Jump to content

Rep:Mod:lx921011inorg

From ChemWiki

Week 1

Optimisation and Analysis of BH3

3-21 G Basis

First of all, a molecule of BH3 was created using Gaussview, followed by setting three B-H bond lengths to 1.55 Å , 1.54 Å and 1.53 Å. The resulting molecule was optimised using B3LYP method and 3-21G basis set. The results were summarised in the following tables.

Table 1: Results for Initial Optimisation of BH3
BH3 optimisation File:BH3 D1 opt.log
File Name BH3_D1_opt
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 3-21G
Charge 0
Spin Singlet
E(RB3LYP) -26.46226418 a.u
E(RB3LYP) -69476.67 kJ/mol
RMS Gradient Norm 0.00011739 a.u.
Imaginary Freq
Dipole Moment 0.00 Debye
Point Group CS
Bond Lengths 1.19 Å, 1.19 Å, 1.19 Å
Bond Angles 120.0o
Job cpu time: 0 days 0 hours 0 minutes 32.7 seconds.
         Item               Value     Threshold  Converged?
 Maximum Force            0.000297     0.000450     YES
 RMS     Force            0.000123     0.000300     YES
 Maximum Displacement     0.001246     0.001800     YES
 RMS     Displacement     0.000617     0.001200     YES
 Predicted change in Energy=-2.806719D-07
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.195          -DE/DX =   -0.0003              !
 ! R2    R(1,3)                  1.1946         -DE/DX =   -0.0001              !
 ! R3    R(1,4)                  1.1943         -DE/DX =    0.0                 !
 ! A1    A(2,1,3)              120.0249         -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              119.969          -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              120.0061         -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)            180.0            -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

It can be deduced from the item table that the calculation was finished because all of the gradient terms are less than 0.001 and all forces and displacements are converged, suggesting an equilibrium was reached. So the calculation was accomplished. In addition, all of the B-H bond lengths are the same up to 3 significant figures. This agrees with the theoretical expectation that all of the bond lengths are the same for BH3 because of the trigonal planar structure of the molecule. It should be noted that the point group is not D3h as predicted by the point group theory, due to the point group not being restricted.

6-31G (d,p) Basis

To compare the nature of different basis sets, a further optimisation based on the results above using 6-31G(d,p) basis set was completed.

Table 2: Results for the Second Optimisation of BH3
BH3 optimisation File:BH3 D1 opt 6-31G dp.log
File Name BH3_D1_opt_6-31G dp.com
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) -26.6153236 a.u.
E(RB3LYP) --69878.52 kJ/mol
RMS Gradient Norm 0.000012 a.u.
Imaginary Freq
Dipole Moment 0.00 Debye
Point Group CS
Bond Lengths 1.19 Å, 1.19 Å, 1.19 Å
Bond Angles 120.0o
Job cpu time 0 days 0 hours 0 minutes 13.5 second
         Item               Value     Threshold  Converged?
 Maximum Force            0.000022     0.000450     YES
 RMS     Force            0.000012     0.000300     YES
 Maximum Displacement     0.000115     0.001800     YES
 RMS     Displacement     0.000067     0.001200     YES
 Predicted change in Energy=-2.904188D-09
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.1923         -DE/DX =    0.0                 !
 ! R2    R(1,3)                  1.1923         -DE/DX =    0.0                 !
 ! R3    R(1,4)                  1.1923         -DE/DX =    0.0                 !
 ! A1    A(2,1,3)              120.0089         -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              119.9851         -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              120.006          -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)            180.0            -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Again, the calculation was successfully finished indicated by the zero values of -DE/DX and converged forces and displacements. It can be concluded that the computed BH3 bond lengths and bond angles are the same for 6-31G (d,p) and 3-21G basis sets, revealing both methods can optimise the structure of BH3 because of the small size of BH3.

Optimisation and Analysis of GaBr3

To use pseudo-potentials and larger basis sets, a molecule of GaBr3 was created in Gaussview. Then, the symmetry was restricted by setting the tolerance of the point group to be very tight (0.0001), followed by optimising it using HPC service. The information and results were presented in the following tables.

Table 3: Results for the Optimisation of GaBr3
GaBr3 Optimisation DOI:10042/26070
File Name GaBr3 HPC output
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set LANL2DZ
Charge 0
Spin Singlet
E(RB3LYP) (a.u.) -41.70082783
E(RB3LYP) (kJ/mol) -109485.51
RMS Gradient Norm (a.u.) 0.00000016
Imaginary Freq
Dipole Moment (Debye) 0.00
Point Group D3h
Bond Lengths 2.35 Å, 2.35 Å, 2.35 Å
Literature Bond Lengths 2.272 Å[1] in GaBr4
Optimised Br-Ga-Br Angles All 120o
Job cpu time 0 days 0 hours 0 minutes 23.4 seconds.
         Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000450     YES
 RMS     Force            0.000000     0.000300     YES
 Maximum Displacement     0.000003     0.001800     YES
 RMS     Displacement     0.000002     0.001200     YES
 Predicted change in Energy=-1.282682D-12
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  2.3502         -DE/DX =    0.0                 !
 ! R2    R(1,3)                  2.3502         -DE/DX =    0.0                 !
 ! R3    R(1,4)                  2.3502         -DE/DX =    0.0                 !
 ! A1    A(2,1,3)              120.0            -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              120.0            -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              120.0            -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)            180.0            -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

The completion of the calculation was confirmed because all of the gradient terms are zero and all of the forces and displacements are converged. From Table 3, all of bond lengths and Br-Ga-Br angles are exactly the same, agreeing the theoretical prediction for a trigonal planar molecule. Thus, the calculated point group is D3h, which is the same as the theoretical prediction. The calculated bond lengths are longer than literature bond lengths for about 0.1 Å, which is very small, suggesting the computed results are resonable using the basis set and calculation method stated above.

Reference

  1. David R. Lide, ed., CRC Handbook of Chemistry and Physics, Internal Version 2005, 9-18.

Optimisation and Analysis of BBr3

A molecule of BBr3 was created based on the optimised structure of BH3 and optimised using a mixture of basis-set and pseudopotentials due to the heavy nature of bromine. The information and results of the calculation were summarised in the following table.

Table 4: Information and Results for the Optimisation of BBr3
BBr3 optimisation DOI:10042/26090
File Name BBr3 HPC output
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set Gen ( 6-31G(d,p) for B and LanL2DZ for Br)
Charge 0
Spin Singlet
E(RB3LYP) (a.u.) -64.43645246
E(RB3LYP) (kJ/mol) -169177.88
RMS Gradient Norm 0.00000776
Imaginary Freq
Dipole Moment (Debye) 0.00
Point Group CS
B-Br Bond Lengths 1.93 Å, 1.93 Å, 1.93 Å
Br-B-Br Angles All 120.0 o
Job cpu time 0 days 0 hours 0 minutes 41.0 seconds
         Item               Value     Threshold  Converged?
 Maximum Force            0.000013     0.000450     YES
 RMS     Force            0.000007     0.000300     YES
 Maximum Displacement     0.000042     0.001800     YES
 RMS     Displacement     0.000027     0.001200     YES
 Predicted change in Energy=-8.100060D-10
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.9339         -DE/DX =    0.0                 !
 ! R2    R(1,3)                  1.9339         -DE/DX =    0.0                 !
 ! R3    R(1,4)                  1.934          -DE/DX =    0.0                 !
 ! A1    A(2,1,3)              120.001          -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              120.0015         -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              119.9975         -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)            180.0            -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

The optimisation was converged, indicated by the values of -DE/DX and converged nature of forces and displacements according to the item table above. Here, the point group is Cs, which is different from GaBr3, due to the fact that the symmetry was not restricted.

