View source for Rep:Mod:shine11

==Inorganic Computational Chemistry==

===Optimisation===
====BH<sub>3</sub>==== 
=====3-21G=====

The log file for the optimisation is [[Media:JS_BH3_OPT3.LOG]]

All bond distances are reported to two decimal places, bond angles are reported to one and the dipole moment is reported to two. This is a result of the fact that the program is only accurate to this level of precision. 

The optimised B-H bond distance is 1.20A<sup>o</sup> and the optimum bond angle is 120.0<sup>o</sup>.

{| class="wikitable"
|-
! scope="col"|
! scope="col"| BH<sub>3</sub>
|-
! scope="row"| File type
| align="right" |.log
|-
! scope="row"| Calculation type
| align="right" |FOPT
|-
! scope="row"| Calculation method
| align="right" |RB3LYP
|-
! scope="row"| Basis set
| align="right" |3-21G
|-
! scope="row"| Final energy/au
| align="right" |-26.4622
|-
! scope="row"| Gradient/au
| align="right" |0.00004507
|-
! scope="row"| Dipole moment/D
| align="right" |0.00
|-
! scope="row"| Point group
| align="right" |D<sub>3h</sub>
|-
! scope="row"| Time taken/s
| align="right" |7.0
|}

<pre>          Item               Value     Threshold  Converged?
 Maximum Force            0.000090     0.000450     YES
 RMS     Force            0.000059     0.000300     YES
 Maximum Displacement     0.000352     0.001800     YES
 RMS     Displacement     0.000230     0.001200     YES
 Predicted change in Energy=-4.580958D-08
 Optimization completed.
    -- Stationary point found.</pre>

=====6-31G(d,p)=====

The log file for this, more accurate optimisation, is [[Media:JS_BH3_OPTACCURATE.LOG]].

The optimised average bond length is 1.20A<sup>o</sup> and the optimised bond angle is 120.0<sup>o</sup>.

{| class="wikitable"
|-
! scope="col"|
! scope="col"| BH<sub>3</sub>
|-
! scope="row"| File type
| align="right" |.log
|-
! scope="row"| Calculation type
| align="right" |FOPT
|-
! scope="row"| Calculation method
| align="right" |RB3LYP
|-
! scope="row"| Basis set
| align="right" |6-31g(d,p)
|-
! scope="row"| Final energy/au
| align="right" |-26.6153
|-
! scope="row"| Gradient/au
| align="right" |0.00000673
|-
! scope="row"| Dipole moment/D
| align="right" |0.00
|-
! scope="row"| Point group
| align="right" |Cs
|-
! scope="row"| Time taken/s
| align="right" |13.0
|}

<pre>         Item               Value     Threshold  Converged?
 Maximum Force            0.000011     0.000450     YES
 RMS     Force            0.000008     0.000300     YES
 Maximum Displacement     0.000056     0.001800     YES
 RMS     Displacement     0.000036     0.001200     YES
 Predicted change in Energy=-9.815639D-10
 Optimization completed.
    -- Stationary point found.</pre>

====GaBr<sub>3</sub>====

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26069 GaBr<sub>3</sub> Optimisation D-space]

The optimised bond length is 2.35A<sup>o</sup> and the optimised bond angle is 120.0<sup>o</sup>. This compares reasonably well to a literature vale of 2.38A<sup>o</sup><ref>H. Ulrich and G Heyne, Physikal. Chem., 1941, B 49, 284</ref>.

{| class="wikitable"
|-
! scope="col"|
! scope="col"| GaBr<sub>3</sub>
|-
! scope="row"| File type
| align="right" |.log
|-
! scope="row"| Calculation type
| align="right" |FOPT
|-
! scope="row"| Calculation method
| align="right" |RB3LYP
|-
! scope="row"| Basis set
| align="right" |LANL2DZ
|-
! scope="row"| Final energy/au
| align="right" |-41.7008
|-
! scope="row"| Gradient/au
| align="right" |0.00000016
|-
! scope="row"| Dipole moment/D
| align="right" |0.00
|-
! scope="row"| Point group
| align="right" |D<sub>3h</sub>
|-
! scope="row"| Time taken/s
| align="right" |52.1
|}

<pre>     Item               Value     Threshold  Converged?
Maximum Force         0.000000    0.000450    YES
RMS Force             0.000000    0.000300    YES
Maximum Displacement  0.000003    0.001800    YES
RMS Displacement      0.000002    0.001200    YES
Predicted change in Energy=-1.282692D-12
 Optimization completed.
    -- Stationary point found.</pre>

====BBr<sub>3</sub>====

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26076 BBr<sub>3</sub> D-space]

The optimised bond length is 1.93A<sup>o</sup> and the optimised bond angle is 120.0<sup>o</sup>. 

{| class="wikitable"
|-
! scope="col"|
! scope="col"| BBr<sub>3</sub>
|-
! scope="row"| File type
| align="right" |.log
|-
! scope="row"| Calculation type
| align="right" |FOPT
|-
! scope="row"| Calculation method
| align="right" |RB3LYP
|-
! scope="row"| Basis set
| align="right" |Gen
|-
! scope="row"| Final energy/au
| align="right" |-64.43644
|-
! scope="row"| Gradient/au
| align="right" |0.00001054
|-
! scope="row"| Dipole moment/D
| align="right" |0.00
|-
! scope="row"| Point group
| align="right" |Cs
|-
! scope="row"| Time taken/s
| align="right" |20.7
|}

<pre>          Item               Value     Threshold  Converged?
Maximum  Force             0.000024   0.000450    YES
RMS      Force             0.000011   0.000300    YES
Maximum  Displacement      0.000167   0.001800    YES
RMS      Displacement      0.000082   0.001200    YES
Predicted change in Energy=-2.420020D-09
 Optimization completed.
    -- Stationary point found.</pre>

====Bond Length Comparison====

{| class="wikitable"
|-
! scope="col"|
! scope="col"|Bond Length/A<sup>o</sup> 
|-
! scope="row"|BH<sub>3</sub>
| align="right" |1.19
|-
! scope="row"|BBr<sub>3</sub> 
| align="right" |1.93
|-
! scope="row"|GaBr<sub>3</sub>
| align="right" |2.35
|}

Changing the ligand from H to Br significantly increases the bond length. The reasons for this are numerous. Firstly, Br has 3 more full s and p orbitals and 1 more full d orbital than H. It is also has three lone pairs, one of which can donate into the empty B p orbital, since the B is sp<sup>2</sup> hybridised. This actually shortens the bond length. The other lone pair in the p orbital can cause repulsion which lengthens the bond. Changing the central atom from B to Ga also increases the bond length. First, Ga has two extra s and p orbitals, and a full d orbital, which will repel the orbitals on Br. Second, the fact that Ga is less electronegative than B will lengthen the bond, since the Ga will attract the electrons in the bond less strongly.

