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3^rd Year Computational Laboratory: Module 2, part 1

BH₃

BH₃ optimisation using 3-21G basis set

optimised B-H bond length: 1.19 Å

optimised H-B-H bond angle: 120.0°

BH₃optimisation - summary table

Summary of the optimised BH3 molecule
File type	.log
Calculation type	FOPT
Calculation method	RB3LYP
Basis set	3-21G
Final energy in atomic units	-26.46226338
Gradient	0.00020672
Dipole moment	0.0000 D
Point group	D3H
Duration of calculation	24s

BH₃optimisation - confirmation

         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.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.1935         -DE/DX =    0.0004              !
 ! R2    R(1,3)                  1.1935         -DE/DX =    0.0004              !
 ! R3    R(1,4)                  1.1935         -DE/DX =    0.0004              !
 ! 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                 !

BH₃ optimisation using 6-31Gdp basis set

.log file can be found here

optimised B-H bond length: 1.19 Å

optimised B-H-B bond angle: 120.0°

energy of 3-21G optimised BH3 molecule: -26.46226338 a.u.

energy of 6-21dp optimised BH3 molecule: -26.61532264 a.u.

difference in energy: 0.15305926 = ~402.00 kJ/mol

BH₃optimisation - summary table

BH3 optimisation
File Name = BH3_OPT2_631_dp
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -26.61532264 a.u.
RMS Gradient Norm = 0.00021663 a.u.
Imaginary Freq =
Dipole Moment = 0.0000 Debye
Point Group = CS
Job cpu time:  0 days  0 hours  0 minutes 42.0 seconds.

BH₃optimisation - confirmation

         Item               Value     Threshold  Converged?
 Maximum Force            0.000434     0.000450     YES
 RMS     Force            0.000284     0.000300     YES
 Maximum Displacement     0.001698     0.001800     YES
 RMS     Displacement     0.001114     0.001200     YES
 Predicted change in Energy=-1.188111D-06
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.1914         -DE/DX =    0.0004              !
 ! R2    R(1,3)                  1.1914         -DE/DX =    0.0004              !
 ! R3    R(1,4)                  1.1914         -DE/DX =    0.0004              !
 ! A1    A(2,1,3)              120.0001         -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              120.0001         -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              119.9999         -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)            180.0            -DE/DX =    0.0                 !

BH₃ frequency

.log file can be found here

BH₃frequency - summary table

BH3 frequency
File Name = filip_bh3_freq
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -26.61532264 a.u.
RMS Gradient Norm = 0.00021659 a.u.
Imaginary Freq = 0
Dipole Moment = 0.0000 Debye
Point Group = C2V
Job cpu time:  0 days  0 hours  0 minutes 34.0 seconds.

BH₃frequency - confirmation

         Item               Value     Threshold  Converged?
 Maximum Force            0.000432     0.000450     YES
 RMS     Force            0.000217     0.000300     YES
 Maximum Displacement     0.001697     0.001800     YES
 RMS     Displacement     0.000848     0.001200     YES
 Predicted change in Energy=-1.101958D-06
 Optimization completed.

Low frequencies ---  -73.0837  -69.5094  -69.4394   -0.0009   -0.0007    0.0006
 Low frequencies --- 1161.3810 1212.0964 1212.1646

BH₃ vibrational analysis

Vibrational modes of BH3
No.	Description	Frequency [cm^-1]	Intensity	Symmetry D3h point group
1	The three hydrogen atoms move in a concerted fashion up and down, perpendicularly to the plane of molecule, meanwhile the boron atom is moving in opposite direction to them to a lesser displacement	1161	93	a2"
2	Two hydrogen atoms move in a symmetrical fashion towards each other and away from each other (scissoring) in a plane of the molecule, whereas both the other hydrogen and boron atom move back and forth in the plane of the molecule within the C2 axis of symmetry containing these two atoms. To a lesser displacement than the other two hydrogens though.	1212	14	e'
3	Two hydrogen atoms move left and right with a fixed distance to each other. The third hydrogen moves also left and right from its position but in a way that on the way to the left it is coming closer to the other hydrogen atom moving to the left and on its way to the right, it is coming towards the hydrogen atom moving to the right. At their maximal displacements, the two fixed hydrogen atoms are each either closest or furthest away possible from the singly moving hydrogen. The boron atom is practically not moving, only to a very slight displacement left and right oppositely to the singly moving hydrogen. All vibrations are happening in the plane of molecule.	1212	14	e'
4	The three hydrogen atoms move in a concerted fashion towards and away of the boron atom which is stationary. All are in plane and to the same displacement. The dipole moment does not change.	2588	0	a1'
5	Two hydrogen atoms vibrate asymmetrically towards and away from the boron atom in plane of the molecule to the same maximal displacement. The last hydrogen and the boron atom vibrate in the plane together very slightly to the left and right.	2722	126	e'
6	Two hydrogen atoms move in a concerted fashion towards and away from the boron atom whereas the third hydrogen moves in the opposite direction, i.e. when the two concerted hydrogens are closest to boron, the third is furthest and vice versa. Boron moves slightly up and down. All vibrations are in the plane of the molecule.	2722	126	e'

IR spectrum of BH3:

there are only three peaks visible in the spectrum as two pairs of vibrations are degenerate so they only produce two peaks and one vibration is totally symmetric preserving the dipole. The requirement for IR active bands is that there must be a change in dipole moment and thus the interaction with electromagnetic field is possible. The last vibration gives rise to the third observed peak.

N.B. e' are degenerate vibrations and if the symmetry was D3h, their two frequency values would be exactly the same (they vary in 3rd decimal place. Due to the C2v symmetry, they slightly vary. C2v point group could not have been avoided despite many attempts to solve the problem.

BH₃ molecular orbitals

http://hdl.handle.net/10042/20492

BH₃molecular orbitals - summary table

BH3 MOs
File Name = BH3_MOs
File Type = .log
Calculation Type = SP
Calculation Method = RB3LYP
Basis Set = 6-31G
Charge = 0
Spin = Singlet
E(RB3LYP) = -7739.67280730 a.u.
RMS Gradient Norm =  a.u.
Imaginary Freq = 
Dipole Moment = 0.0002 Debye
Point Group = C2V
Job cpu time:  0 days  0 hours  0 minutes 27.6 seconds.

BH₃molecular orbitals diagram

the LCAO molecular orbitals look very similarly to the real ones. They lack the exact shape of the orbitals but in average, they represent the electron density quite well. If mixing was included as accurately as possible, there would be even more resemblance between them. The qualitative analysis serves as a very good approximation and proves to be useful and reliable enough to characterise smaller molecules quite quickly and precisely.

the first core molecular orbital is not included in the diagram above due to it being too deep in energy compared to the valence orbitals

TlBr₃

TlBr₃optimisation

Optimised TlBr3 molecule: http://hdl.handle.net/10042/20440

optimised Tl-Br bond length: 2.65 Å

optimised Br-Tl-Br bond angle: 120.0°

literature Tl-Br bond length: 2.51 Å¹

[1] J. Glaser and G. Johansson, On the Structures of the Hydrated Thallium(III) Ion and its Bromide Complexes in Aqueous Solution, Acta Chemica Scandinavica A 36 (1982) 125 - 135

TlBr₃optimisation - summary table

TlBr3 optimisation
File Name = TlBr3optimisation_logfile
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = LANL2DZ
Charge = 0
Spin = Singlet
E(RB3LYP) = -91.21812851 a.u.
RMS Gradient Norm = 0.00000090 a.u.
Imaginary Freq = 
Dipole Moment = 0.0000 Debye
Point Group = D3H
Job cpu time:  0 days  0 hours  0 minutes 18.5 seconds.