Cross Comparison and Summary

To cross-compare the bond distances of BH3, BBr3 and GaBr3, the following table was constructed.

Table 5: Comparison for Bond Distances of BH3, BBr3 and GaBr3
Molecule Bond Distance (Å)
BH3 1.19
BBr3 1.93
GaBr3 2.35

By comparing the bond distance between BH3 and BBr3, it can be concluded that changing ligand to from hydride to bromide increases the bond length. This is due to the larger radius and higher polarisability of the bromide compared to the hydride, resulting in a longer bond due to more covalent nature, and orbital overlap is poorer for BBr3 due to the size mismatch. This comparison is based on the fact that the central atom is the same and both of the ligand act as an one-electron donor. In addition, bromide is more electronegative than hydride, resulting in a more polar bond for BBr3, increasing the bond length, also contributed from a poorer overlap due to energy mismatch.

Through the comparison between BBr3 and GaBr3, it can be deduced that a change of the central atom from boron to gallium increases the bond length. This is due to the larger atomic radius of the gallium compared to boron, and the polarising power of gallium is lower than boron. In terms of electronegativity, Ga is less elctronegative than B, causing the increase in bond polarity. So the Ga-Br bond is weaker than the B-Br bond because of the poorer overlap due to the reasons stated above, thus resulting in a longer bond. This comparison is based on the fact that both B and Ga are sp2 hybridised and act as an one electron acceptor.

During the initial steps of the optimisation of BH3 by 3-21G basis, there is no bond as shown in Figures 1-3. This is due to the nature of the Gaussview. Because it has a distance limit for a bond to be visible. The bond lengths were increased manually before the optimisation. Consequently, the resulting lengths exceed the limit during the initial steps of the optimisation. There are actually three invisible bonds as the hydrogen atoms still orient in a trigonal planar fashion relative to the central B atom,verifying the existence of the chemical bonds, which is in fact the electrostatic attraction between atoms. Then, bond lengths decrease gradually with the process of the optimisation. The first visible bond appears in Step 3. This phenomenon was not observed for the optimisation by 6-31G basis, because the bond lengths had entered the visible region for Gaussview after the initial optimisation by 3-21 G basis.

Figure 1: Optimisation Step 1
Figure 2: Optimisation Step 2
Figure 3: Optimisation Step 3

Frequency Analysis of BH3

First of all, the point group of the optimised BH3 was restricted to D3h by setting the tolerance to be very tight (0.0001), followed by a frequency analysis using the same method and basis set as in optimisation. The information and results were summarised in the following tables.

Table 6: Summary of Frequency Analysis of BH3
BH3 frequency File:BH3 D1 OPT 6-31G DP FREQ NEW.LOG
File Name BH3_D1_OPT_6-31G DP_FREQ_NEW
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) (a.u.) -26.61532363
E(RB3LYP) (kJ/mol) -69878.52
RMS Gradient Norm (a.u.) 0.00000681
Imaginary Freq 0
Dipole Moment (Debye) 0.00
Point Group D3h
Low frequencies --- -7.6863 -1.5828 -0.0054 0.6435 6.8283 7.0093
Low frequencies --- 1162.9673 1213.1631 1213.1658
Table 7: Summary of Vibrational Motions of BH3
No. Mode of Vibration Frequency (cm-1) Intensity Symmetry D3h Point Group
1 1162.97 92.5512 a2 "
Description all H atoms move up or down simultaneously, B atom stationary, bend
2 1213.16 14.0538 e'
Description H atoms on the bottom move towards each other along the plane of the molecule in a scissoring fashion, B atom stationary, bend
3 1213.17 14.0574 e'
Description H atom on the top moves towards each H atom on the bottom in a "scissor" fashion, at the same time, two H atoms on the bottom move in a rocking fashion, bend
4 2582.38 0 a1'
Description All H atoms move linearly and simultaneously towards or away relative to stationary B atom,symmetric stretch
5 2716.56 126.3266 e'
Description One H atom on the bottom moves linearly towards stationary B atom while another moves linearly away, asymmetric stretch
6 2716.56 126.3171 e'
Description H atom on the top moves linearly towards stationary B atom while other two atoms on the bottom move linearly away, or vice versa, asymmetric stretch
Figure 4: Computed IR Spectrum of BH3

The frequency analysis are judged to be successfully completed by the range of the low frequencies which is within ± 15 cm-1 and these frequencies are close to zero. It can be seen from Figure 4 that there are only 3 peaks, which are less than the number of vibrational modes, which is 6, from the results obtained on Table 7. Because the selection rule for IR spectroscopy is there must be a change in dipole moment during the vibrational motion of the molecule. For the vibrational mode 4, the change of dipole moment is cancelled as the bond angles of BH3 are 120o according to Table 2. Thus, this vibrational motion cannot be revealed by IR spectroscopy. In addition, motions 2 and 3 and motions 5 and 6 are two degenrate sets of vibrations, appearing as one peak for each set in the spectrum. So it can be concluded that there are 3 peaks on the IR spectrum.

Frequency Analysis of GaBr3

To compare the difference between the vibrational motions of GaBr3 and BH3, it is necessary to carry out frequency analysis for GaBr3 using the same method and basis set based on the optimised structure of GaBr3 in the previous part. The results and information were summarised as follows.

Table 8: Summary of Frequency Analysis of GaBr3
GaBr3 Frequency DOI:10042/26110
File Name log_82606
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set LANL2DZ
Charge 0
Spin Singlet
E(RB3LYP) (a.u.) -41.70082783
E(RB3LYP) (kJ/mol) -109485.51
RMS Gradient Norm (a.u.) 0.00000011
Imaginary Freq 0
Dipole Moment (Debye) 0
Point Group D3h
Job cpu time 0 days 0 hours 0 minutes 19.4 seconds.
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
Figure 5: Computed IR Spectrum of GaBr3
Table 9: Comparison of Vibration Frequencies between BH3 and GaBr3
No. Frequency (cm-1) Frequency (cm-1)
BH3 (cm-1) Symmtry Label GaBr3 (cm-1) Symmtry Label Type of Motion
1 1162.97 a2" 76.37 e' bend
2 1213.16 e' 76.38 e' bend
3 1213.16 e' 99.70 a2" bend
4 2582.38 a1' 197.34 a1' bend
5 2715.56 e' 316.18 e' bend
6 2715.56 e' 316.19 e' bend

The analysis was successfully accomplished according to the low frequencies, which lie within the range of ±15 cm-1 and are close to zero. By comparing Figures 4 and 5, both of the spectra consist of 3 peaks and a similar pattern is observed, due to the same point group, D3h, hence similar vibrational environments for these two molecules. From Table 9, the vibrational frequencies of GaBr3 is much lower than BH3, due to the greater reduced mass of GaBr3 as both Ga and Br are heavier than B and H. Also, the atomic radii of Ga and Br are greater than B and H, resulting in the less rigidity of the Ga-Br bond compared to the B-H bond because of the poorer overlap. So, the Ga-Br bond vibrates slower than the B-H bond.

According to Table 9, the order of the e' and the a2" bends is reversed from BH3 to GaBr3. This might be rationalised from the magneitude of displacement vectors , e' vibrations of GaBr3 involve the significant displacement vectors of all of the Ga and Br atoms. In contrast, a2" vibration only involves the significant motion of Ga atom and smaller dispalcement of Br atoms,which can be deduced from the smaller displacement vectors as shown in the following table, resulting in a higher vibrational frequency.