Defining a chemical bond is not as trivial as the conventional use of a straight line to indicate covalent bond would make it appear. Typically, it is a potential energy minimum of a system, existing as a result of an attractive electrostatic interaction over a distance that is generally between 1.4-3A<sup>o</sup>. The strength of these interaction can vary greatly, from the covalent bonding in N<sub>2</sub>, to the hydrogen bonds in water. However, many of these interactions exist in molecules, and simply using distance to determine the existence or non-existence of a bond, as Gaussian does, can lead to important interactions not being detected. In molecular orbital theory, any stabilised orbital is considered to be a bonding orbital. Clearly, this is a more accurate method for the determination of bond formation than just using distance, although every single interaction cannot, of course be considered to be a bond. A combination of both methods must be used.

===Frequency Analysis===
====BH<sub>3</sub>==== 

This log file for this process is [[Media:JS_BH3_FREQ3.LOG‎]].

<pre>Low frequencies --- -0.9580 -0.9214 -0.0053 5.3695 11.5406 11.5803
Low frequencies --- 1162.9950 1213.1817 1213.1844
</pre>

{| class="wikitable"
|-
! scope="col"|
! scope="col"| BH<sub>3</sub>
|-
! scope="row"| File type
| align="right" |.log
|-
! scope="row"| Calculation type
| align="right" |FREQ
|-
! scope="row"| Calculation method
| align="right" |RB3LYP
|-
! scope="row"| Basis set
| align="right" |3-21G
|-
! scope="row"| Final energy/au
| align="right" |-26.4622
|-
! scope="row"| Gradient/au
| align="right" |0.00008904
|-
! scope="row"| Dipole moment/D
| align="right" |0.00
|-
! scope="row"| Point group
| align="right" |Cs
|-
! scope="row"| Time taken/s
| align="right" |26.0
|}

<pre>    Item             Value       Threshold Converged?
Maximum Force        0.000221    0.000450  YES
RMS     Force        0.000106    0.000300  YES
Maximum Displacement 0.000724    0.001800  YES
RMS Displacement     0.000445    0.001200  YES 
Predicted change in Energy=-1.667569D-07
Optimization completed.
-- Stationary point found.</pre>

=====Vibration Visualisation=====

The optimised average bond length is 1.20A<sup>o</sup> and the optimised bond angle is 120.0<sup>o</sup>. Force constant related to freq. Gaussian bases bonds on distance

{| class="wikitable"
|-
! scope="col"|Number
! scope="col"|Vibration Form
! scope="col"|Frequency
! scope="col"|Intensity
! scope="col"|Symmetry D<sub>3h</sub>
|-
| scope="row"| 1
| align="right" |[[File:BH3 vib1.png|150px]]
The H move left and right in a concerted manner,

as the B moves in the opposite direction. (bend)
| scope="row"| 1160
| align="right" | 93
| scope="row"| A<sub>2</sub>''
|-
| scope="row"| 2
| align="right" |[[File:BH3 vib2.png|150px]]
The top two H move diagonally in the

shown direction, at the same time, while

the remaining B and H move slightly up and down. (bend)
| scope="row"| 1210
| align="right" |14
| scope="row"| E'
|-
| scope="row"| 3
| align="right" |[[File:BH3 vib3.png|150px]]
The bottom H moves clockwise as the top two move anticlockwise.

The B remains almost totally stationary. (bend)

| scope="row"| 1210
| align="right" |14
| scope="row"| E'
|-
| scope="row"| 4
| align="right" |[[File:BH3 vib4.png|150px]]
The H move out in these directions in a concerted way.

The B does not move. (stretch)

| scope="row"| 2580
| align="right" |0
| scope="row"| A<sub>1</sub>'
|-
| scope="row"| 5
| align="right" |[[File:BH3 vib5.png|150px]]
The top left H moves away from the B as the top right H is moving

towards it. The B and the H remain almost completely still. (stretch)
| scope="row"| 2720
| align="right" |126
| scope="row"| E'
|-
| scope="row"| 6
| align="right" |[[File:BH3 vib6.png|150px]]
The top two H move away from the B,

as the other H moves towards it.

The B remains almost totally motionless. (stretch)
| scope="row"| 2720
| align="right" |126
| scope="row"| E'
|}

The actual IR spectrum is shown below.

[[File:BH3_vibIR.png]]

====GaBr<sub>3</sub>====

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26122 GaBr<sub>3</sub> Frequency D-Space]

<pre>-2.3539 -2.3538 -1.3645 -0.0026 0.0044 0.0276</pre>

The lowest "real" normal mode is 86.9748cm<sup>-1</sup>.

The IR spectrum is below.

