Rep:Mod:pg1910y
Lewis acid/base Pairs
Trihalides of group three elements form dimers in the (....phase) when the halides are in a 1:2 ratio the dimer can be in any of 5 structures all of which are able to inter-convert between the possible structures. The system establishes an equilibrium between all the possible structures. The aim here is to establish, using quantum mechanical means which of the structures will be more stable and hence which structure will be present in the greatest amount.
Each of the isomers have been given a structural label which will be used throughout the project.
Calculations
All calculations will use SDD basis set with the key words 'scf=conver=9' 'opt=tight' and 'int=ultrafine' this means a more complete basis set is being used as opposed to using a combination of 6-31G(d,p) and LanL2DZ especially as I plan to see the effect of having different metal centers has on the equilibrium of the possible structural isomers.
Al2Cl4Br2_S1
| Al2Cl4Br2_S1_OP2 | |
| File Name | PG_Al2Cl4Br2_S1_OP2_log_86252 |
| File Type | .log |
| Calculation Type | FOPT |
| Calculation Method | RB3LYP |
| Basis Set | SDD |
| Charge | 0 |
| Spin | Singlet |
| E(RB3LYP) | -2352.69556157 a.u. |
| RMS Gradient Norm | 0.00000078 a.u. |
| Imaginary Freq | |
| Dipole Moment | 0.0002 Debye |
| Point Group | C1 |
| Job cpu time: | 0 days 0 hours 4 minutes 41.1 seconds. |
| File | [| D-space] |
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000048 0.000060 YES
RMS Displacement 0.000016 0.000040 YES
Predicted change in Energy=-2.423076D-11
Optimization completed.
-- Stationary point found.
Low frequencies --- -0.0024 -0.0012 0.0016 1.2879 1.9076 2.8419 Low frequencies --- 20.1583 55.6840 77.4376
Al2Cl4Br2_S2
| File Name | PG_Al2Cl4Br2_S2_OP_log_86277 |
| File Type | .log |
| Calculation Type | FOPT |
| Calculation Method | RB3LYP |
| Basis Set | SDD |
| Charge | 0 |
| Spin | Singlet |
| E(RB3LYP) | -2352.70112310 |
| RMS Gradient Norm | 0.00000166 |
| Imaginary Freq | |
| Dipole Moment | 0.7155 |
| Point Group | C1 |
| Job cpu time: | 0 days 0 hours 11 minutes 2.7 seconds. |
| File | [| D-space] |
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000059 0.000060 YES
RMS Displacement 0.000021 0.000040 YES
Predicted change in Energy=-1.402301D-10
Optimization completed.
-- Stationary point found.
Low frequencies --- -2.0897 0.0002 0.0010 0.0013 1.1079 1.3849 Low frequencies --- 20.4554 49.0875 77.0510
Al2Cl4Br2_S3
| File Name | PG_Al2Cl4Br2_S3_OP2_log_86278 |
| File Type | .log |
| Calculation Type | FOPT |
| Calculation Method | RB3LYP |
| Basis Set | SDD |
| Charge | 0 |
| Spin | Singlet |
| E(RB3LYP) | -2352.70656956 |
| RMS Gradient Norm | 0.00000039 |
| Imaginary Freq | |
| Dipole Moment | 0.0000 |
| Point Group | C1 |
| Job cpu time: | 0 days 0 hours 14 minutes 12.9 seconds. |
| File | [| D-space] |
Item Value Threshold Converged?
Maximum Force 0.000000 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000010 0.000060 YES
RMS Displacement 0.000003 0.000040 YES
Predicted change in Energy=-3.310876D-12
Optimization completed.
-- Stationary point found.
Low frequencies --- -3.1295 -1.8251 -1.0969 -0.0029 -0.0026 -0.0025 Low frequencies --- 20.3957 43.1170 70.1019
Al2Cl4Br2_S4
| File Name | PG_Al2Cl4Br2_S4_OP_log_86651 |
| File Type | .log |
| Calculation Type | FOPT |
| Calculation Method | RB3LYP |
| Basis Set | SDD |
| Charge | 0 |
| Spin | Singlet |
| E(RB3LYP) | -2352.70647948 a.u. |
| RMS Gradient Norm | 0.00000055 a.u. |
| Imaginary Freq | |
| Dipole Moment | 0.7208 Debye |
| Point Group | C1 |
| Job cpu time: | 0 days 0 hours 11 minutes 50.1 seconds. |
| File | [| D-space] File:PG Al2Cl4Br2 S4 OP.log |
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000041 0.000060 YES
RMS Displacement 0.000018 0.000040 YES
Predicted change in Energy=-2.599515D-11
Optimization completed.