Table 10: Comparison of Bending Motions of GaBr3
No. Animation Frequency (cm-1) Symmetry Label
1 76.37 e' (lowest real mode)
2 76.38 e' (lowest real mode)
3 99.70 a2"

The stretching motion, which involves the dramatic change of bond lengths while the bending motion only requires the slight change in bond lengths. Based on this argument, it can also be deduced from Table 9 that a2" and e' bends, which lie very close ,are lower in energy than a1'and e' stretches. Because bend motions require less energy than stretching motions.

To conclude, the purpose of a frequency analysis is to ensure whether a minimum of the energy of a optimised structure has been reached and to figure out vibrational modes for a molecule, hence computing an IR spectrum. It is based on the result of the optimisation. So same method and basis set must be used to ensure the consistency. Otherwise, the frequency analysis has no significance. The low frequencies are the motions of the centre of the mass, so it is much lower than real frequencies. They are "-6" term in the formula "3N-6" to determine the number of vibration modes for a molecule, where N is the total number of atoms.

Molecular Orbitals of BH3

The analysis of molecular orbitals of BH3 was carried out based on the optimised structure of BH3 by the 6-31G (d,p) basis set. The information of the calculation was summarised in the following table.

Table 11: Summary of MO Calculation of BH3
BH3 MO DOI:10042/26109
File Name LX_BH3_MO
File Type .fch
Calculation Type SP
Calculation Method RB3LYP
Basis Set 6-31G(D,P)
Charge 0
Spin Singlet
Total Energy (a.u.) -26.6153236
Total Energy (kJ/mol) -69878.52
RMS Gradient Norm (a.u.) 0
Imaginary Freq
Dipole Moment (Debye) 0.0001
Point Group
Job cpu time 0 days 0 hours 0 minutes 24 seconds.

A MO diagram of BH3 based on LCAO theory was drawn using Chemdraw with computed MOs on it to compare the difference of these MOs.

Figure 6: MO Diagram of BH3

According to Figure 6, LCAO MOs are simply as a result from the combination of the atomic orbitals, which means the electron density is localised on individual atomic orbitals. But for the real MOs, the electron density is delocalised on the whole molecular orbitals. So, LCAO method cannot give a clear picture on the shape and location of the electron density. But, the positions of nodal planes and nodes as labelled on LCAO MOs on Figure 6 are the same with those on calculated MOs, suggesting the LCAO method can predict accurate positions of nodal planes and nodes. To conclude, LCAO method is not good at predicting the location and shape of the electron density but can give accurate positions of nodal planes and nodes.

Analysis of NH3

First, a molecule of NH3 was created using Gaussview, followed by an optimisation using 6-31G(d,p) basis and DFT method with no symmetry. The information was summarised as follows.

Table 12: Summary of Optimisation of NH3
NH3 optimisation File:LX NH3 OPT 6-31G DP.LOG
File Name LX_NH3_OPT_6-31G DP
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) (a.u.) -56.55776872
E(RB3LYP) (kJ/mol) -148492.40
RMS Gradient Norm 0.00000095
Imaginary Freq
Dipole Moment (Debye) 1.85
Point Group C1
Job cpu time 0 days 0 hours 0 minutes 21.0 seconds.
         Item               Value     Threshold  Converged?
 Maximum Force            0.000002     0.000015     YES
 RMS     Force            0.000001     0.000010     YES
 Maximum Displacement     0.000005     0.000060     YES
 RMS     Displacement     0.000003     0.000040     YES
 Predicted change in Energy=-9.677657D-12
 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)              105.7447         -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              105.7444         -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              105.7444         -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)           -111.8637         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

The calculation was finished because of the converged values of forces and displacements. Also, all of the gradient terms are zero. A frequency analysis was completed to ensure the optimisation result is a minimum. It is necessary to restrict the point group to D3h by setting the tolerance to tight before the analysis.

Table 13: Summary of Frequency Analysis of NH3
NH3 frequency File:LX NH3 FREQ 6-31G DP NEW.LOG
File Name LX_NH3_FREQ_6-31G_DP_NEW
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) (a.u.) -56.55776873
E(RB3LYP) (kJ/mol) -148492.40
RMS Gradient Norm (a.u.) 0.00000133
Imaginary Freq 0
Dipole Moment 1.85
Point Group C3v
Job cpu time 0 days 0 hours 0 minutes 8.0 seconds.
Low frequencies --- -0.0662 -0.0039 0.0017 1.3732 4.3473 4.3478
Low frequencies --- 1089.3706 1693.9316 1693.9316

It can be deduced from the low frequencies that a minimum has been reached as the frequencies lie within ±15 cm-1 and are close to zero and much lower compared to the first vibration at 1089.37 cm-1. So, a NBO analysis can be carried out. The information was summarised as follows.

Table 14: Summary of NBO Analysis of NH3
NH3 NBO File:LX NH3 OPT 6-31GDP NBO.LOG
File Name LX_NH3_OPT_6-31GDP_NBO
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) (a.u.) -56.55776872
E(RB3LYP) (kJ/mol) -148492.40
RMS Gradient Norm (a.u.) 0.00000095
Imaginary Freq
Dipole Moment (Debye) 1.85
Point Group C1
Job cpu time 0 days 0 hours 0 minutes 8.0 seconds.
Figure 7: Charge Distribution of NH3

The range of the charge distribution is -1.00 - +1.00. The specific NMO charges for H are +0.375 and -1.125 for N. This verifies that nitrogen is more electronegative than hydrogen. Also, the sum of charges for nitrogen and hydrogen are zero, confirming neutrality of this molecule. So, NBO analysis was successful.

Finding Association Energies of H3NBH3

A molecule of H3NBH3 was created on Gaussview. Then, it was optimised with no restriction on symmetry using the same method (B3LYP) and basis set (6-31G (d,p)) as used for optimisations of NH3 and BH3. Information and results for this optimisation were summarised as follows.

Table 15: Summary of Optimisation of H3NBH3
NH3BH3 Opt File:LX NH3BH3 OPT 6-31G DP.LOG
File Name LX_NH3BH3_OPT_6-31G DP
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) (a.u.) -83.22468907
E(RB3LYP) (kJ/mol) -218506.39
RMS Gradient Norm (a.u.) 0.00000122
Imaginary Freq
Dipole Moment (Debye) 5.56
Point Group -
         Item               Value     Threshold  Converged?
 Maximum Force            0.000002     0.000015     YES
 RMS     Force            0.000001     0.000010     YES
 Maximum Displacement     0.000027     0.000060     YES
 RMS     Displacement     0.000009     0.000040     YES
 Predicted change in Energy=-9.030556D-11
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,7)                  1.2098         -DE/DX =    0.0                 !
 ! R2    R(2,7)                  1.2098         -DE/DX =    0.0                 !
 ! R3    R(3,7)                  1.2098         -DE/DX =    0.0                 !
 ! R4    R(4,8)                  1.0185         -DE/DX =    0.0                 !
 ! R5    R(5,8)                  1.0185         -DE/DX =    0.0                 !
 ! R6    R(6,8)                  1.0185         -DE/DX =    0.0                 !
 ! R7    R(7,8)                  1.6677         -DE/DX =    0.0                 !
 ! A1    A(1,7,2)              113.874          -DE/DX =    0.0                 !
 ! A2    A(1,7,3)              113.874          -DE/DX =    0.0                 !
 ! A3    A(1,7,8)              104.5972         -DE/DX =    0.0                 !
 ! A4    A(2,7,3)              113.874          -DE/DX =    0.0                 !
 ! A5    A(2,7,8)              104.5972         -DE/DX =    0.0                 !
 ! A6    A(3,7,8)              104.5973         -DE/DX =    0.0                 !
 ! A7    A(4,8,5)              107.8749         -DE/DX =    0.0                 !
 ! A8    A(4,8,6)              107.8749         -DE/DX =    0.0                 !
 ! A9    A(4,8,7)              111.0237         -DE/DX =    0.0                 !
 ! A10   A(5,8,6)              107.8748         -DE/DX =    0.0                 !
 ! A11   A(5,8,7)              111.0241         -DE/DX =    0.0                 !
 ! A12   A(6,8,7)              111.0241         -DE/DX =    0.0                 !
 ! D1    D(1,7,8,4)           -180.0            -DE/DX =    0.0                 !
 ! D2    D(1,7,8,5)            -60.0            -DE/DX =    0.0                 !
 ! D3    D(1,7,8,6)             60.0            -DE/DX =    0.0                 !
 ! D4    D(2,7,8,4)            -60.0            -DE/DX =    0.0                 !
 ! D5    D(2,7,8,5)             60.0            -DE/DX =    0.0                 !
 ! D6    D(2,7,8,6)           -180.0            -DE/DX =    0.0                 !
 ! D7    D(3,7,8,4)             60.0            -DE/DX =    0.0                 !
 ! D8    D(3,7,8,5)            180.0            -DE/DX =    0.0                 !
 ! D9    D(3,7,8,6)            -60.0            -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