[[File:JS GaBr3 spec.png|800px]]

====Vibration Comparison====

{| class="wikitable"
|-
! scope="col"|Number
! scope="col"|Vibration Form
! scope="col"|Frequency BH<sub>3</sub> cm<sup>-1</sup>
! scope="col"|Intensity BH<sub>3</sub> 
! scope="col"|Frequency GaBr<sub>3</sub> cm<sup>-1</sup>
! scope="col"|Intensity GaBr<sub>3</sub>
! scope="col"|Symmetry D<sub>3h</sub>
|-
| scope="row"| 1
| align="right" |[[File:BH3 vib1.png|150px]]
The H move left and right in a concerted manner,

as the B moves in the opposite direction. (bend)
| align="right"| 1160
| align="right" | 93
| align="right"| 120
| align="right" | 4
| align="right"| A<sub>2</sub>''
|-
| scope="row"| 2
| align="right" |[[File:BH3 vib2.png|150px]]
The top two H move diagonally in the

shown direction, at the same time, while

the remaining B and H move slightly up and down. (bend)
| align="right"| 1210
| align="right" |14
| align="right"| 87
| align="right" | 2
| align="right"| E'
|-
| scope="row"| 3
| align="right" |[[File:BH3 vib3.png|150px]]
The bottom H moves clockwise as the top two move anticlockwise.

The B remains almost totally stationary. (bend)

| align="right"| 1210
| align="right" |14
| align="right"| 87
| align="right" | 2
| align="right"| E'
|-
| scope="row"| 4
| align="right" |[[File:BH3 vib4.png|150px]]
The H move out in these directions in a concerted way.

The B does not move. (stretch)

| align="right"| 2580
| align="right" |0
| align="right"| 235
| align="right" | 0
| align="right"| A<sub>1</sub>'
|-
| scope="row"| 5
| align="right" |[[File:BH3 vib5.png|150px]]
The top left H moves away from the B as the top right H is moving

towards it. The B and the H remain almost completely still. (stretch)
| align="right"| 2720
| align="right" |126
| align="right"| 365
| align="right" | 62
| align="right"| E'
|-
| scope="row"| 6
| align="right" |[[File:BH3 vib6.png|150px]]
The top two H move away from the B,

as the other H moves towards it.

The B remains almost totally motionless. (stretch)
| align="right"| 2720
| align="right" |126
| align="right"| 365
| align="right" | 62
| align="right"| E'
|}

The frequencies of BH<sub>3</sub> are much greater than for GaBr<sub>3</sub>, for the same vibrational mode. The main reasons for this are that, first, the frequency is inversely proportional to the reduced mass. Since the reduced mass of GaBr<sub>3</sub> is obviously much greater, its frequencies are reduced. Second, frequency is proportional to the force constant of the bond. The Ga-Br bond is longer than the B-H bond, suggesting that it is a weaker bond. Therefore, its frequencies are again reduced.

Interestingly, bends 2 and 3 are at higher frequency than bend 1 for BH<sub>3</sub>, but are at lower frequency than bend 1 for GaBr<sub>3</sub>. Apart from this, the spectra a reasonably similar, apart from the fact that the GaBr<sub>3</sub> A<sub>2</sub> bend has a lower intensity. Bends 1,2 and 3 are at similar frequencies, since they are bends. Stretches 4,5 and 6 are also at similar frequencies, because they are stretches. The intensity of stretch 4 is zero, since this stretch causes no change in dipole moment of the molecule. There are only three peaks seen due to the degeneracy of the E' vibrations.

This frequency analysis gives eigenvalues that represent the second derivatives of the energy diagram. Therefore, if they are positive, the energy is a minimum. The low frequencies are to do with the idea that each molecule has 3N-6 degrees of freedom, specifically the "-6", meaning the motions of the center of mass of the molecule. Clearly, the same method and basis set must be used for both pieces of analysis, in order for the results to be compared fairly.

===BH<sub>3</sub> MO Analysis===

The line "int=ultrafine scf=conver=9" was used to improve the values for the low frequencies.

The log file for the optimisation is [[Media:JS_BH3_OPT.LOG]]

<pre>   Item                  Value     Threshold  Converged?
 Maximum Force            0.000003     0.000015     YES
 RMS     Force            0.000002     0.000010     YES
 Maximum Displacement     0.000013     0.000060     YES
 RMS     Displacement     0.000008     0.000040     YES
 Predicted change in Energy=-6.228076D-11
 Optimization completed.
    -- Stationary point found</pre>

The log file for the frequency is [[Media:JS BH3 FREQ2.LOG]].

<pre>-11.2361  -11.2272   -5.6980    0.0003    0.0322    0.4463</pre>

The D-space for the population analysis is [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26131 here].

This is the MO diagram with all modeled occupied orbitals and the modeled LUMO.

[[File:JS BH3 MO2.png]]

Comparing the generated orbitals to what MO theory predicted, most of the orbitals appear to be reasonable models of the actual MO, considering the speed of the method. However, the first e' orbital is difficult to view with this program. Also, the rest of the orbitals lack the symmetry that is expected. From this, it also seems that MO theory is useful, for qualitative predictions.

===NH<sub>3</sub> NBO Analysis===

The log file for the optimisation is [[Media:JS NH3 OPT.LOG]].

<pre>         Item               Value     Threshold  Converged?
 Maximum Force            0.000024     0.000450     YES
 RMS     Force            0.000012     0.000300     YES
 Maximum Displacement     0.000079     0.001800     YES
 RMS     Displacement     0.000053     0.001200     YES
 Predicted change in Energy=-1.629715D-09
 Optimization completed.
    -- Stationary point found.</pre>

The log file for the frequency is [[Media:JS NH3 FREQ2.LOG]].

<pre>-9.3920   -8.3783   -6.3678   -0.0017   -0.0017   -0.0009</pre>

This is the [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26136 D-space] for the population analysis.

This is the charge distribution.

[[File:NH3 NBO charge dist.png]]

The charge range was -1.125 to 1.125

{| class="wikitable"
|-
! scope="col"| Atom
! scope="col"| NBO charge
|-
| scope="row"| N
| align="right" | -1.125
|-
| scope="row"| H
| align="right" | +0.375
|}

===NH<sub>3</sub>BH<sub>3</sub> Energy Minimum===

The log file for the optimisation is [[Media:JS NH3BH3 OPT3.LOG]].

