ChemWiki - User contributions [en]

Rep:Mod:Fr216 Federica

2018-05-11T14:17:54Z

Fr216: /* MO analysis */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below and are similar to literature values.<ref name="fe5" />

{| class="wikitable"
|-
! Mode
! Frequency
! Intensity
! Is it IR active?
! Symmetry
! Type
|-
| 1
| 1164
| 93
| YES
| a2''
| bend out of plane
|-
| 2
| 1214
| 14
| YES
| e'
| bend
|-
| 3
| 1214
| 14
| YES
| e'
| bend
|-
| 4
| 2579
| 0
| NO
| a1'
| symmetric stretch
|-
| 5
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
| 6
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|600px|center|thumb]]

*MO analysis

[[File:fr_MO_diagram.png|700px|center|thumb| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid<ref name="fe4" />. MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 kJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 kJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 kJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 kJ/mol

The calculated association energy for NH3BH3 is of -82.965 kJ/mol, which corresponds to 82.96581 kJ/mol in terms of dissociation energy. In terms of what kind of bond we are looking at, it is possible to define it as a dative bond by comparison with literature values. The covalent B-N bond has been found to have a dissociation energy of about 380 kJ/mol<ref name="fe2" />, which is much greater than the valued obtained via the calculations. On the other hand, a dative B-N bond has a dissociation energy of 130.123 ± 4 kJ/mol<ref name="fe6" />, which is very similar to the calculated value. Therefore, the bond is easily recognizable as a dative bond given by the donation of the N lone pair into the empty B p orbital.<ref name="fe1" />

A dative bond is weaker than a covalent bond because while in the first case its rupture gives out species without a net charge (like NH3 and BH3) or two species with both a net charge, the rupture of a covalent bond gives a radical species (far less stable).

This is the reason why BH3NH3 and C2H6 have so different properties despite being isoelectronic<ref name="fe6" />. The C-C bond in ethane is covalent and its rupture gives out two radical species (CH3). This is the reason why the C-C bond dissociation energy is so much higher than the B-N one.

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392
{{DOI|10042/202392}}

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue. No nodes are present in the MO. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair<ref name="fe4" />. In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = - {E(dimer)-[2 x E(monomer)]} = - {- 2352.4163 -[2 x (-1176.1901)]} = 0.0361 a.u. = 94.78056 kJ/mol

The calculation shows how the dimer is lower in energy than the two monomers taken singularly and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising<ref name="fe4" />.

===References===

<references>
<ref name="fe">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
<ref name="fe1">The Journal of Chemical Physics 144, 144315 (2016); https://doi.org/10.1063/1.4945624 </ref>
<ref name="fe2">The table of dissociation energies, accessed Mayb,2018 from: http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf </ref>
<ref name="fe4">L. Patel, presented in part in "lecture notes", Imperial College London, Term 2, 2018. </ref>
<ref name="fe5">Kawaguchi, Kentarou (1992). "Fourier transform infrared spectroscopy of the BH3 ν3 band". The Journal of Chemical Physics. 96 (5): 3411. doi:10.1063/1.461942. ISSN 0021-9606. </ref>
<ref name="fe6">Haaland A. Covalent versus Dative Bonds to Main Group Metals, a Useful Distinction. Angew. Chem. Inf. Ed. Engl. 1989;(28)992-1007.</ref>

</references>

Rep:Mod:Fr216 Federica

2018-05-11T14:11:14Z

Fr216: /* Association Energy calculation for BH3NH3 */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below and are similar to literature values.<ref name="fe5" />

{| class="wikitable"
|-
! Mode
! Frequency
! Intensity
! Is it IR active?
! Symmetry
! Type
|-
| 1
| 1164
| 93
| YES
| a2''
| bend out of plane
|-
| 2
| 1214
| 14
| YES
| e'
| bend
|-
| 3
| 1214
| 14
| YES
| e'
| bend
|-
| 4
| 2579
| 0
| NO
| a1'
| symmetric stretch
|-
| 5
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
| 6
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|600px|center|thumb]]

*MO analysis

[[File:fr_MO_diagram.png|700px|center|thumb| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid<ref name="fe4" />. MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 kJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 kJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 kJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 kJ/mol

The calculated association energy for NH3BH3 is of -82.965 kJ/mol, which corresponds to 82.96581 kJ/mol in terms of dissociation energy. In terms of what kind of bond we are looking at, it is possible to define it as a dative bond by comparison with literature values. The covalent B-N bond has been found to have a dissociation energy of about 380 kJ/mol<ref name="fe2" />, which is much greater than the valued obtained via the calculations. On the other hand, a dative B-N bond has a dissociation energy of 130.123 ± 4 kJ/mol<ref name="fe6" />, which is very similar to the calculated value. Therefore, the bond is easily recognizable as a dative bond given by the donation of the N lone pair into the empty B p orbital.<ref name="fe1" />

A dative bond is weaker than a covalent bond because while in the first case its rupture gives out species without a net charge (like NH3 and BH3) or two species with both a net charge, the rupture of a covalent bond gives a radical species (far less stable).

This is the reason why BH3NH3 and C2H6 have so different properties despite being isoelectronic<ref name="fe6" />. The C-C bond in ethane is covalent and its rupture gives out two radical species (CH3). This is the reason why the C-C bond dissociation energy is so much higher than the B-N one.

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392
{{DOI|10042/202392}}

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair<ref name="fe4" />. In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = - {E(dimer)-[2 x E(monomer)]} = - {- 2352.4163 -[2 x (-1176.1901)]} = 0.0361 a.u. = 94.78056 kJ/mol

The calculation shows how the dimer is lower in energy than the two monomers taken singularly and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising<ref name="fe4" />.

