View source for 3rd Year Computational Chemistry: Module 2 (gc2109)

'''''By Gen Cross'''''

This module aims to illustrate the ability of computational chemistry to predict the structure and relative energies of various inorganic molecules. In addition to predict the IR spectra and Molcular Orbital structures of these optimized structures. Computaional techniques are useful for analyzing unusual bonding systems which are more common in inorganic chemistry, and particulary in cases where analyses is either extremely difficult in a wet lab (e.g. very unstable small moecules) or very toxic compounds.

Throughout this module the Gaussian 09W programme is used to carry out the calculations on the molecules, and GaussView 5.0 is used to draw structures and create input files. These input files are sent to the HPC server for calculation requiring more computational power. The output files gathered from these calcuations are then analysed using GaussView 5.0 to visulise optimizeds structures, bond vibrations and molecular orbitals. During these geometry optimizations, there are generally two main parts the SCF and OPT calculation, dealing with electrons and nuclei respectively. First the Schrodinger equation is solved for the electrons in the molecules using the Born-Oppenheimer approximation. Then the positions of the nuclei are optimized, and the process is repeated until a point at which the gradient of the energy = 0. Generally a minimum point is being searched for as this corresponds to the equilibrium bond lengths for the molecule (there are no forces pushing or pulling the nuclei). However the gradient also = 0 at a maximum point corresponding to a transition state, therefore the second derivative is alse found, when positive this confirms a minium point has been found and the optimal geometry has been found.

=Bonding (ab intio and density functional molecular orbitals)=
==BH<sub>3</sub>==
===Introduction===
This sections aims to show that computational methods can be used to optimize the geometry of a simple inorganic molecule such as BH<sub>3</sub> and once this geometry is found how it can be analysed to predict IR absorptions and the location of molecular and non-bonding orbitals.

===Geometry Optimisation of BH<sub>3</sub> ===
A BH<sub>3</sub> was first drawn on GuassView 5.0 with a trigonal planar structure. Each of the B-H bonds lengths were then set to 1.5 Angstroms. This molecule was optimized using the 'Guassian Calculation Setup' function to submit the molecule to Guassian 09W on the computer,  with  the  '''B3LYP''' method and the '''3-21G''' basis set.  The advantages of this was that it was a quick calculation since the basis set is small, the disadvantage is that the some accuracy maybe lost. On such a simple molecule this inaccuracy will be small so the use of such a basis set is justified. The 3D view of the optimised BH<sub>3</sub> molecule can be seen here <jmol><jmolAppletButton>
<uploadedFileContents>BH3 OPTIMIZATION GC2109.mol</uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 1 2; measure 1 3; measure 1 4; measure 2 1 4</script>
</jmolAppletButton>
</jmol> .

The more relevant information from the '''LOG FILE''' is shown below, but it has also been published in full detail here.

[[Image:BH3 OPT SUMMARY GC2109.jpg|thumb|float:right|300px]]
<pre>
                      Optimized Parameters  
                    (Angstroms and Degrees) 
 -------------------                       ---------------------
  Name  Definition              Value          Derivative Info.               
 ---------------------------------------------------------------
  R1    R(1,2)                  1.1935         -DE/DX =0.0004             
  R2    R(1,3)                  1.1935         -DE/DX =0.0004             
  R3    R(1,4)                  1.1935         -DE/DX =0.0004             
  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                
 ---------------------------------------------------------------</pre>
<pre>
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
Predicted change in Energy=-1.071764D-06
Optimization completed.
    -- Stationary point found.</pre>

It can be seen from the above that the optimization was successful, indicated by the value for the Root Mean Squared of the graph being very close to 0. This is confirmed by Gaussian saying the calculation has converged. It can be seen from the graphs below that the optimisation was complete in 4 iterations.

[[Image:BH3 optimization total energy gc2109.jpg |thumb|centre|600px]]
[[Image:BH3 opt RMS gc2109.jpg|thumb|centre|600px]]

It can be seen from the data in the 'Optimisation Parameters' section and the Jmol diagram that the fully optimised structure for BH<sub>3</sub> has B-H bond lengths of 1.19Å and bond angles of 120 degrees. This agrees well with literature. It can also be seen that the dipole moment of BH<sub>3</sub> is 0 Debye, this is due to its high symmetry point group (D3H).

===Frequency Analysis===
[[Image:Bh3 vibration summarydata gc2109.jpg|thumb|float:right|300px]]

The purposes of carrying out frequency analyses on the optimised structure are 2 fold. First clearly a useful prediction of IR stretches and bond absorptions can be made, to compare with literature from the wet lab. Second, the vibrational analyses is effectively used to check the second derivative of the energy graph, i.e. to check if the stationary point found in the geometry optimisation is indeed a global minimum or is in fact a maximum corresponding to a transition state. Maxima are indicated by negative frequencies in the IR spectrum. It can be seen from the '''LOG FILE''' and the results below that the optimisation carried out above was successful.




















{| class="wikitable" border="1" style="align: center"
|+Table 1 - Vibrational Modes for BH<sub>3</sub>. Full IR Spectrum seen[[Media:BH3 IR spectrum gc2109.jpg| here]]
! Description for Mode of Vibration !! Type of Vibrational Mode !! Intensity of Absorption !! Frequency of Absorption (cm<sup>-1</sup>) !! Literature value for Frequency (cm<sup>-1</sup>)<ref>

Kentarou Kawaguchi,                                                                                                                                             	                      	                                                      		                    		                    		                    		                    					        					        					              					        					        					        					              					        					        					  					                                                                    					                                                                                                                                                        					                                                                                  J. E. Butler,                                                                                                                                             	                      	                                                      		                    		                    		                    		                    					        					        					              					        					        					        					              					        					        					  					                                                                    					                                                                                                                                                        					                                                                                  Chikashi Yamada,                                                                                                                                             	                      	                                                      		                    		                    		                    		                    					        					        					              					        					        					        					              					        					        					  					                                                                    					                                                                                                                                                        					                                                                                  S. H. Bauer,                                                                                                                                             	                      	                                                      		                    		                    		                    		                    					        					        					              					        					        					        					              					        					        					  					                                                                    					                                                                                                                                                        					                                                                                  Tatsuya Minowa,                                                                                                                                             	                      	                                                      		                    		                    		                    		                    					        					        					              					        					        					        					              					        					        					  					                                                                    					                                                                                                                                                        					                                                                                  Hideto Kanamori,                                                                                                                                             	                      	                                                      		                    		                    		                    		                    					        					        					              					        					        					        					              					        					        					  					                                                                    					                                                                                                                                                        					                                                      and                              Eizi Hirota

, J. Chem. Phys. 87, 2438 (1987). http://dx.doi.org/10.1063/1.453135</ref>!! Percentage Error (%) !! Diagram !! Link to 3D animation
|-
! Umbrella deformation 
| A<sub>2</sub> " ||93 || 1146 || 1225 ||6 || [[Image:Mode1 pic gc2109.jpg |thumb|centre|200px]] || [[Media:Mode1 gc2109.gif|Show Animation]]
|-
! Symmetric B-H scissoring 
| E' || 12 || 1205|| 1305 ||8 || [[Image:Mode2 gc2109.gif|thumb|centre|200px]]|| [[Media:Mode2 gc2109.gif|Show Animation]]
|-
! Asymmetric B-H rock 
| E' || 12 || 1205|| 1305|| 8 || [[Image:Mode3 pic gc2109.jpg|thumb|centre|200px]]|| [[Media:Mode3 gc2109.gif|Show Animation]]
|-
! Symmetric B-H stretch 
| A<sub>1</sub>' || 0 || 2592|| - || - ||[[Image:Mode4 pic gc2109.jpg|thumb|centre|200px]]|| [[Media:Mode4 gc2109.gif|Show Animation]]
|-
! Asymmetric B-H stretch (1)
| E' ||104 || 2730|| 2693|| 1 ||[[Image:Mode5 pic gc2109.jpg|thumb|centre|200px]]|| [[Media:Mode5 gc2109.gif|Show Animation]]
|-
! Asymmetric B-H strech (2)
| E' || 104 || 2730|| 2813||3 ||[[Image:Mode6 gc2109.jpg|thumb|centre|200px]]|| [[Media:Mode6 gc2109.gif|Show Animation]]
|-
|}

It can seen from the data in the table above that there are 6 vibrational modes for BH<sub>3</sub>, however in the IR spectrum only 3 absorptions are seen. The 3 missing peaks can be explained by looking at the absorption intensities and their frequencies. It can be seen that the A' B-H stretch has an intensity of 0 because it is a totally symmetric stretch and therefore there is no change in overall dipole moment, an absorption is therefore not seen. In addition each pair of E' absorptions at 1205cm<sup>-1</sup> and 2730cm<sup>-1</sup> are exactly degenerate and therefore their absorptions overlap.

It should be noted that the literature values quoted in the table are themselves computational calculations by ''DeFrees'' and ''McClean'' using HF/6-31G*. That being said a good agreement with the literature is shown.

Analysis of the low frequencies suggests the vibrational results are accurate since they are very close to zero.
<pre>
 Full mass-weighted force constant matrix:
 Low frequencies ---   -0.3716   -0.0098   -0.0018   37.2444   37.9574   37.9592
 Low frequencies --- 1146.0292 1204.8631 1204.8641 </pre>

===Molecular Orbital Analysis===
In order to find the molecular orbitals for BH<sub>3</sub> the previously optimised structure was sent to the HPC server for an Energy analyses with the parameters 'pop=full' and 'full nbo' selected in the calculation set up. Once the calculation was complete the Formatted Checkpoint File was downloaded and the MOs visualised in GaussView 5.0. The '''LOG''' file can be seen here <ref>http://hdl.handle.net/10042/to-12085</ref>.

To check the validity of the quantitative MOs produced computational a molecular orbital diagram was predicted qualitatively using
the linear combination of atomic orbitals method. This is shown below.

{| class="wikitable" border="1" style="text-align: center"
|+Table 6 - MO Diagram for BH<sub>3</sub>
! MO Diagram with Orbitals shown in the XY plane !! Orbitals seen in XZ Plane!! Molecular Orbital
|-
!rowspan="9" |[[Image:Bh3mo diagram gc2109.gif|centre|800px]]
|-
! [[Image:8sidegc2109.jpg|thumb|centre|80px]] || LUMO+3
|-
! [[Image:7sidegc2109.jpg|thumb|centre|80px]] ||LUMO+2
|-
! [[Image:6sidegc2109.jpg|thumb|centre|80px]] ||LUMO+1
|-
! [[Image:5sidegc2109.jpg|thumb|centre|80px]] ||LUMO
|-
! [[Image:4sidegc2109.jpg|thumb|centre|80px]] ||HOMO
|-
! [[Image:3sidegc2109.jpg|thumb|centre|80px]] ||HOMO-1
|-
! [[Image:2sidegc2109.jpg|thumb|centre|80px]] ||HOMO-2
|-
! [[Image:1sidegc2109.jpg|thumb|centre|80px]] ||HOMO-3
|-
|}

The MO diagram above was produced using ChemDraw Pro 12.0

Hydrogen (2.20) <ref>http://en.wikipedia.org/wiki/Electronegativity</ref> is slightly more electronegative than Boron (2.04) and so the H<sub>3</sub> fragment was placed lower in MO diagram. Each of the fragment orbitals were assigned a symmetry group in order to ascertain which orbitals could mix. Finally the electrons were added to the MO diagram. The predicted structure for the MO diagram agrees well with the energies of the MOs calculated computationally so they were added into the figure above. It can be seen that the Boron 1s atomic orbital has been included in the diagram but is not actually involved in bonding as it is too low lying, backed up by the very low energy (-6.73 Ha) relative to the other MOs.

Qualitatively the order of the 2 highest energy MOs is difficult to predict since it can be argued that either should be lower in energy, on the one hand clearly the a1' fragment orbitals are lower in energy originally so it could be argued the resultant 3a' MO should also be lower in energy. Conversely the e' fragment orbitals show worse overlap and so it could be argued this interaction should be smaller leading it to be lower energy MO. In the end the diagram was drawn to agree with the energies found computationally.

Overall it can be seen that the ability of computational methods to predict the MOs for small molecules such as BH<sub>3</sub> is very good. This accuracy would decrease and also require far more computational power and larger basis sets as more complex molecules are analysed.