<pre>         Item               Value     Threshold  Converged?
 Maximum Force            0.000004     0.000450     YES
 RMS     Force            0.000002     0.000300     YES
 Maximum Displacement     0.000026     0.001800     YES
 RMS     Displacement     0.000012     0.001200     YES
 Predicted change in Energy=-2.956782D-10
 Optimization completed.
    -- Stationary point found.</pre>

The log file for the frequency is [[Media:JS NH3BH3 FREQ.LOG]].

<pre>The low frequencies are -6.4842 -4.4175 -0.0011 -0.0009 -0.0008 0.8459.</pre>

===Energy comparison===

E(NH3)=  -56.55776872a.u.
E(BH3)=  -26.6153237196a.u.
E(NH3BH3)= -83.22468907 a.u.

ΔE=E(NH<sub>3</sub>BH<sub>3</sub>)-[E(NH<sub>3</sub>)+E(BH<sub>3</sub>)]

ΔE=(-83.22468907)-[(-26.6153237196)+(-56.55776872)]

= -0.0516 a.u.

= -0.0516*2625.5 KJ/mol

= -135 KJ/mol

===Schlenk Equilibrium===

Considering the grignard reagent MeMgCl, the following species were analysed, excluding Me<sub>2</sub>Mg and MgCl<sub>2</sub>.

[[File:JS_Schlenk eqm chemdraw.png|850px]]

====(1) MeMgCl====

=====Optimisation=====

A mixture of basis sets were used. 6-31G(d,p) was used for the C and H atoms, while LanL2DZ was used for the Mg and Cl atoms. The log file for this optimisation is [[Media:JS Mg mix opt.log]].

The optimised bond length for Mg-Cl is 2.26A<sup>o</sup> and for Mg-Me is 2.07A<sup>o</sup>. The optimised bond angle is 180.0<sup>o</sup>.

{| class="wikitable"
|-
! scope="col"|
! scope="col"| MeMgCl
|-
! scope="row"| File type
| align="right" |.log
|-
! scope="row"| Calculation type
| align="right" |FOPT
|-
! scope="row"| Calculation method
| align="right" |RB3LYP
|-
! scope="row"| Basis set
| align="right" |Gen
|-
! scope="row"| Final energy/au
| align="right" |-55.769
|-
! scope="row"| Gradient/au
| align="right" |0.00000838
|-
! scope="row"| Dipole moment/D
| align="right" |3.13
|-
! scope="row"| Point group
| align="right" |C1
|-
! scope="row"| Time taken/s
| align="right" |68
|}

<pre>        Item               Value     Threshold  Converged?
 Maximum Force            0.000012     0.000450     YES
 RMS     Force            0.000006     0.000300     YES
 Maximum Displacement     0.000396     0.001800     YES
 RMS     Displacement     0.000145     0.001200     YES
 Predicted change in Energy=-2.482616D-09
 Optimization completed.
    -- Stationary point found.</pre>

=====Frequency Analysis=====

This log file for this process is [[Media:JS MEMGCL FREQ.LOG‎]].

<pre>Low frequencies ---  -17.8458   -3.0113   -0.0001   -0.0001    0.0002    4.3589</pre>

{| class="wikitable"
|-
! scope="col"|
! scope="col"| MeMgCl
|-
! scope="row"| File type
| align="right" |.log
|-
! scope="row"| Calculation type
| align="right" |FREQ
|-
! scope="row"| Calculation method
| align="right" |RB3LYP
|-
! scope="row"| Basis set
| align="right" |Gen
|-
! scope="row"| Final energy/au
| align="right" |-55.769
|-
! scope="row"| Gradient/au
| align="right" |0.00000843
|-
! scope="row"| Dipole moment/D
| align="right" |3.13
|-
! scope="row"| Point group
| align="right" |C1
|-
! scope="row"| Time taken/s
| align="right" |38
|}

<pre>          Item               Value     Threshold  Converged?
 Maximum Force            0.000029     0.000450     YES
 RMS     Force            0.000008     0.000300     YES
 Maximum Displacement     0.000472     0.001800     YES
 RMS     Displacement     0.000199     0.001200     YES
 Predicted change in Energy=-3.505925D-09
 Optimization completed.
    -- Stationary point found.</pre>

=====Vibrations=====

{| class="wikitable"
|-
! scope="col"|Number
! scope="col"|Vibration Form
! scope="col"|Frequency
! scope="col"|Intensity
! scope="col"|Symmetry C<sub>3v</sub>
|-
| scope="row"| 1
| align="right" |[[File:Mg1 vib1.png|150px]]
The H move left and right in a concerted manner,

as the B moves in the opposite direction. (bend)
| scope="row"| 97.8
| align="right" | 35
| scope="row"| E
|-
| scope="row"| 2
| align="right" |[[File:Mg1 vib2.png|150px]]
The top two H move diagonally in the

shown direction, at the same time, while

the remaining B and H move slightly up and down. (bend)
| scope="row"| 98.2
| align="right" |35
| scope="row"| E
|-
| scope="row"| 3
| align="right" |[[File:Mg1 vib3.png|150px]]
The bottom H moves clockwise as the top two move anticlockwise.

The B remains almost totally stationary. (bend)

| scope="row"| 357
| align="right" |11
| scope="row"| A<sub>1</sub>
|-
| scope="row"| 4
| align="right" |[[File:Mg1 vib4.png|150px]]
The H move out in these directions in a concerted way.

The B does not move. (stretch)

| scope="row"| 627
| align="right" |58
| scope="row"| A<sub>1</sub>
|-
| scope="row"| 5
| align="right" |[[File:Mg1 vib5.png|150px]]
The top left H moves away from the B as the top right H is moving

towards it. The B and the H remain almost completely still. (stretch)
| scope="row"| 627
| align="right" |104
| scope="row"| E
|-
| scope="row"| 6
| align="right" |[[File:Mg1 vib6.png|150px]]
The top two H move away from the B,

as the other H moves towards it.