===References===

<references>
<ref name="fe">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
<ref name="fe1">The Journal of Chemical Physics 144, 144315 (2016); https://doi.org/10.1063/1.4945624 </ref>
<ref name="fe2">The table of dissociation energies, accessed Mayb,2018 from: http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf </ref>
<ref name="fe4">L. Patel, presented in part in "lecture notes", Imperial College London, Term 2, 2018. </ref>
<ref name="fe5">Kawaguchi, Kentarou (1992). "Fourier transform infrared spectroscopy of the BH3 ν3 band". The Journal of Chemical Physics. 96 (5): 3411. doi:10.1063/1.461942. ISSN 0021-9606. </ref>
<ref name="fe6">Haaland A. Covalent versus Dative Bonds to Main Group Metals, a Useful Distinction. Angew. Chem. Inf. Ed. Engl. 1989;(28)992-1007.</ref>

</references>

Rep:Mod:Fr216 Federica

2018-05-11T14:09:12Z

Fr216: /* Association Energy calculation for BH3NH3 */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below and are similar to literature values.<ref name="fe5" />

{| class="wikitable"
|-
! Mode
! Frequency
! Intensity
! Is it IR active?
! Symmetry
! Type
|-
| 1
| 1164
| 93
| YES
| a2''
| bend out of plane
|-
| 2
| 1214
| 14
| YES
| e'
| bend
|-
| 3
| 1214
| 14
| YES
| e'
| bend
|-
| 4
| 2579
| 0
| NO
| a1'
| symmetric stretch
|-
| 5
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
| 6
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|600px|center|thumb]]

*MO analysis

[[File:fr_MO_diagram.png|700px|center|thumb| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid<ref name="fe4" />. MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 kJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 kJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 kJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 kJ/mol

The calculated association energy for NH3BH3 is of -82.965 kJ/mol, which corresponds to 82.96581 kJ/mol in terms of dissociation energy. In terms of what kind of bond we are looking at, it is possible to define it as a dative bond by comparison with literature values. The covalent B-N bond has been found to have a dissociation energy of about 380 kJ/mol<ref name="fe2" />, which is much greater than the valued obtained via the calculations. On the other hand, a dative B-N bond has a dissociation energy of 130.123 ± 4 kJ/mol<ref name="fe6" />, which is very similar to the calculated value. Therefore, the bond is easily recognizable as a dative bond given by the donation of the N lone pair into the empty B p orbital.<ref name="fe1" />

A dative bond is weaker than a covalent bond because while in the first case its rupture gives out species without a net charge (like NH3 and BH3) or two species with both a net charge, the rupture of a covalent bond gives a radical species (far less stable).

This is the reason why BH3NH3 and C2H6 have so different properties despite being isoelectronic. The C-C bond in ethane is covalent and its rupture gives out two radical species (CH3). This is the reason why the C-C bond dissociation energy is so much higher than the B-N one.

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392
{{DOI|10042/202392}}

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair<ref name="fe4" />. In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = - {E(dimer)-[2 x E(monomer)]} = - {- 2352.4163 -[2 x (-1176.1901)]} = 0.0361 a.u. = 94.78056 kJ/mol

The calculation shows how the dimer is lower in energy than the two monomers taken singularly and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising<ref name="fe4" />.

===References===

<references>
<ref name="fe">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
<ref name="fe1">The Journal of Chemical Physics 144, 144315 (2016); https://doi.org/10.1063/1.4945624 </ref>
<ref name="fe2">The table of dissociation energies, accessed Mayb,2018 from: http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf </ref>
<ref name="fe4">L. Patel, presented in part in "lecture notes", Imperial College London, Term 2, 2018. </ref>
<ref name="fe5">Kawaguchi, Kentarou (1992). "Fourier transform infrared spectroscopy of the BH3 ν3 band". The Journal of Chemical Physics. 96 (5): 3411. doi:10.1063/1.461942. ISSN 0021-9606. </ref>
<ref name="fe6">Haaland A. Covalent versus Dative Bonds to Main Group Metals, a Useful Distinction. Angew. Chem. Inf. Ed. Engl. 1989;(28)992-1007.</ref>

</references>

Rep:Mod:Fr216 Federica

2018-05-11T13:51:10Z

Fr216: /* References */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below and are similar to literature values.<ref name="fe5" />

{| class="wikitable"
|-
! Mode
! Frequency
! Intensity
! Is it IR active?
! Symmetry
! Type
|-
| 1
| 1164
| 93
| YES
| a2''
| bend out of plane
|-
| 2
| 1214
| 14
| YES
| e'
| bend
|-
| 3
| 1214
| 14
| YES
| e'
| bend
|-
| 4
| 2579
| 0
| NO
| a1'
| symmetric stretch
|-
| 5
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
| 6
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|600px|center|thumb]]

*MO analysis

[[File:fr_MO_diagram.png|700px|center|thumb| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid<ref name="fe4" />. MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 kJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 kJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 kJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 kJ/mol

The calculated association energy for NH3BH3 is of -82.965 kJ/mol, which corresponds to 82.96581 kJ/mol in terms of dissociation energy. In terms of what kind of bond we are looking at, it is possible to define it as a dative bond by comparison with literature values. The covalent B-N bond has been found to have a dissociation energy of about 380 kJ/mol<ref name="fe2" />, which is much greater than the valued obtained via the calculations. On the other hand, a dative B-N bond has a dissociation energy of 130.123 ± 4 kJ/mol<ref name="fe5" /> , which is very similar to the calculated value. Therefore, the bond is easily recognizable as a strong dative bond given by the donation of the N lone pair into the empty B p orbital. <ref name="fe1" /> The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has an association energy of about , which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392
{{DOI|10042/202392}}

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair<ref name="fe4" />. In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = - {E(dimer)-[2 x E(monomer)]} = - {- 2352.4163 -[2 x (-1176.1901)]} = 0.0361 a.u. = 94.78056 kJ/mol

The calculation shows how the dimer is lower in energy than the two monomers taken singularly and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising<ref name="fe4" />.