===NBO Analysis===
The same '''LOG''' file <ref>http://hdl.handle.net/10042/to-12086</ref> produced by energy calculation can be used for Natural Bond Order (NBO) analysis because the 'full NBO' option was added previously. The pertinent data from the LOG file can be seen below, and the full version is available here.
[[Image:NBO BH3 summary gc2109.jpg |thumb|float: right|300px]]

<pre>
Summary of Natural Population Analysis:                 
                                                         
                                       Natural Population
            Natural  -----------------------------------------------   
 -----------------------------------------------------------------------
 B      1    0.33161      1.99903     2.66935    0.00000     4.66839
 H      2   -0.11054      0.00000     1.11021    0.00032     1.11054
 H      3   -0.11054      0.00000     1.11021    0.00032     1.11054
 H      4   -0.11054      0.00000     1.11021    0.00032     1.11054
 =======================================================================
 * Total *    0.00000      1.99903     6.00000    0.00097     8.00000 </pre>

<pre>
(Occupancy)   Bond orbital/ Coefficients/ Hybrids
 --------------------------------------------------------------------------------
1. (1.99853) BD ( 1) B   1 - H   2 
                ( 44.48%)   0.6669* B   1 s( 33.33%)p 2.00( 66.67%)
                                        0.0000  0.5774  0.0000  0.0000  0.0000
                                        0.8165  0.0000  0.0000  0.0000
                ( 55.52%)   0.7451* H   2 s(100.00%)
                                        1.0000  0.0000
2. (1.99853) BD ( 1) B   1 - H   3 
                ( 44.48%)   0.6669* B   1 s( 33.33%)p 2.00( 66.67%)
                                        0.0000  0.5774  0.0000  0.7071  0.0000
                                        -0.4082  0.0000  0.0000  0.0000
                ( 55.52%)   0.7451* H   3 s(100.00%)
                                        1.0000  0.0000
3. (1.99853) BD ( 1) B   1 - H   4 
                ( 44.48%)   0.6669* B   1 s( 33.33%)p 2.00( 66.67%)
                                        0.0000  0.5774  0.0000 -0.7071  0.0000
                                        -0.4082  0.0000  0.0000  0.0000
                ( 55.52%)   0.7451* H   4 s(100.00%)
                                        1.0000  0.0000
4. (1.99903) CR ( 1) B   1              s(100.00%)
                                          1.0000  0.0000  0.0000  0.0000  0.0000
                                          0.0000  0.0000  0.0000  0.0000
5. (0.00000) LP*( 1) B   1              s(100.00%)
6. (0.00000) RY*( 1) B   1              s(  0.00%)p 1.00(100.00%)</pre>


Once opened in GaussView 5.0 an optionwas selected to colour the molecule according to electron density. Green indicates a relatively positive charge, whereas Red indicates a negative one. This can be seen in the diagram below, the Green colour of the central Boron and its positive value of 0.33 is in agreement with its well known Lewis Acidic behavior.

[[Image:BH3 NBO picture gc2109.jpg|thumb|centre|300px| Figure x : B= 0.33, H= -0.11 ]]

It can be seen from both the figure above and the natural population analysis that the electron density is equal in each of the Hydrogen atoms, which is to be expected since the molecule is highly symmetric.

Using the Occupancy data above it can also be seen from the '''LOG''' file that 44% of the electron density is deemed to be on the Boron and 56% on the Hydrogen of each B-H bond. In addition the s and p character of each bond can be seen to be 33%:67% (s:p), this is inidicative of sp<sup>2</sup> hybridised bonds and is in agreement with the 120 degree bond angles found in the optimisation.

There is one error in the computational calculations above: while the 4th orbital makes sense the 5th orbital does not. The 4th orbital is a Boron 1s orbital so it should be expected to have 100% s character. However the data suggests the 5th orbital also has 100% s character whereas it should actually be an unoccupied p orbital, which is orbital 6 instead.

==TlBr<sub>3</sub>==
===Geometry Optimisation of TlBr<sub>3</sub>===
As in the BH<sub>3</sub> optimisation the TlBr<sub>3</sub> molecule was drawn with a trigonal planar geometry on GaussView 5.0. However on this occasion the '''LANL2DZ''' basis set was used instead of '''321-G'''. The method was the same '''(DFT/ BLYP)'''. The reason for this is that this basis set uses psuedo potentials which is necessary for larger metal atoms such as Thallium. The pseudo potential carries out the calculation solely on the valence electrons of the Thallium, which is an approximation but should be an accurate one for such a large atom. The LANL2DZ basis set is also larger than the 321-G basis set so should provide a more reliable result for a second row element such as Thallium.

The more relevant information from the LOG FILE is shown below, but it has also been published in full detail here.
 
The 3D view of the optimised TlBr<sub>3</sub> molecule can be seen here <jmol><jmolAppletButton>
<uploadedFileContents>TLBR3 OPTIMISATION GC2109.mol</uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 1 2; measure 2 1 3</script>
</jmolAppletButton>
</jmol> 

[[Image:TlBr3summarygc2109.jpg|thumb|float: right|600px]]

<pre>
Item                        Value      Threshold  Converged?
 Maximum Force            0.000002     0.000450      YES
 RMS     Force            0.000001     0.000300      YES
 Maximum Displacement     0.000022     0.001800      YES
 RMS     Displacement     0.000014     0.001200      YES
 Predicted change in Energy=-6.083881D-11
 Optimization completed.
    -- Stationary point found.</pre>

<pre>
                       Optimized Parameters  
                      (Angstroms and Degrees) 
 --------------------                        ----------------------
  Name  Definition              Value            Derivative Info.               
 ------------------------------------------------------------------
  R1    R(1,2)                  2.651            -DE/DX =    0.0                
  R2    R(1,3)                  2.651            -DE/DX =    0.0                
  R3    R(1,4)                  2.651            -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                
 ------------------------------------------------------------------ </pre>


[[Image:TlBr3 energy graph gc2109.jpg|thumb|centre|600px]]

[[Image:TlBr3 rms gc2109.jpg|thumb|centre|600px]]

It can be seen from the above that the optimisation was carried out in 3 iterations, and a stationary point was found.

[[Image:TlBr3 bond length gc2109.jpg|thumb|centre|300px]]
[[Image:Tlbr3 bond angle.jpg|thumb|centre|300px]]

The optimised structure for TlBr<sub>3</sub> has bond length 2.65Å and 120degree bond angle this is confirmed by the Jmol and the diagrams above. Once again this suggests the molecule is sp2 hybridised.

===Frequency Analysis===
[[Image:Freq summary data gc2109.jpg|thumb|float:right|300px]]
Once again the absence of negative absorptions confirms the geometry optimisation was successful in finding a minimum point.


























{| class="wikitable" border="1" style="align: center"
|+Vibrational Modes for TlBr<sub>3</sub>. Full IR Spectrum seen[[Media:Tlbr3irspecgc2109.jpg| here]]
! Description for Mode of Vibration !! Type of Vibrational Mode !! Intensity of Absorption !! Frequency of Absorption (cm<sup>-1</sup>) !! Diagram !! Link to 3D animation
|-
! Symmetric Tl-Br Scissoring
| A<sub>2</sub> " || 4 || 46 || [[Image:Mode1 tl gc2109.jpg|thumb|centre|200px]] || [[Media:Tl mode1 clip.gif|Show Animation]]
|-
! Asymmetric Tl-Br Rock
| E' || 4 || 46|| [[Image:Mode2 tl gc2109.jpg |thumb|centre|200px]]|| [[Media:Tl mode2 clip.gif|Show Animation]]
|-
! Umbrella Deformation
| E' || 6 || 52|| [[Image:Mode3 tl gc2109.jpg|thumb|centre|200px]]|| [[Media:Tl mode3 clip.gif|Show Animation]]
|-
! Symmetric Tl-Br Stretch
| A<sub>1</sub>' || 0 || 165||[[Image:Mode4 tl gc2109.jpg|thumb|centre|200px]]|| [[Media:Tl mode4 clip.gif|Show Animation]]
|-
! Asymmetric B-H Stretch (1)
| E' || 25 || 211||[[Image:Mode5 tl gc2109.jpg|thumb|centre|200px]]|| [[Media:Tl mode5 clip.gif|Show Animation]]
|-
! Asymmetric B-H Stretch (2)
| E' || 25 || 211||[[Image:Mode6 tl gc2109.jpg|thumb|centre|200px]]|| [[Media:Tl mode6 gc2109.gif|Show Animation]]
|-
|}

It can be seen from the table above that there are 6 vibrational modes for TlBr<sub>3</sub>, and in the IR spectrum there are 2 main peaks, the lower frequency peak (4-6cm<sup>-1</sup>) is broad because 2 peaks have overlapped slightly, the shoulder at 4cm<sup>-1</sup> corresponds to the A2" and E' (Asymmetric Tl-Br Rock) stretches which are degenerate. The two E' (B-H stretches) are completely degenerate and therefore are completely overlapped on spectrum and appear as one peak. The A' (Tl-Br) stretch is completely symmetric and so has an intensity of 0 and does not appear on the spectrum.

The data above shows good general agreement with the literature from the wet lab <ref>Johan Blixt, Julius Glaser, Janos Mink, Ingmar Persson, Per Persson, Magnus Sandstroem, J. Am. Chem. Soc., 1995, 117 (18), pp 5089–5104. http://pubs.acs.org/doi/abs/10.1021/ja00123a011</ref>. However this data can only be used as a rough guide since the spectrum was taken in water. Unfortunately no prior computational literature could be found for TlBr<sub>3</sub> IR absorptions.

Analysis of the low frequencies shows that relative to the real absorptions they are small and close to zero suggesting the results are accurate. as discussed previously the closer the low frequency absorptions are to zero the more reliable the results.
<pre>
 Full mass-weighted force constant matrix:
 Low frequencies ---   -3.4213   -0.0026   -0.0004    0.0015    3.9367    3.9367
 Low frequencies ---   46.4289   46.4292   52.1449 </pre>

==What is a bond?==
It can be seen from some of the Jmol diagrams and pictures of the molecules throughout this module that sometimes a 'bond' is not drawn between two atoms where you would expect one. This is simply because GuassView program has set parameters for when a bond is drawn or not based on how far atoms are apart. The majority of these parameters are based on organic molecules and bond lengths, since inorganic bonds tend to be longer in general there is a high chance GaussView will not draw a bond between many of the atoms. This prompts the question what really is a bond? after-all it is clearly not a line drawn between two atoms. In reality a bond is the attraction of 2 atoms, for covalent bonds this is through the overlap of their atomic orbitals in order that they can share electron density. In metallic bonds this is the delocalisation of free negatively charged electrons across positively charged nuclei. Clearly in reality bonding is far more complex than simply being bonded, double bonded or not bonded at all, as the attraction between atoms does not occur in these digital steps, rather the extent of bonding is on a continuous scale.

=Isomers of Mo(CO)<sub>4</sub>L<sub>2</sub>=
The optimisation of the both the cis, and trans isomers were carried by moving up the basis sets from LANL2MB to LANL2DZ to LANL2DZ + extrabasis set. Vibrational analysis will then be run on the fully optimised structure. During second year inorganic synthesis labs this same complex was studied in the wet lab, in that case the L ligand that was used was the more common PPh<sub>3</sub>. In an ideal scenario this same ligand would be used in the computational calculations, however the large number of electrons in the Phenyl rings would have a large computational cost therefore they are replaced with Cl ligands which is a good choice since it will have a similar steric demand and contribute to bonding in similar manner.

==Geometry Optimisation of Mo(CO)<sub>4</sub>L<sub>2</sub>==
===LanL2MB Basis Set===
Having drawn each of the structures in GaussView 5.0, a loose optimisation was run over the structures using the LanL2MB basis set, which was very quick because it a small basis set, the '''LOG''' file can be found here <ref>http://hdl.handle.net/10042/to-12087</ref>. This is shown below.
===== cis - Mo(CO)<sub>4</sub>L<sub>2</sub> <jmol><jmolAppletButton>
<uploadedFileContents>Lanl2mb cis gc2109.mol</uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 1 2; measure 1 4; measure 1 10; measure 1 11; measure 11 16; measure 5 8; measure 2 6</script>
</jmolAppletButton>
</jmol> =====
[[Image:Cis lanl2mb summary gc2109.jpg|thumb|float:right|300px]]

[[Image:Cis lanl2mb energygraph gc2109.jpg|thumb|left|500px]]

[[Image:Cis lanl2mb RMSgraph gc2109.jpg|thumb|left|500px]]






























<pre>
     Item                    Value       Threshold      Converged?
 Maximum Force              0.000714     0.002500         YES
 RMS     Force              0.000192     0.001667         YES
 Maximum Displacement       0.009868     0.010000         YES
 RMS     Displacement       0.003501     0.006667         YES
 Predicted change in Energy=-4.775072D-06 
 Optimization completed.
    -- Stationary point found. </pre>



===== trans - Mo(CO)<sub>4</sub>L<sub>2</sub> <jmol><jmolAppletButton>
<uploadedFileContents>Lanl2mb trans gc2109.mol</uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 1 2; measure 1 4;measure 2 14; measure 1 5; measure 1 3; measure 4 11; measure 5 10 </script>
</jmolAppletButton>
</jmol>===== 
'''LOG''' file <ref>http://hdl.handle.net/10042/to-12088</ref>
[[Image:Trans lanl2mb summary gc2109.jpg|thumb|float:right|300px]]

[[Image:Trans lanl2mb energygraph gc2109.jpg |thumb|left|500px]]

[[Image:Trans lanl2mb RMSgraph gc2109.jpg|thumb|left|500px]]







































<pre>
      Item                   Value       Threshold     Converged?
 Maximum Force              0.000185     0.002500        YES
 RMS     Force              0.000056     0.001667        YES
 Maximum Displacement       0.002972     0.010000        YES
 RMS     Displacement       0.001019     0.006667        YES
 Predicted change in Energy=-6.046569D-07
 Optimization completed.
    -- Stationary point found.</pre>

===LanL2DZ Basis Set===
cis '''LOG''' file <ref>http://hdl.handle.net/10042/to-12089</ref>, trans '''LOG''' file <ref>http://hdl.handle.net/10042/to-12090</ref>.