TlBr₃optimisation - confirmation

         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=-6.084058D-11
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  2.651          -DE/DX =    0.0                 !
 ! R2    R(1,3)                  2.651          -DE/DX =    0.0                 !
 ! R3    R(1,4)                  2.651          -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                 !

TlBr₃frequency

http://hdl.handle.net/10042/20473

TlBr₃frequency - summary table

TlBr3 frequency
File Name = TlBr3_frequency
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = LANL2DZ
Charge = 0
Spin = Singlet
E(RB3LYP) = -91.21812851 a.u.
RMS Gradient Norm = 0.00000088 a.u.
Imaginary Freq = 0
Dipole Moment = 0.0000 Debye
Point Group = D3H
Job cpu time:  0 days  0 hours  0 minutes 15.9 seconds.

TlBr₃frequency - confirmation


         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.

Low frequencies ---   -3.4213   -0.0026   -0.0004    0.0015    3.9367    3.9367
 Low frequencies ---   46.4289   46.4292   52.1449

Vibrational analysis

Vibrational frequencies: 46, 46, 52, 165, 211 and 211 cm^-1

IR spectrum:

BBr₃

BBr₃optimisation

.log file can be found here

optimised B-Br bond length: 1.93 Å

optimised Br-B-Br bond angle: 120.0°

Discussion

Bond lengths [Å]
BH₃	TlBr₃	BBr₃
1.19	2.65	1.93

the bond length increases in order BH3 < BBr3 < TlBr3, whereas the bond strength in the opposite direction. The bond length depends on the size of an atom, electronegativity of both elements forming the bond and whether there is a good orbital overlap. The size of the atoms present increases in order H < B < Br < Tl.

the larger the central atom, the longer the bond. This can be seen in BBr3 (1.93 Å) and TlBr3 (2.65 Å). The same is true for the ligands, e.g. BH3 (1.19 Å) versus BBr3 (1.93 Å). This is due to the more diffuse orbitals, worse overlap and simply the atoms are further apart.

hydrogens consist of s-type orbitals generally giving good overlap within a small volume and thus the bond lengths involving hydrogens tend to be short. Bromine is large with diffuse orbitals and tend to form weak and long bonds instead. It also has larger electronegativity pulling electrons towards itself when binding unless bound to an element with even higher electronegativity making the nature of a bond more polarised. Boron and Thallium have both the same electronegativity with Thallium being much larger and forming longer and weaker bonds. However, both bromine and thallium can extend their coordination to much higher numbers than hydrogen and boron so can form more bonds.

a bond can be thought of as a build up of the total electon density.² In average, the bond is the place of highest probability of finding an electon. Alternatively, it can be understood as the location of the best orbital overlap. If Gaussview does not draw bonds, it means that the corresponding structure exceeds some pre-defined length inside the program (the structure is not optimised enough). The pre-defined value is picked based on a literature value.

[2] P. Hunt, Molecular Orbitals in Inorganic Chemistry, Lecture 3, p.9

N.B. The point group for BBr3 was determined to be C2v although the correct one is D3h. The latter could not have been achieved even with manually breaking the symmetry and trying to optimize again. The 'nosymm' keyword was not present. The same was true for further analysis of BH3 molecule (MO analysis).

BBr₃optimisation - summary table

BBr3 optimisation
File Name = BBR3_OPT_GEN
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = Gen
Charge = 0
Spin = Singlet
E(RB3LYP) = -64.43645277 a.u.
RMS Gradient Norm = 0.00000384 a.u.
Imaginary Freq = 
Dipole Moment = 0.0002 Debye
Point Group = C2V
Job cpu time:  0 days  0 hours  0 minutes 40.0 seconds.

BBr₃optimisation - confirmation

         Item               Value     Threshold  Converged?
 Maximum Force            0.000008     0.000450     YES
 RMS     Force            0.000005     0.000300     YES
 Maximum Displacement     0.000037     0.001800     YES
 RMS     Displacement     0.000024     0.001200     YES
 Predicted change in Energy=-4.109348D-10
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,4)                  1.9339         -DE/DX =    0.0                 !
 ! R2    R(2,4)                  1.934          -DE/DX =    0.0                 !
 ! R3    R(3,4)                  1.934          -DE/DX =    0.0                 !
 ! A1    A(1,4,2)              120.0021         -DE/DX =    0.0                 !
 ! A2    A(1,4,3)              120.0021         -DE/DX =    0.0                 !
 ! A3    A(2,4,3)              119.9957         -DE/DX =    0.0                 !
 ! D1    D(1,4,3,2)            180.0            -DE/DX =    0.0                 !

BH₃ vs TlBr₃

Vibrational frequencies

Vibrational frequencies [cm^-1]
BH3	TlBr3	Symmetry label D3h
1212	46	e'
1212	46	e'
1161	52	a2"
2588	165	a1'
2722	211	e'
2722	211	e'

Symmetry labels

TlBr3 analysis:

                   E'                     E'                     A2"
Frequencies --    46.4289                46.4292                52.1449
Red. masses --    88.4613                88.4613               117.7209
Fre consts  --     0.1124                 0.1124                 0.1886
                   A1'                    E'                     E'
Frequencies --   165.2685               210.6948               210.6948
Red. masses --    78.9183               101.4032               101.4032
Frc consts  --     1.2700                 2.6522                 2.6522

BH3 analysis:

                   A                      A                      A
Frequencies --  1161.3810              1212.0964              1212.1646
Red. masses --     1.2531                 1.1072                 1.1072
Frc consts  --     0.9958                 0.9584                 0.9585
                    A                      A                      A
Frequencies --  2587.8129              2721.5077              2721.5171
Red. masses --     1.0078                 1.1273                 1.1273
Frc consts  --     3.9765                 4.9196                 4.9196

Discussion

vibrational frequency is proportional to force constant and reduced mass

reduced mass of TlBr3 is much higher than that of BH3 and thus the vibrations are much slower compared to BH3

the lowest vibrational frequency of TlBr3 has symmetry label e' whereas the one for BH3 has symmetry label a2". The opposite is true for the third lowest vibrational mode. The reordering occurs indeed within this first and third lowest vibrational frequency

the two IR spectra both show three peaks and this is due to 2 pairs of vibrations being degenerate and one single vibration being totally symmetric. This leaves the spectra with 3 distinguishable IR active bands. The epsilon (molar extinction coefficient) value in the IR spectrum of BH3 is higher than in the one for TlBr3. The reason why the two spectra are similar in shape and relative distance of their peaks could lie in the fact that both molecules undergo the same types of vibrations. The difference between B and H atoms is similar to the difference between Tl and Br atom. Since both molecules have one large central atom surrounded by 3 smaller ones, the relative distance between the peaks would be comparable (in terms of the overall frequency). The difference in the actual numbers is then however reflected in the frequency we observe. As BH3 has stronger bonds and much lower reduced mass compared to TlBr3, its vibrations are at much higher frequency.