===References===

<references>
<ref name="fe">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
<ref name="fe1">The Journal of Chemical Physics 144, 144315 (2016); https://doi.org/10.1063/1.4945624 </ref>
<ref name="fe2">The table of dissociation energies, accessed Mayb,2018 from: http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf </ref>
<ref name="fe4">L. Patel, presented in part in "lecture notes", Imperial College London, Term 2, 2018. </ref>
<ref name="fe5">Kawaguchi, Kentarou (1992). "Fourier transform infrared spectroscopy of the BH3 ν3 band". The Journal of Chemical Physics. 96 (5): 3411. doi:10.1063/1.461942. ISSN 0021-9606. </ref>
<ref name="fe6">Haaland A. Covalent versus Dative Bonds to Main Group Metals, a Useful Distinction. Angew. Chem. Inf. Ed. Engl. 1989;(28)992-1007.</ref>

</references>

Rep:Mod:Fr216 Federica

2018-05-11T13:47:02Z

Fr216: /* Association Energy calculation for BH3NH3 */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below and are similar to literature values.<ref name="fe5" />

{| class="wikitable"
|-
! Mode
! Frequency
! Intensity
! Is it IR active?
! Symmetry
! Type
|-
| 1
| 1164
| 93
| YES
| a2''
| bend out of plane
|-
| 2
| 1214
| 14
| YES
| e'
| bend
|-
| 3
| 1214
| 14
| YES
| e'
| bend
|-
| 4
| 2579
| 0
| NO
| a1'
| symmetric stretch
|-
| 5
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
| 6
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|600px|center|thumb]]

*MO analysis

[[File:fr_MO_diagram.png|700px|center|thumb| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid<ref name="fe4" />. MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 kJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 kJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 kJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 kJ/mol

The calculated association energy for NH3BH3 is of -82.965 kJ/mol, which corresponds to 82.96581 kJ/mol in terms of dissociation energy. In terms of what kind of bond we are looking at, it is possible to define it as a dative bond by comparison with literature values. The covalent B-N bond has been found to have a dissociation energy of about 380 kJ/mol<ref name="fe2" />, which is much greater than the valued obtained via the calculations. On the other hand, a dative B-N bond has a dissociation energy of 130.123 ± 4 kJ/mol<ref name="fe5" /> , which is very similar to the calculated value. Therefore, the bond is easily recognizable as a strong dative bond given by the donation of the N lone pair into the empty B p orbital. <ref name="fe1" /> The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has an association energy of about , which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392
{{DOI|10042/202392}}

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair<ref name="fe4" />. In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = - {E(dimer)-[2 x E(monomer)]} = - {- 2352.4163 -[2 x (-1176.1901)]} = 0.0361 a.u. = 94.78056 kJ/mol

The calculation shows how the dimer is lower in energy than the two monomers taken singularly and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising<ref name="fe4" />.

===References===

<references>
<ref name="fe">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
<ref name="fe1">The Journal of Chemical Physics 144, 144315 (2016); https://doi.org/10.1063/1.4945624 </ref>
<ref name="fe2">The table of dissociation energies, accessed Mayb,2018 from: http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf </ref>
<ref name="fe4">L. Patel, presented in part in "lecture notes", Imperial College London, Term 2, 2018. </ref>
<ref name="fe5">Kawaguchi, Kentarou (1992). "Fourier transform infrared spectroscopy of the BH3 ν3 band". The Journal of Chemical Physics. 96 (5): 3411. doi:10.1063/1.461942. ISSN 0021-9606. </ref>

</references>

Rep:Mod:Fr216 Federica

2018-05-11T13:32:23Z

Fr216: /* Dissociation energy calculations */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below and are similar to literature values.<ref name="fe5" />

{| class="wikitable"
|-
! Mode
! Frequency
! Intensity
! Is it IR active?
! Symmetry
! Type
|-
| 1
| 1164
| 93
| YES
| a2''
| bend out of plane
|-
| 2
| 1214
| 14
| YES
| e'
| bend
|-
| 3
| 1214
| 14
| YES
| e'
| bend
|-
| 4
| 2579
| 0
| NO
| a1'
| symmetric stretch
|-
| 5
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
| 6
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|600px|center|thumb]]

*MO analysis

[[File:fr_MO_diagram.png|700px|center|thumb| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid<ref name="fe4" />. MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 kJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 kJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 kJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 kJ/mol

The calculated association energy for NH3BH3 is of -82.965 kJ/mol, which corresponds to 82.96581 kJ/mol in terms of dissociation energy. The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. <ref name="fe1" /> The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has an association energy of about 380 KJ/mol<ref name="fe2" />, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392
{{DOI|10042/202392}}

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair<ref name="fe4" />. In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = - {E(dimer)-[2 x E(monomer)]} = - {- 2352.4163 -[2 x (-1176.1901)]} = 0.0361 a.u. = 94.78056 kJ/mol

The calculation shows how the dimer is lower in energy than the two monomers taken singularly and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising<ref name="fe4" />.

===References===

<references>
<ref name="fe">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
<ref name="fe1">The Journal of Chemical Physics 144, 144315 (2016); https://doi.org/10.1063/1.4945624 </ref>
<ref name="fe2">The table of dissociation energies, accessed Mayb,2018 from: http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf </ref>
<ref name="fe4">L. Patel, presented in part in "lecture notes", Imperial College London, Term 2, 2018. </ref>
<ref name="fe5">Kawaguchi, Kentarou (1992). "Fourier transform infrared spectroscopy of the BH3 ν3 band". The Journal of Chemical Physics. 96 (5): 3411. doi:10.1063/1.461942. ISSN 0021-9606. </ref>

</references>

Rep:Mod:Fr216 Federica

2018-05-11T13:30:07Z

Fr216: /* Association Energy calculation for BH3NH3 */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below and are similar to literature values.<ref name="fe5" />