The B remains almost totally motionless. (stretch)
| scope="row"| 627
| align="right" |104
| scope="row"| E
|-
| scope="row"| 7
| align="right" |[[File:Mg1 vib7.png|150px]]
The H move left and right in a concerted manner,

as the B moves in the opposite direction. (bend)
| scope="row"| 3040
| align="right" | 18
| scope="row"| A<sub></sub>1
|-
| scope="row"| 8
| align="right" |[[File:Mg1 vib8.png|150px]]
The top two H move diagonally in the

shown direction, at the same time, while

the remaining B and H move slightly up and down. (bend)
| scope="row"| 3120
| align="right" |12
| scope="row"| E
|-
| scope="row"| 9
| align="right" |[[File:Mg1 vib9.png|150px]]
The bottom H moves clockwise as the top two move anticlockwise.

The B remains almost totally stationary. (bend)

| scope="row"| 3120
| align="right" |12
| scope="row"| E
|}

[[File:JSMg1IR.png|850px]]

====(2) Me<sub>2</sub>Mg<sub>2</sub>Cl<sub>2</sub>L<sub>2</sub>, L = Et<sub>2</sub>O====
=====Optimisation=====
Here is the optimisation file [[Media:JS MG2 MIX ET2O OPT3.LOG]]

{| class="wikitable"
|-
! scope="col"|
! scope="col"|MG2, L = ET2O
|-
! scope="row"| File type
| align="right" |.log
|-
! scope="row"| Calculation type
| align="right" |FOPT
|-
! scope="row"| Calculation method
| align="right" |RB3LYP
|-
! scope="row"| Basis set
| align="right" |Gen
|-
! scope="row"| Final energy/au
| align="right" |-579.0039
|-
! scope="row"| Gradient/au
| align="right" |0.00000342
|-
! scope="row"| Dipole moment/D
| align="right" |9.51
|-
! scope="row"| Point group
| align="right" |C1
|-
! scope="row"| Time taken
| align="right" |1h 43min 
|}

<pre>         Item               Value     Threshold  Converged?
 Maximum Force            0.000010     0.000450     YES
 RMS     Force            0.000002     0.000300     YES
 Maximum Displacement     0.000537     0.001800     YES
 RMS     Displacement     0.000115     0.001200     YES
 Predicted change in Energy=-2.800254D-09
 Optimization completed.
    -- Stationary point found.</pre>

=====Frequency=====
This is the frequency analysis file [[Media:JS Mg2 Et2O FREQ.log]]

{| class="wikitable"
|-
! scope="col"|
! scope="col"| Mg2, L=Et2O
|-
! scope="row"| File type
| align="right" |.log
|-
! scope="row"| Calculation type
| align="right" |FREQ
|-
! scope="row"| Calculation method
| align="right" |RB3LYP
|-
! scope="row"| Basis set
| align="right" |Gen
|-
! scope="row"| Final energy/au
| align="right" |-579.004
|-
! scope="row"| Gradient/au
| align="right" |0.00000343
|-
! scope="row"| Dipole moment/D
| align="right" |9.50
|-
! scope="row"| Point group
| align="right" |C1
|-
! scope="row"| Time taken
| align="right" |1h 8min 40s
|}

<pre>Low frequencies ---   -4.2354    0.0005    0.0007    0.0008    4.7788    8.7652</pre>

=====Vibrations=====

Unfortunately, there were 120 generated vibrational modes for these molecules, making it difficult to analyse each mode individually. Therefore, only the key modes are shown, meaning the ones that involve the Mg and Cl atoms.

{| class="wikitable"
|-
! scope="col"|Number
! scope="col"|Vibration Form
! scope="col"|Frequency
! scope="col"|Intensity
! scope="col"|Symmetry if the structure

was ideal C<sub>2v</sub>
|-
| scope="row"| 1
| align="right" |[[File:Mg2Et2O vib1.png|350px]]
The two Cl move in and out,

at the same time(symmetrically). (stretch)
| scope="row"| 47.3
| align="right" |0
| scope="row"| A<sub>1</sub>
|-
| scope="row"| 2
| align="right" |[[File:Mg2Et2O vib2.png|350px]]
The two Cl move up and down

at the same time. (bend)

| scope="row"| 76.6
| align="right" |1
| scope="row"| A<sub>1</sub>
|-
| scope="row"| 3
| align="right" |[[File:Mg2Et2O vib3.png|350px]]
The Mg and the Cl move diagonally

in a asymmetric fashion. (stretch)

| scope="row"| 103
| align="right" |2
| scope="row"| A<sub>1</sub>
|-
| scope="row"| 4
| align="right" |[[File:Mg2Et2O vib4.png|350px]]
The two Cl move up and down

at the same time. (bend)
| scope="row"| 128
| align="right" |5
| scope="row"| A<sub>1</sub>
|-
| scope="row"| 5
| align="right" |[[File:Mg2Et2O vib5.png|350px]]
The two Cl move in as the two Mg atoms
move out, symmetrically. (stretch)
| scope="row"| 189
| align="right" |2
| scope="row"| A<sub>1</sub>
|-
| scope="row"| 6
| align="right" |[[File:Mg2Et2O vib7.png|350px]]
Each Mg and Cl stretches symmetrically. (stretch)
| scope="row"| 218
| align="right" | 2
| scope="row"| A<sub></sub>1
|-
| scope="row"| 7
| align="right" |[[File:Mg2Et2O vib7.png|350px]]
The two Cl stretch asymmetrically,

as do the Mg, but in the opposite direction. (stretch)
| scope="row"| 284
| align="right" |50
| scope="row"| A<sub>2</sub>
|-
| scope="row"| 8
| align="right" |[[File:Mg2Et2O vib8.png|350px]]
Again, the two Cl stretch asymmetrically,

as do the Mg, but in the opposite direction. (stretch)

| scope="row"| 287
| align="right" |85
| scope="row"| A<sub>2</sub>
|-
| scope="row"| 9
| align="right" |[[File:Mg2Et2O vib9.png|350px]]
The Mg and the Cl move in and out symmetrically,

in a concerted manner. (stretch)

| scope="row"| 304
| align="right" |21
| scope="row"| A<sub>1</sub>
|}

[[File:JS Mg2Et2O spectrum.png|750px]]

A key point to note, that is evidenced by the following spectra, as well as the population analysis, is that the diagram at the beginning of this section is only a very rough estimate of where the electrons actually lie. Specifically, there appears to be a high amount of electron density between the two Cl atoms. The term "bond" is not used here, due to the vagueness of its definition, discussed above. The modes 1, 5, 7 and 9 seem to show this. An advantage of using this program is that the symmetric stretches of Cl-Cl can still be viewed, despite the fact that they are not IR active, since they do not cause a change in the dipole of the molecule. These all have A<sub>1</sub> symmetry. Due to  the fact that the frequency of the vibration is inversely proportional to the reduced mass, the Cl-Cl stretches and bends are at a low frequency. In addition, there seems to be a so called "bond" between the Mg and Cl atoms, shown by modes 2, 3, 4 and 6. Furthermore, mode 9 suggests the presence of a bond between the Mg atoms.