The optimisation was finished because all forces and displacements are converged and all gradient terms are zero, suggesting a stationary point was reached. To ensure a minimum had been achieved, a frequency analysis was carried out using the same method and basis set with the restriction of the point group to D3h using very tight tolerance (0.0001):

Table 16: Summary of Frequency Analysis of H3NBH3
NH3BH3 Frequency File:LX NH3BH3 FREQ 6-31G DP.LOG
File Name LX_NH3BH3_FREQ_6-31G DP
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Charge 0
Spin Singlet
E(RB3LYP) (a.u.) -83.22468909
E(RB3LYP) (kJ/mol) -218506.39
RMS Gradient Norm 0.00000134
Imaginary Freq 0
Dipole Moment (Debye) 5.56
Point Group C3v
Job cpu time 0 days 0 hours 0 minutes 21.0 seconds.
Low frequencies --- -5.1591 -0.2901 -0.0423 -0.0012 1.2790 1.3465
Low frequencies --- 263.3038 632.9632 638.4672

According to the item table, a minimum was reached for H3NBH3 as low frequencies are close to zero, lying within the range of ±15 cm-1 and low frequencies are low.

To find the association energy of H3NBH3, the following table was constructed.

Table 17: Results for Energy Calculation of H3NBH3
Energy
BH3 (a.u.) -26.61532363
NH3 (a.u.) -56.55776872
H3NBH3 (a.u.) -83.22468907
Dissociation Energy (a.u.) -0.05159672
Dissociation Energy (kJ/mol) -135.47

According to Table 17, H3NBH3 is more stable than the NH3 and BH3, due to the formation of a new dative covalent bond by the donation of a lone pair from the sp3 orbital on N to the empty p orbital on BH3, lowering the total energy of the whole system. So this process is spontaneous.

Mini Project: Investigating Aromaticity

Figure 8: Aromatic Molecules

The molecules as shown on Figure 8, are isoelectronic and have 6 π-electrons, resulting in the aromaticity as predicted by Hückel's rule (n=1). Starting from benzene as a reference molecule, the MOs of these four molecules, especially occupied π-MOs, were analysed in detail using computational methods to investigate the aromaticity and the effect of changing one C-H fragment on benzene to other isoelectronic fragments such as N+-H and B--H on chemical properties. In addition, NBO analysis was also carried out to give charge distribution patterns to predict the reactivities and regioselectivities.








Optimisation

First and foremost, the optimisations of the structures of these four molecules were completed using B3LYP method and 6-31G (d,p) basis set without restriction on symmetry. The information and results were summarised in the following tables.

Table 18: Summary of Optimisations
Benzene Optimisation Boratabenzene Optimisation Pyridinium Optimisation Borazine Optimisation
File Name lx-Benzene-opt lx-borataben-opt lx-pyridinium-opt lx-Borazine-opt
File Type .log .log .log .log
Calculation Type FOPT FOPT FOPT FOPT
Calculation Method RB3LYP RB3LYP RB3LYP RB3LYP
Basis Set 6-31G(d,p) 6-31G(d,p) 6-31G(d,p) 6-31G(d,p)
Charge 0 -1 1 0
Spin Singlet Singlet Singlet Singlet
E(RB3LYP) (a.u.) -232.2582028 -219.0205229 -248.6680607 -242.6845997
E(RB3LYP) (kJ/mol) -609793.82 -575038.30 -652877.90 -637168.32
RMS Gradient Norm 0.00000012 0.00000036 0.00000044 0.00000016
Imaginary Freq
Dipole Moment (Debye) 0 9.2828 8.6349 0
Point Group C1 C1 C1 C1
Job cpu time 0 days 0 hours 6 minutes 44.6 seconds. 0 days 0 hours 8 minutes 24.0 seconds. 0 days 0 hours 7 minutes 8.0 seconds. 0 days 0 hours 9 minutes 47.4 seconds.
Dspace DOI:10042/26155 DOI:10042/26154 DOI:10042/26152 DOI:10042/26153

Item Table of Benzene:

         Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000002     YES
 RMS     Force            0.000000     0.000001     YES
 Maximum Displacement     0.000002     0.000006     YES
 RMS     Displacement     0.000001     0.000004     YES
 Predicted change in Energy=-7.235345D-13
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.3963         -DE/DX =    0.0                 !
 ! R2    R(1,6)                  1.3963         -DE/DX =    0.0                 !
 ! R3    R(1,7)                  1.0863         -DE/DX =    0.0                 !
 ! R4    R(2,3)                  1.3963         -DE/DX =    0.0                 !
 ! R5    R(2,8)                  1.0863         -DE/DX =    0.0                 !
 ! R6    R(3,4)                  1.3963         -DE/DX =    0.0                 !
 ! R7    R(3,9)                  1.0863         -DE/DX =    0.0                 !
 ! R8    R(4,5)                  1.3963         -DE/DX =    0.0                 !
 ! R9    R(4,10)                 1.0863         -DE/DX =    0.0                 !
 ! R10   R(5,6)                  1.3963         -DE/DX =    0.0                 !
 ! R11   R(5,11)                 1.0863         -DE/DX =    0.0                 !
 ! R12   R(6,12)                 1.0863         -DE/DX =    0.0                 !
 ! A1    A(2,1,6)              120.0            -DE/DX =    0.0                 !
 ! A2    A(2,1,7)              120.0            -DE/DX =    0.0                 !
 ! A3    A(6,1,7)              120.0            -DE/DX =    0.0                 !
 ! A4    A(1,2,3)              120.0            -DE/DX =    0.0                 !
 ! A5    A(1,2,8)              120.0001         -DE/DX =    0.0                 !
 ! A6    A(3,2,8)              120.0            -DE/DX =    0.0                 !
 ! A7    A(2,3,4)              120.0001         -DE/DX =    0.0                 !
 ! A8    A(2,3,9)              120.0            -DE/DX =    0.0                 !
 ! A9    A(4,3,9)              120.0            -DE/DX =    0.0                 !
 ! A10   A(3,4,5)              120.0            -DE/DX =    0.0                 !
 ! A11   A(3,4,10)             120.0            -DE/DX =    0.0                 !
 ! A12   A(5,4,10)             120.0            -DE/DX =    0.0                 !
 ! A13   A(4,5,6)              120.0            -DE/DX =    0.0                 !
 ! A14   A(4,5,11)             120.0001         -DE/DX =    0.0                 !
 ! A15   A(6,5,11)             119.9999         -DE/DX =    0.0                 !
 ! A16   A(1,6,5)              120.0            -DE/DX =    0.0                 !
 ! A17   A(1,6,12)             120.0            -DE/DX =    0.0                 !
 ! A18   A(5,6,12)             120.0            -DE/DX =    0.0                 !
 ! D1    D(6,1,2,3)             -0.0001         -DE/DX =    0.0                 !
 ! D2    D(6,1,2,8)           -179.9999         -DE/DX =    0.0                 !
 ! D3    D(7,1,2,3)            179.9999         -DE/DX =    0.0                 !
 ! D4    D(7,1,2,8)              0.0001         -DE/DX =    0.0                 !
 ! D5    D(2,1,6,5)              0.0            -DE/DX =    0.0                 !
 ! D6    D(2,1,6,12)           180.0            -DE/DX =    0.0                 !
 ! D7    D(7,1,6,5)           -180.0            -DE/DX =    0.0                 !
 ! D8    D(7,1,6,12)             0.0            -DE/DX =    0.0                 !
 ! D9    D(1,2,3,4)              0.0002         -DE/DX =    0.0                 !
 ! D10   D(1,2,3,9)            180.0            -DE/DX =    0.0                 !
 ! D11   D(8,2,3,4)            180.0            -DE/DX =    0.0                 !
 ! D12   D(8,2,3,9)             -0.0001         -DE/DX =    0.0                 !
 ! D13   D(2,3,4,5)             -0.0001         -DE/DX =    0.0                 !
 ! D14   D(2,3,4,10)           179.9999         -DE/DX =    0.0                 !
 ! D15   D(9,3,4,5)           -180.0            -DE/DX =    0.0                 !
 ! D16   D(9,3,4,10)             0.0            -DE/DX =    0.0                 !
 ! D17   D(3,4,5,6)              0.0            -DE/DX =    0.0                 !
 ! D18   D(3,4,5,11)           180.0            -DE/DX =    0.0                 !
 ! D19   D(10,4,5,6)          -180.0001         -DE/DX =    0.0                 !
 ! D20   D(10,4,5,11)            0.0            -DE/DX =    0.0                 !
 ! D21   D(4,5,6,1)              0.0001         -DE/DX =    0.0                 !
 ! D22   D(4,5,6,12)           180.0            -DE/DX =    0.0                 !
 ! D23   D(11,5,6,1)          -179.9999         -DE/DX =    0.0                 !
 ! D24   D(11,5,6,12)            0.0            -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Item Table of Boratabenzene:

