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Y2COMP:bd316

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BH3

Basis set - 6-31G

Computational level - B3LYP

The results of the optimisation are as follows:

 Item               Value     Threshold  Converged?
 Maximum Force            0.000001     0.000450     YES
 RMS     Force            0.000000     0.000300     YES
 Maximum Displacement     0.000002     0.001800     YES
 RMS     Displacement     0.000001     0.001200     YES 
BH3

The results of the frequency analysis are as follows:

File:BD316 BH3 SYM FREQ.LOG

 Low frequencies ---   -9.0337   -9.0167   -0.0526    0.0009    0.5551    3.5044
 Low frequencies --- 1162.9922 1213.1509 1213.1511 

The frequencies of the vibrational modes

BH3 has point group D3h.

Frequency (cm-1) Intensity (arbitrary units) Symmetry IR active? Type
1163 93 A2" yes symmetric bend
1213 14 E' very slight asymmetric bend
1213 14 E' very slight symmetric bend
2583 0 A1' no symmetric stretch
2716 126 E' yes asymmetric stretch
2716 126 E' yes asymmetric stretch

The IR spectrum:

In the spectrum, only three of the six vibrations are visible. This is because, firstly, one of the vibrations, that corresponding to the symmetric stretch at 2583 cm-1, is IR-silent. This because it is totally symmetric and hence does not result in a change in dipole moment. Secondly, there are two sets of two degenerate vibrations, the peaks for which occur at the same frequency and hence are indistinguishable.


Smf115 (talk) 01:14, 17 May 2018 (BST)Well written and thorough explaination of the number of peaks seen in the spectrum and correctly assigned modes.

The MOs of BH3

The computed MO4 appears to show a lesser contribution from the 2S B atomic orbital than from the H3 fragment orbital, unlike the qualitative LCAO molecular orbital which predicts a greater relative contribution from the B 2S atomic orbital. It is difficult to qualitatively predict with accuracy the relative energies of the various orbitals; this discrepancy suggests that in fact the H3 fragment orbital is higher in energy than the boron 2S atomic orbital.

NH3

Basis set - 6-31G

Computational level - B3LYP

The results of the optimisation are as follows:

 Item               Value     Threshold  Converged?
 Maximum Force            0.000002     0.000015     YES
 RMS     Force            0.000002     0.000010     YES
 Maximum Displacement     0.000029     0.000060     YES
 RMS     Displacement     0.000017     0.000040     YES
 Predicted change in Energy=-1.087432D-10 
NH3


The results of the frequency are as follows:

 Low frequencies ---   -7.9447   -5.4530   -5.4526    0.0008    0.0035    0.0116
 Low frequencies --- 1089.4132 1693.9304 1693.9304 

File:BD316 NH3 OPT631 FREQ4.LOG

The frequencies of vibrational modes

Frequency (cm-1) Intensity (arbitrary units) Symmetry IR active? Type
1089 145 A1 yes symmetric bend
1694 14 E very slight asymmetric bend
1694 14 E very slight symmetric bend
3461 1 A1 very slight symmetric stretch
3590 0 E no asymmetric stretch
3590 0 E no asymmetric stretch

BH3NH3

Basis set - 6-31G

Computational level - B3LYP

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     0.000010     0.000040     YES
 Predicted change in Energy=-9.107835D-11

Results of the optimisation

BH3NH3

The results of the frequency analysis are as follows:

File:BH3NH3BD316FREQ.LOG

Low frequencies ---   -1.8806    0.0004    0.0007    0.0008    5.8284    6.3699
 Low frequencies ---  263.3965  632.9709  638.5079

Ammonia-borane association energies

E(NH3) = -56.5578 a.u. E(BH3) = -26.6153 a.u. E(H3NBH3) = -83.2247 a.u.

ΔE = (E(NH3) + E(BH3)) - E(H3NBH3)

Dissociation energy = 0.0516 a.u. = 129 kJ mol-1

The bond dissociation energy of the CC bond in H3 is 618.3 +- 15.4 kJ mol-1.1 The NB bond is significantly weaker than this, which is perhaps indicative of the weaker interaction of the orbitals which form the BN bonds, due to the difference in energy between the boron and nitrogen orbitals and the worse overlap due to the difference in size.

BBr3

Basis set - Gen

Computational level - RB3LYP

The results of the optimisation are as follows:

 Item               Value     Threshold  Converged?
 Maximum Force            0.000008     0.000450     YES
 RMS     Force            0.000005     0.000300     YES
 Maximum Displacement     0.000036     0.001800     YES
 RMS     Displacement     0.000024     0.001200     YES
 Predicted change in Energy=-4.086094D-10 

DOI:10042/202294

BH3

Frequency analysis:

DOI:10042/202317

Project : aromaticity of benzene and borazine

Benzene

Basis set - 6-31G Computational level - B3LYP

Item               Value     Threshold  Converged?
 Maximum Force            0.000013     0.000015     YES
 RMS     Force            0.000004     0.000010     YES
 Maximum Displacement     0.000054     0.000060     YES
 RMS     Displacement     0.000017     0.000040     YES
 Predicted change in Energy=-1.965796D-09

Benzene

The results of a frequency analysis on the optimised structure of benzene are as follows:

 Low frequencies ---   -3.9416   -0.0010    0.0003    0.0005    5.4503    7.6074
 Low frequencies ---  414.5266  414.5883  621.0905 

File:BD316BENZENEFREQ.LOG

Borazine

Basis set - 6-31G

Computational level - B3LYP

Item               Value     Threshold  Converged?
 Maximum Force            0.000009     0.000015     YES
 RMS     Force            0.000003     0.000010     YES
 Maximum Displacement     0.000027     0.000060     YES
 RMS     Displacement     0.000008     0.000040     YES
 Predicted change in Energy=-4.809258D-10 

