H 0.264 to 0.285(CH3), 0.234(CH2OH), 0.532(CH2OH) From 0.269 to 0.309 0.269

Compare to the charge distribution of [N(CH3)4]+ molecule, OH group is an electron donating group and push the electrons towards the central atom which results in the increase charge value of Central N atom and other C and H atoms in the system. On the contrary, CN group is an electron withdrawing group which pull electrons from the central atom and results in the decrease value of N central atom.

HOMO and LUMO comparison

HOMO and LUMO graph
[N(CH3)3(CH2OH)]+ [N(CH3)3(CH2CN)]+ [N(CH3)4]+
HOMO
LUMO

Note: The HOMO of [N(CH3)4]+ is triply degenerate.

HOMO and LUMO energy
[N(CH3)3(CH2OH)]+ [N(CH3)3(CH2CN)]+ [N(CH3)4]+
HOMO -0.48763 -0.50047 -0.57934 (degenerate)
LUMO -0.12459 -0.18183 -0.13303
HOMO-LUMO gap (KJ•mol-1) 953 837 1172

The HOMO of [N(CH3)4]+ molecule is triply degenerate due to the Td symmetry. When one methyl group was replaced by -OH or -CN group, this degeneracy was broken and the structure became more stable due to the electronegative of O and N atom. The HOMO-LUMO gap also decreased.

Interesting aspect of [N(CH3)3(CH2OH)]+

During the optimization of [N(CH3)3(CH2OH)]+, there are two possible structure (Symmetry) for which O-H bond could be both periplanar or antiperiplanar to the next C-N bond. The result shows that periplanar structure are preferred since the two lone pair electrons in O atom is favoring on opposite site with two adjacent C-H bond. These could be explained by both steric effect and stabilization of C-H anti-bonding orbital.

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