         Item               Value     Threshold  Converged?
 Maximum Force            0.000001     0.000002     YES
 RMS     Force            0.000000     0.000001     YES
 Maximum Displacement     0.000005     0.000006     YES
 RMS     Displacement     0.000001     0.000004     YES
 Predicted change in Energy=-2.592632D-12
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.4052         -DE/DX =    0.0                 !
 ! R2    R(1,5)                  1.4052         -DE/DX =    0.0                 !
 ! R3    R(1,6)                  1.0915         -DE/DX =    0.0                 !
 ! R4    R(2,3)                  1.3988         -DE/DX =    0.0                 !
 ! R5    R(2,7)                  1.0969         -DE/DX =    0.0                 !
 ! R6    R(3,8)                  1.0968         -DE/DX =    0.0                 !
 ! R7    R(3,12)                 1.5141         -DE/DX =    0.0                 !
 ! R8    R(4,5)                  1.3988         -DE/DX =    0.0                 !
 ! R9    R(4,10)                 1.0968         -DE/DX =    0.0                 !
 ! R10   R(4,12)                 1.5141         -DE/DX =    0.0                 !
 ! R11   R(5,11)                 1.0969         -DE/DX =    0.0                 !
 ! R12   R(9,12)                 1.2184         -DE/DX =    0.0                 !
 ! A1    A(2,1,5)              120.415          -DE/DX =    0.0                 !
 ! A2    A(2,1,6)              119.7929         -DE/DX =    0.0                 !
 ! A3    A(5,1,6)              119.7921         -DE/DX =    0.0                 !
 ! A4    A(1,2,3)              122.1794         -DE/DX =    0.0                 !
 ! A5    A(1,2,7)              117.4558         -DE/DX =    0.0                 !
 ! A6    A(3,2,7)              120.3648         -DE/DX =    0.0                 !
 ! A7    A(2,3,8)              116.012          -DE/DX =    0.0                 !
 ! A8    A(2,3,12)             120.0607         -DE/DX =    0.0                 !
 ! A9    A(8,3,12)             123.9274         -DE/DX =    0.0                 !
 ! A10   A(5,4,10)             116.0124         -DE/DX =    0.0                 !
 ! A11   A(5,4,12)             120.0605         -DE/DX =    0.0                 !
 ! A12   A(10,4,12)            123.9271         -DE/DX =    0.0                 !
 ! A13   A(1,5,4)              122.1798         -DE/DX =    0.0                 !
 ! A14   A(1,5,11)             117.4556         -DE/DX =    0.0                 !
 ! A15   A(4,5,11)             120.3645         -DE/DX =    0.0                 !
 ! A16   A(3,12,4)             115.1046         -DE/DX =    0.0                 !
 ! A17   A(3,12,9)             122.4473         -DE/DX =    0.0                 !
 ! A18   A(4,12,9)             122.4481         -DE/DX =    0.0                 !
 ! D1    D(5,1,2,3)              0.0002         -DE/DX =    0.0                 !
 ! D2    D(5,1,2,7)           -179.9999         -DE/DX =    0.0                 !
 ! D3    D(6,1,2,3)            180.0001         -DE/DX =    0.0                 !
 ! D4    D(6,1,2,7)              0.0            -DE/DX =    0.0                 !
 ! D5    D(2,1,5,4)             -0.0002         -DE/DX =    0.0                 !
 ! D6    D(2,1,5,11)          -180.0001         -DE/DX =    0.0                 !
 ! D7    D(6,1,5,4)           -180.0001         -DE/DX =    0.0                 !
 ! D8    D(6,1,5,11)             0.0            -DE/DX =    0.0                 !
 ! D9    D(1,2,3,8)           -180.0001         -DE/DX =    0.0                 !
 ! D10   D(1,2,3,12)            -0.0001         -DE/DX =    0.0                 !
 ! D11   D(7,2,3,8)              0.0            -DE/DX =    0.0                 !
 ! D12   D(7,2,3,12)           180.0001         -DE/DX =    0.0                 !
 ! D13   D(2,3,12,4)             0.0            -DE/DX =    0.0                 !
 ! D14   D(2,3,12,9)          -180.0            -DE/DX =    0.0                 !
 ! D15   D(8,3,12,4)           180.0            -DE/DX =    0.0                 !
 ! D16   D(8,3,12,9)             0.0            -DE/DX =    0.0                 !
 ! D17   D(10,4,5,1)           180.0001         -DE/DX =    0.0                 !
 ! D18   D(10,4,5,11)            0.0            -DE/DX =    0.0                 !
 ! D19   D(12,4,5,1)             0.0001         -DE/DX =    0.0                 !
 ! D20   D(12,4,5,11)         -180.0            -DE/DX =    0.0                 !
 ! D21   D(5,4,12,3)             0.0            -DE/DX =    0.0                 !
 ! D22   D(5,4,12,9)           180.0            -DE/DX =    0.0                 !
 ! D23   D(10,4,12,3)         -180.0            -DE/DX =    0.0                 !
 ! D24   D(10,4,12,9)            0.0            -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Item Table of Pyridinium