The loosely optimised structures were then manually altered using the 'Dihedral Angle' function on GaussView 5.0. This was done so that future optimisation would not find a false minimum, rather than the global minimum. The trans isomer was made to have eclipsed PCl<sub>3</sub> groups by making the dihedral angle between Chlorine atoms 0 degrees. For the cis isomer the dihedral angle between one Cl atom and a carbonyl was forced to be 180degrees and then this same carbonyl group was given a 0 degree dihedral angle with a Cl atom on the other PCl<sub>3</sub> group.

Having completed this manual alteration both structures were re-optimised with the higher LanL2DZ basis set, the calculations were given the additional words 'int=unltrafine scf=conver=9' in the Gaussian Calculation Set-up. This is shown below.

===== cis - Mo(CO)<sub>4</sub>L<sub>2</sub> <jmol><jmolAppletButton>
<uploadedFileContents>Cis lanl2dz gc2109 optimised.mol</uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 1 2; measure 1 4; measure 1 10; measure 1 11; measure 11 16; measure 5 8; measure 2 6</script>
</jmolAppletButton>
</jmol>=====
[[Image:Cis lanl2dz summary gc2109.jpg|thumb|float:right|300px]]

[[Image:Cis lanl2dz energygraph gc2109.jpg|thumb|left|500px]]

[[Image:Cis lanl2dz RMSgraph gc2109.jpg|thumb|left|500px]]





































<pre>
      Item                  Value       Threshold     Converged?
 Maximum Force             0.000016     0.000450        YES
 RMS     Force             0.000005     0.000300        YES
 Maximum Displacement      0.000989     0.001800        YES
 RMS     Displacement      0.000270     0.001200        YES
 Predicted change in Energy=-7.775720D-09
 Optimization completed.
    -- Stationary point found.</pre>

===== trans - Mo(CO)<sub>4</sub>L<sub>2</sub> <jmol><jmolAppletButton>
<uploadedFileContents>Trans lanl2dz gc2109 - Copy.mol</uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 1 2; measure 1 4; measure 2 14; measure 1 5; measure 1 3; measure 4 11; measure 5 10</script>
</jmolAppletButton>
</jmol>=====
[[Image:Trans lanl2dz summary gc2109.jpg|thumb|float:right|300px]]

[[Image:Trans lanl2dz energygraph gc2109.jpg|thumb|left|500px]]

[[Image:Trans lanl2dz RMSgraph gc2109.jpg |thumb|left|500px]]




































<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000037     0.000450     YES
 RMS     Force            0.000012     0.000300     YES
 Maximum Displacement     0.000976     0.001800     YES
 RMS     Displacement     0.000169     0.001200     YES
 Predicted change in Energy=-3.384020D-08
 Optimization completed.
    -- Stationary point found. </pre>

===LanL2DZ plus Extra Basis Set, Including contribution of Phosphorus d Atomic Orbitals===
cis '''LOG''' file <ref>http://hdl.handle.net/10042/to-12091</ref>, trans '''LOG''' file <ref>http://hdl.handle.net/10042/to-12092</ref>.

===== cis - Mo(CO)<sub>4</sub>L<sub>2</sub> <jmol><jmolAppletButton>
<uploadedFileContents>Cis gc2109 extra basis.mol </uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 1 2; measure 1 4; measure 1 10; measure 1 11; measure 11 16; measure 5 8; measure 2 6</script>
</jmolAppletButton>
</jmol>=====
[[Image:Cis extra basis summary gc2109.jpg|thumb|float:right|300px]]

[[Image:Cis extrabasis energygraph gc2109.jpg|thumb|left|500px]]

[[Image:Cis extrabasis RMSgraph gc2109.jpg|thumb|left|500px]]





































<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000138     0.000450     YES
 RMS     Force            0.000044     0.000300     YES
 Maximum Displacement     0.001079     0.001800     YES
 RMS     Displacement     0.000409     0.001200     YES
 Predicted change in Energy=-2.380857D-07
 Optimization completed.
    -- Stationary point found. </pre>

===== trans - Mo(CO)<sub>4</sub>L<sub>2</sub> <jmol><jmolAppletButton>
<uploadedFileContents>Trans gc2109 extra basis.mol</uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 1 2; measure 1 4; measure 2 14; measure 1 5; measure 1 3; measure 4 11; measure 5 10</script>
</jmolAppletButton>
</jmol>=====
[[Image:Trans extra basis summary gc2109.jpg|thumb|float:right|300px]]

[[Image:Trans extrabasis energygraph gc2109.jpg|thumb|left|500px]]
[[Image:Trans extra basis RMSgraph gc2109.jpg|thumb|left|500px]]




































<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000027     0.000450     YES
 RMS     Force            0.000006     0.000300     YES
 Maximum Displacement     0.000336     0.001800     YES
 RMS     Displacement     0.000081     0.001200     YES
 Predicted change in Energy=-9.511944D-09
 Optimization completed.
    -- Stationary point found. </pre>

====Structural Analysis of Optimized Geometries====
{| class="wikitable" border="1" style="align: center"
|+Bond Lengths for both Isomers
! Bond !! Cis Isomer Bond Length (A) !! Trans Isomer Bond Length (A) !! Lit. Bond Length (cis) <ref>F. Albert. Cotton, Donald J. Darensbourg, Simonetta. Klein, Brian W. S. Kolthammer. Inorg. Chem., 1982, 21 (4), pp 1651–1655
  http://pubs.acs.org/doi/pdf/10.1021/ic00134a075</ref> !!Percentage Error (%)(cis)!! Lit. Bond Length (trans)<ref>D. W. Bennett, J. Chem. Cryst., 34(6), 2004, pp 353 - 359. http://www.springerlink.com/content/u5383x017700g761/fulltext.pdf</ref>!! Percentage Error (trans) (%)
|-
! C=O
| 1.17, 1.18 ||1.17, 1.18 || 1.15 || 2 || 1.15||  2
|-
! P-Cl
| 2.12 ||2.12 || - || - || - || -
|-
! Mo-C
| 2.02, 2.05|| 2.06 ||1.98, 2.05 || 0 || 1.87 || 10
|-
! Mo-P
|2.48 || 2.42 || 2.56 || 3 || 2.37 || 2
|-
|}

N.B The literature values for the cis isomer correspond to a Mo(CO)<sub>4</sub>(PPhMe<sub>2</sub>)(PPh<sub>3</sub>) molecule, whereas the literature values for the trans isomer correspond to a Mo(CO)<sub>4</sub>(PPh<sub>3</sub>)<sub>2</sub> molecule. This small difference in ligands should have little effect on the bond lengths seen above.

It can be seen from the percentage differences above that the results are in good agreement with the literature. A look at the bond lengths in the Jmol diagram reveals that as the optimisation is carried at higher level basis set the bond lengths in general shorten and become closer to the literature values seen. It can be concluded from this that taking into account the low lying d orbitals of heavier elements is worthwhile.

====Analysis of Stabilities of the Isomers====
From the summary files of the optimisation of each of the isomers the relative energies of the molecules can be used to predict which isomer is more stable, and therefore the thermodynamic product. It can be seen that after the final optimisation (including the extra basis set) the trans isomer is more stable, -623.6942 Hartrees, compared with -623.6929 Hartrees for the cis isomer. A conversion to the more familiar KJ/mol units can be carried by multiplying by 2625.50 <ref>http://mccammon.ucsd.edu/~dzhang/energy-unit-conv-table.html</ref>. This gives an energy difference of 3.41KJ/mol in favour of the trans isomer. This result is consistent with literature and the second year synthesis labs which found that the cis isomer is converted to the trans isomer at elevated temperatures. However the difference found computationally is not satisfactory to come to this conclusion since it is known that there is roughly a 10KJ/mol error in these calculations <ref>3rd Year Computational Chemistry Online Manual, Module 2, 2011</ref>.

The results do though show that taking account of the phosphorus d orbitals using the extrabasis made a big difference to the results: without the extra basis set optimisation it would have been found that the cis isomer is the most stable form by computational calculations.

Despite the possible error in the calculations, the final result is that the trans-isomer is more stable and this intuitively makes sense due to the high steric demand of the PPh<sub>3</sub>/ PCl<sub>3</sub> groups. Further increasing the size of these groups would accentuate the difference in energy. The only way the cis isomer could become the thermodynamic product would be to introduce a stabilising interaction between the 2 phosphorus groups, this could be achieved by adding an amine or hydroxyl group on one of the groups to enable Hydrogen bonding.

===Frequency Analysis===
cis '''LOG''' file <ref>http://hdl.handle.net/10042/to-12093</ref>, trans '''LOG''' file <ref>http://hdl.handle.net/10042/to-12094</ref>.

The fully optimised structures for both isomers were sent back to the HPC servers to find their vibrational frequencies. The absence of negative absorptions in both spectra (the lowest frequency absorptions are shown), indicate the optimisations carried out previously were successful.
==== cis - Mo(CO)<sub>4</sub>L<sub>2</sub> ====
[[Image:Freq summary data gc2109 cis extra basis.jpg|thumb|float:right|300px]]


























{| class="wikitable" border="1" style="align: center"
|+ Vibrational Modes for cis - Mo(CO)<sub>4</sub>L<sub>2</sub>
! Mode of Vibration !! Type of Vibrational Mode !! Intensity of Absorption !! Frequency of Absorption (cm<sup>-1</sup>) !! Literature value for Frequency (cm<sup>-1</sup>)<ref>Florence M. Nareetsile and N.J. Coville, Bull. Chem. Soc. Ethiop. 2011, 25(2). http://www.ajol.info/index.php/bcse/article/viewFile/65884/53602</ref>!! Percentage Error (%) !! Diagram !! Link to 3D animation
|-
! Rotation of the PCl<sub>3</sub> groups
| - || 0 || 12 || - || -|| [[Image:MODE1 12 CIS GC2109.jpg|thumb|centre|200px]] || [[Media:Mode1 cis gc2109.gif|Show Animation]]
|-
! Rotation of the PCl<sub>3</sub> groups
| - || 0 || 20|| - || -|| [[Image:MODE2 20 CIS GC2109.jpg|thumb|centre|200px]]|| [[Media:Mode2 cis gc2109.gif|Show Animation]]
|-
! Asymmetric Carbonyl Stretch (1)
| B<sub>2</sub>' || 1605 || 1938|| 1874|| 3 || [[Image:MODE3 1938 CIS GC2109.jpg|thumb|centre|200px]]|| [[Media:Mode3 cis gc2109.gif|Show Animation]]
|-
! Asymmetric Carbonyl Stretch (2)
| B<sub>2</sub> || 813 || 1942|| 1910|| 2 ||[[Image:MODE4 1942 CIS GC2109.jpg|thumb|centre|200px]]|| [[Media:Mode4 cis gc2109.gif|Show Animation]]
|-
! Stretch for all 4 Carbonyls (asymmetric)
| A<sub>1</sub>' || 588 || 1952|| 1926|| 1 ||[[Image:MODE5 1952 CIS GC2109.jpg|thumb|centre|200px]]|| [[Media:Mode5 cis gc2109.gif|Show Animation]]
|-
! Stretch for all 4 Carbonyls (symmetric)
|  A<sub>1</sub>' ||544||2019 ||2021|| 0 ||[[Image:MODE6 2019 CIS GC2109.jpg|thumb|centre|200px]]|| [[Media:Mode6 cis gc2109.gif|Show Animation]]
|-
|}

It can be seen from the above data that the cis isomer has 4 unique absorption corresponding to C=O stretches. The B2' and B2 stretches are overalaid on the IR spectrum and so can not be resolved from each other. This can be seen clearly in zoomed in IR spectrum below. The computational calculations agree well literature from the wet lab with the largest percentage difference seen above is 3%.

