A molecule of BH3 was created with the three B-H bond lengths being altered to 1.53, 1.54 and 1.55 Angstroms.
To optimise the BH3 molecule created in Gaussian the following settings were implemented and then the calculation was set to run. Method: DFT, B3LYP Basis set: 3-21G Calculation type: OPT
Summary for BH3(Table 1)
Title
Value
Units
File Type
.log
Calculation Type
FOPT
Calculation Method
RB3LYP
Basis Set
3-21G
Charge
0
Spin
Singlet
E(RB3LYP)
-26.46226429
au
RMS Gradient Norm
0.00008851
au
Dipole Moment
0.00
Debye
Point Group
CS
Job cpu time
23.0
seconds
Analysing the Optimised Molecule of BH3
The optimised BH3 log file is linked here and the calculation summary is shown in Table 1.
The point group isn't D3h as expected as the bond lengths are all slightly different, also the calculations require very accurate numbers which are hard to provide when drawing the molecule on screen. You can tell the molecule has been optimised as the gradient is less than 0.001 au; another way to check that it has optimised properly is by viewing the .log file and checking the final "Maximum Force", "RMS Force", "Maximum Displacement" and "RMS Displacement" are all converged (RMS = Root Mean Squared). This is confirmed in the section from the .log file below.
In Gaussview, we can produce two graphs showing the Optimisation Step number vs. Total energy/Gradient. Each optimisation step is shown in the 7 static images below, following left-to-right.
Optimisation steps for BH3
Animation of optimised BH3.
Animation of optimised BH3.
Animation of optimised BH3.
Animation of optimised BH3.
Animation of optimised BH3.
Animation of optimised BH3.
Animation of optimised BH3.
The gradient is the steepness of the slope on a potential energy surface (PES), when the gradient is at its lowest, it is most stable (i.e. gradient = 0 at minima or maxima).
The optimisation step images show that at some inter-atomic distances there is no physical bond, however this is because the program has a set distance that it will place a physical bond in the image. A chemical bond is actually an attractive interaction between the two atoms, and may still be present at distances further than the physical bond drawn in Guassian.
Optimisation Step No vs. Total Energy3.
Optimisation Step No vs. Total Energy3.
Summary for BH3 using new basis set(Table 2)
Title
Value
Units
File Type
.log
Calculation Type
FOPT
Calculation Method
RB3LYP
Basis Set
6-31G(d,p)
Charge
0
Spin
Singlet
E(RB3LYP)
-26.61532358
au
RMS Gradient Norm
0.00008206
au
Dipole Moment
0.00
Debye
Point Group
CS
Job cpu time
22.0
seconds
Using a better basis set
This time the calculation has been ran using a higher-level basis-set - 6-31G (d,p). The summary can be seen in Table 2 and the .log file can be found here.
The optimised bond distances and bond angle can be found on GaussView:
Optimised B-H bond distances = 1.19 Å .
Optimised H-B-H bond angles = 120.00, 120.01, 120.00 degrees.
Analysing the total energies of the two different basis sets we can see that the 6-31(d,p) has a lower value. This does not mean it was a better computation! This is because you cannot compare the values of two different basis sets.
The text below from the .log file confirms that the optimisation worked (i.e. all 'Items' converged).
A trigonal planar molecule of GaBr3 was drawn. The symmetry was constrained to D3h and the tolerance increased to "Very tight (0.0001)".
The following settings were implemented:
Calculation type: OPT
Method: DFT, B3LYP
Basis set: LanL2DZ
The LanL2DZ basis set is medium-level basis-set.
The calculation was submitted to the HPC and published on D-space[1]. The summary is presented in Table 3.
Optimised Ga-Br bond distance: 2.35 Å
Optimised Br-Ga-Br bond angle: 120.00 deg
The literature value for Ga-Br bond distance was measured at 2.239 ± 0.007 Å at 357 K.[2], this is in agreement with our optimised Ga-Br bond length.
Below is a cut from the .log file and is confirmation that the calculation worked:
For molecules such as BBr3, we need to use a mixture of basis pseudo-potentials and basis-sets as they contain both heavy and light elements.
The basis set "GEN" is used to allow definition of basis sets on each atom, and the additional keyword "pseudo=read gfinput" was added to allow definition of pseudo-potentials on each atom. The snippet of text below was appended to the file, this specifies the basis sets for each atom and the pseudo-potential for the Br atoms.