Comparing these modes to those for MeMgCl, they are very different, in terms of their frequencies, suggesting that the solvent molecule is interacting with the molecule quite profoundly. For instance, mode number 3 for MeMgCl has a frequency 250cm<sup>-1</sup> greater than mode number 3 for the one above, which is the same mode. This indicates that the Mg has become electron deficient. This is the only mode that can be compared fairly, based on the fact that the ligand is also affecting the reduced mass, as well as the force constant. Therefore, it is not a clear indication of the presence of electron density.

=====Molecular orbitals=====
This is the [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26382 D-space] for the population analysis.

{| class="wikitable"
|-
! scope="col"|Number
! scope="col"|MO
! scope="col"|Energy/a.u.
! scope="col"|Atoms involved
! scope="col"|Orbitals That Are Overlapping
|-
| scope="row"| 61(LUMO)
| align="right" |[[File:Mg2Et2O MO11.png|200px]]
| scope="row"| -0.02344
| align="right" |Cl + Mg
| scope="row"| Probably p<sub>x</sub>, p<sub>y</sub> and p<sub>z</sub> to give a δ bond.
|-
| scope="row"| 60(HOMO)
| align="right" |[[File:Mg2Et2O MO10.png|200px]]
| scope="row"| -0.20946
| align="right" |Cl + Mg + C + H
| scope="row"|p<sub>x</sub> to form π bond.

σ* between Mg and Me.
|-
| scope="row"| 57
| align="right" |[[File:Mg2Et2O MO9.png|200px]]
| scope="row"| -0.29044
| align="right" |Cl
| scope="row"| p<sub></sub>y to form π* bond.
|-
| scope="row"| 56
| align="right" |[[File:Mg2Et2O MO8.png|200px]]
| scope="row"| -0.29731
| align="right" |Cl
| scope="row"| p<sub>y</sub> to form π bond.
|-
| scope="row"| 53
| align="right" |[[File:Mg2Et2O MO7.png|200px]]
| scope="row"|-0.31822
| align="right" |Cl
| scope="row"| p<sub>x</sub> to form π* bond.
|-
| scope="row"| 52
| align="right" |[[File:Mg2Et2O MO6.png|200px]]
| scope="row"| -0.32726
| align="right" |Cl
| scope="row"| p<sub>x</sub> to form π bond.
|-
| scope="row"| 51
| align="right" |[[File:Mg2Et2O MO5.png|200px]]
| scope="row"| -0.32981
| align="right" |Cl
| scope="row"| p<sub>z</sub> to form σ bond.
|-
| scope="row"| 47
| align="right" |[[File:Mg2Et2O MO4.png|200px]]
| scope="row"| -0.34083
| align="right" |Cl + Mg
| scope="row"| p<sub>z</sub> to form σ bond.
|-
| scope="row"|45
| align="right" |[[File:Mg2Et2O MO3.png|200px]]
| scope="row"| -0.3615
| align="right" |Cl + O + C + H
| scope="row"| Explained below.
|-
| scope="row"| 20
| align="right" |[[File:Mg2Et2O MO2.png|200px]]
| scope="row"| -0.75058
| align="right" |Cl
| scope="row"| s to form σ* bond.
|-
| scope="row"| 17
| align="right" |[[File:Mg2Et2O MO1.png|200px]]
| scope="row"| -0.76274
| align="right" |Cl
| scope="row"| s to form σ bond.
|}

Molecular orbital 45 is the p<sub>x</sub> orbital on Cl, overlapping with the Mg-O bond. Considering the C-O bond, it formed by the s orbital on the Mg mixing with an O orbital, since they are both have a<sub>1</sub> symmetry. The O orbital consists of an sp<sup>3</sup> orbital on the C, mixing with the p<sub>z</sub> orbital on the O.

[[File:JSMg2Et2O MOdiagram.png|300px]]

The vast majority of these modes indicate that there is a reasonably large amount of electron density between the Cl atoms, that is, it could be said that there is a "bond" between them. Interestingly, energy level 45 shows that, in addition, the O can overlap with the central Mg and Cl atoms as well. Also, energy level 47 shows a high level of electron density between all of the central Mg and Cl atoms, as does the LUMO. This explains why  the IR spectrum indicates the existence of Mg-Mg and Mg-Cl "bonds". Furthermore, the HOMO involves the central atoms, as well as the methyl group. The majority of the electron density is on the Me, since it is the C that is electronegative and acting as a nucleophile, shown in the NBO analysis below.

=====Natural Bond Orbital Analysis=====

This image of charge distribution is from -1.375 to 1.375, with green indicating positive charge.

[[File:JS Mg2Et2O charge.png|250px]]

{| class="wikitable"
|-
! scope="col"| Atom
! scope="col"| Mean NBO charge
|-
| scope="row"| Mg
| align="right" | +1.280
|-
| scope="row"| C
| align="right" | -1.374
|-
| scope="row"| Cl
| align="right" | -0.654
|-
| scope="row"| O
| align="right" | -0.66
|}

The C is the most electronegative atom, which can then act as a nucleophile in C-C bond forming reactions, as expected. The Mg is electropositive, stabilized by the electronegative O, which comes from the solvent.