-- Stationary point found.
Low frequencies --- 0.0011 0.0027 0.0030 2.2372 2.3603 4.1121 Low frequencies --- 20.3886 44.4063 76.2956
Al2Cl4Br2_S5
| File Name | PG_Al2Cl4Br2_S5_OP_log_86279 |
| File Type | .log |
| Calculation Type | FOPT |
| Calculation Method | RB3LYP |
| Basis Set | SDD |
| Charge | 0 |
| Spin | Singlet |
| E(RB3LYP) | -2352.70664911 |
| RMS Gradient Norm | 0.00000044 |
| Imaginary Freq | |
| Dipole Moment | 0.7847 |
| Point Group | C1 |
| Job cpu time: | 0 days 0 hours 13 minutes 28.9 seconds. |
| File | [| D-space] File:PG Al2Cl4Br2 S5 OP.log |
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000026 0.000060 YES
RMS Displacement 0.000009 0.000040 YES
Predicted change in Energy=-1.613605D-11
Optimization completed.
-- Stationary point found.
Low frequencies --- -0.0027 -0.0020 0.0017 2.3274 2.4412 3.8334 Low frequencies --- 20.8580 44.6463 69.9724
Comparison of Energies
| Structure | Energy difference (A.U) |
symmetry |
|---|---|---|
| S1 | 0.01100799 | D2h |
| S2 | 0.00544646 | C1 |
| S3 | 0.00000000 | C2h |
| S4 | 0.00009008 | C2v |
| S5 | -0.00007955 | C2v |
Here is a table compiling together the differences in energy compared to the lowest energy. It is not possible to use the values outputted directly from the computations as they are not absoluts values for the energy of the molecules, however what we are able to look at is the change in energy from one structure to another.
What we see from the table is that out of the four isomers (S1-S4) that would be formed with the dimerisation of two AlCl2Br monomers S3 is the most stable.
In the S3 isomer, both bridging atoms are Chlorine and the remaining chlorine and bromine atoms are distributed in a trans- arrangement on either side of the molecule. This doesn't immediately make sense if the interactions in the dimer were still considered as an electron donor/acceptor interaction, as Bromine being a larger and less electronegative atom would make a better п-donor then Chlorine, therefor S1 or S2 would perhaps be the most stable. When thought of as two monomers starting at a distance and coming closer together, the interactions would indeed start out as a distinct donor-acceptor interaction, with the p-orbital of the halide atom aligning with the vacant p-orbital of aluminum, electron density starts moving towards the aluminium. once the dimer is formed, however, the bridges between the two monomers do not consist of two electron donor-acceptor interactions but rather 2 3c-4e- interactions.
As we can see from the diagram, showing the computed bond lengths (Å) to 2.d.p., the bond lengths of Al--Cl(terminal) are the same at 2.16Å whilst the Al--Cl(bridging) are significantly longer at 2.41Å (~13% increase). This difference would suggest a difference in bonding character between the two bonds.
I also included in my calculations a structure that is another isomer of Al2Cl4Br2 but wouldn't be formed from the dissemination of AlCl2Br. This was to see if there would be any greater stability of the structure. What we see from the calculations, is that whist innitially the values would indicate that it is more stable, the difference is smaller then the error expected from the calculations so it not possible to definitively say that it is more stable or not.
Effect of Br position on stability
Working from S3 as the most stable of the isomers we can qualitatively analyse the effect on stability that changing the position of Br within the molecule. What we see is that when the bromine atoms are arranged cis- to one another the stability of the system reduces, however this difference is only a change of ~0.2 KJmol-1, with the possible accuracy of these calculations (even with the better basis set), this difference probably does not amount to much so we can not conclusively say it effects stability. A more noticeable effect that this change in structure causes is the breakdown in symmetry which is seen in the vibrational properties of the molecule. This will be discussed more in the section on IR.
