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Sam's Computational Chemistry Wiki Page Week 1

First Optimisation

The beginning of this project starts with the optimisation of a borane molecule, see image right. A conventional molecule of BH3 was created and the bond lengths increased to 1.5 angstroms. An optimisation calculation was then performed using Gaussian to identify the optimum bond lengths and angles for the BH3 molecule along with other information regarding the nature of the molecule.


Image of an optimised borane molecule.
Image of an optimised borane molecule.

Information Regarding BH3 optimisation

Borane Optimisation Results Summary
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 3-21g
Final Energy -26.46226338 a.u.
Gradient 0.00020672 a.u.
Dipole moment 0.00
Point Group D3h
Calculation Time 00:00:17:0

Time format hh:mm:ss:

Link to .log file for BH3 optimisation

File:BH3OPTIMISATION.LOG

The following extract from the log file shows successful convergence of the optimisation

        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

"Bonds" in gausview are a structural convenience. What definition would you choose for the existence of a bond?

By solving the Schrodinger equation for the system we have we can determine its energy. If the atoms in the system have a lower energy than the same number of free atoms that have no interactions with each other, then there must be some bonding that is present. As bonding occurs to lower the total energy of atoms/molecules.

The optimisation is calculated for the desired molecule in the gas phase. The results obtained for this optimisation might differ for a molecule in a solid phase due to packing forces distorting the molecule.

Below are two images showing the how the bond length is altered to find an energy minima.


Optimisation with improved basis set

The accuracy of the results obtained from the calculations run in gaussian is highly dependent on the choice of basis set of orbitals. A higher level basis set will entail longer equations that better describe the orbitals in question but will ultimately lead to longer calculation times. However with simple molecules such as BH3 the calculation time is increased by a matter of seconds and not hours or days.

The energy determined from the 6-31G optimisation was slightly lower than expected by a significant amount. The energy reported was 26.61641998 a.u., compared with the reported -26.61532363 a.u. It was noticed that the optimisation had not been performed using the 3-21G optimised structure. Instead it had been performed using a structure selected from the optimisation plot that was slightly higher in energy. Repeating the optimisation using the correct structure from the first optimisation an energy value of -26.61532363 a.u., the same as the expected value. The results summary for the first erroneous 6-31G basis set optimisation have not be included.

Further Optimisation of BH3
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G d,p
Energy -26.61532181v a.u.
Gradient 0.00027724 a.u.
Dipole Moment 0.00
Point Group C3h
Calculation Time 00:00:09:0

Time format hh:mm:ss:

Below is a link to the .log file for the 6-31G d,p optimisation of BH3

File:Corrected 6-31G optimisation.log

It was noticed that a change in point group had occurred in this second optimisation, this would have been because symmetry was not restricted to the D3h point group, but it is not critical to have the true symmetry at this stage.


Enhanced Basis Sets

Analysis of TlBr3

This stage in the project involved studying a molecule of TlBr3, which in ways is comparible to borane. Thallium is in the same group as boron and in this molecule its valency is the same. Although the existance of this molecule is questionable, as is the existance of BH3, due to the inert pair effect and lower oxidation states becoming preferred by lower group elements. In order perform accurate calculations for these heavier atoms pseudo potentials must be used to account for the large number of core electrons present. The complexity of these calculations demanded the use High Performance Computing(HPC) in order to run them successfully and quickly.

A larger basis set optimisation was performed for a molecule of TlBl3 using (HPC) with the LanL2DZ basis set that includes a pseudopotential(Los Alamos ECP) to account for the core electrons(non-valence) in these heavy atoms. Before running the calculation it was specified in the input file that TlBr3 was restricted to D3h symmetry and the tolerances were set to 'very tight'. Below is the ouput log file from the optimisation and results summary.