         Item               Value     Threshold  Converged?
 Maximum Force            0.000001     0.000002     YES
 RMS     Force            0.000000     0.000001     YES
 Maximum Displacement     0.000005     0.000006     YES
 RMS     Displacement     0.000001     0.000004     YES
 Predicted change in Energy=-4.632836D-12
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.3987         -DE/DX =    0.0                 !
 ! R2    R(1,5)                  1.3987         -DE/DX =    0.0                 !
 ! R3    R(1,6)                  1.0852         -DE/DX =    0.0                 !
 ! R4    R(2,3)                  1.3838         -DE/DX =    0.0                 !
 ! R5    R(2,7)                  1.0835         -DE/DX =    0.0                 !
 ! R6    R(3,8)                  1.0832         -DE/DX =    0.0                 !
 ! R7    R(3,12)                 1.3524         -DE/DX =    0.0                 !
 ! R8    R(4,5)                  1.3838         -DE/DX =    0.0                 !
 ! R9    R(4,10)                 1.0832         -DE/DX =    0.0                 !
 ! R10   R(4,12)                 1.3524         -DE/DX =    0.0                 !
 ! R11   R(5,11)                 1.0835         -DE/DX =    0.0                 !
 ! R12   R(9,12)                 1.0169         -DE/DX =    0.0                 !
 ! A1    A(2,1,5)              120.0616         -DE/DX =    0.0                 !
 ! A2    A(2,1,6)              119.9693         -DE/DX =    0.0                 !
 ! A3    A(5,1,6)              119.9691         -DE/DX =    0.0                 !
 ! A4    A(1,2,3)              119.0802         -DE/DX =    0.0                 !
 ! A5    A(1,2,7)              121.474          -DE/DX =    0.0                 !
 ! A6    A(3,2,7)              119.4458         -DE/DX =    0.0                 !
 ! A7    A(2,3,8)              123.9412         -DE/DX =    0.0                 !
 ! A8    A(2,3,12)             119.2362         -DE/DX =    0.0                 !
 ! A9    A(8,3,12)             116.8226         -DE/DX =    0.0                 !
 ! A10   A(5,4,10)             123.941          -DE/DX =    0.0                 !
 ! A11   A(5,4,12)             119.2366         -DE/DX =    0.0                 !
 ! A12   A(10,4,12)            116.8223         -DE/DX =    0.0                 !
 ! A13   A(1,5,4)              119.0801         -DE/DX =    0.0                 !
 ! A14   A(1,5,11)             121.4747         -DE/DX =    0.0                 !
 ! A15   A(4,5,11)             119.4452         -DE/DX =    0.0                 !
 ! A16   A(3,12,4)             123.3053         -DE/DX =    0.0                 !
 ! A17   A(3,12,9)             118.3472         -DE/DX =    0.0                 !
 ! A18   A(4,12,9)             118.3475         -DE/DX =    0.0                 !
 ! D1    D(5,1,2,3)             -0.0001         -DE/DX =    0.0                 !
 ! D2    D(5,1,2,7)           -180.0            -DE/DX =    0.0                 !
 ! D3    D(6,1,2,3)           -180.0002         -DE/DX =    0.0                 !
 ! D4    D(6,1,2,7)              0.0            -DE/DX =    0.0                 !
 ! D5    D(2,1,5,4)             -0.0002         -DE/DX =    0.0                 !
 ! D6    D(2,1,5,11)           179.9999         -DE/DX =    0.0                 !
 ! D7    D(6,1,5,4)           -180.0001         -DE/DX =    0.0                 !
 ! D8    D(6,1,5,11)             0.0            -DE/DX =    0.0                 !
 ! D9    D(1,2,3,8)            180.0            -DE/DX =    0.0                 !
 ! D10   D(1,2,3,12)             0.0003         -DE/DX =    0.0                 !
 ! D11   D(7,2,3,8)             -0.0001         -DE/DX =    0.0                 !
 ! D12   D(7,2,3,12)           180.0001         -DE/DX =    0.0                 !
 ! D13   D(2,3,12,4)            -0.0002         -DE/DX =    0.0                 !
 ! D14   D(2,3,12,9)          -180.0001         -DE/DX =    0.0                 !
 ! D15   D(8,3,12,4)           180.0001         -DE/DX =    0.0                 !
 ! D16   D(8,3,12,9)             0.0001         -DE/DX =    0.0                 !
 ! D17   D(10,4,5,1)           180.0            -DE/DX =    0.0                 !
 ! D18   D(10,4,5,11)           -0.0001         -DE/DX =    0.0                 !
 ! D19   D(12,4,5,1)             0.0002         -DE/DX =    0.0                 !
 ! D20   D(12,4,5,11)          180.0001         -DE/DX =    0.0                 !
 ! D21   D(5,4,12,3)             0.0            -DE/DX =    0.0                 !
 ! D22   D(5,4,12,9)          -180.0001         -DE/DX =    0.0                 !
 ! D23   D(10,4,12,3)          180.0002         -DE/DX =    0.0                 !
 ! D24   D(10,4,12,9)            0.0001         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

Item Table of Borazine

         Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000002     YES
 RMS     Force            0.000000     0.000001     YES
 Maximum Displacement     0.000002     0.000006     YES
 RMS     Displacement     0.000001     0.000004     YES
 Predicted change in Energy=-9.528920D-13
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,12)                 1.1951         -DE/DX =    0.0                 !
 ! R2    R(2,8)                  1.0097         -DE/DX =    0.0                 !
 ! R3    R(3,11)                 1.1951         -DE/DX =    0.0                 !
 ! R4    R(4,7)                  1.0097         -DE/DX =    0.0                 !
 ! R5    R(5,10)                 1.1951         -DE/DX =    0.0                 !
 ! R6    R(6,9)                  1.0097         -DE/DX =    0.0                 !
 ! R7    R(7,10)                 1.4306         -DE/DX =    0.0                 !
 ! R8    R(7,11)                 1.4306         -DE/DX =    0.0                 !
 ! R9    R(8,11)                 1.4306         -DE/DX =    0.0                 !
 ! R10   R(8,12)                 1.4306         -DE/DX =    0.0                 !
 ! R11   R(9,10)                 1.4306         -DE/DX =    0.0                 !
 ! R12   R(9,12)                 1.4306         -DE/DX =    0.0                 !
 ! A1    A(4,7,10)             118.5662         -DE/DX =    0.0                 !
 ! A2    A(4,7,11)             118.566          -DE/DX =    0.0                 !
 ! A3    A(10,7,11)            122.8677         -DE/DX =    0.0                 !
 ! A4    A(2,8,11)             118.5661         -DE/DX =    0.0                 !
 ! A5    A(2,8,12)             118.5662         -DE/DX =    0.0                 !
 ! A6    A(11,8,12)            122.8677         -DE/DX =    0.0                 !
 ! A7    A(6,9,10)             118.5656         -DE/DX =    0.0                 !
 ! A8    A(6,9,12)             118.5656         -DE/DX =    0.0                 !
 ! A9    A(10,9,12)            122.8688         -DE/DX =    0.0                 !
 ! A10   A(5,10,7)             121.4341         -DE/DX =    0.0                 !
 ! A11   A(5,10,9)             121.434          -DE/DX =    0.0                 !
 ! A12   A(7,10,9)             117.1319         -DE/DX =    0.0                 !
 ! A13   A(3,11,7)             121.434          -DE/DX =    0.0                 !
 ! A14   A(3,11,8)             121.4341         -DE/DX =    0.0                 !
 ! A15   A(7,11,8)             117.132          -DE/DX =    0.0                 !
 ! A16   A(1,12,8)             121.434          -DE/DX =    0.0                 !
 ! A17   A(1,12,9)             121.4341         -DE/DX =    0.0                 !
 ! A18   A(8,12,9)             117.1319         -DE/DX =    0.0                 !
 ! D1    D(4,7,10,5)             0.0            -DE/DX =    0.0                 !
 ! D2    D(4,7,10,9)           180.0001         -DE/DX =    0.0                 !
 ! D3    D(11,7,10,5)         -180.0            -DE/DX =    0.0                 !
 ! D4    D(11,7,10,9)            0.0001         -DE/DX =    0.0                 !
 ! D5    D(4,7,11,3)             0.0            -DE/DX =    0.0                 !
 ! D6    D(4,7,11,8)          -180.0            -DE/DX =    0.0                 !
 ! D7    D(10,7,11,3)          180.0            -DE/DX =    0.0                 !
 ! D8    D(10,7,11,8)            0.0001         -DE/DX =    0.0                 !
 ! D9    D(2,8,11,3)             0.0001         -DE/DX =    0.0                 !
 ! D10   D(2,8,11,7)          -179.9999         -DE/DX =    0.0                 !
 ! D11   D(12,8,11,3)          179.9998         -DE/DX =    0.0                 !
 ! D12   D(12,8,11,7)           -0.0002         -DE/DX =    0.0                 !
 ! D13   D(2,8,12,1)            -0.0001         -DE/DX =    0.0                 !
 ! D14   D(2,8,12,9)           179.9999         -DE/DX =    0.0                 !
 ! D15   D(11,8,12,1)         -179.9998         -DE/DX =    0.0                 !
 ! D16   D(11,8,12,9)            0.0001         -DE/DX =    0.0                 !
 ! D17   D(6,9,10,5)             0.0            -DE/DX =    0.0                 !
 ! D18   D(6,9,10,7)           179.9999         -DE/DX =    0.0                 !
 ! D19   D(12,9,10,5)          180.0            -DE/DX =    0.0                 !
 ! D20   D(12,9,10,7)           -0.0001         -DE/DX =    0.0                 !
 ! D21   D(6,9,12,1)             0.0            -DE/DX =    0.0                 !
 ! D22   D(6,9,12,8)           180.0            -DE/DX =    0.0                 !
 ! D23   D(10,9,12,1)          180.0            -DE/DX =    0.0                 !
 ! D24   D(10,9,12,8)            0.0            -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