When we put bromine atoms in the place of the bridging chlorines we see a far more significant change in energy ~14.30 KJmol-1 for one substution (S2) and ~28.90 KJmol-1 for the second (S1). This can most likely be put down to there being a poorer orbital energy overlap between Br-Al compared with Cl-Al, coupled with the reduced electronegativity and greater atomic radii which will lead to longer and weaker bonds.
Association Energy
After running an optimisation on a molecule of AlCl2Br it should be possible to compare the energy of 2 monomer units to the energy of the dimer with the difference in energy being the association energy of dimerisation
|
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000002 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-6.355071D-11
Optimization completed.
-- Stationary point found.
|
Low frequencies --- -2.2635 0.0030 0.0032 0.0041 1.2290 2.7066 Low frequencies --- 117.7454 128.5576 172.1364
-2352.70656956 - 2x(-1176.33752124) = -0.03152756 a.u. = -82.8 kJmol-1
It is quite clear then that there is a significant and favourable stabilisation associated with the dimerisation of two monomers. i.e. the Dimer is more stable then its separate monomers
Comparing this value to RT (~2.5 KJmol-1) means that the earlier assumption that the structures are able to isomerise into to other structures will not be the case, at least where both bonds are broken, to then be reformed with a different structural arrangement of groups. The possibility of a single bond breaking followed by rotation and reforming a bond to a different halogen as a possible pathway to isomerisation has not been ruled out, however considering the stability of the dimer this is becoming less likely.
Frequency analysis and spectra
| Structure | Spectra | Structure | Spectra | |
|---|---|---|---|---|
| Structure 1 D2h |
 |
Structure 3 C2h |
| |
| Structure 2 C1 |
 |
Structure 4 C2v |
|
All of the structures have 18 possible vibrations that they can perform, the major difference between all three is the symmetry of the molecule vibrating, all the molecules undergo essentially the same stretches, twists and vibrations but not all of them show up in the Infrared spectrum.
To be seen in the IR spectrum a vibrations must be associate with a change in the dipole of a molecule, this reasoning helps to explain why the more symmetrical molecules show less peaks in the IR spectrum of the molecule as more of the vibrational modes will themselves be symmetric and hence will not have the necessary change in dipole to show up.
Adding a Bridging Bromide S3-->S2
When we change the distribution of the halides so that one of the bridging halides is a bromine we see a dramatic change in the spectra due to the loss of symmetry but also a swapping of the order of the vibrational modes of the molecule. Bellow is a table showing the stretches of the vibrations where the stretches have changed order, to better show the change, the vidrations of S2 will be rearranged so that they best match those of S3
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|
What we can be intantly notice that in a lot of these casee; S2M4, S2M11, S2M10 and S2M12 the rearrangements are coupled with a lowering in energy of the corresponding S3 stretch. In all of these cases it can be directly linked to the increase in mass of the bridging atom as in these vibrations, these are the atoms being displaced most there will also be a contribution due to the weakening of the bonds being stretched.
In the case of S2M4 whilst there is still a lot of movement from the bridging atoms, you also get a large energetic contribution due to the decrease in mass and a strengthening of bond for one of the terminal atoms.
In truth, in all the cases of mode switching and indeed all the vibrations when comparing S2 with S3 there is going to be a sliding scale of contributions between the increase in mass and weakening of the bonds to the bridging atom and the reduction in mass and strengthening of the bonds to the terminal atoms.
Adding a Bridging Bromide S3-->S1
As with the section above, we can see that there is quite a few vibrational modes that are rearranging in energy but now that there are two heavier atoms forming weaker bonds as the bridging atoms and two lighter atoms forming stronger bonds taking the place of the heavier atoms we see a different set of vibrational modes have rearranged.
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|
For S1M4 and S1M6 there is only a small displacement of the bridging atoms whilst most to the displacement or stretch is being performed by the now lighter terminal atoms leading to a higher energy vibration. Making the vibrations higher in energy, whilst in S1M3, S1M5, S1M11 and S1M10 there is a large displacement of the bridging atoms lowering the energy of the vibration. For S1M10 and S1M11 there is a very dramatic change in energy, this is bacause, along with the above explanation there is also a larger variation in the bonds connecting the aluminium atoms to the bridging atoms.