{| class="wikitable"
|-
! Mode
! Frequency
! Intensity
! Is it IR active?
! Symmetry
! Type
|-
| 1
| 1164
| 93
| YES
| a2''
| bend out of plane
|-
| 2
| 1214
| 14
| YES
| e'
| bend
|-
| 3
| 1214
| 14
| YES
| e'
| bend
|-
| 4
| 2579
| 0
| NO
| a1'
| symmetric stretch
|-
| 5
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
| 6
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|600px|center|thumb]]

*MO analysis

[[File:fr_MO_diagram.png|700px|center|thumb| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid<ref name="fe4" />. MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 kJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 kJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 kJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 kJ/mol

The calculated association energy for NH3BH3 is of -82.965 kJ/mol, which corresponds to 82.96581 kJ/mol in terms of dissociation energy. The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. <ref name="fe1" /> The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has an association energy of about 380 KJ/mol<ref name="fe2" />, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392
{{DOI|10042/202392}}

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair<ref name="fe4" />. In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising<ref name="fe4" />.

===References===

<references>
<ref name="fe">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
<ref name="fe1">The Journal of Chemical Physics 144, 144315 (2016); https://doi.org/10.1063/1.4945624 </ref>
<ref name="fe2">The table of dissociation energies, accessed Mayb,2018 from: http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf </ref>
<ref name="fe4">L. Patel, presented in part in "lecture notes", Imperial College London, Term 2, 2018. </ref>
<ref name="fe5">Kawaguchi, Kentarou (1992). "Fourier transform infrared spectroscopy of the BH3 ν3 band". The Journal of Chemical Physics. 96 (5): 3411. doi:10.1063/1.461942. ISSN 0021-9606. </ref>

</references>

Rep:Mod:Fr216 Federica

2018-05-11T13:24:20Z

Fr216: /* Dissociation energy calculations */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below and are similar to literature values.<ref name="fe5" />

{| class="wikitable"
|-
! Mode
! Frequency
! Intensity
! Is it IR active?
! Symmetry
! Type
|-
| 1
| 1164
| 93
| YES
| a2''
| bend out of plane
|-
| 2
| 1214
| 14
| YES
| e'
| bend
|-
| 3
| 1214
| 14
| YES
| e'
| bend
|-
| 4
| 2579
| 0
| NO
| a1'
| symmetric stretch
|-
| 5
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
| 6
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|600px|center|thumb]]

*MO analysis

[[File:fr_MO_diagram.png|700px|center|thumb| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid<ref name="fe4" />. MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. <ref name="fe1" /> The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol<ref name="fe2" />, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392
{{DOI|10042/202392}}

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair<ref name="fe4" />. In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising<ref name="fe4" />.

===References===

<references>
<ref name="fe">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
<ref name="fe1">The Journal of Chemical Physics 144, 144315 (2016); https://doi.org/10.1063/1.4945624 </ref>
<ref name="fe2">The table of dissociation energies, accessed Mayb,2018 from: http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf </ref>
<ref name="fe4">L. Patel, presented in part in "lecture notes", Imperial College London, Term 2, 2018. </ref>
<ref name="fe5">Kawaguchi, Kentarou (1992). "Fourier transform infrared spectroscopy of the BH3 ν3 band". The Journal of Chemical Physics. 96 (5): 3411. doi:10.1063/1.461942. ISSN 0021-9606. </ref>

</references>

Rep:Mod:Fr216 Federica

2018-05-11T13:23:38Z

Fr216: /* Dissociation energy calculations */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below and are similar to literature values.<ref name="fe5" />

{| class="wikitable"
|-
! Mode
! Frequency
! Intensity
! Is it IR active?
! Symmetry
! Type
|-
| 1
| 1164
| 93
| YES
| a2''
| bend out of plane
|-
| 2
| 1214
| 14
| YES
| e'
| bend
|-
| 3
| 1214
| 14
| YES
| e'
| bend
|-
| 4
| 2579
| 0
| NO
| a1'
| symmetric stretch
|-
| 5
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
| 6
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|600px|center|thumb]]

*MO analysis

[[File:fr_MO_diagram.png|700px|center|thumb| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid<ref name="fe4" />. MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. <ref name="fe1" /> The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol<ref name="fe2" />, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392
{{DOI|10042/202392}}

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair<ref name="fe4" />. In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising<ref name="fe4">.

===References===

<references>
<ref name="fe">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
<ref name="fe1">The Journal of Chemical Physics 144, 144315 (2016); https://doi.org/10.1063/1.4945624 </ref>
<ref name="fe2">The table of dissociation energies, accessed Mayb,2018 from: http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf </ref>
<ref name="fe4">L. Patel, presented in part in "lecture notes", Imperial College London, Term 2, 2018. </ref>
<ref name="fe5">Kawaguchi, Kentarou (1992). "Fourier transform infrared spectroscopy of the BH3 ν3 band". The Journal of Chemical Physics. 96 (5): 3411. doi:10.1063/1.461942. ISSN 0021-9606. </ref>

</references>

Rep:Mod:Fr216 Federica

2018-05-11T13:22:34Z

Fr216: /* Specific additional information */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below and are similar to literature values.<ref name="fe5" />

{| class="wikitable"
|-
! Mode
! Frequency
! Intensity
! Is it IR active?
! Symmetry
! Type
|-
| 1
| 1164
| 93
| YES
| a2''
| bend out of plane
|-
| 2
| 1214
| 14
| YES
| e'
| bend
|-
| 3
| 1214
| 14
| YES
| e'
| bend
|-
| 4
| 2579
| 0
| NO
| a1'
| symmetric stretch
|-
| 5
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
| 6
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|600px|center|thumb]]

*MO analysis

[[File:fr_MO_diagram.png|700px|center|thumb| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid<ref name="fe4" />. MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. <ref name="fe1" /> The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol<ref name="fe2" />, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392
{{DOI|10042/202392}}

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair<ref name="fe4" />. In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