Borazine

The results of a frequency analysis on the optimised structure of borazine are as follows:

 Low frequencies ---   -7.2362   -0.0005    0.0000    0.0009    4.3039    7.4691
 Low frequencies ---  289.5823  289.7102  404.4530 

File:BD316BORAZINEEXPTFREQ.LOG

Comparison and analysis

Charge analysis

The following table shows the results of an NBO charge analysis on the benzene and borazine:

Benzene Borazine
NBO charges
H atoms: 0.239 H(-B) atoms: -0.077; H(-N) atoms : +0.432
C atoms: -0.239 N atoms: -1.102; B atoms: 0.747

NBO charges demonstrate the distribution of charge in the molecule. This is determined by the relative electronegativities of the various substituents - the tendencies of the atoms to attract the electron density within the molecular orbitals.

In benzene, the carbon atoms, with an electronegativity of 2.55, are electron-rich, whereas the H atoms, with an electronegativity value of 2.20, are electron-deficient. This is because the electron density localised between the C and H atoms is attracted more strongly by the carbon atoms. This effect is more pronounced between the N and H atoms in borazine, because nitrogen is more electronegative than carbon. The boron atoms in borazine are electron-deficient relative to the hydrogen atoms to which they are attached, because boron is more electropositive than hydrogen, with an electronegativity value of 2.04.


Smf115 (talk) 01:07, 17 May 2018 (BST)Great mention of the electronegativities. Considering other points such as symmetry and the neutral charge overall would be an improvement, alongisde the correct colour range for the charge districution across both molecules.

Molecular orbital analysis

Below is a comparison of three selected comparable molecular orbitals of benzene and borazine. For the purposes of analsysis the axis system is defined as:

Benzene Borazine
Benzene LUMO Borazine LUMO
This is the lowest unoccupied MO for both benzene and borazine. The benzene MO shows a larger contribution from the anti-bonding pair of carbon atoms than from the bonding quartet. The borazine MO shows a larger contribution from the anti-bonding pair of boron atoms than from the anti-bonding pair of nitrogen atoms - this is consistent with the fact that the boron fragment orbitals will be higher in energy than the nitrogen fragment orbitals, because they are more electropositive, and so will display larger contributions in the higher energy, antibonding-combination MOs. Both MOs display roughly comparable, moderately strong (qualitative) overall anti-bonding character.
Benzene MO17 Borazine MO17
This, for both compounds, is the result of the fully-bonding linear combination of the Pz on each of the C/N/B atoms the lowest energy MO of the aromatic pi system. The contribution from each carbon atom in the benzene MO is the same. It is (just) visible that in the borazine MO the nitrogen atoms have a slightly greater contribution than the boron atoms. Both MOs display (roughly equal) strong bonding charcter.
Benzene MO24 Borazine MO24
These are strongly anti-bonding combinations of both the Px (sigma-type) atomic orbitals on the atoms in the ring and the 1s atomic orbitals of the hydrogen atoms. Sigma type through-bond interactions are stronger than pi-type through space interactions because the orbitals overlap more strongly. Hence, MOs 24 are more strongly anti-bonding and higher in energy than, for example, the LUMOs. These are anti-bonding combinations of fully-bonding C6 / B3N3 and H6 fragment orbitals.

Smf115 (talk) 01:06, 17 May 2018 (BST)Great comparison of the MOs and nice extra information with the LCAOs (although check the phases of the LUMO LCAO!)

Aromaticity

An aromatic compound displays unusual or 'special' stability relative to the comparable conjugated linear molecule. For example, the aromatic stabilisation energy of benzene has been reported as 152 kJ mol-1.2 All aromatic compounds are planar, cyclic and display bond lengths intermediate between that of the expected length of the single bond and that of the expected length of the double bond.3 However, these criteria are not fully sufficient as a predictor for aromaticity.

Both benzene and borazine are aromatic. In benzene each carbon atom contributes one electron to the delocalised aromatic pi system (the fully-bonding orbital for which is MO17 above); in borazine, each N Pz orbital contributes two electrons to this and the B Pz orbitals are empty but accept electron density. The lowest energy fully-bonding molecular orbital for this aromatic system is MO17 above. The presence of these conjugated Pz orbitals is not necessarily a reliable predictor of aromatic character, as it was considered to be in some of the earliest concepts of aromaticity.3 Some molecules may even be cyclic, planar, have a contiguous array of pi electrons and be 'anti-aromatic', displaying special instability relative to the linear analogue (although said systems will often contort to adopt non-planar geometries to avoid the anti-aromaticity).

Benzene and borazine demonstrate Hückel aromaticity, in that they have (4n+2) pi electrons. Cyclic planar systems are anti-aromatic by Hückel's criteria if they have (4n) pi electrons.4 Hückel et. al. developed his quantum mechanical description of aromaticity in the 1930s, as a refinement on the concepts of aromaticity developed by Kekule, Erlenmeyer and others in the late 19th century.3,4

Smf115 (talk) 01:04, 17 May 2018 (BST)A good, well referenced answer. A further development on MO 17 being just one MO which contributes to the delocalisation of the electron density in the molecule would have been good. The use of MO 17 as a reference was really good though, tieing in the molecules just studied.

Smf115 (talk) 01:15, 17 May 2018 (BST)Overall a very good report with a few mistakes made but very good MO analysis in the second section.

References

1 - https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf

2 - https://pubs.acs.org/doi/abs/10.1021/ja001274p

3 - https://onlinelibrary.wiley.com/doi/epdf/10.1002/chem.200700250

4 - https://link.springer.com/content/pdf/bfm%3A978-90-481-3560-8%2F1.pdf