[[Image:Cis ir spectrum gc2109.jpg |thumb|centre|600px|IR spectrum for cis - Mo(CO)<sub>4</sub>L<sub>2</sub>]]

[[Image:Cis ir spectrum gc2109 zoomed.jpg |thumb|centre|600px |IR spectrum for cis - Mo(CO)<sub>4</sub>L<sub>2</sub> zoomed in on the carbonyl region]]

==== trans - Mo(CO)<sub>4</sub>L<sub>2</sub>====
[[Image:Trans freq extra basis final gc2109.jpg |thumb|float:right|300px]]




























{| class="wikitable" border="1" style="align: center"
|+Vibrational Modes for trans - Mo(CO)<sub>4</sub>L<sub>2</sub>
! Description for Mode of Vibration !! Type of Vibrational Mode !! Intensity of Absorption !! Frequency of Absorption (cm<sup>-1</sup>) !! Literature value for Frequency (cm<sup>-1</sup>)<ref>Anthony W. Brown and Anthony L. Diaz, J. Chem. Educ., 2010, 87 (9), pp 975–977. http://pubs.acs.org/doi/pdf/10.1021/ed1002477 </ref>!! Percentage Error (%) !! Diagram !! Link to 3D animation
|-
! Symmetric Rotation of PCl<sub>3</sub> bonds
| - || 5 || 46 || - || -|| [[Image:Mode 1 5cm gc2109 trans.jpg|thumb|centre|200px]] || [[Media:Mode 1 trans gc2109.gif|Show Animation]]
|-
! Asymmetric Rotation of PCl<sub>3</sub> bonds 
| - || 6 || 46|| - || -|| [[Image:Mode 2 6cm gc2109 trans.jpg |thumb|centre|200px]]|| [[Media:Mode 2 trans gc2109.gif|Show Animation]]
|-
! Asymmetric trans -Carbonyl stretch (1)
| E<sub>u</sub> || 1475 || 1950|| 1887|| 3 || [[Image:Mode 3 1950cm gc2109 trans.jpg|thumb|centre|200px]]|| [[Media:Mode 3 trans gc2109.gif|Show Animation]]
|-
! Asymmetric trans -Carbonyl stretch (2)
| E<sub>u</sub> || 1467 || 1951|| 1887|| 3 ||[[Image: Mode 4 1951cm gc2109 trans.jpg|thumb|centre|200px]]|| [[Media:Mode 4 trans gc2109.gif|Show Animation]]
|-
! Stretching Mode for all Carbonyls
| B<sub>1g</sub> || 1 || 1977|| - ||- ||[[Image:Mode 5 1977 gc2109 trans.jpg|thumb|centre|200px]]|| [[Media:Mode 5 trans gc2109.gif|Show Animation]]
|-
! Stretching Mode for all Carbonyls
| A<sub>1g</sub> || 4 || 2031|| -|| -||[[Image:Mode 6 2031 gc2109 trans.jpg|thumb|centre|200px]]|| [[Media:Mode 6 trans gc2109.gif|Show Animation]]
|-
|}

In contrast with the cis isomer, the trans isomer only has 1 unique vibrational absorption at 1950cm<sup>-1</sup>. This peak corresponds to the two E stretches which are degenerate. The absorptions at 1977cm<sup>-1</sup> and 2031cm<sup>-1</sup> are not seen in the vibrational spectrum because they are highly symmetric, little to no dipole moment being formed and so a very low intensity. The single peak corresponding to the C=O functionality can be seen clearly in the zoomed in IR spectrum. Again the computational calculations agree well literature from the wet lab with a low percentage difference.

[[Image:Spectrum gc2109 trans.jpg |thumb|centre|600px|IR spectrum for trans - Mo(CO)<sub>4</sub>L<sub>2</sub>]]

[[Image:Spectrum gc2109 trans zoomed.jpg|thumb|centre|600px|IR spectrum for trans - Mo(CO)<sub>4</sub>L<sub>2</sub> zoomed in on the carbonyl region]]

=Mini Project - Aromaticity in Metal Clusters =
==Introduction==
In recent years it was noticed by ''Li et al'' that all metal clusters such as Al<sub>4</sub><sup>2-</sup> can exhibit a large amount of resonance in a planar 4-membered ring, and that this aromaticity is not the same as that seen in normal Huckel aromatics such as C<sub>4</sub>H<sub>4</sub><sup>2+</sup>. By doing a count of each of the species valence electrons it is clear that they are not aromatic: the C<sub>4</sub>H<sub>4</sub><sup>2+</sup> 18 electrons whereas the all metal M<sub>4</sub><sup>2-</sup> species have only 14 electrons. The carbon di-cation exhibits classical bonding with 8 2-centre, 2-electron bonds (4 C-C + 4 C-H) and one 4-centre π aromatic bond, giving the molecule 4n+2 Huckel aromaticity. The metal clusters on the other hand are fundamentally electron deficient which gives rise to their unusual bonding: 8 electrons are taken up due to each metal having a lone pair, 2 are used in a 4-centre 2-electron π bond giving the metal cluster its π aromaticity. This leaves 4 electrons for 4 σ which is clearly not possible in a classical sense. It was found by ''Fowler et al.'' <ref>Fowler, R.W.A. Havenith, E. Steine

Chemical Physics Letters Volume 359, Issues 5–6, 27 June 2002, Pages 530–536</ref> that in Al<sub>4</sub><sup>2-</sup> it is the σ electrons in the ring that are responsible for a diamagnetic current induced by an external magnetic field. This is strong evidence to suggest that species such as Al<sub>4</sub><sup>2-</sup> are both σ and π aromatic.
In this Mini Project several isomers of Na<sub>2</sub>Al<sub>4</sub> will be investigated using the computational techniques learnt during the previous parts of the module. The role of the sodium is simply to stabilize the otherwise unstable aluminium dianion, this should not effect the electronic structure of the M<sub>4</sub><sup>2-</sup> dianion to a large extent.<ref>Alexander I. Boldyrev* and Aleksey E. Kuznetsov,
Inorg. Chem., 2002, 41 (3), pp 532–53

DOI: 10.1021/ic010840u

</ref>

The aim is to first to optimise the isomers of Aluminium and Gallium to find the most thermodynamically favoured arrangement, and once these are found to use MO and NBO analyses to illustrate the presence of both π and σ aromaticity.

==Optimisations==
First the structures were given a loose optimisation using the LanL2DZ pseudo potential basis set. Following this the 6113G(d) basis set was used to optimise the structures taking into account all the electrons and the d orbitals. This optimisation was completed an all the isomers, from these the D4h (square), Cs and D4h (pyramidal) were selected to be further optimised using the MP2 method.

The summary and '''LOG''' files for each of the optimisations is shown below:
{| class="wikitable" style="text-align:center"
|+ Optimisations for The Al Isomers
|- 
! !! D4h (square) !! Cs !! D4h (pyramidal) !! C2v  !! D2h
|-
| LanL2DZ|| - ||[[Image:Cs Al l2.jpg|thumb|250px|centre]]<jmol><jmolAppletButton>
<uploadedFileContents>Al Cs LanL2DZ.mol </uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 1 2; measure 1 4</script>
</jmolAppletButton>
</jmol> '''LOG''' file <ref>http://hdl.handle.net/10042/to-12103</ref>  ||[[Image:Bipy Al l2.jpg|thumb|250px|centre]]<jmol><jmolAppletButton>
<uploadedFileContents>Bipy Al L2Dz.mol </uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 1 2; measure 1 4</script>
</jmolAppletButton>
</jmol> '''LOG''' file <ref>http://hdl.handle.net/10042/to-12095</ref> ||[[Image:Al cis L2 summary.jpg|thumb|250px|centre]]<jmol><jmolAppletButton>
<uploadedFileContents>Cis Al L2DZ.mol </uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 1 2; measure 1 4</script>
</jmolAppletButton>
</jmol> '''LOG''' file <ref>http://hdl.handle.net/10042/to-12112</ref> ||[[Image:Al oppo L2 summary.jpg|thumb|250px|centre]] <jmol><jmolAppletButton>
<uploadedFileContents>Opposite Al LANL2DZ.mol </uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 1 2; measure 1 4</script>
</jmolAppletButton>
</jmol> '''LOG''' file <ref>http://hdl.handle.net/10042/to-12111</ref>
|-
| BLYP/ 6113-G(d)|| [[Image:Al sq gc2109.jpg|thumb|250px|centre]] <jmol><jmolAppletButton>
<uploadedFileContents>Al square gc2109 6113.mol</uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 1 2; measure 1 4</script>
</jmolAppletButton>
</jmol> '''LOG''' file <ref>http://hdl.handle.net/10042/to-12127</ref> ||[[Image:Al 6113 Cs summary.jpg  |thumb|250px|centre]] <jmol><jmolAppletButton>
<uploadedFileContents>Al Cs 6113.mol</uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 1 2; measure 1 4</script>
</jmolAppletButton>
</jmol> '''LOG''' file <ref>http://hdl.handle.net/10042/to-12097</ref>||[[Image:Al 6113 bipy summary.jpg|thumb|250px|centre]] <jmol><jmolAppletButton>
<uploadedFileContents>Bipy Al 6113.mol </uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 1 2; measure 1 4</script>
</jmolAppletButton>
</jmol> '''LOG''' file <ref>http://hdl.handle.net/10042/to-12096</ref>||[[Image:Al cis 6113 summary.jpg|thumb|250px|centre]]<jmol><jmolAppletButton>
<uploadedFileContents>Cis Al 6113.mol </uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 1 2; measure 1 4</script>
</jmolAppletButton>
</jmol> '''LOG''' file <ref>http://hdl.handle.net/10042/to-12116</ref> ||[[Image:Al oppo 6113 summary.jpg|thumb|250px|centre]]<jmol><jmolAppletButton>
<uploadedFileContents>Opposite Al 6113.mol </uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 1 2; measure 1 4</script>
</jmolAppletButton>
</jmol> '''LOG''' file <ref>http://hdl.handle.net/10042/to-12117</ref>
|-
| MP2/ 6113-G(d)||[[Image:Al mp2 square summary.jpg|thumb|250px|centre]]<jmol><jmolAppletButton>
<uploadedFileContents>Al square MP2 gc2109.mol</uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 1 2; measure 1 4</script>
</jmolAppletButton>
</jmol>'''LOG''' file <ref>http://hdl.handle.net/10042/to-12102</ref> ||[[Image:Al mp2 Cs summary.jpg|thumb|250px|centre]]<jmol><jmolAppletButton>
<uploadedFileContents>Al MP2 Cs.mol</uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 1 2; measure 1 4</script>
</jmolAppletButton>
</jmol> '''LOG''' file <ref>http://hdl.handle.net/10042/to-12099</ref>||[[Image:Al mp2 bipy summary.jpg|thumb|250px|centre]] <jmol><jmolAppletButton>
<uploadedFileContents>Al MP2 bipy.mol</uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 1 2; measure 1 4</script>
</jmolAppletButton>
</jmol>'''LOG''' file <ref>http://hdl.handle.net/10042/to-12101</ref>||- ||-
|-
|}