===References===

<references>
<ref name="fe">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
<ref name="fe1">The Journal of Chemical Physics 144, 144315 (2016); https://doi.org/10.1063/1.4945624 </ref>
<ref name="fe2">The table of dissociation energies, accessed Mayb,2018 from: http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf </ref>
<ref name="fe4">L. Patel, presented in part in "lecture notes", Imperial College London, Term 2, 2018. </ref>
<ref name="fe5">Kawaguchi, Kentarou (1992). "Fourier transform infrared spectroscopy of the BH3 ν3 band". The Journal of Chemical Physics. 96 (5): 3411. doi:10.1063/1.461942. ISSN 0021-9606. </ref>

</references>

Rep:Mod:Fr216 Federica

2018-05-11T13:21:34Z

Fr216: /* Specific additional information */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below and are similar to literature values.<ref name="fe5" />

{| class="wikitable"
|-
! Mode
! Frequency
! Intensity
! Is it IR active?
! Symmetry
! Type
|-
| 1
| 1164
| 93
| YES
| a2''
| bend out of plane
|-
| 2
| 1214
| 14
| YES
| e'
| bend
|-
| 3
| 1214
| 14
| YES
| e'
| bend
|-
| 4
| 2579
| 0
| NO
| a1'
| symmetric stretch
|-
| 5
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
| 6
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|600px|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid<ref name="fe4" />. MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. <ref name="fe1" /> The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol<ref name="fe2" />, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392
{{DOI|10042/202392}}

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair<ref name="fe4" />. In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

===References===

<references>
<ref name="fe">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
<ref name="fe1">The Journal of Chemical Physics 144, 144315 (2016); https://doi.org/10.1063/1.4945624 </ref>
<ref name="fe2">The table of dissociation energies, accessed Mayb,2018 from: http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf </ref>
<ref name="fe4">L. Patel, presented in part in "lecture notes", Imperial College London, Term 2, 2018. </ref>
<ref name="fe5">Kawaguchi, Kentarou (1992). "Fourier transform infrared spectroscopy of the BH3 ν3 band". The Journal of Chemical Physics. 96 (5): 3411. doi:10.1063/1.461942. ISSN 0021-9606. </ref>

</references>

Rep:Mod:Fr216 Federica

2018-05-11T13:20:27Z

Fr216: /* Specific additional information */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below and are similar to literature values.<ref name="fe5" />

{| class="wikitable"
|-
! Mode
! Frequency
! Intensity
! Is it IR active?
! Symmetry
! Type
|-
| 1
| 1164
| 93
| YES
| a2''
| bend out of plane
|-
| 2
| 1214
| 14
| YES
| e'
| bend
|-
| 3
| 1214
| 14
| YES
| e'
| bend
|-
| 4
| 2579
| 0
| NO
| a1'
| symmetric stretch
|-
| 5
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
| 6
| 2712
| 126
| YES
| e'
| asymmetric stretch
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid<ref name="fe4" />. MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. <ref name="fe1" /> The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol<ref name="fe2" />, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392
{{DOI|10042/202392}}

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair<ref name="fe4" />. In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

===References===

<references>
<ref name="fe">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
<ref name="fe1">The Journal of Chemical Physics 144, 144315 (2016); https://doi.org/10.1063/1.4945624 </ref>
<ref name="fe2">The table of dissociation energies, accessed Mayb,2018 from: http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf </ref>
<ref name="fe4">L. Patel, presented in part in "lecture notes", Imperial College London, Term 2, 2018. </ref>
<ref name="fe5">Kawaguchi, Kentarou (1992). "Fourier transform infrared spectroscopy of the BH3 ν3 band". The Journal of Chemical Physics. 96 (5): 3411. doi:10.1063/1.461942. ISSN 0021-9606. </ref>

</references>

Rep:Mod:Fr216 Federica

2018-05-11T13:15:50Z

Fr216: /* Specific additional information */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below and are similar to literature values.<ref name="fe5" />

{| class="wikitable"
|-
! Mode
! Frequency
! Intensity
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| 93
| YES
| a2''
|-
| 2
| 1214
| 14
| YES
| e' bend
|-
| 3
| 1214
| 14
| YES
| e' bend
|-
| 4
| 2579
| 0
| NO
| a1'
|-
| 5
| 2712
| 126
| YES
| e'
|-
| 6
| 2712
| 126
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid<ref name="fe4" />. MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. <ref name="fe1" /> The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol<ref name="fe2" />, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392
{{DOI|10042/202392}}

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair<ref name="fe4" />. In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

===References===

<references>
<ref name="fe">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
<ref name="fe1">The Journal of Chemical Physics 144, 144315 (2016); https://doi.org/10.1063/1.4945624 </ref>
<ref name="fe2">The table of dissociation energies, accessed Mayb,2018 from: http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf </ref>
<ref name="fe4">L. Patel, presented in part in "lecture notes", Imperial College London, Term 2, 2018. </ref>
<ref name="fe5">Kawaguchi, Kentarou (1992). "Fourier transform infrared spectroscopy of the BH3 ν3 band". The Journal of Chemical Physics. 96 (5): 3411. doi:10.1063/1.461942. ISSN 0021-9606. </ref>

</references>

Rep:Mod:Fr216 Federica

2018-05-11T13:07:01Z

Fr216: /* Computational basis set: B - 6-31G and Br - LanL2DZ */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below and are similar to literature values.<ref name="fe5" />

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid<ref name="fe4" />. MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. <ref name="fe1" /> The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol<ref name="fe2" />, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392
{{DOI|10042/202392}}

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair<ref name="fe4" />. In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

===References===

<references>
<ref name="fe">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
<ref name="fe1">The Journal of Chemical Physics 144, 144315 (2016); https://doi.org/10.1063/1.4945624 </ref>
<ref name="fe2">The table of dissociation energies, accessed Mayb,2018 from: http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf </ref>
<ref name="fe4">L. Patel, presented in part in "lecture notes", Imperial College London, Term 2, 2018. </ref>
<ref name="fe5">Kawaguchi, Kentarou (1992). "Fourier transform infrared spectroscopy of the BH3 ν3 band". The Journal of Chemical Physics. 96 (5): 3411. doi:10.1063/1.461942. ISSN 0021-9606. </ref>