The computation was ran on the HPC[3].The summary is shown in Table 4.
Optimised B-Br bond distance = 1.93 Å
Optimised Br-B-Br bond angle = 120.0 deg
The snippet of text below confirms the calculation was successful.
Comparison of Bond Lengths of Optimised Structures / Å (Table 5)
BH3
BBr3
GaBr3
1.19
1.930
2.35
If we first compare the B-H and B-Br bond lengths we can see that they are all quite similar. Br and H are similar as they both need to gain 1 electron to complete their octet. The B-Br bond is slightly longer. The B-H bond is expected to be shorter as their orbitals are closer matched in size, which leads to better overlap and therefore a shorter, stronger bond. Another factor is that Br is rather large in comparison to H, and so the two atomic centres cannot possibly get as close as the boron and hydrogen centres can.
B-Br lengths are shorter than Ga-Br lengths. B and Ga are similar as they are both group 13 elements and are both Lewis acids. The main difference is their size. This will cause their properties, including bond lengths, to alter. The size difference of the two atoms, once again, means that the two atomic centres of Ga and Br cannot get as close the atomic centres of B and Br. Ga also has more electrons than B, making it more electropositive, and therefore not as good of a Lewis acid in comparison.
It is also interesting to note that the optimised structure of the molecules gives different bond lengths for each bond except in gallium(III) tribromide where they are all the same.
I have already summarised above in Section Understanding Optimisations how sometimes Gaussian does not display bonds even though there may be a bond present. A chemical bond is an attractive interaction between atoms/molecules. Sometimes the bond distance is too far away for Gaussian to consider it as a physical bond, even though there may be an attractive force present between the two atoms. There are various classifications of bonds. There are classically strong ones such as covalent and ionic interactions, and there are weak ones such as dipole-dipole interaction, van der Waals interactions and hydrogen bonding.
Day 3
Vibrational Analysis of BH3
Summary for BH3 (Table 5)
Title
Value
Units
File Type
.log
Calculation Type
FREQ
Calculation Method
RB3LYP
Basis Set
6-31G(d,p)
Charge
0
Spin
Singlet
E(RB3LYP)
-26.61532358
au
RMS Gradient Norm
0.00008203
au
Imaginary Freq
0
Dipole Moment
0.00
Debye
Point Group
CS
Job cpu time
8.0
seconds
To carry out a vibrational analysis of BH3 first the optimised (6-31G(d,p)) BH3 structure was opened and then a Gaussian calculation was set up to job type "freq" (short for frequency). The link to the calculation is here.
The low frequencies in the file did not come out as 0 ± 15cm-1:
So I redrew and re-optimised BH3 with basis set 3-61G(d,p), this time without changing the bond lengths. The link to the log file is here. I then repeated the process above so that the job type is for frequency (click here).
The "zero" frequencies are now within ±15cm-1. The top 6 low frequencies are the frequencies which correspond to the "-6" from the number of vibrational modes rule 3N-6 and correspond to the motion of the centre of mass. The bottom row with 3 frequencies are the "real" frequencies.
The IR spectrum shows that there are only three peaks. Initially we may expect six because that's how many vibrational modes are calculated; however, the one at 2582.28 cm-1 has a zero intensity - this is because it is a totally symmetrical vibration. The peak at 1213.18 and 1213.19 cm-1 will overlap into one peak, their intensities are the same to 2 d.p. and their symmetry is the same. Finally, there are two peaks with identical frequencies at 2715.45 cm-1 with equal intensities up to 2 d.p., and the same symmetry of E'. This brings us to three peaks: 1163.00, 1213.18, 2715.45 cm-1.
IR spectrum BH3
Vibrations of BH3 (Table 7)
No
Form of the Vibration
Frequency/cm-1
Intensity
Symmetry D3h point group
1
BH3.All H-atoms moving up and down in a concerted motion out of the plane of the molecule. The Boron atom moves up when the hydrogens move down and vice-versa.
1163
93
A2"
2
BH3.Two H-atoms are moving closer together and then further apart symmetrically within the plane of the molecule. The other hydrogen and boron atoms are static.