once the optimisation is completed, all subsequent calculations and analyses involving the optimised molecule have to be performed using the same basis set and method. This basically ensures the same conditions (level of accuracy). If a different basis set or method were used for frequency analysis, the following result is quite likely to differ from the one which would be obtained if that different basis set or method were used initially to optimise the molecule.

frequency analysis allows to calculate many useful parameters about a molecule, e.g. force constants and reduced masses leading to vibrations and more importantly the types of vibrations present. That can then be used to estimate the IR spectrum. Also, one can study the change in dipole moment and hence investigate the molecule's interactions with electromagnetic field.

low frequencies represent the motion of the center of mass (the central atom). Since this is the heavier atom, it does not move much and so these frequencies should be low. If they are not, the molecule is probably not optimised well enough.

NH₃

NH₃ optimisation

NH3 optimisation: http://hdl.handle.net/10042/20501

.log file can be found here

NH₃optimisation - summary table

NH3 optimisation
File Name = NH3_optimisation
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -56.55776856 a.u.
RMS Gradient Norm = 0.00000885 a.u.
Imaginary Freq = 
Dipole Moment = 1.8464 Debye
Point Group = C1
Job cpu time:  0 days  0 hours  0 minutes 20.9 seconds.

NH₃optimisation - confirmation

         Item               Value     Threshold  Converged?
 Maximum Force            0.000024     0.000450     YES
 RMS     Force            0.000012     0.000300     YES
 Maximum Displacement     0.000079     0.001800     YES
 RMS     Displacement     0.000053     0.001200     YES
 Predicted change in Energy=-1.629727D-09
 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)              105.7413         -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              105.7486         -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              105.7479         -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)           -111.8631         -DE/DX =    0.0                 !

NH₃ frequency

NH3 frequency: http://hdl.handle.net/10042/20502

NH₃frequency - summary table

NH3 frequency
File Name = NH3_frequency
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -56.55776856 a.u.
RMS Gradient Norm = 0.00000878 a.u.
Imaginary Freq = 0
Dipole Moment = 1.8464 Debye
Point Group = C1
Job cpu time:  0 days  0 hours  0 minutes 13.6 seconds.

NH₃frequency - confirmation

         Item               Value     Threshold  Converged?
 Maximum Force            0.000021     0.000450     YES
 RMS     Force            0.000009     0.000300     YES
 Maximum Displacement     0.000077     0.001800     YES
 RMS     Displacement     0.000039     0.001200     YES
 Predicted change in Energy=-1.592773D-09
 Optimization completed.
    -- Stationary point found.

Low frequencies ---  -30.8045    0.0007    0.0008    0.0008   20.2188   28.2150
 Low frequencies --- 1089.5530 1694.1235 1694.1861

NH₃ molecular orbitals

NH3 MOs: http://hdl.handle.net/10042/20505

NH₃molecular orbitals - summary table

NH3 MOs
File Name = NH3_MOs
File Type = .log
Calculation Type = SP
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -56.55776852 a.u.
RMS Gradient Norm =  a.u.
Imaginary Freq = 
Dipole Moment = 1.8464 Debye
Point Group = C1
Job cpu time:  0 days  0 hours  0 minutes 13.3 seconds.

NH₃ charge distribution

Charge limits: Green to red = +1.0 to -1.0

Specific NBO charges for NH3

NH₃BH₃

NH₃BH₃ optimisation

NH3BH3 optimisation: http://hdl.handle.net/10042/20506

.log file can be found here

NH₃BH₃optimisation - summary table

NH3BH3 optimisation
File Name = NH3BH3_optimisation
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -83.22469032 a.u.
RMS Gradient Norm = 0.00005935 a.u.
Imaginary Freq = 
Dipole Moment = 5.5648 Debye
Point Group = C1
Job cpu time:  0 days  0 hours  1 minutes 24.4 seconds.

NH₃BH₃optimisation - confirmation

         Item               Value     Threshold  Converged?
 Maximum Force            0.000121     0.000450     YES
 RMS     Force            0.000057     0.000300     YES
 Maximum Displacement     0.000508     0.001800     YES
 RMS     Displacement     0.000294     0.001200     YES
 Predicted change in Energy=-1.611643D-07
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,7)                  1.0186         -DE/DX =   -0.0001              !
 ! R2    R(2,7)                  1.0186         -DE/DX =   -0.0001              !
 ! R3    R(3,7)                  1.0186         -DE/DX =   -0.0001              !
 ! R4    R(4,8)                  1.21           -DE/DX =   -0.0001              !
 ! R5    R(5,8)                  1.21           -DE/DX =   -0.0001              !
 ! R6    R(6,8)                  1.21           -DE/DX =   -0.0001              !
 ! R7    R(7,8)                  1.6681         -DE/DX =   -0.0001              !
 ! A1    A(1,7,2)              107.873          -DE/DX =    0.0                 !
 ! A2    A(1,7,3)              107.873          -DE/DX =    0.0                 !
 ! A3    A(1,7,8)              111.0212         -DE/DX =    0.0                 !
 ! A4    A(2,7,3)              107.8692         -DE/DX =    0.0                 !
 ! A5    A(2,7,8)              111.0298         -DE/DX =    0.0                 !
 ! A6    A(3,7,8)              111.0297         -DE/DX =    0.0                 !
 ! A7    A(4,8,5)              113.8796         -DE/DX =    0.0                 !
 ! A8    A(4,8,6)              113.8796         -DE/DX =    0.0                 !
 ! A9    A(4,8,7)              104.5972         -DE/DX =    0.0                 !
 ! A10   A(5,8,6)              113.8728         -DE/DX =    0.0                 !
 ! A11   A(5,8,7)              104.591          -DE/DX =    0.0                 !
 ! A12   A(6,8,7)              104.591          -DE/DX =    0.0                 !
 ! D1    D(1,7,8,4)            179.9998         -DE/DX =    0.0                 !
 ! D2    D(1,7,8,5)            -59.9967         -DE/DX =    0.0                 !
 ! D3    D(1,7,8,6)             59.9963         -DE/DX =    0.0                 !
 ! D4    D(2,7,8,4)            -60.0005         -DE/DX =    0.0                 !
 ! D5    D(2,7,8,5)             60.003          -DE/DX =    0.0                 !
 ! D6    D(2,7,8,6)            179.996          -DE/DX =    0.0                 !
 ! D7    D(3,7,8,4)             60.0001         -DE/DX =    0.0                 !
 ! D8    D(3,7,8,5)           -179.9964         -DE/DX =    0.0                 !
 ! D9    D(3,7,8,6)            -60.0034         -DE/DX =    0.0                 !