</references>

Rep:Mod:Fr216 Federica

2018-05-11T11:49:34Z

Fr216: /* Molecules optimization and analysis */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below and are similar to literature values.<ref name="fe5" />

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid<ref name="fe4" />. MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. <ref name="fe1" /> The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol<ref name="fe2" />, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair<ref name="fe4" />. In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

===References===

<references>
<ref name="fe">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
<ref name="fe1">The Journal of Chemical Physics 144, 144315 (2016); https://doi.org/10.1063/1.4945624 </ref>
<ref name="fe2">The table of dissociation energies, accessed Mayb,2018 from: http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf </ref>
<ref name="fe4">L. Patel, presented in part in "lecture notes", Imperial College London, Term 2, 2018. </ref>
<ref name="fe5">Kawaguchi, Kentarou (1992). "Fourier transform infrared spectroscopy of the BH3 ν3 band". The Journal of Chemical Physics. 96 (5): 3411. doi:10.1063/1.461942. ISSN 0021-9606. </ref>

</references>

Rep:Mod:Fr216 Federica

2018-05-11T11:40:39Z

Fr216: /* References */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid<ref name="fe4" />. MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. <ref name="fe1" /> The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol<ref name="fe2" />, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair (lit). In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

===References===

<references>
<ref name="fe">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
<ref name="fe1">The Journal of Chemical Physics 144, 144315 (2016); https://doi.org/10.1063/1.4945624 </ref>
<ref name="fe2">The table of dissociation energies, accessed Mayb,2018 from: http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf </ref>
<ref name="fe4"> L. Patel, presented in part in "lecture notes", Imperial College London, Term 2, 2018. </ref>

</references>

Rep:Mod:Fr216 Federica

2018-05-11T11:39:10Z

Fr216: /* Specific additional information */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid<ref name="fe4" />. MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. <ref name="fe1" /> The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol<ref name="fe2" />, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair (lit). In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

===References===

<references>
<ref name="fe">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
<ref name="fe1">The Journal of Chemical Physics 144, 144315 (2016); https://doi.org/10.1063/1.4945624 </ref>
<ref name="fe2">The table of dissociation energies, accessed Mayb,2018 from: http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf </ref>

</references>

Rep:Mod:Fr216 Federica

2018-05-11T11:29:59Z

Fr216: /* Association Energy calculation for BH3NH3 */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. <ref name="fe1" /> The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol<ref name="fe2" />, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair (lit). In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

===References===

<references>
<ref name="fe">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
<ref name="fe1">The Journal of Chemical Physics 144, 144315 (2016); https://doi.org/10.1063/1.4945624 </ref>
<ref name="fe2">The table of dissociation energies, accessed Mayb,2018 from: http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf </ref>

</references>

Rep:Mod:Fr216 Federica

2018-05-11T11:27:10Z

Fr216: /* References */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. <ref name="fe1" /> The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol<ref name="fe2" />, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair (lit). In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

===References===

<references>
<ref name="fe">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
<ref name="fe1">The Journal of Chemical Physics 144, 144315 (2016); https://doi.org/10.1063/1.4945624 </ref>
<ref name="fe2">The table of dissociation energies, accessed Mayb,2018 from: http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf </ref>

</references>

Rep:Mod:Fr216 Federica

2018-05-11T11:27:00Z

Fr216: /* References */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. <ref name="fe1" /> The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol<ref name="fe2" />, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair (lit). In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

===References===

<references>
<ref name="fe">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
<ref name="fe2">The Journal of Chemical Physics 144, 144315 (2016); https://doi.org/10.1063/1.4945624 </ref>
<ref name="fe2">The table of dissociation energies, accessed Mayb,2018 from: http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf </ref>

</references>

Rep:Mod:Fr216 Federica

2018-05-11T11:21:59Z

Fr216: /* References */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. <ref name="fe1" /> The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol<ref name="fe2" />, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair (lit). In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

===References===

<references>
<ref name="fe">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
<ref name="fe2"> </ref>
</references>

Rep:Mod:Fr216 Federica

2018-05-11T11:17:01Z

Fr216: /* Association Energy calculation for BH3NH3 */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. <ref name="fe1" /> The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol<ref name="fe2" />, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair (lit). In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

===References===

<references>
<ref name="fe">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
</references>

Rep:Mod:Fr216 Federica

2018-05-11T11:04:07Z

Fr216: /* References */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. (lit) The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair (lit). In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

===References===

<references>
<ref name="fe">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
</references>

Rep:Mod:Fr216 Federica

2018-05-11T11:03:58Z

Fr216: /* References */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. (lit) The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair (lit). In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

===References===

<references>
<ref name="fe1">P. Hunt, presented in part in "tutorial 1 notes", Imperial College London, May, 2018. </ref>
</references>

Rep:Mod:Fr216 Federica

2018-05-11T11:01:53Z

Fr216: /* Specific additional information */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3<ref name="fe" />]]

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. (lit) The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair (lit). In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

===References===

Rep:Mod:Fr216 Federica

2018-05-11T11:00:16Z

Fr216: /* Molecules optimization and analysis */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3]]

''insert reference to Patricia hunt''

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. (lit) The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair (lit). In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

===References===

Rep:Mod:Fr216 Federica

2018-05-11T10:56:50Z

Fr216: /* MO analysis */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3]]

''insert reference to Patricia hunt''

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. (lit) The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair (lit). In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

Rep:Mod:Fr216 Federica

2018-05-11T10:56:29Z

Fr216: /* MO analysis */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3]]

''insert reference to Patricia hunt''

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. (lit) The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

MO43 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO43 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair (lit). In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