Link to D-space published file DOI:10042/22473

Image of an optimised TlBr3 molecule.
Image of an optimised TlBr3 molecule.
HPC TlBr3 Optimisation Results Summary
File Type .log
Calculation Type FOPT
Calculation Method RCCSD-FC
Basis Set LANL2DZ
Total Energy -89.23013903 a.u.
RMS Gradient 0.00653397 a.u.
Dipole Moment 0.000 Debye
Point Group D3h
Calculation Time 0:04:33:1

The following table shows the successful convergence of the optimisation of TlBr3

       Item               Value     Threshold  Converged?
Maximum Force            0.000015     0.000450     YES
RMS     Force            0.000010     0.000300     YES
Maximum Displacement     0.000154     0.001800     YES
RMS     Displacement     0.000101     0.001200     YES
Predicted change in Energy=-3.591615D-09

The optimised bond length determined by the calculation was 2.601 angstroms and an optimised bond angle of 120 degrees. Comparing this with the reported 2.618 for the gas phase[1].

Analysis of BBr3

Following on from the TlBr3 optimisation, a second optimisation of a different molecule, BBr3, was performed using the HPC. A difference between this optimisation and the previous was that the GEN basis set was used. This allowed for the basis sets of the individual atoms to be specified which was necessary as the bromine atoms, being a heavy element, required a pseudo potential which boron did not. The boron atom was given a B-31G d,p basis set and the bromine atoms were given LanL2DZ basis sets. Below is a table summarising the results of the optimisation and a second table showing the successful convergence of the calculation.

BBr3 Optimisation Results Summary
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set Gen
Energy -64.42903742
Gradient 0.01418126
Dipole Moment 0.00 Debye
Point Group D3h
Calculation Time 00:00:28:0

Time format hh:mm:ss:

        Item               Value     Threshold  Converged?
Maximum Force            0.000008     0.000450     YES
RMS     Force            0.000005     0.000300     YES
Maximum Displacement     0.000036     0.001800     YES
RMS     Displacement     0.000023     0.001200     YES

Link to BBr3 file published on D-space DOI:10042/22852

Comparison of Bond Lengths from Optimised Geometries

The bond lengths of the optimised structures for the three compounds that have been investigated so far have been tabulated, see table right.

Bond Length Comparison
Bond Bond Length/
angstroms
B-H 1.193
B-Br 1.934
Tl-Br 2.601

It can be noticed that there is an increase in bond length of 0.741 angstroms when changing the ligands from hydrogen to bromine. This would likely be due bromine's valence electrons being located in very diffuse orbitals and they considerably different in energy. As such would there woukld be poor overlap with the orbitals of boron as they are 2 periods apart in the periodic table. In contrast, hydrogen has considerably smaller orbitals that are much closer in size and energy to boron and so overlap is much greater and as a result the bond is shorter and most likely stronger than the B-Br bond. Bromine and hydrogen, despite being significantly different in size and mass, share the same common valency of 1, whilst bromine can adopt higher valencies it is typically observed forming only a single bond.

Changing the central atom from boron to thallium also had a significant impact on the bond length, increasing by 0.667 angstroms. This is likely for the same reason that changing from a small ligand to a larger ligand increased the bond length, poorer orbital overlap. Thallium is 4 periods below boron in the periodic table so it would be expected to have similar chemistry, although the inert pair would likely give rise to some differences. Its significantly larger size and electron count means that its valence electrons are in very diffuse orbitals. Coupled with the large valence orbitals of bromine gives an even poor orbital overlap than observed in BBr3. This gives rise to a much longer bond which is evident from the optimised structure.


Frequency Analysis

BH3

In this part of the project, the previously generated optimised structure of BH3 will be reused by performing a frequency analysis to determine its molecular vibrations.