NH₃BH₃ frequency

NH3BH3 frequency: http://hdl.handle.net/10042/20507

NH₃BH₃frequency - summary table

NH3BH3 frequency
File Name = NH3BH3_frequency
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -83.22469032 a.u.
RMS Gradient Norm = 0.00005931 a.u.
Imaginary Freq = 0
Dipole Moment = 5.5648 Debye
Point Group = C1
Job cpu time:  0 days  0 hours  0 minutes 58.7 seconds.

NH₃BH₃frequency - confirmation

         Item               Value     Threshold  Converged?
 Maximum Force            0.000113     0.000450     YES
 RMS     Force            0.000059     0.000300     YES
 Maximum Displacement     0.000583     0.001800     YES
 RMS     Displacement     0.000343     0.001200     YES
 Predicted change in Energy=-1.712668D-07
 Optimization completed.
    -- Stationary point found.

Low frequencies ---    0.0009    0.0012    0.0014   18.5248   23.7751   41.0186
 Low frequencies ---  266.2845  632.2308  639.8256

NH₃BH₃ energy analysis

BH3: -26.61532264 a.u.

NH3: -56.55776856 a.u.

BH3NH3: -83.22469032 a.u.
- ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159912 a.u. = -135.52 kJ/mol

the dissociation energy of the N->B dative bond is thus 135.52 kJ/mol. This is a reasonable value as single bonds are usually in a range of few hundreds kJ/mol. The actual literature value was found to be 130 kJ/mol.³

[3] S. Xie, Y. Song, and Z. Liu, Can. J. Chem. 87, 1235–1247 (2009)

3^rd Year Computational Laboratory: Module 2, part 2, Ionic Liquids: Designer Solvents

[N(CH₃)₄]⁺

[N(CH₃)₄]⁺ optimisation

[N(CH₃)₄]⁺ optimisation: http://hdl.handle.net/10042/20557

[N(CH₃)₄]⁺ optimisation - summary table

N(CH3)4 optimisation
File Name = [N(CH3)4]_optimisation
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 1
Spin = Singlet
E(RB3LYP) = -214.18127212 a.u.
RMS Gradient Norm = 0.00010472 a.u.
Imaginary Freq = 
Dipole Moment = 2.9934 Debye
Point Group = C1
Job cpu time:  0 days  0 hours  4 minutes 20.9 seconds.

[N(CH₃)₄]⁺ optimisation - confirmation

         Item               Value     Threshold  Converged?
 Maximum Force            0.000270     0.000450     YES
 RMS     Force            0.000054     0.000300     YES
 Maximum Displacement     0.000790     0.001800     YES
 RMS     Displacement     0.000209     0.001200     YES
 Predicted change in Energy=-4.731250D-07
 Optimization completed.
    -- Stationary point found.

[N(CH₃)₄]⁺ frequency

[N(CH₃)₄]⁺ frequency: http://hdl.handle.net/10042/20584

[N(CH₃)₄]⁺ frequency - summary table

N(CH3)4 frequency
File Name = [N(CH3)4]_frequency
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 1
Spin = Singlet
E(RB3LYP) = -214.18127212 a.u.
RMS Gradient Norm = 0.00010477 a.u.
Imaginary Freq = 0
Dipole Moment = 2.9934 Debye
Point Group = C1
Job cpu time:  0 days  0 hours  8 minutes 52.1 seconds.

[N(CH₃)₄]⁺ frequency - confirmation

         
         Item               Value     Threshold  Converged?
 Maximum Force            0.000364     0.000450     YES
 RMS     Force            0.000105     0.000300     YES
 Maximum Displacement     0.000825     0.001800     YES
 RMS     Displacement     0.000306     0.001200     YES
 Predicted change in Energy=-5.687183D-07
 Optimization completed.
    -- Stationary point found.

Low frequencies ---  -11.2532   -0.0005   -0.0001    0.0007    9.6421   13.2689
 Low frequencies ---  181.9903  280.1494  287.2544

[N(CH₃)₄]⁺ molecular orbitals

[N(CH₃)₄]⁺ molecular orbitals: http://hdl.handle.net/10042/20665

[N(CH₃)₄]⁺ molecular orbitals - summary table

N(CH3)4 MOs
File Name = [N(CH3)4]_MOs
File Type = .log
Calculation Type = SP
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 1
Spin = Singlet
E(RB3LYP) = -214.18126893 a.u.
RMS Gradient Norm =  a.u.
Imaginary Freq = 
Dipole Moment = 0.0013 Debye
Point Group = C1
Job cpu time:  0 days  0 hours  1 minutes  9.4 seconds.

[P(CH₃)₄]⁺

[P(CH₃)₄]⁺ optimisation

[P(CH₃)₄]⁺ optimisation: http://hdl.handle.net/10042/20563

[P(CH₃)₄]⁺ optimisation - summary table

P(CH3)4 optimisation
File Name = [P(CH3)4]_optimisation
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 1
Spin = Singlet
E(RB3LYP) = -500.82700332 a.u.
RMS Gradient Norm = 0.00003441 a.u.
Imaginary Freq = 
Dipole Moment = 3.7357 Debye
Point Group = C1
Job cpu time:  0 days  0 hours  4 minutes 27.7 seconds.

[P(CH₃)₄]⁺ optimisation - confirmation


         Item               Value     Threshold  Converged?
 Maximum Force            0.000075     0.000450     YES
 RMS     Force            0.000026     0.000300     YES
 Maximum Displacement     0.001055     0.001800     YES
 RMS     Displacement     0.000294     0.001200     YES
 Predicted change in Energy=-9.220745D-08
 Optimization completed.
    -- Stationary point found.

[P(CH₃)₄]⁺ frequency

[P(CH₃)₄]⁺ frequency: http://hdl.handle.net/10042/20591

[P(CH₃)₄]⁺ frequency - summary table

P(CH3)4 frequency
File Name = [P(CH3)4]_frequency
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 1
Spin = Singlet
E(RB3LYP) = -500.82700332 a.u.
RMS Gradient Norm = 0.00003444 a.u.
Imaginary Freq = 0
Dipole Moment = 3.7357 Debye
Point Group = C1
Job cpu time:  0 days  0 hours  8 minutes 20.7 seconds.

[P(CH₃)₄]⁺ frequency - confirmation


         Item               Value     Threshold  Converged?
 Maximum Force            0.000083     0.000450     YES
 RMS     Force            0.000034     0.000300     YES
 Maximum Displacement     0.002272     0.001800     NO 
 RMS     Displacement     0.000935     0.001200     YES
 Predicted change in Energy=-1.113948D-07

N.B. for frequency analysis, only the forces are required to converge. Moreover, the difference between the actual value and the threshold value is not that large.