File:MO43 to post.png

2018-05-11T10:56:22Z

Fr216:

File:MO56 to post.png

2018-05-11T10:55:32Z

Fr216: Fr216 uploaded a new version of File:MO56 to post.png

File:MO56 to post.png

2018-05-11T10:54:16Z

Fr216: Fr216 uploaded a new version of File:MO56 to post.png

File:MO54 to post.png

2018-05-11T10:53:41Z

Fr216: Fr216 uploaded a new version of File:MO54 to post.png

Rep:Mod:Fr216 Federica

2018-05-11T10:40:58Z

Fr216: /* Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3]]

''insert reference to Patricia hunt''

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. (lit) The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

=====MO analysis =====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair (lit). In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

Rep:Mod:Fr216 Federica

2018-05-11T10:40:07Z

Fr216: /* MO analysis */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3]]

''insert reference to Patricia hunt''

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. (lit) The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair (lit). In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

Rep:Mod:Fr216 Federica

2018-05-11T10:38:44Z

Fr216: /* Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3]]

''insert reference to Patricia hunt''

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. (lit) The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair (lit). In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame|Summary table for monomer AlCl2Br]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

====MO analysis ====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

Rep:Mod:Fr216 Federica

2018-05-11T10:37:51Z

Fr216: /* Mini project - Lewis Acids and Bases */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3]]

''insert reference to Patricia hunt''

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. (lit) The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair (lit). In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

====MO analysis ====

The 3 valence MO chosen for the analysis are: MO56, MO54 and MO43.

MO56 is an unfilled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has an highly antibonding character.

[[File:MO56 to post.png|center|frame]]

MO54 is a filled orbital. The main orbital interactions are highlighted in blue and the nodes in red. Overall, it has a non-bonding character.

[[File:MO54 to post.png|center|frame]]

File:MO54 to post.png

2018-05-11T10:37:07Z

Fr216:

File:MO56 to post.png

2018-05-11T10:25:05Z

Fr216:

Rep:Mod:Fr216 Federica

2018-05-11T10:24:10Z

Fr216: /* Dissociation energy calculations */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3]]

''insert reference to Patricia hunt''

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. (lit) The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair (lit). In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element, and it tries to compensate by dimerising (lit).

====MO analysis ====

Rep:Mod:Fr216 Federica

2018-05-11T10:22:49Z

Fr216: /* Mini project - Lewis Acids and Bases */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3]]

''insert reference to Patricia hunt''

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. (lit) The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown below, and the label corresponds to their point group.

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|Summary table for trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

====Confomer with bridging Br groups ====

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|Summary table for confomer with bridging Br groups]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity and presence of lone pair (lit). In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

A computational analysis was performed on the AlCl2Br monomer to get the dissociation energy of the lowest energy dimer.

=====Computational basis set: Al, Cl - 6-31G(d,p) and Br - LanL2DZ=====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable. This is not surprising considering that Al is an electrodeficient Group 13 element,

Rep:Mod:Fr216 Federica

2018-05-11T10:04:23Z

Fr216: /* Mini project - Lewis Acids and Bases */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3]]

''insert reference to Patricia hunt''

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. (lit) The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown in the following figure:

[[File:fr_5isomers.png|frame|center|The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

====Confomer with bridging Br groups ====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|5 isomers of Al2Cl4Br2]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity. In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable.

File:Fr 5isomers.png

2018-05-11T10:04:03Z

Fr216: Fr216 uploaded a new version of File:Fr 5isomers.png

Rep:Mod:Fr216 Federica

2018-05-11T10:00:30Z

Fr216: /* Mini project - Lewis Acids and Bases */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3]]

''insert reference to Patricia hunt''

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. (lit) The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown in the following figure:

[[File:fr_5isomers.png|thumb|center|200x100px|alt=White diagonal cross over blue background|5 isomers]]
[[File:fr_5isomers.png|frame|center|200x200px|alt=The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

====Confomer with bridging Br groups ====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|5 isomers of Al2Cl4Br2]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity. In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable.

Rep:Mod:Fr216 Federica

2018-05-11T09:57:49Z

Fr216: /* Mini project - Lewis Acids and Bases */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3]]

''insert reference to Patricia hunt''

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. (lit) The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown in the following figure:

[[File:fr_5isomers.png|frame|center|200x200px|alt=The five isomers of Al2Cl4Br2.]]

====Confomer with trans-Br groups====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

====Confomer with bridging Br groups ====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|5 isomers of Al2Cl4Br2]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity. In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable.

Rep:Mod:Fr216 Federica

2018-05-11T09:53:03Z

Fr216: /* Mini project - Lewis Acids and Bases */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3]]

''insert reference to Patricia hunt''

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. (lit) The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown in the following figure:

[[File:fr_5isomers.png|thumb|5 isomers of Al2Cl4Br2]]

====Confomer with trans-Br groups====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

====Confomer with bridging Br groups ====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|5 isomers of Al2Cl4Br2]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity. In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable.

Rep:Mod:Fr216 Federica

2018-05-11T09:52:44Z

Fr216: /* Mini project - Lewis Acids and Bases */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3]]

''insert reference to Patricia hunt''

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. (lit) The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown in the following figure:

[[File:fr_5isomers.png|center|frame|5 isomers of Al2Cl4Br2]]

====Confomer with trans-Br groups====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

====Confomer with bridging Br groups ====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|5 isomers of Al2Cl4Br2]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity. In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable.

File:Fr 5isomers.png

2018-05-11T09:52:33Z

Fr216:

Rep:Mod:Fr216 Federica

2018-05-11T09:35:40Z

Fr216: /* Association Energy calculation for BH3NH3 */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3]]

''insert reference to Patricia hunt''

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively strong dative bond. It is given by the donation of the N lone pair into the empty B p orbital. (lit) The relative strength of the bond can be assessed by comparison with equivalent molecules: a covalent B-N bond has a dissociation energy of about 380 KJ/mol, which is much smaller than the predicted energy for NH3BH3. This proves that the bond is weaker and hence the bond we are dealing with is weaker than a polar covalent bond.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown in the following figure:

[[File:federica_5_isomers.png|center|frame|5 isomers of Al2Cl4Br2]]

====Confomer with trans-Br groups====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

====Confomer with bridging Br groups ====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|5 isomers of Al2Cl4Br2]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity. In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable.