File:2 BH3 FREQ REPEAT.LOG

Low frequencies --- -0.9033 -0.7343 -0.0054 6.7375 12.2491 12.2824

Low frequencies --- 1163.0003 1213.1853 1213.1880
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
                    1                      2                      3
                   A2"                    E'                     E'
Frequencies --  1163.0003              1213.1853              1213.1880
Red. masses --     1.2531                 1.1072                 1.1072
Frc consts  --     0.9986                 0.9601                 0.9601
IR Inten    --    92.5478                14.0553                14.0589
 Atom  AN      X      Y      Z        X      Y      Z        X      Y      Z
    1   5     0.00   0.00   0.16     0.00   0.10   0.00    -0.10   0.00   0.00
    2   1     0.00   0.00  -0.57     0.00   0.08   0.00     0.81   0.00   0.00
    3   1     0.00   0.00  -0.57    -0.39  -0.59   0.00     0.14   0.39   0.00
    4   1     0.00   0.00  -0.57     0.39  -0.59   0.00     0.14  -0.39   0.00


        Item               Value     Threshold  Converged?
Maximum Force            0.000005     0.000450     YES
RMS     Force            0.000002     0.000300     YES
Maximum Displacement     0.000019     0.001800     YES
RMS     Displacement     0.000009     0.001200     YES


BH<sub3 Frequency Analysis Results Summary
File Type .chk
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set RB3LYP
Total Energy -26.1532363 a.u.
RMS Gradient 0.00000237 a.u.
Dipole Moment 0.0000 D
Point Group D3h
Calculation Time 0:00:10
BH3 molecular vibrations
no. Vibration Form Frequency Intensity Symmetry label of Vibration
1
A bending type vibration, boron atom remains stationary whilst the three hydrogen atoms rise above
and then fall below the σh plane of the molecule in a concerted symmetric fashion
1163.00 92.55
2
A bending type vibration, the boron atom and one hydrogen atom remain stationary whilst
the remaining hydrogen atoms move towards each other and then away in the σh plane
1213.19 14.06
3
A bending type vibration, the boron atom and two of the hydrogen atoms remain
stationary whilst the remaining hydrogen atom moves toward one of the
stationary hydrogen atoms then moves towards the second stationary hydrogen atom, remaining in the σh plane
1213.19 14.06
4
A symmetric stretching vibration, boron atom remains stationary whilst the hydrogen atoms move
away and then back towards the boron atom in a symmetric fashion whilst remaining in the σh plane
2582.26 0.00
5
An asymmetric stretching vibration, one hydrogen atom remains stationary
whilst the other two hydrogen atoms move towards and away the
boron atom. As one moves closer the other moves away. Vibration is in the σh plane
2715.43 126.33
6
An asymmetric stretching vibration, one hydrogen atom moves away from
the boron atom as the other two move closer to the boron and as the single
hydrogen atom moves closer to the boron, the other hydrogen atoms move further away
2715.43 126.32

Below is the predicted vibrational spectrum for the optimised BH3 molecule.

predicted vibrational spectrum for the optimised BH3 molecule

TlBr3

After completing the BH3 frequency analysis, a frequency analysis was performed for the optimised TlBr3 structure for comparison.

Link to File for TlBr3 frequency analysis published on the D-space DOI:10042/22892

TlBr3 Frequency Analysis Results Summary
File Type .log
Calculation Type FREQ
Calculation Method RCCSD-FC
Basis Set LANL2DZ
Energy -89.23366292 a.u.
Gradient 0.00000735 a.u.
Dipole Moment 0.00 Debye
Point Group D3h
Calculation Time 00:50:59:8

Table showing successful convergence

        Item               Value     Threshold  Converged?
Maximum Force            0.000015     0.000450     YES
RMS     Force            0.000007     0.000300     YES
Maximum Displacement     0.000153     0.001800     YES
RMS     Displacement     0.000076     0.001200     YES


Below is the predicted Vibrational spectrum for TlBr<su8b>3

vibrational spectrum for TlBr3

As can be seen, the vibrations of significant intensity for both molecules have some key differences. The peaks in the TlBr3 spectrum are of significantly lower intensity and occur at lower frequencies than the equivalent vibrations for BH3. Also the peaks in the TlBr3 spectrum are noticeably broader.