Low frequencies ---  -17.5556    0.0018    0.0024    0.0031    2.2658   15.3518
 Low frequencies ---  155.1983  184.5950  192.4405

[P(CH₃)₄]⁺ molecular orbitals

[P(CH₃)₄]⁺ molecular orbitals: http://hdl.handle.net/10042/20678

[P(CH₃)₄]⁺ molecular orbitals - summary table

P(CH3)4 MOs
File Name = [P(CH3)4]_MOs
File Type = .log
Calculation Type = SP
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 1
Spin = Singlet
E(RB3LYP) = -500.82699801 a.u.
RMS Gradient Norm =  a.u.
Imaginary Freq = 
Dipole Moment = 0.0021 Debye
Point Group = C1
Job cpu time:  0 days  0 hours  1 minutes 11.7 seconds.

[S(CH₃)₃]⁺

[S(CH₃)₃]⁺ optimisation

[S(CH₃)₃]⁺ optimisation: http://hdl.handle.net/10042/20564

[S(CH₃)₃]⁺ optimisation - summary table

S(CH3)3 optimisation
File Name = [S(CH3)3]_optimisation
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 1
Spin = Singlet
E(RB3LYP) = -517.68327867 a.u.
RMS Gradient Norm = 0.00006722 a.u.
Imaginary Freq = 
Dipole Moment = 3.1533 Debye
Point Group = C1
Job cpu time:  0 days  0 hours  2 minutes 54.2 seconds.

[S(CH₃)₃]⁺ optimisation - confirmation

Item               Value     Threshold  Converged?
 Maximum Force            0.000145     0.000450     YES
 RMS     Force            0.000039     0.000300     YES
 Maximum Displacement     0.001734     0.001800     YES
 RMS     Displacement     0.000500     0.001200     YES
 Predicted change in Energy=-2.931400D-07
 Optimization completed.
    -- Stationary point found.

[S(CH₃)₃]⁺ frequency

[S(CH₃)₃]⁺ frequency: http://hdl.handle.net/10042/20605

[S(CH₃)₃]⁺ frequency - summary table

S(CH3)3 frequency
File Name = [S(CH3)3]_frequency
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 1
Spin = Singlet
E(RB3LYP) = -517.68327867 a.u.
RMS Gradient Norm = 0.00006719 a.u.
Imaginary Freq = 0
Dipole Moment = 3.1533 Debye
Point Group = C1
Job cpu time:  0 days  0 hours  3 minutes 59.0 seconds.

[S(CH₃)₃]⁺ frequency - confirmation

         Item               Value     Threshold  Converged?
 Maximum Force            0.000270     0.000450     YES
 RMS     Force            0.000067     0.000300     YES
 Maximum Displacement     0.001798     0.001800     YES
 RMS     Displacement     0.000647     0.001200     YES
 Predicted change in Energy=-3.305774D-07
 Optimization completed.
    -- Stationary point found.

Low frequencies ---  -13.7961  -11.8440    0.0012    0.0039    0.0040   22.1581
 Low frequencies ---  159.2984  195.2522  199.2714

[S(CH₃)₃]⁺ MOs

[S(CH₃)₃]⁺ MOs: http://hdl.handle.net/10042/20694

[S(CH₃)₃]⁺ MOs - summary table

S(CH3)3 MOs
File Name = [S(CH3)3]_MOs
File Type = .log
Calculation Type = SP
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 1
Spin = Singlet
E(RB3LYP) = -517.68327822 a.u.
RMS Gradient Norm =  a.u.
Imaginary Freq = 
Dipole Moment = 0.9640 Debye
Point Group = C1
Job cpu time:  0 days  0 hours  0 minutes 42.2 seconds.

Discussion

General analysis

Both N and P atoms adopt tetrahedral geometry to minimize the steric crowding of methyl groups which are thus in the same environment. This is confirmed by inspection of C-X-C bond angles (109.5° and 109.4° respectively compared to 109.7° for tetrahedral arrangement). On the other hand, S is found to be in a trigonal pyramidal structure due to its lone pair which is quite large and pushes the methyl groups closer together by a lot reducing the C-S-C from normal trigonal pyramidal (~107°) to slightly distorted molecular structure with bond angle 102.7°.

The shortest and strongest bond among the three C-X bonds is between nitrogen and carbon. P and S atoms form weaker bonds mainly due to them being larger atoms with diffuse orbitals resulting in smaller orbital overlap. Only N is in the same period as C. The literature values for C-N (ammonium salt)⁴, C-P⁵ and C-S⁵ are 1.50 Å, 1.87 Å and 1.81 Å respectively. The computed values fit this quite well.

The charge distribution in these three systems can be rationalized based on Pauling electronegativity which increases in order P < H < C < S < N and effective nuclear charge of every atom. The larger atomic number, the higher Z_eff and the more electron density would be attracted to this atom. The formal oxidation state of all hydrogens is (+I), the one of all carbons is (-IV), nitrogen and phosphorus carry (+III) and sulphur (+II) oxidation number respectively. Although each complex has +1 charge, in every structure it is distributed differently among the atoms so that the minimum energy is found and the charge is stabilized best.

In [N(CH₃)₄]⁺, the nitrogen atom is so electronegative that it inductively pulls electron density away from carbons. It does so to such extent that the charge on nitrogen lowers to -0.295 and all carbons therefore experience much lower negative charge (-0.483).

In [P(CH₃)₄]⁺, the phosphorus atom is now less electronegative than carbon and hence carries high positive charge of +1.667. On the contrary, the charge of each carbon decreased dramatically to -1.060 because of incoming electron density from phosphorus.

In [S(CH₃)₃]⁺, the electronegativities of sulphur and carbon are comparable. The positive charge in the complex would be mostly stabilized on sulphur but the actual charge is not +1 (but +0.917) as sulphur itself withdraws little electron density from carbons due to its marginally higher electronegativity. The carbon electon density is somewhat lowered by this effect displaying lower negative charge (-0.846) than in the complex with electopositive phosphorus but higher than in the complex with electronegative nitrogen.

The charge for hydrogens does not change by much across these three complexes oscillating in a range of +0.269 to +0.298.

The charge distribution completely relates to the contribution of each of the two atoms to the C-X bond. The atom with higher electronegativity has got higher electron density around itself and thus contributes to the bond more than its bonding partner. The higher the difference in electronegativity, the bigger the difference in contributions:

[N(CH₃)₄]⁺ Δχ_C-N=0.49, contribution factor ~34:66

[P(CH₃)₄]⁺ Δχ_C-P=0.36, contribution factor ~60:40

[S(CH₃)₃]⁺ Δχ_C-S=0.03, contribution factor ~49:51

The p-type orbitals dominate the MO character of all carbons and heteroatoms whereas MOs of hydrogens are almost exclusively formed from s-type orbitals. The highest contribution of p-type character is observed on sulphur atom (s:p = ~1:5). Apart from p-type, s-type orbitals also participate in carbons and heteroatoms but to a much lesser extent (s:p = ~1:3 - ~1:4). Only traces of d-type orbitals have been indicated.