All of optimisations were finished, deduced from the converged values of forces and displacements. Also, all of the gradient terms -DE/DX are zero. So an equilibrium was reached for each optimisation. Also, the computed energies are very negative according to Table 18, suggesting the stabilisation caused by aromaticity.

Frequency Analysis

To ensure the results for optimisations are minimum, frequency analyses of these molecules were carried based on optimised structures in the previous step.

Table 19: Summary of Frequency Analyses
Benzene Frequency Boratabenzene Frequency Pyridinium Frequency Borazine Frequency
File Name lx-benzene-freq lx-Boratabenzene-Freq lx-Pyridinium-freq lx-Borazine-Freq
File Type .log .log .log .log
Calculation Type FREQ FREQ FREQ FREQ
Calculation Method RB3LYP RB3LYP RB3LYP RB3LYP
Basis Set 6-31G(d,p) 6-31G(d,p) 6-31G(d,p) 6-31G(d,p)
Charge 0 -1 1 0
Spin Singlet Singlet Singlet Singlet
E(RB3LYP) (a.u.) -232.258202 -219.020523 -248.6680609 -242.6845992
E(RB3LYP) (kJ/mol) -609793.82 -575038.30 -652877.90 -637168.32
RMS Gradient Norm 0.00000045 0.00000868 0.00002064 0.00000152
Imaginary Freq 0 0 0 0
Dipole Moment (Debye) 0 2.84 1.87 0
Point Group D6h C2v C2v D3h
Job cpu time 0 days 0 hours 2 minutes 50.3 seconds. 0 days 0 hours 4 minutes 19.3 seconds. 0 days 0 hours 4 minutes 21.4 seconds. 0 days 0 hours 3 minutes 32.2 seconds.
Low Frequencies Line 1 -10.2160 -5.5939 -5.5939 -0.0056 -0.0055 0.0008 -7.0558 -0.0007 0.0003 0.0004 3.7283 4.7592 -9.3463 -2.9476 -0.0006 -0.0004 0.0002 1.5571 -3.7961 -3.7936 -3.2442 -0.0037 0.0164 0.0253
Low Frequencies Line 2 414.5469 414.5469 621.0423 371.2949 404.4219 565.0804 391.9229 404.3452 620.2019 289.7365 289.7373 404.5429
Dspace DOI:10042/26156 DOI:10042/26159 DOI:10042/26157 DOI:10042/26158

It can be deduced from Table 19 that all of the optimised structures obtained are minimum, indicated by the first line of low frequencies as all the frequencies are close to zero and lie within the range of ± 15 cm-1. In addition, the low frequencies are low compared to real frequencies.

To further verify the validity of the optimised structures, the computed bond lengths and angles and literature values were presented as follows.

Table 20: Comparison of Bond Lengths and Bond Angles
Benzene Computed Values Literature Values
C-C Length (Å) 1.40 1.40[1]
C-H Length (Å) 1.10 1.10[1]
Pyridinium Computed Values Literature Values
C-N+ (Å) 1.36 1.39[2]
Borazine Computed Values Literature Values
B-N (Å) 1.44 1.44[3]
B-N-B Angle (o) 117 118[3]
Boratabenzene Computed Values Literature Values
C-B- Length (Å) 1.51 1.45 and 1.48 [4]
C-B--C Angle (o) 116 116 [4]

It can be deduced from Table 20 that the computed bond lengths and bond angles that are close to literature values,confirming the optimisations were successful. So the method and basis set used are reliable enough to produce bond lengths and bond angles for the molecules under investigation.

To compare IR spectra of different molecules, the following table was constructed.

Table 21: Summary of IR Spectra
' IR Spectrum
Benzene
Boratabenzene
Pyridinium
Borazine

It is clear from Table 21 that benzene produces the simplest IR spectrum due to the most symmetrical structure, causing the greatest number vibrations to be IR inactive due to the cancellation in dipole moments. This is followed by borazine as its structure is more symmetrical than pyridinium and boratabenzene which have the least symmetrical structures. Consequently, pyridinium and boratabenzene have the most complex IR spectra.

References

  1. 1.0 1.1 David R. Lide, ed., CRC Handbook of Chemistry and Physics,Internal Version 2005, 9-25. Cite error: Invalid <ref> tag; name "Benzene" defined multiple times with different content
  2. David R. Lide, ed., CRC Handbook of Chemistry and Physics, Internal Version 2005, 9-7.
  3. 3.0 3.1 David R. Lide, ed., CRC Handbook of Chemistry and Physics, Internal Version 2005, 9-16. Cite error: Invalid <ref> tag; name "Borazine" defined multiple times with different content
  4. 4.0 4.1 D. A. Hoic, W. M. Davis and G. C. Fu, Journal of the American Chemical Society, 1995, 117, 8480-8481.

Investigating Molecular Orbitals

MO calculations were completed based on the optimised structures in the previous step by the consistent method (B3LYP) and basis set (6-31G (d,p)). The information was presented in the following table.

Table 22: Summary of Frequency Analyses
File Name Benzene MO Boratabenzene MO Pyridinium-MO Borazine-MO
File Type .fch .fch .fch .fch
Calculation Type SP SP SP SP
Calculation Method RB3LYP RB3LYP RB3LYP RB3LYP
Basis Set 6-31G(D,P) 6-31G(D,P) 6-31G(D,P) 6-31G(D,P)
Charge 0 -1 1 0
Spin Singlet Singlet Singlet Singlet
Total Energy (a.u.) -232.2582107 -219.0205306 -248.668074 -242.6845983
Total Energy (kJ/mol) -609793.84 -575038.32 -652877.93 -637168.32
RMS Gradient Norm 0 0 0 0
Imaginary Freq
Dipole Moment (Debye) 0.00 2.85 1.87 0.00
Point Group
Dspace DOI:10042/26171 DOI:10042/26170 DOI:10042/26168 DOI:10042/26169

To construct a basis for the comparison of MOs, the central part of the MO diagram of benzene was drawn, including both σ and π orbitals. Orbitals 1-6 was not included as they are formed from 1s orbitals of carbon, which are very stable and have little effect on bonding. Each LCAOs was drawn by desconstructing the corresponding MO.