1213
14
E'
3
BH3.The molecule looks as if it is rocking. As two hydrogens swing around in one direction in unison, whilst the other opposes them by rocking in the opposite direction but with more intensity. This happens within the plane of the molecule. The boron atom sways with the rocking of the hydrogens.
1213
14
E'
4
BH3.All hydrogen atoms are moving in and out of the centre (stretching) in unison within the plane of the molecule. The boron atom is static.
2582
0
A1'
5
BH3.The molecule is rocking. One BH bond is not stretching. The other two are stretching in and out of the centre within the plane of the molecule. As one hydrogen atom moves towards the boron atom, the other will move out.
2715
1262
E'
6
BH3.Two BH bonds are moving in and out of the centre at the same intensity and in a concerted fashion. the other BH bond is stretching in and out of the centre more intensely, stretching further away and closer towards the centre. This is within the plane of the molecule. As the two less intense stretching BH bonds become shorter, the more intense BH stretch becomes longer, and vice-versa.
2715
126
E'
Vibrational Analysis of GaBr3
Summary for GaBr3 (Table 8)
Title
Value
Units
File Type
.log
Calculation Type
FREQ
Calculation Method
RB3LYP
Basis Set
LANL2DZ
Charge
0
Spin
Singlet
E(RB3LYP)
-41.70082783
au
RMS Gradient Norm
0.00000011
au
Imaginary Freq
0
Dipole Moment
0.00
Debye
Point Group
D3h
Job cpu time
13.9
seconds
The vibrational analysis job (Job Type "freq") was ran on the optimised GaBr3 on the HPC[4].
Lowest "real" mode is 76.4 cm-1. The IR spectrum is presented below. We once again see only three peaks for the same reason that BH3 only had three peaks.
IR spectrum GaBr3
Vibrations of BH3 (Table 9)
No
Form of the Vibration
Frequency/cm-1
Intensity
Symmetry D3h point group
1
GaBr3.The molecule looks as if it is rocking. As two Br atoms swing around in one direction in unison, whilst the other opposes them by rocking in the opposite direction but with more intensity. This happens within the plane of the molecule. The Ga atom sways with the rocking of the bromine atoms.
76
3
E'
2
GaBr3.Two Br atoms are moving closer together and then further apart symmetrically within the plane of the molecule. The other Br and Ga atoms are moving 'away' together when the two other Br atoms come closer together.
76
3
E'
3
GaBr3.All Br atoms moving up and down in a concerted motion out of the plane of the molecule. The Ga atom moves up when the Br atoms move down and vice-versa, but in a more intense manner.
100
9
A2"
4
GaBr3.All Br atoms are moving in and out of the centre (stretching) in unison within the plane of the molecule. The Ga atom is static.
197
0
A1'
5
GaBr3.The molecule is rocking. One GaBr bond is not stretching. The other two are stretching in and out of the centre within the plane of the molecule. As one Br atom moves towards the Ga atom, the other will move out. The Ga centre is also "swaying", as a Br comes in, Ga sways towards it.
316
57
E'
6
GaBr3.Two GaBr bonds are moving in and out of the centre at the same intensity and in a concerted fashion. the other GaBr bond is stretching in and out of the centre more intensely, stretching further away and closer towards the centre. This is within the plane of the molecule. As the two less intense stretching GaBr bonds become shorter, the more intense GaBr stretch becomes longer, and vice-versa.
316
57
E'
Comparing vibrational frequencies of BH3 and GaBr3 / cm-1 (Table 10)
BH3
Symmetry
GaBr3
Symmetry
1163
A2"
76
E'
1213
E'
76
E'
1213
E'
100
A2"
2582
A1'
197
A1'
2715
E'
316
E'
2715
E'
316
E'
Comparing vibrational frequencies of BH3 and GaBr3 / cm-1 (Table 11)
Symmetry
BH3
GaBr3
A2"
1163
100
E'
1213
76
E'
1213
76
A1'
2582
197
E'
2715
316
E'
2715
316
All motions which have been described very similarly for both molecules belong to the same symmetry group; the frequencies that match motions (as described in tables 8 and 9) are displayed in Table 11. You can see that there has been a reordering of vibrational modes; A2 is shown at a higher frequency than E' in the GaBr3 molecule, whereas it is reversed for BH3.