Comparison of BH3 and TlBr3 vibrational frequencies
BH3 TlBr3
Frequency/cm-1 Intensity Frequency/cm-1 Intensity
1163.00 92.55 50.39 4.44
1213.19 14.06 50.39 4.44
1213.19 14.06 58.18 5.5815
2582.26 0.00 179.41 0.00
2715.43 126.33 224.96 24.53
2715.43 126.32 224.96 24.53


Population Analysis

After confirming that an energy minima had been reached, a population analysis of BH3 was run with the aim of computing the molecular orbitals of BH3. Below is the .log file from the population analysis

File:BH3 POP ANALYSIS.LOG

A molecular orbital diagram was constructed for BH3 and images of the computed molecular orbitals were put alongside the corresponding orbitals created by LCAO.

Molecular Orbital diagram of BH3
Molecular Orbital diagram of BH3


NH3 Analysis

.log file for optimised NH3

File:NH3 OPTIMISATION.LOG

.log file for frequency analysis of NH3

File:NH3 FREQ REPEAT 631G.LOG

.log file for NH3 population analysis

File:NH3 pop analysis 631G.log

Optimised NH3 molecule

Successful Convergence for NH3 optimisation


        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


Results summary NH3 Optimisation
File Type .log
Calculation FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Energy - 56.55776856 a.u.
Gradient 0.00000885 a.u.
Dipole Moment 1.846 Debye
Point Group C1

After reading through the log file for the NH3 frequency analysis it was noted that the low frequencies varied from -30.70 to 28.30 cm-1 which is considered outside of acceptable limits. The frequency analysis was then repeated with the keyword "int=grid=ultrafine" to and C3v restricted symmetry.

Low frequencies ---  -10.7082   -8.7207   -7.6506   -0.0017   -0.0014   -0.0006
Low frequencies --- 1089.2623 1693.9134 1693.9171
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:

Item Value Threshold Converged?

Maximum Force            0.000007     0.000450     YES
RMS     Force            0.000003     0.000300     YES
Maximum Displacement     0.000033     0.001800     YES
RMS     Displacement     0.000012     0.001200     YES



Association Energies

A molecule of NH3BH3 was contrsucted in Gaussview from an ethyl fragment, an additional valence had to be added to both the nitrogen and boron atoms as this was somewhat of an unconventional molecule, with the objective of determining the energy of the dative bond formed between the nitrogen and boron atoms. The molecule was optimised using a 6-31G(d,p) basis set at B3LYP level [the keyword nosymm was used] as it was found through earlier runs that when this keyword wasn't included for the optimisation, the low frequencies determined in the subsequent frequency analysis would be outside of acceptable limits at -28.48.

After performing the optimisation, a frequency analysis was performed to determine whether an energy minima had been found. The symmetry of the molecule was set to very tight and the keyword "int=grid=ultrafine" was used. The most outlying low frequency was -19.79

Optimisation Convergence

    Item               Value     Threshold  Converged? 
Maximum Force            0.000165     0.000450     YES
RMS     Force            0.000035     0.000300     YES
Maximum Displacement     0.000912     0.001800     YES
RMS     Displacement     0.000385     0.001200     YES
Predicted change in Energy=-1.139026D-07
Optimization completed.
NH3BH3 Optimisation Results Summary
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Energy -83.22468957 a.u.
Gradient 0.00005572 a.u.
Dipole Moment 5.56 Debye
Point Group C1
Calculation Time 00:01:08
NH3BH3 Frequency Analysis Results Summary
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G(d,p)
Energy -83.22468891 a.u.
Gradient 0.00005350 a.u.
Dipole Moment 5.5629 Debye
Point Group C1
Calculation Time 00:01:59

Frequency Analysis Convergence

        Item               Value     Threshold  Converged?
Maximum Force            0.000195     0.000450     YES
RMS     Force            0.000054     0.000300     YES
Maximum Displacement     0.001003     0.001800     YES
RMS     Displacement     0.000418     0.001200     YES
Predicted change in Energy=-1.446886D-07
Optimization completed.