Looking at the log file gives a significant amount of information about the central atoms.

<pre>
1. (1.97330) BD ( 1)Mg   1 -Cl   3 
                (  5.76%)   0.2399*Mg   1 s( 23.62%)p 3.23( 76.38%)
                                            0.4858  0.0130 -0.5089 -0.0444 -0.1705
                                           -0.0157  0.6871  0.0388
                ( 94.24%)   0.9708*Cl   3 s( 30.28%)p 2.30( 69.72%)
                                            0.5503  0.0007  0.7286  0.0012  0.1048
                                            0.0005 -0.3942  0.0030
     2. (1.97364) BD ( 1)Mg   1 -Cl   4 
                (  5.93%)   0.2435*Mg   1 s( 24.67%)p 3.05( 75.33%)
                                            0.4965  0.0111 -0.4100 -0.0316 -0.2557
                                           -0.0247 -0.7184 -0.0467
                ( 94.07%)   0.9699*Cl   4 s( 30.58%)p 2.27( 69.42%)
                                            0.5530  0.0005  0.6706  0.0013  0.1856
                                            0.0007  0.4582 -0.0029
 4. (1.97265) BD ( 1)Mg   2 -Cl   3 
                (  5.89%)   0.2427*Mg   2 s( 24.73%)p 3.04( 75.27%)
                                           -0.4972 -0.0105 -0.4259 -0.0316  0.1065
                                            0.0117 -0.7460 -0.0471
                ( 94.11%)   0.9701*Cl   3 s( 29.52%)p 2.39( 70.48%)
                                           -0.5434 -0.0001  0.6809  0.0014 -0.0389
                                           -0.0002  0.4895 -0.0033
     5. (1.97283) BD ( 1)Mg   2 -Cl   4 
                (  5.74%)   0.2395*Mg   2 s( 23.67%)p 3.22( 76.33%)
                                           -0.4863 -0.0150 -0.5228 -0.0335  0.2379
                                            0.0185  0.6563  0.0343
                ( 94.26%)   0.9709*Cl   4 s( 29.49%)p 2.39( 70.51%)
                                           -0.5431 -0.0001  0.7394  0.0011 -0.1085
                                            0.0008 -0.3827  0.0028
</pre>

Considering the Mg-Cl bonds, it is clearly a relatively accurate approximation to say that the Mg atoms are sp<sup>3</sup> hybridised. This means that their ideal bond angle should be somewhere around 109<sup>o</sup>. The fact that their average bond angles are actually 98.6<sup>o</sup> and 122.9<sup>o</sup> suggests that there is a significant amount of ring strain. This is obviously greater in the Mg3 molecule, which could be one reason why it is the least stable molecule. Looking at the Cl atoms, which constitute almost 95% of the bonds, they are all almost exactly 3:7 s:p orbitals. These would, again, prefer an angle of around 115<sup>o</sup>. The fact that the internal angles are almost 90<sup>o</sup>, again, suggests that a large amount of ring strain is present.

No Mg-Mg or Cl-Cl bonds are officially detected by Gaussian, due to the previously stated fact that it detects the existence of bonds based on the distances between the atoms. It is clear from the analysis that they can be said to exist, however.

====(2) Me<sub>2</sub>Mg<sub>2</sub>Cl<sub>2</sub>L<sub>2</sub>, L = THF====
=====Optimisation=====

This is the [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26377 D-space] for the optimisation.

{| class="wikitable"
|-
! scope="col"|
! scope="col"|MG2, L = THF
|-
! scope="row"| File type
| align="right" |.log
|-
! scope="row"| Calculation type
| align="right" |FOPT
|-
! scope="row"| Calculation method
| align="right" |RB3LYP
|-
! scope="row"| Basis set
| align="right" |Gen
|-
! scope="row"| Final energy/au
| align="right" |-576.581
|-
! scope="row"| Gradient/au
| align="right" |0.00017625
|-
! scope="row"| Dipole moment/D
| align="right" |10.41
|-
! scope="row"| Point group
| align="right" |C1
|-
! scope="row"| Time taken
| align="right" |4h 7min 46s
|}

<pre>         Item               Value     Threshold  Converged?
 Maximum Force            0.000008     0.000450     YES
 RMS     Force            0.000002     0.000300     YES
 Maximum Displacement     0.001290     0.001800     YES
 RMS     Displacement     0.000296     0.001200     YES
 Predicted change in Energy=-4.797915D-09
 Optimization completed.
    -- Stationary point found.</pre>

=====Frequency=====
[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26383 Here] is the D-space for the frequency analysis.

{| class="wikitable"
|-
! scope="col"|
! scope="col"|MG2, L = THF
|-
! scope="row"| File type
| align="right" |.log
|-
! scope="row"| Calculation type
| align="right" |FREQ
|-
! scope="row"| Calculation method
| align="right" |RB3LYP
|-
! scope="row"| Basis set
| align="right" |Gen
|-
! scope="row"| Final energy/au
| align="right" |-576.581
|-
! scope="row"| Gradient/au
| align="right" |0.00000763
|-
! scope="row"| Dipole moment/D
| align="right" |10.45
|-
! scope="row"| Point group
| align="right" |C1
|-
! scope="row"| Time taken
| align="right" |54min 20s
|}

<pre>Low frequencies ---  -11.6009   -0.0004   -0.0004   -0.0003    2.8476    7.2269</pre>

=====Molecular orbitals=====
This is the [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26384 D-space] for the population analysis.
====(3) Me<sub>2</sub>Mg<sub>2</sub>Cl<sub>2</sub>L<sub>2</sub>, L = THF====
=====Optimisation=====

[https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26380 This] is the D-space for the optimisation.