Full list of S3 vibrations
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MOs of S3
Energy calgulations [| D-space] File:PG Al2Cl4Br2 S3 EN.log
|
Here we will look at a few of the MO orbitals that have been calculated for the most stable of the structures, S3. While the arrangements of the atoms will differ from structure to structure, because chlorine and bromine come from the same group and hence share a similar electronic structure. It is not expected that that there would be much difference in the overall make up of the MOs.
To aid discussion discussion of the orbitals will either be done with reference to the diagram above, where the four-members ring structure of the aluminium and bridging chlorides lie in the XY plane. This will mainly be relevant only when discussing the aluminium or bridging bridging chloride orbitals. Or orbitals will be referred to by their alignment to their σ-bond, this will be more useful when discussing the terminal chlorides or bromides. |
Orbital 31
 
|
This is the Lowest energy of the bonding orbitals, consisting purely of two S-orbitals from the bridging chlorides. This would not normally be thought of as a bonding interacting when considering a more primitive level of bonding theory, due do the large distance between them (~3.3 Å)
Overall, theis is a highly bonding orbital giving strong interactions between the two bridging chlorides, however will not contribute significantly to the total stability of the molecule as a whole. |
Orbital 37
 
|
This orbital is a combination of the two Px orbitals from the bridging chlorides with the aluminium S-orbitals of matching phase giving a YZ nodal plane through the chlorines the two aluminium Sorbitals also have an inphase interaction with the P-orbitals of their connected halides each adding an additional nodal point.
Overall This is a highly bonding interaction with strong interactions with. Additionally this orbital is one of the three main orbitals that contribute to the bridging interaction. |
Orbital 38
 
|
similar to orbital 37 this consists of the two Cl P(y) orbitals pointing into the ring structure giving an in phase overlap, this also has an in phase overlap with the aluminium S-orbitals (which are in phase with respect to each other) each aluminium S-orbital in phase interactions with the P-orbitals of their connected halides.
Overall, this is a highly bonding orbital with strong interactions. There are six nodal points from each P-orbital. Additionally this orbital is one of the three main orbitals that contribute to the bridging interaction. |
Orbital 41
 
|
This orbital consists of four P(z) orbitals from the ring structure, all overlapping in plane, giving a nodal plane the bisects the ring in the XY plane. Each of the aluminium P(z) orbitals also have in phase overlap with their connected halide P-orbitals
Overall this is a highly bonding orbital with a nodal plane and four nodal points. Additionally this orbital is one of the three main orbitals that contribute to the bridging interaction. |
Orbital 43
 
|
This orbital only consists of four P-orbitals, while initially it would appear that aluminium is also contributing, however on closer inspection the obitals are deforming around the aluminium atom. The P-orbitals are from the four terminal halides, aligned along the Al-X bond. The orbitals from the halides on the same aluminium are out of phase to one another, and are also out of phase with the halide situated on the other aluminium on the same face of the ring structure. There is possibly a weak through space interaction between one halide and the halide situated diagonally across from it (i.e. Cl- -Cl and Br- -Br)
Overall this orbital is probably anti-bonding but due to its repetitively low energy is not very destabilising. There are four nodes from the P-orbitals |
Orbital 54
 
|
This orbital represents the HOMO of the molecule. It is made up of two in plane but non-overlapping P(z) orbitals that are slightly twisted towards the the bromines and aligning into the same direction as the terminal chlorines, they are out of phase with respect to both of them. All of the terminal halides has P-orbitals perpendicular to the Al-X bond, aligned in the XZ plane. they are out of phase with respect to the neighbour on the same aluminium but in phase with the neighbour on the same face of the ring on the other aluminium.