Although the positive charge is often assigned to the nitrogen atom in [N(CH₃)₄]⁺, according to the charge distribution analysis, this is not a very realistic situation. Nitrogen is too electronegative and pulls electron density towards itself. A positive charge spread mainly on hydrogens and somewhat less on carbons would be a better representation for this complex. It is always better to designate the positive charge to the whole molecule rather than a separate single atom unless charge distribution analysis has already been done and verified. In addition, R groups (R=alkyl) are electron releasing via induction always decreasing the partial charge on central nitrogen. Consequently, depicting a positive charge on this atom is imprecise.

[4] F. H. Allen, et. al. Tables of bond Lengths determined by X-Ray and Neutron Diffraction. Part 1. Bond Lengths in Organic Compounds, J. Chem. Soc. II 1987, S1-S19.

[5] R. C. Weast, Handbook of Chemistry & Physics (65th ed.), CRC Press, ISBN 0-8493-0465-2.

Interactions in molecular orbitals

Molecular orbitals in [N(CH₃)₄]⁺
MO	Through space interactions	Through bond interactions	Overall character and number of nodes	Delocalisation
6	Weakly bonding between hydrogens on adjacent carbons and strongly bonding between adjacent carbons.	Very strongly bonding C-N bonds (sp3-sp3 overlap) and strongly bonding C-H bonds (sp3-s overlap)	Totally symmetric molecular orbital with overall very strong bonding interactions. Contains 5 sp3-type based atomic nodes (4 carbons and 1 nitrogen) and 0 nodal planes	Delocalisation occurs over the whole molecule as it possesses only bonding interactions.
10	Very weakly bonding between hydrogens on adjacent carbons.	Very strongly antibonding C-N bonds (sp3-sp3 overlap) and strongly bonding interactions in C-H bonds (sp3-s overlap).	There are 5 sp3-type atomic nodes and 1 spherical nodal plane. Overall, the molecular orbital is strongly bonding.	Delocalisation occurs to a lower extent and happens in CH3 regions and around N atom.
14	Weakly to medium bonding interactions between top, bottom, and all the middle hydrogens and strong antibonding interactions between middle and top or bottom hydrogens.	Strong bonding C-H bonds (sp3-s overlap), non-bonding C-N bonds.	Overall non-bonding or very weakly bonding due to 4 atomic nodes and 2 nodal planes.	Delocalisation can only occur in one of the three bonding parts of the molecule.
19	Medium strength bonding interactions between hydrogens at the same level but antibonding between hydrogens separated by a nodal plane. Non-bonding interactions among all the carbons.	Strongly bonding interactions in C-N and C-H bonds (sp3-sp3 and sp3-s overlap respectively).	The presence of 5 atomic nodes and 3 nodal planes makes the orbital weakly antibonding despite some bonding interactions.	Delocalisation restricted to atomic orbitals on the bottom and in the middle of the depicted diagram.
20	Weakly bonding interactions between hydrogens not being separated by a nodal plane (left front, right front, left back and right back in the diagram). Weakly antibonding between hydrogens which are separated by a nodal plane.	Strongly bonding or non-bonding (~1:1) interactions for C-H bonds and also for C-N bonds.	Contains 5 atomic nodes and 4 nodal planes making the orbital strongly antibonding.	Delocalisation can only occur on the left or right of the depicted molecule.

[N(CH₃)₃(CH₂OH)]⁺

[N(CH₃)₃(CH₂OH)]⁺ optimisation

[N(CH₃)₃(CH₂OH)]⁺ optimisation: http://hdl.handle.net/10042/20716

[N(CH₃)₃(CH₂OH)]⁺ optimisation - summary table

OH optX
File Name = OH opt2
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 1
Spin = Singlet
E(RB3LYP) = -289.39472261 a.u.
RMS Gradient Norm = 0.00001557 a.u.
Imaginary Freq = 
Dipole Moment = 1.8145 Debye
Point Group = C1
Job cpu time:  0 days  0 hours 19 minutes 23.1 seconds.

[N(CH₃)₃(CH₂OH)]⁺ optimisation - confirmation

        Item               Value     Threshold  Converged?
 Maximum Force            0.000030     0.000450     YES
 RMS     Force            0.000007     0.000300     YES
 Maximum Displacement     0.000924     0.001800     YES
 RMS     Displacement     0.000263     0.001200     YES
 Predicted change in Energy=-2.595792D-08
 Optimization completed.
    -- Stationary point found.

[N(CH₃)₃(CH₂OH)]⁺ frequency

[N(CH₃)₃(CH₂OH)]⁺ frequency: http://hdl.handle.net/10042/20720

[N(CH₃)₃(CH₂OH)]⁺ frequency - summary table

OH freqX
File Name = OH freq2
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 1
Spin = Singlet
E(RB3LYP) = -289.39472261 a.u.
RMS Gradient Norm = 0.00001549 a.u.
Imaginary Freq = 0
Dipole Moment = 1.8145 Debye
Point Group = C1
Job cpu time:  0 days  0 hours 12 minutes  5.7 seconds.

[N(CH₃)₃(CH₂OH)]⁺ frequency - confirmation

         Item               Value     Threshold  Converged?
 Maximum Force            0.000076     0.000450     YES
 RMS     Force            0.000015     0.000300     YES
 Maximum Displacement     0.000779     0.001800     YES
 RMS     Displacement     0.000282     0.001200     YES
 Predicted change in Energy=-2.811110D-08
 Optimization completed.
    -- Stationary point found.

Low frequencies ---   -8.3571    0.0009    0.0010    0.0013    9.3119   23.2991
 Low frequencies ---  135.6194  212.4618  256.7404

[N(CH₃)₃(CH₂OH)]⁺ molecular orbitals

[N(CH₃)₃(CH₂OH)]⁺ molecular orbitals: http://hdl.handle.net/10042/20726

[N(CH₃)₃(CH₂OH)]⁺ molecular orbitals - summary table

N(CH3)3(CH2OH)+ MOs
File Name = OH MOs2
File Type = .log
Calculation Type = SP
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 1
Spin = Singlet
E(RB3LYP) = -289.39471439 a.u.
RMS Gradient Norm =  a.u.
Imaginary Freq = 
Dipole Moment = 2.1373 Debye
Point Group = C1
Job cpu time:  0 days  0 hours  1 minutes 47.0 seconds.

[N(CH₃)₃(CH₂CN)]⁺

[N(CH₃)₃(CH₂CN)]⁺ optimisation

[N(CH₃)₃(CH₂CN)]⁺ optimisation: http://hdl.handle.net/10042/20569

[N(CH₃)₃(CH₂CN)]⁺ optimisation - summary table

[N(CH3)3(CH2CN)]+ optimisation
File Name = [N(CH3)3(CH2CN)]_optimisation
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 1
Spin = Singlet
E(RB3LYP) = -306.39377650 a.u.
RMS Gradient Norm = 0.00001756 a.u.
Imaginary Freq = 
Dipole Moment = 13.0927 Debye
Point Group = C1
Job cpu time:  0 days  0 hours 18 minutes 17.8 seconds.