{| class="wikitable"
|-
! scope="col"|
! scope="col"|MG2, L = THF
|-
! scope="row"| File type
| align="right" |.log
|-
! scope="row"| Calculation type
| align="right" |FOPT
|-
! scope="row"| Calculation method
| align="right" |RB3LYP
|-
! scope="row"| Basis set
| align="right" |Gen
|-
! scope="row"| Final energy/au
| align="right" |-576.555
|-
! scope="row"| Gradient/au
| align="right" |0.00025064
|-
! scope="row"| Dipole moment/D
| align="right" |13.28
|-
! scope="row"| Point group
| align="right" |C1
|-
! scope="row"| Time taken
| align="right" |4h 26min 9s
|}

<pre>         Item               Value     Threshold  Converged?
 Maximum Force            0.002152     0.000450     YES
 RMS     Force            0.000281     0.000300     YES
 Maximum Displacement     0.454039     0.001800     YES
 RMS     Displacement     0.110593     0.001200     YES
 Predicted change in Energy=-5.882623D-04</pre>

=====Frequency=====

This is the [https://spectradspace.lib.imperial.ac.uk:8443/dspace/handle/10042/26381 D-space] for the frequency analysis.

{| class="wikitable"
|-
! scope="col"|
! scope="col"|MG2, L = THF
|-
! scope="row"| File type
| align="right" |.log
|-
! scope="row"| Calculation type
| align="right" |FREQ
|-
! scope="row"| Calculation method
| align="right" |RB3LYP
|-
! scope="row"| Basis set
| align="right" |Gen
|-
! scope="row"| Final energy/au
| align="right" |-576.559
|-
! scope="row"| Gradient/au
| align="right" |0.00001015
|-
! scope="row"| Dipole moment/D
| align="right" |11.41
|-
! scope="row"| Point group
| align="right" |C1
|-
! scope="row"| Time taken
| align="right" |4h 40min 59s
|}

=====Molecular orbitals=====

This is the log file [[Media:JS Mg3 THF NBO.log]] and this is the checkpoint file [[Media:JS Mg3 THF NBO FINAL.fchk]] for the population analysis.

====Energy Comparison====

{| class="wikitable"
|-
! scope="col"|
! scope="col"|Energy of Molecule/a.u.
|-
! scope="row"|Mg2, L = Et<sub>2</sub>O
| align="right" |-579.0039
|-
! scope="row"|Mg2, L = THF
| align="right" |-576.581
|-
! scope="row"|Mg3, L = THF
| align="right" |-576.555 
|}

Looking at these values, it is clear that considering their absolute values in KJ/mol would be pointless, due to their magnitude. However, when the structures are viewed, they all look sensible. Therefore, their energies can be compared to each other.

Interestingly, Mg2 with L=THF is more stable than Mg3 with L=THF. This suggests that, overall, the intramolecular forces between the protons on the THF ligands and the methyl groups are attractive, and are lowering the energy of the molecule. Viewing the molecules below shows that the Mg3 molecule, shown <jmol>
<jmolAppletButton>
<uploadedFileContents>JS Mg3 mix OPT THF.mol</uploadedFileContents>
<text>here</text>
</jmolAppletButton>
</jmol>, is trying to maximise this interaction. The <jmol>
<jmolAppletButton>
<uploadedFileContents>JS Mg2THFOPT.mol</uploadedFileContents>
<text>Mg2</text>
</jmolAppletButton>
</jmol>, is already close to the optimum distance.

The shortest distance between the protons is 2.33A<sup>o</sup> in the Mg molecule, but 2.67A<sup>o</sup> in Mg2. However, Mg2 has many more of these interactions than Mg2. Presumably, the molecule with Et<sub>2</sub>O ligands is the most stable due to the lack of ring strain. In addition, it is easier for <jmol>
<jmolAppletButton>
<uploadedFileContents>JS MG2 MIX ET2O OPT3.mol</uploadedFileContents>
<text>this</text>
</jmolAppletButton>
</jmol> molecule to form the H-H interactions.

====MO Comparison====

{| class="wikitable"
|-
! scope="col"|Number
! scope="col"|MO
! scope="col"|Energy Mg2, L=Et<sub>2</sub>O/a.u.
! scope="col"|Energy Mg2, L=THF/a.u.
! scope="col"|Energy Mg3, L=THF/a.u.
! scope="col"|Atoms involved
! scope="col"|Orbitals That Are Overlapping
|-
| scope="row"| 61(LUMO)
| align="right" |[[File:Mg2Et2O MO11.png|200px]]
| scope="row"| -0.02344
| scope="row"| +0.02436
| scope="row"| +0.02756
| align="right" |Cl + Mg
| scope="row"| Probably p<sub>x</sub>, p<sub>y</sub> and p<sub>z</sub> to give a δ bond.
|-
| scope="row"| 60(HOMO)
| align="right" |[[File:Mg2Et2O MO10.png|200px]]
| scope="row"| -0.20946
| scope="row"| -0.20707
| scope="row"| -0.20541
| align="right" |Cl + Mg + C + H
| scope="row"|p<sub>x</sub> to form π bond.

σ* between Mg and Me.

|}

The orbitals of each molecule have almost identical geometry, therefore analysing the energy of these orbitals are key to understanding their chemistry. Based on this, the Mg2, L=Et<sub>2</sub>O, is the best electrophile, from the fact that it has the lowest lying LUMO. Mg3, L=THF, is the best nucleophile, with its highest energy HOMO.

====Conclusion====

This particular grignard reagent is a reasonably reactive molecule. The reasons for this are numerous, and are shown clearly by the population analysis, with the Mg3 molecule being the slightly better nucleophile. This analysis also shows that both solvents stabilize the molecules, with Et<sub>2</sub>O dong a slightly better job, shown by their relative energies. In addition, the population analysis shows explicitly what exactly is happening, in terms of bonding between the central atoms. Using molecular orbital theory, it was possible to explain what exactly was mixing in the majority of the key orbitals. As well as this, the vibrational analysis was in agreement with the population analysis and used to reinforce the data. The log file from the population analysis, in particular, was useful in analysing the position of the electron density between the central atoms. The two difficulties encountered were that, first, the Mg3, L=Et<sub>2</sub>, molecule was not successfully generated. Second, the issue that Gaussian is unable to label the interactions between Mg-Mg and Cl-Cl as bonds.

===References===

<references/>