{| class="wikitable" style="text-align:center"
|+ Optimisations for The Ga Isomers
|- 
! !! D4h (square) !! Cs !! D4h (pyramidal) !! C2v  !! D2h
|-
| LanL2DZ||-||[[Image:Ga l2dz Cs summary.jpg|thumb|250px|centre]]<jmol><jmolAppletButton>
<uploadedFileContents>Ga Cs L2DZ.mol </uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 3 4; measure 3 5</script>
</jmolAppletButton>
</jmol> '''LOG''' file <ref>http://hdl.handle.net/10042/to-12104</ref> ||[[Image:Ga l2dz bipy summary.jpg|thumb|250px|centre]]<jmol><jmolAppletButton>
<uploadedFileContents>Bipy Ga L2DZ.mol</uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 3 4; measure 3 5</script>
</jmolAppletButton>
</jmol> '''LOG''' file <ref>http://hdl.handle.net/10042/to-12107</ref> ||[[Image:Ga cis L2 summary.jpg |thumb|250px|centre]]<jmol><jmolAppletButton>
<uploadedFileContents>Cis Ga L2DZ.mol </uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 3 4; measure 3 6</script>
</jmolAppletButton>
</jmol> '''LOG''' file <ref>http://hdl.handle.net/10042/to-12115</ref>  ||[[Image:Ga oppo L2 summary.jpg|thumb|250px|centre]] <jmol><jmolAppletButton>
<uploadedFileContents>Opposite Ga LANL2DZ.mol</uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 3 4; measure 3 6</script>
</jmolAppletButton>
</jmol> '''LOG''' file <ref>http://hdl.handle.net/10042/to-12114</ref> 
|-
| BLYP/ 6113-G(d)||[[Image:Ga gc2109.jpg |thumb|250px|centre]] <jmol><jmolAppletButton>
<uploadedFileContents>Ga Square 6113 gc2190.mol </uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 3 4; measure 3 5</script>
</jmolAppletButton>
</jmol> '''LOG''' file <ref>http://hdl.handle.net/10042/to-12128</ref> ||[[Image:Ga 6113 Cs summary.jpg |thumb|250px|centre]] <jmol><jmolAppletButton>
<uploadedFileContents>Ga Cs Attempt 2 6113.mol</uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 3 4; measure 3 5</script>
</jmolAppletButton>
</jmol> '''LOG''' file <ref>http://hdl.handle.net/10042/to-12105</ref> ||[[Image:Ga 6113 bipy summary.jpg|thumb|250px|centre]] <jmol><jmolAppletButton>
<uploadedFileContents>Ga bipy 6113.mol</uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 3 4; measure 3 5</script>
</jmolAppletButton>
</jmol> '''LOG''' file <ref>http://hdl.handle.net/10042/to-12106</ref>||[[Image:Ga cis 6113 summary.jpg|thumb|250px|centre]]<jmol><jmolAppletButton>
<uploadedFileContents>Cis Ga 6113.mol</uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 3 4; measure 3 5</script>
</jmolAppletButton>
</jmol> '''LOG''' file <ref>http://hdl.handle.net/10042/to-12118</ref> ||[[Image:Ga oppo 6113 summary.jpg |thumb|250px|centre]]<jmol><jmolAppletButton>
<uploadedFileContents>Opposite Ga 6113.mol</uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 3 4; measure 3 5</script>
</jmolAppletButton>
</jmol> '''LOG''' file <ref>http://hdl.handle.net/10042/to-12113</ref>
|-
| MP2/ 6113-G(d)||[[Image:Ga mp2 square summary.jpg|thumb|250px|centre]]<jmol><jmolAppletButton>
<uploadedFileContents>Ga square MP2 gc2109.mol</uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 3 4; measure 3 5</script>
</jmolAppletButton>
</jmol> '''LOG''' file <ref>http://hdl.handle.net/10042/to-12109</ref> ||[[Image:Ga mp2 Cs summary.jpg|thumb|250px|centre]]<jmol><jmolAppletButton>
<uploadedFileContents>Ga MP2 Cs.mol </uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 3 5; measure 3 4</script>
</jmolAppletButton>
</jmol> '''LOG''' file <ref>http://hdl.handle.net/10042/to-12108</ref>||[[Image:Ga mp2 bipy summary.jpg|thumb|250px|centre]]<jmol><jmolAppletButton>
<uploadedFileContents>Bipy Ga MP2.mol </uploadedFileContents>
<text>VIEW 3D</text>
<script>background=black; measure 3 5; measure 3 4</script>
</jmolAppletButton>
</jmol>'''LOG''' file <ref>http://hdl.handle.net/10042/to-12110</ref> ||- ||-
|-
|}

It can seen from the energies in the summary files and the Jmol diagrams that in general as you move down the table the energy of the molecules goes down, and the bond lengths in the structures goes down.

It can also be seen that the energy of the Cs isomer is the most thermodynamically stable in the case of both aluminium and gallium. The energies produced by the calculations as a whole are in perfect agreement with the literature, with the D4h (pyramidal) structure being the second most stable isomer. For both Gallium and Aluminium the D2h isomer was clearly the least stable isomer by some margin.

It should be noted that the Gallium isomers were all more stable than there Aluminium counterparts due to their more diffuse atomic orbitals allowing for greater overlap.

Since the Cs and D4h (pyramidal) isomers are the most stable these geometries are concentrated on most for the future calculations.

==Molecular Orbital Analysis==
{| class="wikitable" style="text-align:center"
|+ MOs for The Al Isomers
|- 
! !! D4h (square) <ref>http://hdl.handle.net/10042/to-12120</ref>!! Cs <ref>http://hdl.handle.net/10042/to-12098</ref> !! D4h (pyramidal) <ref>http://hdl.handle.net/10042/to-12119</ref> !! C2v  <ref>http://hdl.handle.net/10042/to-12122</ref> !! D2h <ref>http://hdl.handle.net/10042/to-12121</ref>
|-
| LUMO||[[Image:Al square LUMO.jpg |thumb|125px|centre]] ||[[Image:Al Cs LUMO.jpg |thumb|125px|centre]] ||[[Image:Al bipy LUMO.jpg|thumb|125px|centre]] ||[[Image:Al cis LUMO.jpg|thumb|125px|centre]] ||[[Image:Al oppo LUMO.jpg|thumb|125px|centre]] 
|-
| HOMO||[[Image:Al square HOMO.jpg|thumb|125px|centre]] ||[[Image:Al Cs HOMO.jpg|thumb|125px|centre]] ||[[Image:Al bipy HOMO.jpg|thumb|125px|centre]] ||[[Image:Al cis HOMO.jpg |thumb|125px|centre]] ||[[Image:Al oppo HOMO.jpg |thumb|125px|centre]]
|-
| HOMO-1||[[Image:Al square HOMO-1.jpg|thumb|125px|centre]] ||[[Image:Al Cs HOMO-1.jpg|thumb|125px|centre]] ||[[Image:Al bipy HOMO-1.jpg|thumb|125px|centre]] ||[[Image:Al cis HOMO-1.jpg|thumb|125px|centre]] ||[[Image:Al oppo HOMO-1.jpg|thumb|125px|centre]]
|-
| HOMO-2||[[Image:Al square HOMO-2.jpg |thumb|125px|centre]] ||[[Image:Al Cs HOMO-2.jpg|thumb|125px|centre]] ||[[Image:Al bipy HOMO-2.jpg |thumb|125px|centre]] ||[[Image:Al cis HOMO-2.jpg|thumb|125px|centre]] ||[[Image:Al oppo HOMO-2.jpg|thumb|125px|centre]] 
|-
| HOMO-3||[[Image:Al square HOMO-3.jpg|thumb|125px|centre]] ||[[Image:Al Cs HOMO-3.jpg|thumb|125px|centre]] ||[[Image:Al bipy HOMO-3.jpg |thumb|125px|centre]] ||[[Image:Al cis HOMO-3.jpg|thumb|125px|centre]] ||[[Image:Al oppo HOMO-3.jpg|thumb|125px|centre]] 
|-
| HOMO-4||[[Image:Al square HOMO-4.jpg|thumb|125px|centre]] ||[[Image:Al Cs HOMO-4.jpg|thumb|125px|centre]] ||[[Image:Al bipy HOMO-4.jpg|thumb|125px|centre]] ||[[Image:Al cis HOMO-4.jpg |thumb|125px|centre]] ||[[Image:Al oppo HOMO-4.jpg|thumb|125px|centre]] 
|-
| HOMO-5||[[Image:Al square HOMO-5.jpg|thumb|125px|centre]] ||[[Image:Al Cs HOMO-5.jpg |thumb|125px|centre]] ||[[Image:Al bipy HOMO-5.jpg|thumb|125px|centre]] ||[[Image:Al cis HOMO-5.jpg|thumb|125px|centre]] ||[[Image:Al oppo HOMO-5.jpg |thumb|125px|centre]] 
|-
| HOMO-6|| - ||[[Image:Al Cs HOMO-6.jpg |thumb|125px|centre]] ||[[Image:Al bipy HOMO-6.jpg|thumb|125px|centre]] ||[[Image:Al cis HOMO-6.jpg |thumb|125px|centre]] ||[[Image:Al oppo HOMO-6.jpg  |thumb|125px|centre]] 
|-
|}

{| class="wikitable" style="text-align:center"
|+ MOs for The Ga Isomers
|- 
! !! D4h (square)<ref>http://hdl.handle.net/10042/to-12124</ref> !! Cs <ref>http://hdl.handle.net/10042/to-12123</ref>!! D4h (pyramidal) <ref>http://hdl.handle.net/10042/to-12110</ref> !! C2v  <ref>http://hdl.handle.net/10042/to-12126</ref>!! D2h<ref>http://hdl.handle.net/10042/to-12125</ref>
|-
| LUMO||[[Image:Galumosquaregc2109.jpg|thumb|125px|centre]] ||[[Image:Ga Cs LUMO.jpg|thumb|125px|centre]] ||[[Image:Ga bipy LUMO.jpg|thumb|125px|centre]] ||[[Image:Ga cis LUMO.jpg|thumb|125px|centre]] ||[[Image:Ga oppo LUMO.jpg|thumb|125px|centre]] 
|-
| HOMO||[[Image:Ga square HOMO.jpg|thumb|125px|centre]] ||[[Image:Ga Cs HOMO.jpg|thumb|125px|centre]] ||[[Image:Ga bipy HOMO.jpg |thumb|125px|centre]] ||[[Image:Ga cis HOMO.jpg|thumb|125px|centre]] ||[[Image:Ga oppo HOMO.jpg|thumb|125px|centre]]
|-
| HOMO-1||[[Image:Ga square HOMO+1.jpg|thumb|125px|centre]] ||[[Image:Ga Cs HOMO-1.jpg|thumb|125px|centre]] ||[[Image:Ga bipy HOMO-1.jpg|thumb|125px|centre]] ||[[Image:Ga cis HOMO-1.jpg|thumb|125px|centre]] ||[[Image:Ga oppo HOMO-1.jpg|thumb|125px|centre]]
|-
| HOMO-2||[[Image:Ga square HOMO+2.jpg|thumb|125px|centre]] ||[[Image:Ga Cs HOMO-2.jpg|thumb|125px|centre]] ||[[Image:Ga bipy HOMO-2.jpg|thumb|125px|centre]] ||[[Image:Ga cis HOMO-2.jpg |thumb|125px|centre]] ||[[Image:Ga oppo HOMO-2.jpg|thumb|125px|centre]] 
|-
| HOMO-3||[[Image:Ga square HOMO+3.jpg|thumb|125px|centre]] ||[[Image:Ga Cs HOMO-3.jpg|thumb|125px|centre]] ||[[Image:Ga bipy HOMO-3.jpg|thumb|125px|centre]] ||[[Image:Ga cis HOMO-3.jpg|thumb|125px|centre]] ||[[Image:Ga oppo HOMO-3.jpg|thumb|125px|centre]] 
|-
| HOMO-4||[[Image:Ga square HOMO+4.jpg|thumb|125px|centre]] ||[[Image:Ga Cs HOMO-4.jpg|thumb|125px|centre]] ||[[Image:Ga bipy HOMO-4.jpg|thumb|125px|centre]] ||[[Image:Ga cis HOMO-4.jpg|thumb|125px|centre]] ||[[Image:Ga oppo HOMO-4.jpg |thumb|125px|centre]] 
|-
| HOMO-5||[[Image:Ga square HOMO+5.jpg |thumb|125px|centre]] ||[[Image:Ga Cs HOMO-5.jpg|thumb|125px|centre]] ||[[Image:Ga bipy HOMO-5.jpg|thumb|125px|centre]] ||[[Image:Ga cis HOMO-5.jpg|thumb|125px|centre]] ||[[Image:Ga oppo HOMO-5.jpg|thumb|125px|centre]] 
|-
| HOMO-6|| - ||[[Image:Ga Cs HOMO-6.jpg|thumb|125px|centre]] ||[[Image:Ga bipy HOMO-6.jpg|thumb|125px|centre]] ||[[Image:Ga cis HOMO-6.jpg|thumb|125px|centre]] ||[[Image:Ga oppo HOMO-6.jpg |thumb|125px|centre]] 
|-
|}

The MO diagrams above correlate well with those seen in the literature.<ref>Constantinos A. Tsipis, Coordination Chemistry Reviews, Volume 249, Issue 24, 15 December 2005, Pages 2740–2762</ref> It can be seen that in general the MO's have a very similar structure for all of the isomers, although the order of them is different between some of the isomers. This is an indication that the sodium does indeed have little effect on the electronic structure of the dianion. In addition the MOs are clearly very similar for the Aluminium and Gallium which is to be expected.

It can be seen from the MO diagrams that the HOMO corresponds to the π aromatic electrons across the 4 metal centres. The HOMO-3 to HOMO-6 molecular orbitals correspond to the Aluminium / Gallium lone pairs. Finally the HOMO-1 and HOMO-2 molecular orbitals correspond to the σ bonding orbitals.

A comparison between the MOs above and the MOs for  C<sub>4</sub>H<sub>4</sub><sup>2+</sup> shows that the electronic structures of these molecules is quite different. Most importantly there is a difference between the HOMO-2 of each of the species, the carbon ring has a HOMO-2 which corresponds to π bond, whereas the HOMO-2 in the metal clusters corresponds to an aromatic σ bonding interaction. This will be analysed further in the NBO analyses.