Low Frequencies from frequency analysis.

Low frequencies ---  -19.7874   -0.0003    0.0007    0.0009    8.3509    8.9871
Low frequencies ---  262.3874  631.2874  637.7886
NH3 Frequency Analysis Results Summary
File Type .log
Calculation Type FREQ
Calculation Method RB3LYP
Basis Set 6-31G d,p
Energy -56.55776872 a.u.
Gradient 0.00000262 a.u.
Dipole Moement 1.84 Debye
Point Group C3v
Calculation Time 00:00:22:0

Optimisation of NH3

.log file for optimisation of NH3 File:SAMBROOKES NH3BH3 OPT.LOG


        Item               Value     Threshold  Converged?
Maximum Force            0.000166     0.000450     YES
RMS     Force            0.000035     0.000300     YES
Maximum Displacement     0.000908     0.001800     YES
RMS     Displacement     0.000321     0.001200     YES
Predicted change in Energy=-1.131674D-07
Optimization completed.
   -- Stationary point found.
NH3BH3 Optimisation Results Summary
File Type .log
Calculation Type FOPT
Calculation Method RB3LYP
Basis Set 6-31G d,p
Energy -83.21699260 a.u.
Gradient 0.00977410 a.u.
Dipole Moment 5.75 Debye
Point Group C3
Calculation Time 00:00:40:0

.log file for NH3BH3 frequency analysis File:SAMBROOKES NH3BH3 FREQ 4THREPEAT.LOG

Item Value Threshold Converged?

Maximum Force            0.000195     0.000450     YES
RMS     Force            0.000054     0.000300     YES
Maximum Displacement     0.001003     0.001800     YES
RMS     Displacement     0.000418     0.001200     YES
Predicted change in Energy=-1.446886D-07
Optimization completed.
   -- Stationary point found.
Low frequencies ---  -19.7874   -0.0003    0.0007    0.0009    8.3509    8.9871
Low frequencies ---  262.3874  631.2874  637.7886
Harmonic frequencies (cm**-1), IR intensities (KM/Mole), Raman scattering
activities (A**4/AMU), depolarization ratios for plane and unpolarized
incident light, reduced masses (AMU), force constants (mDyne/A),
and normal coordinates:
                    1                      2                      3
                    A                      A                      A
Frequencies --   262.3873               631.2874               637.7886
Red. masses --     1.0078                 5.0083                 1.0452
Frc consts  --     0.0409                 1.1760                 0.2505
IR Inten    --     0.0000                14.1381                 3.5619
NH3BH3 Frequency Analysis Results Summary
File Type .log
Calculation Type FREQ
Basis Set 6-31G d,p
Energy -83.22468891 a.u.
Gradient 0.00005350 a.u.
Dipole Moment 5.56 Debye
Point Group C3
Calculation Time 00:01:59

Association Energy Value

Using the energies calculated from the optimisation of BH3 and values from the optimisations performed previously for NH3 and NH3BH3 the association energy for the formation of the nitrogen-boron bond was determined. All of the energies used were calculated using the 6-31G d,p basis set and the B3LYP method as the choice of basis set will influence the energies calculated for a particular therefore having a direct influence on subsequent calculations that use these results.

Association Energy = E(NH3BH3) - (E(NH3) + E(BH3)) = -83.22468957 - ( -56.55776856 + -26.61641998) = - 0.05050103 a.u.

1 a.u. = 4.35974394 x 10-18 J, therefore the association energy is equal to -132.59 kJ mol-1.

References

1. W.M. Hayens (ed). 'CRC Handbook of Chemistry and Physics'. 93rd Ed. Boca Raton. CRC Press. 2013