The large difference between the frequencies of each compound are because a high frequency means a high energy vibration, the BH3 vibrations have a much higher energy than the gallium compound
The spectra are similar because they both show three peaks even though the molecules have six vibrational modes.
A2" and E', and A1' and E', lie fairly close together in both spectra, with A1' and E' at a higher frequency than A2" and E'. The reason they are fairly close together is because A1' and E' motions include the stretching of the bonds whereas A2" and E' do not include any stretching.
The method and basis set for these calculations must be set the same in order to make the calculations comparable.
The purpose for carrying out a frequency analysis is to ensure you have a minimum energy level and not a maximum (e.g. a transition state).
As said above, the top 6 low frequencies are the frequencies which correspond to the "-6" from the number of vibrational modes rule 3N-6 and correspond to the motion of the centre of mass. The bottom row with 3 frequencies are the "real" frequencies. These are the frequencies at which we will see observable peaks at.
Molecular Orbitals of BH3
Summary for BH3 (Table 12)
Title
Value
Units
File Type
.fch
Calculation Type
SP
Calculation Method
RB3LYP
Basis Set
6-31G(D,P)
Charge
0
Spin
Singlet
E(RB3LYP)
-26.61532363
au
RMS Gradient Norm
0.00000000
au
Dipole Moment
0.00
Debye
Point Group
Wall Time
6
seconds
To generate MO's of BH3 the optimised structure was ran on the HPC[5] with the following settings:
Job type: Energy.
Additional keywords: "pop=full"
NBO tab -> Type: Full NBO.
The .fchk file was downloaded and the the MO's could be visualised in GaussView. The MO diagram (below) was drawn in ChemDraw, with each MO level containing the LCAO MO's and the Gaussian-generated MO's. You can see that the LCAO models are in very good agreement with the generated MO's. The only difference is that the LCAO's do not show how much space the orbitals are actually taking up, alternatively the generated orbitals don't show the relative contributions of atomic orbitals. I think the accuracy of the qualitative MO is pretty good when comparing the two models, this means that the diagram is useful as a qualitative model.
MO diagram for BH3
NBO analysis of NH3
Summary for optimised NH3 (Table 13)
Title
Value
Units
File Type
.log
Calculation Type
FOPT
Calculation Method
RB3LYP
Basis Set
6-31G(d,p)
Charge
0
Spin
Singlet
E(RB3LYP)
-56.55776856
au
RMS Gradient Norm
0.00000885
au
Imaginary Freq
Dipole Moment
1.85
Debye
Point Group
C1
Job cpu time
20.0
seconds
To optimise a molecule of NH3 the following settings were implemented:
The snippet above shows the top 6 low frequencies are not within ±15, so the frequency analysis was re-run with the additional keywords "opt=tight scf=conver=9 int=ultrafine"). As you can see below, it worked. The link to the file is here
Using the .log file we can carry out a NBO analysis. We use the .log file for NBO analysis, and the .chk files for MO analysis.
The charge distributions are displayed where bright green is a highly positive charge and bright red is a highly negative charge
(Colour range: -1.125(red) to 1.125(green)).
The specific NBO charges can be shown quantitavely (N= -1.125. H = 0.375). This is shown in the far right image and the snippet below from the .log file below under the heading "natural charge".
Charge distribution NH3
Charge distribution NH3
Summary of Natural Population Analysis:
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
N 1 -1.12515 1.99982 6.11104 0.01429 8.12515
H 2 0.37505 0.00000 0.62250 0.00246 0.62495
H 3 0.37505 0.00000 0.62250 0.00246 0.62495
H 4 0.37505 0.00000 0.62249 0.00246 0.62495
=======================================================================
* Total * 0.00000 1.99982 7.97852 0.02166 10.00000
The snippet below describes the bonding in the NH3. It can, for example, show the contribution of each atoms orbitals to the bond. The first bond shows that the nitrogen orbitals and hydrogen orbitals contribute 68.83% and 31.17% respectively to the bond. The nitrogen contribution consists of 24.87% s- and 75.05% p-orbital (an sp3 hybrid orbital), and the hydrogen atom gives 99.91% s-orbital (essentially entirely s-orbital). Reasing the analysis we can see the nitrgoen atom has formed four sp3 hybrid orbitals, three interact with different hydrogen atoms, and one interacts with its lone-pair (bond 5 in the list). Orbitial four has the heading CR which indicates it is a core-orbital (i.e. the 1s AO of nitrogen).