Figure 9: MO Diagram of Benzene

From Figure 9, MO 17, 20 and 21 are π orbitals, formed by the side-on overlap between 2p orbitals on each carbon. This means there are totally 6 π-electrons for the whole system, obeying Hückel's rule (n=1). Moreover, the π-electron density is delocalised across the six-membered ring. So the aromaticity presents in the system.

MOs 17,20,21 were chosen to be compared among benzene, boratabenzene, pyridinium and borazine. Because they are π-bonding MOs, which have more effect on reactivity than σ-bonding MOs. Also, MOs 21 are HOMOs in all of the four isoelectronic molecules,which can be studied to give more insight to reactivity. The following table was constructed.

Table 23: Comparison of MOs 17, 20 and 21
No. Benzene Energy (a.u.) Boratabenzene Energy (a.u.) Pyridinium Energy (a.u.) Borazine Energy (a.u.)
17 -0.35994 -0.13210 -0.64062 -0.36134
20 -0.24690 -0.03492 -0.50487 -0.27594
21 -0.24690 0.01095 -0.47886 -0.27593

MOs presented in Table 23 are similar to some extent. They are all π-bonding MOs apart from MO 21 of boratabenzene which is almost non-bonding, deduced from the signs of energies. All of the MOs are occupied. This means totally 6 π-electrons exist. So aromaticity presents in all of the four isoelectronic molecules under investigation.

However, MOs of the same orbital number are different in shapes and energies. It can be deduced from Table 23 that the AOs of boron contribute the least to the MOs, due to the least elctronegativity. For example, the degree of the curvature of the electrodensity for MO 17 of boratabenzene is smaller in the region adjacent to boron compared to the region adjacent to each carbon, suggesting less contribution from corresponding AOs. According to the same reason, nitrogen has the largest LCAOs contribution, which can be deduced from MO 17 for pyridinium, indicated by the greater curvature around it.

By comparing the energies of orbitals in similar shapes, there is a general trend that B--H fragment increases the energy while N+-H fragment decreases the energy. This can be rationalised by more electronegative N-H fragment lowers the energy of corresponding AOs, and hence the energy of corresponding MOs is lowered as well according to LCAO theory. This situation is reversed for B--H fragment as boron is less electronegative than carbon. For instance, MO 17 is the most stable for pyridinium while the least stable for boratabenzene. As for borazine, all of C-H fragments are replaced by either N+-H or B--H, so energies for MOs were closer to benzene compared to boratabenzene and pyridinium. Due to the effect of N+-H and C-H fragments on energies, the degenracy between MOs 20 and 21 is broken from benzene to boratabenzene and pyridinium. But, these two orbitals are much closer in energy for borazine, because of the equal number of N+-H and B--H fragments, resulting in some change in energy being cancelled.

Interestingly, MOs formed by the combination of three 2p orbitals on each side of six-membered rings have different orbital numbers for boratabenzene and pyridinium (21 for boratabenzene and 20 for pyridinium), suggesting the order of MOs is reversed from pyridinium to boratabenzene. This can be explained by evaluating the anti-bonding character between two lobes of different colors as labelled on Table 23. Also, this due to the electropositive nature of boron which rises the energy of corresponding AOs and MOs, and electronegative nitrogen lowers the energy of the MO in this type.

Regarding the full MO diagram, it can be concluded from the argument stated above that substitution of a C-H fragment to a N+-H fragment generally decreases the energies of the MOs involving this fragment and hence lowers the energy of the whole system as indicated on Table 18. This situation is reversed for the substitution of a B--H fragment. The number of degenrate orbitals on the full MO diagram is therefore reduced for pyridinium, boratabenzene and borazine in comparison to benzene.

NBO Analysis

To compare the reactivity, the pattern of charge distribution of molecules was predicted by NBO analysis with a color range of -0.5-0.5.

Table 24: Comparison of Charge Distribution
Benzene Boratabenzene
Charge Distribution
Charge Range [-0.239,0.239] [-0.588,0.202]
Pyridinium Borazine
Charge Distribution
Charge Range [-0.476,0.483] [-1.102,0.747]

It is clear from Table 24 that benzene has the most symmetrical charge distribution as all of the fragments are the same, and it has the narrowest charge range, resulting from the less polarity of the C-C and C-H bonds and hence less nucleophilicity and electrophilicity. This distribution pattern is broken in other three molecules due to substitutions of polar fragments. Consequently, addition reactions are extremely hard for benzene. So benzene is the most unreactive compound. Borazine has the widest charge range, resulting from polar B-N,N-H and B-H bonds, making addition reactions relatively easy due to more nucleoophilic and electrophilic nature.

For pyridinium, it is interesting to see that ortho and para carbons are more positive than meta carbons. Same situation exists in borazine, where ortho and para carbons are more negative than meta carbons as shown on Table 24. This is illustrated in terms of resonance structures on Figure 10.

Figure 10: Resonance Structures of Pyridinium and Boratabenzene

According to Figure 10, the positive and negative charges are more likely on para and meta carbons than meta carbons. Therefore, meta carbons have the least positive or negative charge as shown on Table 24. There are 2 resonace forms for ortho carbons while only one resonance form for para carbon. This verifies the result of patterns of charge distribution where ortho carbons are more positive or negative than para carbons. It can be inferred that reactions such as nucleophilic and electrophilic substitutions are most likely to happen at ortho carbons of pyridinium and boratabenzene respectively, due to the polarity of C-B and C-N bonds.

Conclusion

This project focuses using computational methods to investigate the aromaticity of four isoelectronic compounds as shown on Figure 8. The optimisations were judged to successfully finish because the optimised bond lengths and angles are fairly close to literature values. In addition, all of the forces and displacements are converged and gradient terms are zero according to item tables. Frequency analysis shows that boratabenzene and pyridinium produce more complex IR spectra than benzene due to the less symmetrical structures. From MO analysis, substitution of the C-H fragment to the N+-H fragment decreases the energies of the corresponding MOs due to more electronegativity of nitrogen, while substitution of the B--H increases the corresponding energies. This explains why pyridinium has the most negative energy while boratabenzene has the most positive energy, which can be seen from Tables 22 and 23. The degenracy of certain MOs is broken as a result of the substitutions. NBO analysis reveals borazine is the most reactive compound and benzene is the least reactive, indicated by the charge ranges. So borazine is the most susceptible to addition reactions across the polar B-N bonds. Substitutions of N+-H and B--H fragments on benzene to produce pyridinium and boratabenzene can activate ortho positions on the six-membered ring, deduced from charge distributions and resonance forms, making further reactions such as substitutions and additions possible at ortho positions for the resulting aromatic compounds compared to benzene. Overall, the computational method is reliable enough to predict structure, molecular orbitals and reactivities for the molecules under investigation.

Future Works

Several future works can be completed to establish a better overview of the aromaticity.

  • Investigate MOs and NBOs of aromatic molecules such as naphthalene, quinolinium and isoquinolinium the effect of the ring size on aromatic stabilisation, reactivity and regioselectivity.
  • Fully compute cyclopentadienyl anion, which also has 6 π-electrons, to find similarities and differences with the molecules investigated in this project.
  • Rather than predict reactivities from NBO and MO analysis, we can model the transition states for borazine, boratabenzene and pyridinium for additions and substitutions to further understand reactivities and regioselectivities.