{| class="wikitable" border="1"
|+ MOs for C<sub>4</sub>H<sub>4</sub><sup>2+</sup>
|-align="bottom" | caption
! HOMO !! HOMO-1 !! HOMO-2 !! HOMO-3 !! HOMO-4 !! HOMO-5 !! HOMO-6
|-
|  [[Image:Homo gc2109.jpg|thumb|125px]] ||  [[Image:Homo-1 gc2109.jpg |thumb|125px]] || [[Image:Homo-2 gc2109.jpg|thumb|125px]] ||  [[Image:Homo-3 gc2109.jpg |thumb|125px]] ||  [[Image:Homo-4 gc2109.jpg|thumb|125px ]] || [[Image:Homo-5 gc2109.jpg |thumb|125px]] || [[Image:Homo-6 gc2109.jpg|thumb|125px]] 
|}

===Effect of Sodium===
To analyse the stabilising effect of sodium on the dianion the energy of a lone sodium atom was found by optimising its structure GaussView 5.0. This was found to be -161.8460 a.u. Next the energy of the Al<sub>4</sub><sup>2-</sup> fragment is taken from the earlier optimisation, =-7699.4640. The energy of these fragments added together is then compared with the energy of a molecule which is bonded to the sodium atoms (-1291.6439), to reveal the stability gained from the sodium.

Therefore Stabilisation Energy = -1291.6439 - ((2 x -161.8460)-967.7997)= -0.1522 a.u. or -399KJ/mol.

Clearly this is a very stabilising interaction.

==NBO Analyses==
{| class="wikitable" style="text-align:center"
|+ NBOs for The Al Isomers
|- 
! !! D4h (square) !! Cs !! D4h (pyramidal)
|-
| NBO||[[Image:Al square MP2.jpg|thumb|350px|centre]] ||[[Image:Al Cs MP2.jpg|thumb|350px|centre]] ||[[Image:Al bipy MP2.jpg|thumb|350px|centre]] 
|-
|}

{| class="wikitable" style="text-align:center"
|+ NBOs for The Ga Isomers
|- 
! !! D4h (square) !! Cs !! D4h (pyramidal)
|-
| NBO||[[Image:Ga square MP2.jpg|thumb|350px|centre]] ||[[Image:Ga Cs MP2.jpg|thumb|350px|centre]] ||[[Image:Ga bipy MP2.jpg|thumb|350px|centre]] 
|-
|}

It can be seen from the NBOs above that the electrons are spread fairly evenly across the molecules, this is particularly evident in the D4h square molecules, where the electrons are spread exactly evenly, which is to be expected since the molecules are so symmetric. As a result of its higher electronegativity there is more electron density on the Boron atoms than the Sodium atoms in general

N.B some data has been removed from the Second Order Perturbation information shown below so that the more relevant and important data is clearer.
===Analysis of Aluminium Cs===
<pre>
Second Order Perturbation Theory Analysis of Fock Matrix in NBO Basis

     Threshold for printing:   0.50 kcal/mol
    (Intermolecular threshold: 0.05 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
   1. BD (   1)Al   1 -Al   2        /176. BD*(   1)Al   1 -Al   3           41.54    0.34    0.108
   1. BD (   1)Al   1 -Al   2        /179. BD*(   1)Al   2 -Al   4           41.54    0.34    0.108
   2. BD (   1)Al   1 -Al   3        /175. BD*(   1)Al   1 -Al   2           25.63    0.34    0.089
   2. BD (   1)Al   1 -Al   3        /177. BD*(   1)Al   1 -Al   4           26.99    0.36    0.093
   2. BD (   1)Al   1 -Al   3        /178. BD*(   1)Al   2 -Al   3           22.75    0.36    0.086
   2. BD (   1)Al   1 -Al   3        /180. BD*(   1)Al   3 -Al   4           48.56    0.30    0.112
   3. BD (   1)Al   1 -Al   4        /176. BD*(   1)Al   1 -Al   3           45.36    0.38    0.121
   3. BD (   1)Al   1 -Al   4        /179. BD*(   1)Al   2 -Al   4           21.18    0.38    0.083
   4. BD (   1)Al   2 -Al   3        /176. BD*(   1)Al   1 -Al   3           21.18    0.38    0.083
   4. BD (   1)Al   2 -Al   3        /179. BD*(   1)Al   2 -Al   4           45.36    0.38    0.121
   5. BD (   1)Al   2 -Al   4        /175. BD*(   1)Al   1 -Al   2           25.63    0.34    0.089
   5. BD (   1)Al   2 -Al   4        /177. BD*(   1)Al   1 -Al   4           22.75    0.36    0.086
   5. BD (   1)Al   2 -Al   4        /178. BD*(   1)Al   2 -Al   3           26.99    0.36    0.093
   5. BD (   1)Al   2 -Al   4        /180. BD*(   1)Al   3 -Al   4           48.56    0.30    0.112
   6. BD (   1)Al   3 -Al   4        /176. BD*(   1)Al   1 -Al   3           35.26    0.38    0.106
   6. BD (   1)Al   3 -Al   4        /179. BD*(   1)Al   2 -Al   4           35.26    0.38    0.106
  39. LP (   1)Al   3                / 37. LP*(   1)Al   1                   19.88    0.02    0.030
  39. LP (   1)Al   3                / 38. LP*(   1)Al   2                  154.65    0.02    0.083
  40. LP*(   1)Al   4                / 37. LP*(   1)Al   1                  154.65    0.02    0.083
  40. LP*(   1)Al   4                / 38. LP*(   1)Al   2                   19.88    0.02    0.030
  37. LP*(   1)Al   1                / 41. LP*(   1)Na   5                   46.05    0.03    0.056
  38. LP*(   1)Al   2                / 41. LP*(   1)Na   5                   46.05    0.03    0.056
  39. LP (   1)Al   3                / 41. LP*(   1)Na   5                   39.90    0.06    0.064
  40. LP*(   1)Al   4                / 41. LP*(   1)Na   5                   39.90    0.06    0.064
   6. BD (   1)Al   3 -Al   4        / 45. LP*(   1)Na   6                   22.78    0.58    0.105
  45. LP*(   1)Na   6                /174. RY*(  21)Na   6      </pre>

The data below is strong evidence for the resonance and σ aromaticity discussed previously. It can be seen from line 39. that there is a very large stabilizing interaction of 155kcal/mol corresponding to the donation of electrons from the lone pair on Al(3) into the antibonding lone pair on Al(2). An equal interaction is seen from the antibonding lone pair on Al(1) into the antibonding Al(2). It can be seen that in general there is a large amount of stabilisation gained in the molecule by resonance.

<pre>
  (Occupancy)   Bond orbital/ Coefficients/ Hybrids
 ---------------------------------------------------------------------------------
     1. (1.73592) BD ( 1)Al   1 -Al   2 
                ( 50.00%)   0.7071*Al   1 s( 37.15%)p 1.68( 62.51%)d 0.01(  0.34%)
                                            0.0000 -0.0011  0.6094  0.0033 -0.0080
                                            0.0013 -0.0001  0.0003 -0.0154 -0.0039
                                            0.0078 -0.0022 -0.0001 -0.0003 -0.3007
                                            0.0143 -0.0135 -0.0001  0.0003  0.0000
                                           -0.7307  0.0102  0.0005 -0.0059  0.0000
                                            0.0006  0.0067  0.0059  0.0042  0.0574
                ( 50.00%)   0.7071*Al   2 s( 37.15%)p 1.68( 62.51%)d 0.01(  0.34%)
                                            0.0000 -0.0011  0.6094  0.0033 -0.0080
                                            0.0013 -0.0001  0.0003 -0.0154 -0.0039
                                            0.0078 -0.0022 -0.0001 -0.0003 -0.3007
                                            0.0143 -0.0135 -0.0001  0.0003  0.0000
                                            0.7307 -0.0102 -0.0005  0.0059  0.0000
                                            0.0006 -0.0067 -0.0059  0.0042  0.0574
     2. (1.60474) BD ( 1)Al   1 -Al   3 
                ( 39.74%)   0.6304*Al   1 s( 19.32%)p 4.16( 80.40%)d 0.01(  0.28%)
                                            0.0000 -0.0009  0.4377  0.0330  0.0226
                                           -0.0014  0.0000 -0.0002  0.0495  0.0140
                                           -0.0029 -0.0006 -0.0002 -0.0012 -0.6380
                                           -0.0544  0.0011 -0.0048 -0.0005  0.0005
                                            0.6249  0.0276  0.0018  0.0007  0.0002
                                            0.0093 -0.0094  0.0392  0.0298 -0.0156
                ( 60.26%)   0.7763*Al   3 s( 16.06%)p 5.21( 83.72%)d 0.01(  0.22%)
                                            0.0000 -0.0001  0.3997  0.0284  0.0008
                                           -0.0010  0.0002 -0.0002  0.0492  0.0068
                                            0.0119  0.0034 -0.0002 -0.0002  0.6527
                                            0.0284  0.0131  0.0018  0.0006 -0.0006
                                           -0.6384  0.0048  0.0066 -0.0074  0.0000
                                           -0.0060  0.0091  0.0350  0.0126 -0.0266
     3. (1.75442) BD ( 1)Al   1 -Al   4 
                ( 47.34%)   0.6880*Al   1 s( 43.69%)p 1.28( 55.97%)d 0.01(  0.35%)
                                            0.0000 -0.0010  0.6599 -0.0360 -0.0107
                                            0.0008  0.0000  0.0003 -0.0135 -0.0117
                                            0.0078 -0.0020 -0.0001  0.0003  0.7011
                                           -0.0071 -0.0032  0.0125  0.0002  0.0005
                                            0.2591 -0.0184  0.0118 -0.0008  0.0000
                                           -0.0065  0.0004 -0.0006 -0.0485 -0.0326
                ( 52.66%)   0.7257*Al   4 s( 42.42%)p 1.35( 57.30%)d 0.01(  0.28%)
                                            0.0000 -0.0008  0.6510 -0.0075  0.0172
                                            0.0006 -0.0001  0.0003  0.0116 -0.0096
                                           -0.0049 -0.0007 -0.0001 -0.0001 -0.6938
                                           -0.0184  0.0099 -0.0033 -0.0004  0.0000
                                            0.3008 -0.0177 -0.0143 -0.0008 -0.0001
                                            0.0032 -0.0017 -0.0108 -0.0441 -0.0268
     4. (1.75442) BD ( 1)Al   2 -Al   3 
                ( 47.34%)   0.6880*Al   2 s( 43.69%)p 1.28( 55.97%)d 0.01(  0.35%)
                                            0.0000 -0.0010  0.6599 -0.0360 -0.0107
                                            0.0008  0.0000  0.0003 -0.0135 -0.0117
                                            0.0078 -0.0020 -0.0001  0.0003  0.7011
                                           -0.0071 -0.0032  0.0125  0.0002 -0.0005
                                           -0.2591  0.0184 -0.0118  0.0008  0.0000
                                           -0.0065 -0.0004  0.0006 -0.0485 -0.0326
                ( 52.66%)   0.7257*Al   3 s( 42.42%)p 1.35( 57.30%)d 0.01(  0.28%)
                                            0.0000 -0.0008  0.6510 -0.0075  0.0172
                                            0.0006 -0.0001  0.0003  0.0116 -0.0096
                                           -0.0049 -0.0007 -0.0001 -0.0001 -0.6938
                                           -0.0184  0.0099 -0.0033 -0.0004  0.0000
                                           -0.3008  0.0177  0.0143  0.0008  0.0001
                                            0.0032  0.0017  0.0108 -0.0441 -0.0268
     5. (1.60474) BD ( 1)Al   2 -Al   4 
                ( 39.74%)   0.6304*Al   2 s( 19.32%)p 4.16( 80.40%)d 0.01(  0.28%)
                                            0.0000 -0.0009  0.4377  0.0330  0.0226
                                           -0.0014  0.0000 -0.0002  0.0495  0.0140
                                           -0.0029 -0.0006 -0.0002 -0.0012 -0.6380
                                           -0.0544  0.0011 -0.0048 -0.0005 -0.0005
                                           -0.6249 -0.0276 -0.0018 -0.0007 -0.0002
                                            0.0093  0.0094 -0.0392  0.0298 -0.0156
                ( 60.26%)   0.7763*Al   4 s( 16.06%)p 5.21( 83.72%)d 0.01(  0.22%)
                                            0.0000 -0.0001  0.3997  0.0284  0.0008
                                           -0.0010  0.0002 -0.0002  0.0492  0.0068
                                            0.0119  0.0034 -0.0002 -0.0002  0.6527
                                            0.0284  0.0131  0.0018  0.0006  0.0006
                                            0.6384 -0.0048 -0.0066  0.0074  0.0000
                                           -0.0060 -0.0091 -0.0350  0.0126 -0.0266
     6. (1.71270) BD ( 1)Al   3 -Al   4 
                ( 50.00%)   0.7071*Al   3 s( 41.20%)p 1.42( 58.60%)d 0.00(  0.21%)
                                            0.0000 -0.0009  0.6415 -0.0201 -0.0011
                                            0.0006 -0.0002  0.0002  0.0336 -0.0031
                                           -0.0131 -0.0043  0.0000 -0.0001  0.2961
                                            0.0150 -0.0009  0.0022  0.0001 -0.0001
                                            0.7047 -0.0064  0.0025  0.0052 -0.0007
                                            0.0009 -0.0026  0.0086 -0.0126  0.0426
                ( 50.00%)   0.7071*Al   4 s( 41.20%)p 1.42( 58.60%)d 0.00(  0.21%)
                                            0.0000 -0.0009  0.6415 -0.0201 -0.0011
                                            0.0006 -0.0002  0.0002  0.0336 -0.0031
                                           -0.0131 -0.0043  0.0000 -0.0001  0.2961
                                            0.0150 -0.0009  0.0022  0.0001  0.0001
                                           -0.7047  0.0064 -0.0025 -0.0052  0.0007
                                            0.0009  0.0026 -0.0086 -0.0126  0.0426</pre>

The occupancy data above suggests the geometry of the Al atoms in the ring is sp2 like however there are clear distortions from this due to the strain produced by the ring. The fact that all the interaction before the non-bonding core s orbital is reached are bonding interactions strongly suggests electrons are being spread across the structure leading to aromaticity.