[N(CH₃)₃(CH₂CN)]⁺ optimisation - confirmation

         Item               Value     Threshold  Converged?
 Maximum Force            0.000044     0.000450     YES
 RMS     Force            0.000009     0.000300     YES
 Maximum Displacement     0.000561     0.001800     YES
 RMS     Displacement     0.000155     0.001200     YES
 Predicted change in Energy=-1.656738D-08
 Optimization completed.
    -- Stationary point found.

[N(CH₃)₃(CH₂CN)]⁺ frequency

[N(CH₃)₃(CH₂CN)]⁺ frequency: http://hdl.handle.net/10042/20643

[N(CH₃)₃(CH₂CN)]⁺ frequency - summary table

[N(CH3)3(CH2CN)]+ frequency
File Name = [N(CH3)3(CH2CN)]_frequency
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 1
Spin = Singlet
E(RB3LYP) = -306.39377650 a.u.
RMS Gradient Norm = 0.00001761 a.u.
Imaginary Freq = 0
Dipole Moment = 13.0926 Debye
Point Group = C1
Job cpu time:  0 days  0 hours 12 minutes  7.2 seconds.

[N(CH₃)₃(CH₂CN)]⁺ frequency - confirmation

         Item               Value     Threshold  Converged?
 Maximum Force            0.000056     0.000450     YES
 RMS     Force            0.000018     0.000300     YES
 Maximum Displacement     0.001834     0.001800     NO 
 RMS     Displacement     0.000605     0.001200     YES
 Predicted change in Energy=-3.139986D-09

Low frequencies ---   -0.0002    0.0007    0.0009    5.4931   11.0165   16.8454
 Low frequencies ---   93.2738  154.2316  213.7761

[N(CH₃)₃(CH₂CN)]⁺ molecular orbitals

[N(CH₃)₃(CH₂CN)]⁺ molecular orbitals: http://hdl.handle.net/10042/20710

[N(CH₃)₃(CH₂CN)]⁺ molecular orbitals - summary table

[N(CH3)3(CH2CN)]+ MOs
File Name = [N(CH3)3(CH2CN)]_MOs
File Type = .log
Calculation Type = SP
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 1
Spin = Singlet
E(RB3LYP) = -306.39376999 a.u.
RMS Gradient Norm =  a.u.
Imaginary Freq = 
Dipole Moment = 5.7640 Debye
Point Group = C1
Job cpu time:  0 days  0 hours  1 minutes 43.6 seconds.

Discussion

Effects of different substituents on charge distribution


[N(CH₃)₄]⁺	[N(CH₃)₃CH₂OH]⁺	[N(CH₃)₃CH₂CN]⁺

The picture in the middle confirmes that OH group is electron withdrawing by induction and electron donating via resonance due to oxygen lone pairs. The resonance effect generally predominates and this can be seen in this case as well. The electron density on nitrogen, three carbons and hydrogens (especially the closest ones to OH group) increased dramatically after introducing the OH substituent. The only element experiencing a stronger inductive than resonance effect of oxygen is carbon adjacent to OH group. The electronegative oxygen pulls electron density away from it and increases its charge from -0.483 to +0.088.

CN group however is an electron withdrawing group by resonance as the nitrogen atom tries to break a bond with carbon in order to gain a lone pair. This is a result of high electronegativity of nitrogen. The effect can be justified by comparing charge distributions with and without CN substituent. In case a substituent is present, all atoms except three carbons further away from cyano group (and these decreased only slightly; by 0.004-0.006) lost some electron density and their charges have increased.

HOMO-LUMO comparison

Item	[N(CH₃)₄]⁺	[N(CH₃)₃CH₂OH]⁺	[N(CH₃)₃CH₂CN]⁺
HOMO
Energy [a.u.]	-0.57917	-0.46630	-0.50048
Interactions	Medium strength bonding interactions between hydrogens at the same planar level but antibonding between hydrogens separated by a nodal plane. Non-bonding interactions among all the carbons. The presence of 5 atomic nodes and 3 nodal planes makes the orbital strongly antibonding.	Strongly antibonding through space interactions between OH hydrogen and CH2 hydrogens creating 2 atomic nodes and 2 nodal planes. There is also an antibonding atomic orbital between carbon and hydrogen on 2 of the CH3 groups creating another 2 atomic nodes. Overall, the molecular orbital is strongly antibonding.	Strongly antibonding interaction within cyano group and bonding interaction in 2 C-H bonds adjacent to CN group can be observed. Additionally, there are 2 C-H (not adjacent to cyano group) antibonding orbitals and through space weak antibonding interactions between two hydrogens on CH2 group. Molecular orbital is overall antibonding with 2 major nodal planes and 4 atomic nodes.
LUMO
Energy [a.u.]	-0.13308	-0.11991	-0.18181
Interactions	Symmetrically antibonding molecular orbital consisting of 5 spherical antibonding regions. There are weak bonding interactions among the three hydrogens on each CH3 group but the other interactions, mainly ones corresponding to the bonds are either non-bonding or strongly antibonding, e.g. C-N single bonds.	This molecular orbital can be divided into approximately 3 regions. First contains nitrogen in the middle surrounded by a spherical nodal region which itself is bonding. Further still, there are 4 antibonding regions with respect to the middle region. All bonding interactions are either non-bonding or antibonding. Overall, this is a highly antibonding orbital which however includes all the atomic orbitals compared to the HOMO which does so only to the half of them.	There are various antibonding interactions present, the main ones being an antibonding character of C-N triple bond and an antibonding C-N single bonds. Weak bonding through space interactions between hydrogens on CH3 groups are also encountered. It is difficult to determine the number of atomic nodes and nodal planes but as far as the main ones are considered, there is 5 of each.

The shape of the HOMO-LUMO orbitals involving substituents changes dramatically as the HOMO contains only half of the atomic orbitals whereas LUMO consists of all of them. LUMO is thus more delocalised. Also, the number of nodal planes and atomic nodes increases making the character of the molecular orbital more antibonding and less likely to be occupied. For [N(CH₃)₄]⁺, the number of atomic orbitals forming the molecular orbital is significant in both cases but the character changes markedly. 5 nodal planes in LUMO (some of them spherical) compared to 3 in HOMO make the LUMO higher in energy.

The HOMO-LUMO energy gaps have been calculated to be 0.44609, 0.34639 and 0.31867 a.u. for [N(CH₃)₄]⁺, [N(CH₃)₃CH₂OH]⁺ and [N(CH₃)₃CH₂CN]⁺ respectively. It is the highest difference between two adjacent energy levels in the whole molecular orbitals diagram except one gap which is slightly larger but occurs towards the top of the diagram and is chemically unimportant(above level 130). As both HOMO and LUMO are antibonding, the more elctron density present, the higher the orbital will be in energy due to stronger antibonding interactions. This correlates with the data as the electron releasing hydroxyl group is highest in energy followed by unsubstituted [N(CH₃)₄]⁺ and electron withdrawing cyano group. The reason why the latter two are swapped in HOMOs may simply lie in the fact that the HOMO of [N(CH₃)₄]⁺ is 21^st level whereas the one of N(CH₃)₃CH₂CN]⁺ is 27^th.