The section below describes the interactions between various MOs such as between bonding and non/anti-bonding MOs. This is not of much interest when looking at NH3 but could be more interesting in other molecules.
Second Order Perturbation Theory Analysis of Fock Matrix in NBO Basis
Threshold for printing: 0.50 kcal/mol
E(2) E(j)-E(i) F(i,j)
Donor NBO (i) Acceptor NBO (j) kcal/mol a.u. a.u.
===================================================================================================
within unit 1
5. LP ( 1) N 1 / 16. RY*( 1) H 2 1.01 1.43 0.034
5. LP ( 1) N 1 / 17. RY*( 2) H 2 0.67 2.17 0.034
5. LP ( 1) N 1 / 20. RY*( 1) H 3 1.01 1.43 0.034
5. LP ( 1) N 1 / 21. RY*( 2) H 3 0.67 2.17 0.034
5. LP ( 1) N 1 / 24. RY*( 1) H 4 1.01 1.43 0.034
5. LP ( 1) N 1 / 25. RY*( 2) H 4 0.67 2.17 0.034
The section below titled "Natural Bond Orbitals (Summary)" summarises the energy and population of the bonds (including the lone-pair). We can see that each 'bond' has a two electrons, and the energy of the lone-pair bond is almost half that of the N-H bonds, it is also higher in energy. We can also see that the energy of the core 1s orbital is much, much lower than all other MOs. This is why we do not normally include these orbitals in our quantitative MO diagrams.
Natural Bond Orbitals (Summary):
Principal Delocalizations
NBO Occupancy Energy (geminal,vicinal,remote)
====================================================================================
Molecular unit 1 (H3N)
1. BD ( 1) N 1 - H 2 1.99909 -0.60417
2. BD ( 1) N 1 - H 3 1.99909 -0.60417
3. BD ( 1) N 1 - H 4 1.99909 -0.60416
4. CR ( 1) N 1 1.99982 -14.16768
5. LP ( 1) N 1 1.99721 -0.31756 24(v),16(v),20(v),17(v)
Association energies: Ammonia-Borane
Reaction: NH3 + BH3 -> NH3BH3.
Already calculated energies of NH3 (-56.55776856 au) and BH3 (-26.61532363 au)
Optimise for NH3BH3 link to filehere.
Job type: Optimisation
Method: DFT B3LYP
Basis set: 6-31G(d,p)
Summary for optimisation of NH3BH3 (Table 16)
Title
Value
Units
File Type
.log
Calculation Type
FOPT
Calculation Method
RB3LYP
Basis Set
6-31G(d,p)
Charge
0
Spin
Singlet
E(RB3LYP)
-83.22468896
au
RMS Gradient Norm
0.00011161
au
Imaginary Freq
0
Dipole Moment
5.57
Debye
Point Group
C3
Job cpu time
21.0
seconds
Item Value Threshold Converged?
Maximum Force 0.000233 0.000450 YES
RMS Force 0.000083 0.000300 YES
Maximum Displacement 0.000981 0.001800 YES
RMS Displacement 0.000370 0.001200 YES
Predicted change in Energy=-4.041556D-07
Optimization completed.
The energy difference (dissociation) of the reaction is:
ΔE = -83.22468896 - (-56.55776856 + -26.61532363) = -0.05153677 au = -135.31 KJ/mol
Accuracy
Energy has an error of ~10kJ/mol = 3.808798324x10-3 (BUT It is standard to report numbers to 2dp (two decimal places) in kJ/mol, thus 0.01 kJ/mol is 0.0000038 au, so when reporting energies in au you must record them upto at least 7dp (recording upto 8dp is better and then drop the last two when reporting the data in a publication))
Dipole moment to 2dp
Frequencies error around 10% as we are using a harmonic approximation.
Intensities are rounded to an integer
Bond distances are accurate to ~0.01Å
Bond angles are accurate to ~0.1 deg
Week 2 - Mini Project: Lewis Acids & Bases
We know that BH3 does not exist as a monomer but exists as a dimer with 2 bridging hydrogens in the form B2H6. This is a similar case for Grignard reagents which are kept in a Schlenk equilibrium[7] where some the molecule has bridging halides within the equilibrium. This project is based on analysing and investing the conformers, vibrations and MOs of Al2Cl4Br2. There are four structural isomers of this molecule that can be formed from AlCl2Br monomers.