===Analysis of Aluminium D4h pyramidal===
<pre>
Second Order Perturbation Theory Analysis of Fock Matrix in NBO Basis

     Threshold for printing:   0.50 kcal/mol
    (Intermolecular threshold: 0.05 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
   2. BD (   1)Al   1 -Al   3        / 37. LP (   1)Al   2                   35.49    0.15    0.068
   2. BD (   1)Al   1 -Al   3        / 40. LP (   1)Al   4                   35.49    0.15    0.068
   2. BD (   1)Al   1 -Al   3        /176. BD*(   1)Al   1 -Al   2           33.18    0.28    0.087
   2. BD (   1)Al   1 -Al   3        /178. BD*(   1)Al   1 -Al   4           33.18    0.28    0.087
   2. BD (   1)Al   1 -Al   3        /179. BD*(   1)Al   2 -Al   3           33.18    0.28    0.087
   2. BD (   1)Al   1 -Al   3        /180. BD*(   1)Al   3 -Al   4           33.18    0.28    0.087
   5. BD (   1)Al   3 -Al   4        /177. BD*(   1)Al   1 -Al   3           31.55    0.38    0.101
  37. LP (   1)Al   2                /176. BD*(   1)Al   1 -Al   2           51.13    0.13    0.108
  37. LP (   1)Al   2                /178. BD*(   1)Al   1 -Al   4           19.33    0.13    0.066
  37. LP (   1)Al   2                /179. BD*(   1)Al   2 -Al   3           51.12    0.13    0.108
  37. LP (   1)Al   2                /180. BD*(   1)Al   3 -Al   4           19.33    0.13    0.066
  40. LP (   1)Al   4                /176. BD*(   1)Al   1 -Al   2           19.33    0.13    0.066
  40. LP (   1)Al   4                /178. BD*(   1)Al   1 -Al   4           51.13    0.13    0.108
  40. LP (   1)Al   4                /179. BD*(   1)Al   2 -Al   3           19.33    0.13    0.066
  40. LP (   1)Al   4                /180. BD*(   1)Al   3 -Al   4           51.12    0.13    0.108</pre>

It can be seen from the data above that while there is still a large amount of resonance stabilisation in the D4h geometry it is to a lesser extent and there are no interactions above 100kcal/mol like those seen in the Cs geometry. This may explain why the Cs geometry is more thermodynamically stable.

<pre>

(Occupancy)   Bond orbital/ Coefficients/ Hybrids
 ---------------------------------------------------------------------------------
     1. (1.78942) BD ( 1)Al   1 -Al   2 
                ( 43.80%)   0.6618*Al   1 s( 41.30%)p 1.41( 58.33%)d 0.01(  0.37%)
                                            0.0000 -0.0012  0.6422 -0.0076 -0.0216
                                            0.0007  0.0000  0.0003  0.3749 -0.0230
                                           -0.0201 -0.0033  0.0000 -0.0001  0.6604
                                            0.0000  0.0034  0.0058 -0.0008  0.0000
                                           -0.0750 -0.0004 -0.0007 -0.0008  0.0001
                                            0.0134 -0.0019 -0.0112 -0.0541 -0.0219
                ( 56.20%)   0.7497*Al   2 s( 49.92%)p 1.00( 49.73%)d 0.01(  0.35%)
                                            0.0000 -0.0012  0.7065  0.0021 -0.0100
                                            0.0000  0.0000  0.0004  0.4490 -0.0113
                                           -0.0159 -0.0004  0.0003  0.0001 -0.5383
                                            0.0140  0.0049 -0.0016  0.0008  0.0000
                                            0.0726 -0.0019 -0.0008  0.0002 -0.0001
                                           -0.0010 -0.0006 -0.0084 -0.0579 -0.0056
     2. (1.62717) BD ( 1)Al   1 -Al   3 
                ( 50.00%)   0.7071*Al   1 s( 17.58%)p 4.66( 81.97%)d 0.03(  0.44%)
                                            0.0000 -0.0005  0.4173  0.0284  0.0300
                                           -0.0018  0.0001  0.0004  0.5563  0.0246
                                            0.0079  0.0092  0.0003 -0.0005 -0.7066
                                           -0.0312 -0.0101 -0.0117 -0.0004  0.0001
                                            0.0948  0.0042  0.0014  0.0016  0.0001
                                            0.0469 -0.0067  0.0116  0.0111  0.0441
                ( 50.00%)   0.7071*Al   3 s( 17.58%)p 4.66( 81.97%)d 0.03(  0.44%)
                                            0.0000 -0.0005  0.4173  0.0284  0.0300
                                           -0.0018  0.0001 -0.0004 -0.5563 -0.0246
                                           -0.0079 -0.0092 -0.0003  0.0005  0.7066
                                            0.0313  0.0101  0.0117  0.0004 -0.0001
                                           -0.0948 -0.0042 -0.0014 -0.0016 -0.0001
                                            0.0469 -0.0067  0.0116  0.0111  0.0441
     3. (1.78942) BD ( 1)Al   1 -Al   4 
                ( 43.80%)   0.6618*Al   1 s( 41.30%)p 1.41( 58.33%)d 0.01(  0.37%)
                                            0.0000 -0.0012  0.6422 -0.0076 -0.0216
                                            0.0007  0.0000  0.0001 -0.7357  0.0055
                                            0.0015 -0.0049  0.0007 -0.0003 -0.2021
                                            0.0221  0.0202  0.0046 -0.0002  0.0000
                                            0.0135 -0.0026 -0.0024 -0.0006  0.0000
                                           -0.0136  0.0031  0.0016  0.0546 -0.0231
                ( 56.20%)   0.7497*Al   4 s( 49.92%)p 1.00( 49.73%)d 0.01(  0.35%)
                                            0.0000 -0.0012  0.7065  0.0021 -0.0100
                                            0.0000  0.0000 -0.0002  0.4178 -0.0109
                                           -0.0009  0.0016 -0.0009 -0.0003 -0.5626
                                            0.0142  0.0165  0.0000 -0.0001  0.0000
                                            0.0751 -0.0019 -0.0020  0.0000  0.0000
                                           -0.0280  0.0044  0.0044  0.0509 -0.0069
     4. (1.78942) BD ( 1)Al   2 -Al   3 
                ( 56.20%)   0.7497*Al   2 s( 49.92%)p 1.00( 49.73%)d 0.01(  0.35%)
                                            0.0000 -0.0012  0.7065  0.0021 -0.0100
                                            0.0000  0.0000  0.0002 -0.4178  0.0109
                                            0.0009 -0.0016  0.0009  0.0003  0.5626
                                           -0.0142 -0.0165  0.0000  0.0001  0.0000
                                           -0.0751  0.0019  0.0020  0.0000  0.0000
                                           -0.0280  0.0044  0.0044  0.0509 -0.0069
                ( 43.80%)   0.6618*Al   3 s( 41.30%)p 1.41( 58.33%)d 0.01(  0.37%)
                                            0.0000 -0.0012  0.6422 -0.0076 -0.0216
                                            0.0007  0.0000 -0.0001  0.7357 -0.0055
                                           -0.0015  0.0049 -0.0007  0.0003  0.2021
                                           -0.0221 -0.0202 -0.0046  0.0002  0.0000
                                           -0.0135  0.0026  0.0024  0.0006  0.0000
                                           -0.0136  0.0031  0.0016  0.0546 -0.0231
     5. (1.78942) BD ( 1)Al   3 -Al   4 
                ( 43.80%)   0.6618*Al   3 s( 41.30%)p 1.41( 58.33%)d 0.01(  0.37%)
                                            0.0000 -0.0012  0.6422 -0.0076 -0.0216
                                            0.0007  0.0000 -0.0003 -0.3749  0.0230
                                            0.0201  0.0033  0.0000  0.0001 -0.6604
                                            0.0000 -0.0034 -0.0058  0.0008  0.0000
                                            0.0750  0.0004  0.0007  0.0008 -0.0001
                                            0.0134 -0.0019 -0.0112 -0.0541 -0.0219
                ( 56.20%)   0.7497*Al   4 s( 49.92%)p 1.00( 49.73%)d 0.01(  0.35%)
                                            0.0000 -0.0012  0.7065  0.0021 -0.0100
                                            0.0000  0.0000 -0.0004 -0.4490  0.0113
                                            0.0159  0.0004 -0.0003 -0.0001  0.5383
                                           -0.0140 -0.0049  0.0016 -0.0008  0.0000
                                           -0.0726  0.0019  0.0008 -0.0002  0.0001
                                           -0.0010 -0.0006 -0.0084 -0.0579 -0.0056
     6. (2.00000) CR ( 1)Al   1           s(100.00%)
                                            1.0000  0.0000  0.0000  0.0000  0.0000
                                            0.0000  0.0000  0.0000  0.0000  0.0000
                                            0.0000  0.0000  0.0000  0.0000  0.0000
                                            0.0000  0.0000  0.0000  0.0000  0.0000
                                            0.0000  0.0000  0.0000  0.0000  0.0000
                                            0.0000  0.0000  0.0000  0.0000  0.0000</pre>

The bonding in the D4h structure is very similar to that in the Cs geometry, again orbitals 1 to 5 are all bonding interactions and this suggests aromaticity.

===Analysis of Gallium Cs===
<pre>
Second Order Perturbation Theory Analysis of Fock Matrix in NBO Basis

     Threshold for printing:   0.50 kcal/mol
    (Intermolecular threshold: 0.05 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
  72. LP*(   1)Na   1                / 73. LP*(   2)Na   1                   18.83    0.09    0.085

 from unit  1 to unit  2
  72. LP*(   1)Na   1                / 76. LP*(   1)Na   2                   24.01    0.09    0.081

 from unit  1 to unit  3

 from unit  2 to unit  1

 within unit  2
  76. LP*(   1)Na   2                / 78. LP*(   3)Na   2                  141.66    0.02    0.160

 from unit  2 to unit  3

 from unit  3 to unit  1
  80. LP (   1)Ga   3                / 72. LP*(   1)Na   1                   37.31    0.06    0.064
  82. LP*(   2)Ga   4                / 72. LP*(   1)Na   1                   42.37    0.03    0.055
  84. LP*(   2)Ga   5                / 72. LP*(   1)Na   1                   37.00    0.06    0.063
  85. LP*(   1)Ga   6                / 72. LP*(   1)Na   1                   44.19    0.03    0.054

 from unit  3 to unit  2
   2. BD (   1)Ga   3 -Ga   5        / 76. LP*(   1)Na   2                   34.48    0.65    0.136
 252. BD*(   1)Ga   5 -Ga   6        / 76. LP*(   1)Na   2                   28.81    0.02    0.040