The larger the gap present, the harder it is to promote an electron from HOMO to LUMO and the less reactive and more stable the compound is. The magnitude of the energy gap also influences magnetic properties and colour not applicable to these complexes though. The smaller gap for substituted complexes means they are more likely to react with incoming electrophiles and nucleophiles (depending on charge at particular atom which has been discussed earlier). According to the data, cyano group is slightly more reactive than hydroxyl group. For the overall reactivity, however, the actual energy also has to be taken into account as a molecule with high HOMO-LUMO energy levels is unlikely to undergo addition reactions whereas the one with low lying HOMO-LUMO orbitals will be less prone to elimination reactions.

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3rd Year Computational Laboratory: Module 2, part 1

BH3

BH3 optimisation using 3-21G basis set

BH3optimisation - summary table

BH3optimisation - confirmation

BH3 optimisation using 6-31Gdp basis set

BH3optimisation - summary table

BH3optimisation - confirmation

BH3 frequency

BH3frequency - summary table

BH3frequency - confirmation

BH3 vibrational analysis

BH3 molecular orbitals

BH3molecular orbitals - summary table

BH3molecular orbitals diagram

TlBr3

TlBr3optimisation

TlBr3optimisation - summary table

TlBr3optimisation - confirmation

TlBr3frequency

TlBr3frequency - summary table

TlBr3frequency - confirmation

Vibrational analysis

BBr3

BBr3optimisation

Discussion

BBr3optimisation - summary table

BBr3optimisation - confirmation

BH3 vs TlBr3

Vibrational frequencies

Symmetry labels

Discussion

NH3

NH3 optimisation

NH3optimisation - summary table

NH3optimisation - confirmation

NH3 frequency

NH3frequency - summary table

NH3frequency - confirmation

NH3 molecular orbitals

NH3molecular orbitals - summary table

NH3 charge distribution

Specific NBO charges for NH3

NH3BH3

NH3BH3 optimisation

NH3BH3optimisation - summary table

NH3BH3optimisation - confirmation

NH3BH3 frequency

NH3BH3frequency - summary table

NH3BH3frequency - confirmation

NH3BH3 energy analysis

3rd Year Computational Laboratory: Module 2, part 2, Ionic Liquids: Designer Solvents

[N(CH3)4]+

[N(CH3)4]+ optimisation

[N(CH3)4]+ optimisation - summary table

[N(CH3)4]+ optimisation - confirmation

[N(CH3)4]+ frequency

[N(CH3)4]+ frequency - summary table

[N(CH3)4]+ frequency - confirmation

[N(CH3)4]+ molecular orbitals

[N(CH3)4]+ molecular orbitals - summary table

[P(CH3)4]+

[P(CH3)4]+ optimisation

[P(CH3)4]+ optimisation - summary table

[P(CH3)4]+ optimisation - confirmation

[P(CH3)4]+ frequency

[P(CH3)4]+ frequency - summary table

[P(CH3)4]+ frequency - confirmation

[P(CH3)4]+ molecular orbitals

[P(CH3)4]+ molecular orbitals - summary table

[S(CH3)3]+

[S(CH3)3]+ optimisation

[S(CH3)3]+ optimisation - summary table

[S(CH3)3]+ optimisation - confirmation

[S(CH3)3]+ frequency

[S(CH3)3]+ frequency - summary table

[S(CH3)3]+ frequency - confirmation

[S(CH3)3]+ MOs

[S(CH3)3]+ MOs - summary table

Discussion

3^rd Year Computational Laboratory: Module 2, part 1

BH₃

BH₃ optimisation using 3-21G basis set

BH₃optimisation - summary table

BH₃optimisation - confirmation

BH₃ optimisation using 6-31Gdp basis set

BH₃optimisation - summary table

BH₃optimisation - confirmation

BH₃ frequency

BH₃frequency - summary table

BH₃frequency - confirmation

BH₃ vibrational analysis

BH₃ molecular orbitals

BH₃molecular orbitals - summary table

BH₃molecular orbitals diagram

TlBr₃

TlBr₃optimisation

TlBr₃optimisation - summary table

TlBr₃optimisation - confirmation

TlBr₃frequency

TlBr₃frequency - summary table

TlBr₃frequency - confirmation

BBr₃

BBr₃optimisation

BBr₃optimisation - summary table

BBr₃optimisation - confirmation

BH₃ vs TlBr₃

NH₃

NH₃ optimisation

NH₃optimisation - summary table

NH₃optimisation - confirmation

NH₃ frequency

NH₃frequency - summary table

NH₃frequency - confirmation

NH₃ molecular orbitals

NH₃molecular orbitals - summary table

NH₃ charge distribution

NH₃BH₃

NH₃BH₃ optimisation

NH₃BH₃optimisation - summary table

NH₃BH₃optimisation - confirmation

NH₃BH₃ frequency

NH₃BH₃frequency - summary table

NH₃BH₃frequency - confirmation

NH₃BH₃ energy analysis

3^rd Year Computational Laboratory: Module 2, part 2, Ionic Liquids: Designer Solvents

[N(CH₃)₄]⁺

[N(CH₃)₄]⁺ optimisation

[N(CH₃)₄]⁺ optimisation - summary table

[N(CH₃)₄]⁺ optimisation - confirmation

[N(CH₃)₄]⁺ frequency

[N(CH₃)₄]⁺ frequency - summary table

[N(CH₃)₄]⁺ frequency - confirmation

[N(CH₃)₄]⁺ molecular orbitals

[N(CH₃)₄]⁺ molecular orbitals - summary table

[P(CH₃)₄]⁺

[P(CH₃)₄]⁺ optimisation

[P(CH₃)₄]⁺ optimisation - summary table

[P(CH₃)₄]⁺ optimisation - confirmation

[P(CH₃)₄]⁺ frequency

[P(CH₃)₄]⁺ frequency - summary table

[P(CH₃)₄]⁺ frequency - confirmation

[P(CH₃)₄]⁺ molecular orbitals

[P(CH₃)₄]⁺ molecular orbitals - summary table

[S(CH₃)₃]⁺

[S(CH₃)₃]⁺ optimisation

[S(CH₃)₃]⁺ optimisation - summary table

[S(CH₃)₃]⁺ optimisation - confirmation

[S(CH₃)₃]⁺ frequency

[S(CH₃)₃]⁺ frequency - summary table

[S(CH₃)₃]⁺ frequency - confirmation

[S(CH₃)₃]⁺ MOs

[S(CH₃)₃]⁺ MOs - summary table

[N(CH₃)₃(CH₂OH)]⁺

[N(CH₃)₃(CH₂OH)]⁺ optimisation

[N(CH₃)₃(CH₂OH)]⁺ optimisation - summary table

[N(CH₃)₃(CH₂OH)]⁺ optimisation - confirmation

[N(CH₃)₃(CH₂OH)]⁺ frequency

[N(CH₃)₃(CH₂OH)]⁺ frequency - summary table

[N(CH₃)₃(CH₂OH)]⁺ frequency - confirmation