This puts the basis sets 6-31G(d,p) on Al and Cl atoms and the psuedo-potential (PP) LANL2DZ on the Br atoms. The snippets below show that the data has converged and that the optimisation is complete. Conformer 1
Item Value Threshold Converged?
Maximum Force 0.000149 0.000450 YES
RMS Force 0.000075 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000468 0.001200 YES
Predicted change in Energy=-2.769504D-07
Optimization completed.
Conformer 2
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000456 0.001800 YES
RMS Displacement 0.000186 0.001200 YES
Predicted change in Energy=-6.120255D-08
Optimization completed.
Conformer 3
Item Value Threshold Converged?
Maximum Force 0.000019 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000409 0.001800 YES
RMS Displacement 0.000139 0.001200 YES
Predicted change in Energy=-6.549991D-09
Optimization completed.
Conformer 4
Item Value Threshold Converged?
Maximum Force 0.000383 0.000450 YES
RMS Force 0.000137 0.000300 YES
Maximum Displacement 0.001263 0.001800 YES
RMS Displacement 0.000526 0.001200 YES
Predicted change in Energy=-3.326973D-07
Optimization completed.
Conformer Energies
Energy for Al2Cl4Br2 conformers(Table 18)
Units
Isomer 1
Isomer 2
Isomer 3
Isomer 4
E(a.u.)
-2352.40630684
-2352.41109811
-2352.41626678
-2352.41629358
E(relative, a.u.)
0.00998674
0.00519547
0.0000268
0
E(relative, kJ/mol)
26.22
13.64
0.07
0
Here are the energies of the different conformers in kJ/mol (Table 18). We can see that Isomer 4 is the most stable (lowest in energy).
The relative energies make sense in terms of molecule stability. Isomers 3 and 4 have bridging cholrine atoms only, this gives them extra stability because chlorine and aluminium are in the same row meaning they will have a better orbital overlap than bridging bromine atoms. Isomer 3 has the next higest energy as it has one bridign bromine, and isomer one has the highest energy with two bridging bromine atoms. The difference in stability between isomer 3 and 4 are that the bromines are on opposite sides of the molecule so there are less repulsions between the two bromine atoms than if they were on the same side such as in isomer 3.
Dissociation Energy
Summary for monomer AlCl2Br (Table 19)
Title
Value
Units
File Type
.log
Calculation Type
FOPT
Calculation Method
RB3LYP
Basis Set
GEN
Charge
0
Spin
Singlet
E(RB3LYP)
-1176.19013679
au
RMS Gradient Norm
0.00004196
au
Imaginary Freq
Dipole Moment
0.11
Debye
Point Group
C2V
Job cpu time
1m12.2s
mins secs
The monomer was optimised and it's summary placed in Table 19[12].
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984438D-08
Optimization completed.
The dissociation energy for lowest energy conformer to the monomers is:
ΔE = 2(Monomer) - (Dimer)
ΔE = 2(-1176.19013679) - (-2352.41629358) = 0.03602 a.u.
ΔE = 0.02603326 a.u. = 94.57 kJ/mol
The dimer is more stable than the combination of energies from 2 monomers. This makes sense as aluminium has an empty p-orbital acting as a Lewis acid, the dimer helps the aluminium in obtaining its electron octet by donating electrons into the p-orbital via the bridging chlorine atoms in 3c-2e bonds.
Analysing the motions I can see that the motions labelled 11-14 are Al-X (where X is bridging) stretching, and 15- 18 are Al-Y (where Y is terminal) stretching. All vibrational modes before 11 are non-bond-stretching. The molecule's with less symmetry have more bands, i.e. Isomer 2 is C1 symmetry and therefore has the most signals. If there is an overall dipole moment in the motion then a signal should be visible in the spectra.
Analysing vibrational modes 15-18
This includes all vibration's above 420 cm-1. Vibrational modes 16 and 17 are 'symmetric' for a fully symmetric molecule. Therefore, I will refer to these two vibrational modes as the 'symmetric' stretches.
All isomers should show vibrational modes 15 and 18 at a relatively strong intensity as these are unsymmetrical stretches.