 within unit  3
   1. BD (   1)Ga   3 -Ga   4        /250. BD*(   1)Ga   3 -Ga   6           28.91    0.42    0.104
   1. BD (   1)Ga   3 -Ga   4        /251. BD*(   1)Ga   4 -Ga   6           21.12    0.63    0.106
   2. BD (   1)Ga   3 -Ga   5        / 81. LP*(   1)Ga   4                   17.67    0.52    0.090
   2. BD (   1)Ga   3 -Ga   5        /250. BD*(   1)Ga   3 -Ga   6           42.28    0.40    0.122
   3. BD (   1)Ga   3 -Ga   6        / 81. LP*(   1)Ga   4                   19.59    0.19    0.055
   3. BD (   1)Ga   3 -Ga   6        / 83. LP (   1)Ga   5                   22.65    0.15    0.055
   3. BD (   1)Ga   3 -Ga   6        /248. BD*(   1)Ga   3 -Ga   4           37.81    0.28    0.093
   3. BD (   1)Ga   3 -Ga   6        /249. BD*(   1)Ga   3 -Ga   5           78.88    0.22    0.118
   3. BD (   1)Ga   3 -Ga   6        /251. BD*(   1)Ga   4 -Ga   6           39.92    0.29    0.099
   3. BD (   1)Ga   3 -Ga   6        /252. BD*(   1)Ga   5 -Ga   6           36.87    0.31    0.100
   4. BD (   1)Ga   4 -Ga   6        /248. BD*(   1)Ga   3 -Ga   4           19.85    0.57    0.097
   4. BD (   1)Ga   4 -Ga   6        /250. BD*(   1)Ga   3 -Ga   6           55.67    0.37    0.133
  60. CR (   3)Ga   6                /250. BD*(   1)Ga   3 -Ga   6           29.11    8.16    0.489
  80. LP (   1)Ga   3                / 82. LP*(   2)Ga   4                  148.46    0.03    0.085
  81. LP*(   1)Ga   4                /248. BD*(   1)Ga   3 -Ga   4           91.71    0.09    0.126
  81. LP*(   1)Ga   4                /249. BD*(   1)Ga   3 -Ga   5          117.47    0.03    0.077
  83. LP (   1)Ga   5                / 81. LP*(   1)Ga   4                   99.59    0.04    0.077
  83. LP (   1)Ga   5                /249. BD*(   1)Ga   3 -Ga   5          196.70    0.07    0.139
  84. LP*(   2)Ga   5                / 85. LP*(   1)Ga   6                  138.19    0.03    0.084
 248. BD*(   1)Ga   3 -Ga   4        /251. BD*(   1)Ga   4 -Ga   6          373.00    0.01    0.108
 249. BD*(   1)Ga   3 -Ga   5        /248. BD*(   1)Ga   3 -Ga   4           89.97    0.06    0.101
 249. BD*(   1)Ga   3 -Ga   5        /252. BD*(   1)Ga   5 -Ga   6           45.63    0.09    0.097
 251. BD*(   1)Ga   4 -Ga   6        /252. BD*(   1)Ga   5 -Ga   6          135.75    0.02    0.093</pre>
It can be seen from stabilisation energies above that with Gallium the resonances are very high, even higher than those found in aluminium. However it should be taken into consideration that Gallium is larger than aluminium and therefore had larger orbitals, so these larger resonances are to be expected.

<pre>
      (Occupancy)   Bond orbital/ Coefficients/ Hybrids
 ---------------------------------------------------------------------------------
     1. (1.81751) BD ( 1)Ga   3 -Ga   4 
                ( 45.04%)   0.6711*Ga   3 s( 41.62%)p 1.39( 58.03%)d 0.01(  0.34%)
                                            0.0000  0.0000 -0.0009  0.6451 -0.0058
                                           -0.0063 -0.0011  0.0001  0.0000  0.0000
                                            0.0002  0.0030  0.0116  0.0057 -0.0008
                                           -0.0003  0.0000  0.0000 -0.0001 -0.7065
                                            0.0209  0.0018 -0.0015 -0.0009  0.0001
                                            0.0000  0.0000  0.2833  0.0171  0.0086
                                           -0.0007  0.0000  0.0000 -0.0002  0.0065
                                           -0.0009  0.0002 -0.0004 -0.0005 -0.0004
                                            0.0085 -0.0050 -0.0002 -0.0497 -0.0050
                                            0.0003 -0.0279 -0.0034
                ( 54.96%)   0.7414*Ga   4 s( 53.22%)p 0.87( 46.47%)d 0.01(  0.32%)
                                            0.0000  0.0000 -0.0010  0.7293 -0.0162
                                           -0.0036 -0.0008  0.0000  0.0000  0.0000
                                            0.0002  0.0124  0.0067  0.0057  0.0011
                                            0.0008  0.0000  0.0000  0.0000  0.4258
                                            0.0051 -0.0010  0.0028  0.0025  0.0000
                                            0.0000  0.0005  0.5321  0.0065  0.0017
                                            0.0005 -0.0007  0.0000  0.0001 -0.0050
                                            0.0008  0.0002 -0.0056  0.0002  0.0002
                                            0.0127  0.0017 -0.0003 -0.0308 -0.0017
                                           -0.0001 -0.0445 -0.0029
     2. (1.75387) BD ( 1)Ga   3 -Ga   5 
                ( 39.63%)   0.6295*Ga   3 s( 39.59%)p 1.52( 60.04%)d 0.01(  0.37%)
                                            0.0000  0.0000 -0.0011  0.6291 -0.0126
                                           -0.0007 -0.0005  0.0004  0.0000  0.0000
                                            0.0001  0.0421  0.0085  0.0055 -0.0018
                                            0.0000  0.0000  0.0000 -0.0001  0.2871
                                           -0.0094 -0.0024  0.0010  0.0009  0.0000
                                            0.0000  0.0002 -0.7183  0.0058  0.0027
                                            0.0002 -0.0020  0.0000  0.0002  0.0061
                                           -0.0010 -0.0002  0.0061 -0.0012 -0.0004
                                           -0.0031 -0.0013  0.0004 -0.0331  0.0021
                                            0.0008  0.0503  0.0027
                ( 60.37%)   0.7770*Ga   5 s( 50.18%)p 0.99( 49.59%)d 0.00(  0.23%)
                                            0.0000  0.0000 -0.0012  0.7083 -0.0046
                                           -0.0003  0.0003  0.0002  0.0000  0.0000
                                            0.0001  0.0612  0.0016  0.0050 -0.0023
                                            0.0003  0.0000  0.0000 -0.0001  0.5482
                                           -0.0233 -0.0034  0.0029  0.0000  0.0000
                                            0.0000 -0.0003  0.4370 -0.0070 -0.0025
                                           -0.0025  0.0015  0.0000  0.0002  0.0017
                                           -0.0004  0.0001  0.0011  0.0004  0.0004
                                            0.0281 -0.0007  0.0005 -0.0194  0.0028
                                            0.0009  0.0332  0.0019
     3. (1.57277) BD ( 1)Ga   3 -Ga   6 
                ( 58.50%)   0.7648*Ga   3 s( 18.24%)p 4.45( 81.10%)d 0.04(  0.66%)
                                            0.0000  0.0000 -0.0007  0.4267  0.0175
                                            0.0001  0.0020 -0.0005  0.0000  0.0000
                                           -0.0002  0.0589 -0.0145  0.0005 -0.0019
                                            0.0006  0.0000  0.0000 -0.0001  0.6402
                                           -0.0351 -0.0028  0.0050 -0.0022  0.0000
                                            0.0000  0.0005  0.6294  0.0068  0.0013
                                            0.0060  0.0010  0.0000  0.0000 -0.0094
                                            0.0011  0.0002 -0.0177  0.0016 -0.0004
                                           -0.0647  0.0043  0.0001  0.0219  0.0015
                                            0.0005 -0.0384 -0.0021
                ( 41.50%)   0.6442*Ga   6 s( 21.25%)p 3.67( 78.02%)d 0.03(  0.73%)
                                            0.0000  0.0000 -0.0011  0.4600  0.0293
                                           -0.0061 -0.0010 -0.0004  0.0000  0.0000
                                           -0.0002  0.0609 -0.0193  0.0046 -0.0008
                                            0.0015  0.0000  0.0000 -0.0012 -0.6286
                                            0.0449  0.0025 -0.0084  0.0009  0.0000
                                            0.0000 -0.0004 -0.6151  0.0172  0.0093
                                           -0.0013  0.0021  0.0000 -0.0003  0.0155
                                           -0.0018 -0.0001  0.0174 -0.0020  0.0000
                                           -0.0571  0.0043  0.0002  0.0530  0.0017
                                            0.0001 -0.0260 -0.0023
     4. (1.75040) BD ( 1)Ga   4 -Ga   6 
                ( 55.72%)   0.7464*Ga   4 s( 46.65%)p 1.14( 52.98%)d 0.01(  0.38%)
                                            0.0000  0.0000 -0.0013  0.6829  0.0116
                                            0.0018  0.0014  0.0001  0.0000  0.0000
                                            0.0003 -0.0027  0.0010  0.0021  0.0022
                                            0.0003  0.0000  0.0000 -0.0005 -0.4926
                                            0.0023 -0.0018 -0.0044  0.0000  0.0000
                                            0.0000  0.0001 -0.5358 -0.0034  0.0025
                                            0.0019 -0.0010  0.0000 -0.0002  0.0038
                                            0.0001 -0.0002  0.0080 -0.0010  0.0003
                                            0.0125  0.0016 -0.0001  0.0196  0.0020
                                            0.0003  0.0559  0.0041
                ( 44.28%)   0.6655*Ga   6 s( 37.34%)p 1.67( 62.22%)d 0.01(  0.45%)
                                            0.0000  0.0000 -0.0011  0.6110  0.0013
                                            0.0037  0.0017  0.0002  0.0000  0.0000
                                            0.0003 -0.0225  0.0080  0.0010  0.0027
                                           -0.0001  0.0000  0.0000 -0.0003 -0.2806
                                           -0.0123 -0.0028 -0.0017 -0.0001  0.0000
                                            0.0000  0.0000  0.7366 -0.0026 -0.0059
                                           -0.0016  0.0004 -0.0001 -0.0002 -0.0016
                                            0.0008  0.0002 -0.0139  0.0017 -0.0003
                                            0.0052 -0.0032 -0.0002  0.0008  0.0014
                                            0.0003  0.0648  0.0049
     5. (1.76421) BD ( 1)Ga   5 -Ga   6 
                ( 58.23%)   0.7631*Ga   5 s( 49.18%)p 1.03( 50.48%)d 0.01(  0.33%)
                                            0.0000  0.0000 -0.0009  0.7013 -0.0007
                                           -0.0060 -0.0005  0.0000  0.0000  0.0000
                                            0.0002  0.0156  0.0073  0.0053 -0.0011
                                           -0.0001  0.0000  0.0000 -0.0001 -0.5372
                                            0.0119  0.0012 -0.0003 -0.0014  0.0001
                                            0.0000 -0.0001 -0.4641 -0.0180 -0.0086
                                           -0.0008 -0.0004  0.0000 -0.0002  0.0036
                                           -0.0006 -0.0002  0.0050  0.0001  0.0004
                                            0.0077  0.0038 -0.0002 -0.0411 -0.0046
                                            0.0003 -0.0389 -0.0039
                ( 41.77%)   0.6463*Ga   6 s( 41.53%)p 1.40( 58.01%)d 0.01(  0.46%)
                                            0.0000  0.0000 -0.0009  0.6437 -0.0302
                                           -0.0011 -0.0003  0.0002  0.0000  0.0000
                                            0.0003 -0.0145  0.0163  0.0043  0.0017
                                            0.0002  0.0000  0.0000  0.0003  0.7153
                                           -0.0147 -0.0024  0.0066  0.0023  0.0000
                                            0.0000 -0.0005 -0.2596 -0.0148 -0.0064
                                           -0.0002 -0.0001  0.0000  0.0002 -0.0123
                                            0.0017 -0.0002 -0.0024  0.0008 -0.0002
                                            0.0112 -0.0039 -0.0003 -0.0565 -0.0025
                                           -0.0001 -0.0325 -0.0018
     6. (2.00000) CR ( 1)Na   1           s(100.00%)
                                            1.0000  0.0000  0.0000  0.0000  0.0000
                                            0.0000  0.0000  0.0000  0.0000  0.0000
                                            0.0000  0.0000  0.0000  0.0000  0.0000
                                            0.0000  0.0000  0.0000  0.0000  0.0000
                                            0.0000  0.0000  0.0000  0.0000  0.0000
                                            0.0000  0.0000  0.0000  0.0000  0.0000 </pre>
The bonding picture for the Gallium geometries is again the same as in the Aluminium molecules.

==Vibrational Spectroscopy Analysis==
Frequency analysis was run simply to check that the optimisations run previously had reached global minima. Presence of the low frequency absoprtions close to zero suggests this is the case.

An example for Aluminium in the Cs geometry is shown below:

<pre>
 Full mass-weighted force constant matrix:
 Low frequencies ---   -1.8179   -1.8125   -0.0020    0.0006    0.0018   16.9290
 Low frequencies ---   68.8340   68.8341   84.5201 </pre>

==Conclusion of Mini Project==
In conclusion the experiment has been successful in illustrating that it is possible for all metal clusters to have both π and σ aromaticity. In addition the geometry analyses has shown that the Cs geometry is the most stable of the ones investigated. NBO analysis has suggested the reason for this due to greater σ aromaticity between the metal atoms.

=Conclusion=
Computational techniques have been shown to be very useful in the calculation of almost all aspects of inorganic molecules despite their often unusual bonding. Geometry optimisations using the appropriate basis set have produced geometries with relative energies that agree well with literature. From these geometries it has been seen than IR spectra can be predicted to a good accuracy and molecular orbitals and NBO analysis provide an insight into the nature of where electrons are located in complex molecules which is simply not accessible by experiments in the wet lab.

=References=
<references/>