It can be seen that there is a noticeable difference in the size of the orbitals. Bromine has large diffuse orbitals, expected as it is bellow chlorine on the periodic table, but more interestingly the bridging chlorines have smaller and tighter orbitals than their terminal counterparts, this is perhaps reflecting the fact that these chorines are sharing four electrons rather then two, so are likely to be more electron deficient. Overall, this orbital is likely to be anti-bonding, but not particularly strongly so as all interactions are through-space. There are six nodes from the P-orbitals. |
Orbital 55
 
|
This orbital represents the LUMO of the molecule, it appears to be the anti-bonding partner to orbital 38 discussed earlier. Consisting of two aluminium S-orbitals, inphase with each other, two P(y) orbitals which are in phase with each other bit are out of phase with respecto to the Aluminium S-orbitals. The terminal halides each have P-orbitals directed towards their connected aluminium but are out of phase with its S-orbital. This give six strongly anti-bonding interactions, but with two favourable but likely weak through-space interactions. There are six nodes from the p-orbitals and four nodal points and two nodal planes
Overall this orbital will be strongly anti-bonding. |
All MOs
The table bellow shows all of the calculated MOs of all non-core MOs up to and includont the LUMO+1
| Orbital 31 |
Orbital 32  |
Orbital 33  |
Orbital 34 
|
Orbital 35  |
Orbital 36  |
Orbital 37 |
Orbital 38 
|
Orbital 39  |
Orbital 40  |
Orbital 41 |
Orbital 42 
|
| Orbital 43 |
Orbital 44  |
Orbital 45  |
Orbital 46 
|
Orbital 47  |
Orbital 48  |
Orbital 49  |
Orbital 50 
|
Orbital 51  |
Orbital 52  |
Orbital 53  |
Orbital 54
|
| Orbital 54 HOMO |
Orbital 55 LUMO |
Orbital 56 LUMO+1  |
Charge Distribution
We can see from the calculated charge distributions that the bridging chlorides are quite a bit more electron deficient than the terminal chlorides, this corresponds with the 3C-2e-1 model of the bond discussed earlier. As the bridging chlorides are shearing more of their electron density, they have a lower charge on them.
The Effect of Replacing the Aluminium with Gallium
I wanted to see if there there might be a noticeable change in the order of the stabilities of the structural isomers. My thoughts being that there might be better energetic overlap between the Gallium and Bromine orbitals that may lead to more favorable interactions
| S1 | S2 | S3 | S4 | |
|---|---|---|---|---|
|
File Name |
PG_Ga2Cl4Br2_S1_OP_log_87111 | PG_Ga2Cl4Br2_S2_OP_log_87108 | PG_Ga2Cl4Br2_S3_OP_log_87109 | PG_Ga2Cl4Br2_S4_OP_log_87110 |
| File Type | .log | .log | .log | .log |
| Calculation Type | FOPT | FOPT | FOPT | FOPT |
| Calculation Method | RB3LYP | RB3LYP | RB3LYP | RB3LYP |
| Basis Set | SDD | SDD | SDD | SDD |
| Charge | 0 | 0 | 0 | 0 |
| Spin | Singlet | Singlet | Singlet | Singlet |
| E(RB3LYP) | -1871.950089 | -1871.955099 | -1871.959893 | -1871.959787 a.u. |
| RMS Gradient Norm | 0.0000007 | 0.00000076 | 0.00000055 | 0.00000011 a.u. |
| Imaginary Freq | ||||
| Dipole Moment | 0.0001 | 0.9669 | 0 | 0.9386Debye |
| Point Group | C1 | C1 | C1 | C1 |
| Job cpu time: | 0 days 0 hours 9 minutes 27.8 seconds. | 0 days 0 hours 11 minutes 21.2 seconds. | 0 days 0 hours 10 minutes 38.6 seconds. | 0 days 0 hours 10 minutes 48.4 seconds. |
| File: | File:PG Ga2Cl4Br2 S1 OP.log | File:PG Ga2Cl4Br2 S2 OP.log | File:PG Ga2Cl4Br2 S3 OP.log | File:PG Ga2Cl4Br2 S4 OP.log
|
| Isomer | Energy difference (a.u.) |
Energy difference (kJmol-1 |
|---|---|---|
| S1 | 0.00980427 | |
| S2 | 0.00479409 | |
| S3 | 0 | |
| S4 | 0.00010536 |
As can be seen from the calculations, there seems to be no change in the order of the stability of the dimers.