Isomer 1 has no terminal Br atoms and only has two of its vibrational modes (15 (467cm-1) and 18(617cm-1)) which represent terminal Al-Y stretches, this is due to the symmetry. This is the most symmetrical of the four isomers, and so the 'symmetrical stretches' of vibrational modes 16 and 17 cancel each other out to give zero intensity.
Isomer 2 has a dominant peak at 423 cm-1, however each of the peaks for modes 15-18 are all intense (all >100) compared to the other three isomers. This is due to this isomer being the least symmetric so each 'symmetrical stretch' is more dominant than it would be in the other three.
Isomer 3 has less symmetry than isomer 1 and more than isomer 2, so we can expect to see the 'symmetrical stretches' with an intensity between the two. This is what we see. Mode 16 (461 cm-1) and 17 (570 cm-1) have intensities of 35 and 32 respectively.
Isomer 4 is a very symmetrical molecule, but not entirely symmetric! Therefore, we still see the 'symmetrical stretches', but in very low intensity. (Mode 16 (459 cm-1) 0.4 int; Mode 17 (574 cm-1) 5 int).
Analysing vibrational modes 11-14
This includes all vibration's below 420 cm-1. Vibrational modes 11 and 13 are 'symmetric' for a fully symmetric molecule. Therefore, I will refer to these two vibrational modes as the 'symmetric stretches'.
The animations in GuassView show that the bridging Br is a lot less active when it comes to displacing it in the vibrations.
Isomer 1 being the most symmetrical has a zero intensity for the two 'symmetric modes' as expected.
Isomer 2 being the most unsymmetrical molecule shows the all four peaks at relatively high intensity in this region as expected. (211 cm-1, 0.21 int; 257 cm-1, 10 int; 289 cm-1, 49 int; 385 cm-1, 152 int.)
The centre of isomer 3 is highly symmetrical with two bridging chlorine atoms, but overall the molecule is unsymmetrical. Vibrational mode 11 has a zero intensity. Mode 13 has an intensity of only 2, still very small as this molecule is still quite symmetrical. Mode 14 (420 cm-1) has a relatively low intensity compared to vibrational mode 14 for the other isomers (10 times less), this is because this particular stretch is very symmetrical for the symmetry of this isomer. [See image Conformer 3. Vib mode 14.
Isomer 4 is highly symmetrical as explained above. Therefore the 'symmetrical stretches' will have very low intensities. This is true. Mode 11 (264 cm-1) and mode 13 (308 cm-1) with intensities 0.05 and 0.008 respectively. These are very low.
Population Analysis on Isomer 4 (Lowest Energy Isomer)
A population analysis was ran on isomer 4 on the HPC [17] with the following settings:
Job type: Energy.
Additional keywords: "pop=full"
NBO tab -> Type: Full NBO
The non-core occupied MOs are the ones numbered 31 and upward (HOMO being MO 54). The table below lists five of these MO's describing the interactions between each.
MO N<supo
Labelled MO
Jmol of MO
31
MO 31
Orbital 31
38
MO 38
Orbital 38
41
MO 41
Orbital 41
50
MO 50
Orbital 50
54
MO 54
Orbital 54
Observations:
MO 41 is particularly interesting because it clearly shows an orbital that is not formed along a bond but is formed between the two bridging chlorine atoms. From just a purely quantitative observation you can see that these two atoms are close together and so we expect there to be some interaction. This proves this prediction further. The MO shows that this is a bonding interaction, the reason for no physical bond drawn is probably because the distance between the two chlorine atoms is too far.
Another interesting observation is MO 31 and 38 show that there is delocalisation around the 4 atoms central to the molecule (two Al and two bridging Cl). IT is well known that the bridging Al-Cl-Al bond is a 3c-2e type bond which is a form of delocalisation.
All the MOs with nodal planes show that these are seen only on the atoms themselves.
MO 50 consists primarily of through space antibonding interactions. Although none of the orbitals are close together so this is a relatively weak anti-bonding MO.
MO 54 only has anti-bonding interactions and is the HOMO. It is worth noting that the antibonding interactions between bridging Cl and terminal Br is stronger than that between bridging and terminal chlorine atoms. This is probably largely to do with the bromine's increased size relative to chlorine.