Rep:Mod:Fr216 Federica

2018-05-11T09:12:27Z

Fr216: /* Computational basis set = 6-31G(d,p) */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

====Specific additional information====

*Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

The IR spectrum does not show 6 peaks because not all the modes are IR active. This is because one of the selection rules for an IR mode to be active is that it requires a change in the dipole moment and ''mode 4'' is totally symmetric causing the dipole moment stays constant. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum, showing overall only 4 peaks.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

*MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3]]

''insert reference to Patricia hunt''

There is no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This implies that the fragments might be closer in energy than the original prediction. The valence electrons are sitting in a bonding orbital, suggesting that the molecule is not willing to give up electrons (act as a base or nucleophile). On the other hand, it has a vacant non-bonding orbital at relatively low energy showing that it is a good electrons acceptor. This not only agrees with the idea that BH3 is electron deficient (VSEPR theory), but also with laboratory experiments where it acts as an acid.(lit) MO theory can be useful in predicting orbital interactions and reactivity between fragments in very complex systems, even where the VSEPR or crystal field theories cannot give an explanation.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively weak dative bond. A covalent B-N bond has a dissociation energy of about 380 KJ/mol, while the predicted one for this molecule is much smaller, implying that the bond itself is much weaker.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown in the following figure:

[[File:federica_5_isomers.png|center|frame|5 isomers of Al2Cl4Br2]]

====Confomer with trans-Br groups====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

====Confomer with bridging Br groups ====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|5 isomers of Al2Cl4Br2]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity. In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable.

Rep:Mod:Fr216 Federica

2018-05-11T08:50:50Z

Fr216: /* BBr3 */

=Molecules optimization and analysis=

===BH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3_OPT_2_SYM_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr216_Summary_bh3.png|center|frame| Summary table for BH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
Predicted change in Energy=-1.635270D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1948 -DE/DX = -0.0002 !
! R2 R(1,3) 1.1944 -DE/DX = -0.0001 !
! R3 R(1,4) 1.1947 -DE/DX = -0.0002 !
! A1 A(2,1,3) 119.9855 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0157 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9989 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculations results:
<pre>
Low frequencies --- -0.2263 -0.1037 -0.0054 47.9770 49.0378 49.0383
Low frequencies --- 1163.7209 1213.6704 1213.6731
</pre>

*Frequency analysis log file: [[Media:FR_BH3_FREQUENCY.LOG| FR_BH3_freq.log]]

*Specific additional information:

-Vibrations: the vibration table is shown below.

{| class="wikitable"
|-
! Mode
! Frequency
! Is it IR active?
! Symmetry
|-
| 1
| 1164
| YES
| a2''
|-
| 2
| 1214
| YES
| e' bend
|-
| 3
| 1214
| YES
| e' bend
|-
| 4
| 2579
| NO
| a1'
|-
| 5
| 2712
| YES
| e'
|-
| 6
| 2712
| YES
| e'
|-
|}

BH3 is a non-linear molecule (D3h point group) and its IR modes can be predicted via the ''3N-6'' equation.

<div class="center" style="width:auto; margin-left:auto; margin-right:auto;">3N-6=(3x4)-6=6 vibrational degrees of freedom</div>

However, the IR spectrum does not show 6 peaks because not all the modes are IR active. One of the selection rules for an IR mode to be active is that it requires a change in the dipole moment. Mode 4 is totally symmetrical and hence does not appear in the spectrum. Modes 2,3 and 5,6 are degenerate and appear only once in the spectrum.

[[File:Fr216_Spectrum_bh3.png|center|frame]]

- MO analysis

[[File:fr_MO_diagram.png|center|frame| MO diagram for BH3]]

''insert reference to Patricia hunt''

There are no significant difference between the predicted orbitals and the real MOs. That said, the predicted contributions from each fragment to the MO is slightly too big. This suggests that the fragments might be closer in energy than the original prediction. This means that MO theory can be useful in predicting the possible orbital interactions between fragments in very complex systems.

===NH3 ===
====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr216_Summary_nh3.png|center|frame|Summary table for NH3]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
Predicted change in Energy=-9.844603D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7446 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7446 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7446 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8637 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0047 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

*Frequency analysis log file: [[Media:FR_NH3_OPT_FREQ.LOG| FR_NH3_freq.log]]

===BH3NH3===

====Computational basis set = 6-31G(d,p)====

<jmol><jmolApplet>
<title>optimised BH3NH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>FR_BH3NH3_OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below: [[File:Fr216_Summary_bh3nh3.png|center|frame]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000513 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
Predicted change in Energy=-1.631175D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,8) 1.21 -DE/DX = -0.0001 !
! R2 R(2,8) 1.21 -DE/DX = -0.0001 !
! R3 R(3,8) 1.21 -DE/DX = -0.0001 !
! R4 R(4,7) 1.0186 -DE/DX = -0.0001 !
! R5 R(5,7) 1.0186 -DE/DX = -0.0001 !
! R6 R(6,7) 1.0186 -DE/DX = -0.0001 !
! R7 R(7,8) 1.6681 -DE/DX = -0.0001 !
! A1 A(4,7,5) 107.8685 -DE/DX = 0.0 !
! A2 A(4,7,6) 107.8685 -DE/DX = 0.0 !
! A3 A(4,7,8) 111.0294 -DE/DX = 0.0 !
! A4 A(5,7,6) 107.8686 -DE/DX = 0.0 !
! A5 A(5,7,8) 111.0303 -DE/DX = 0.0 !
! A6 A(6,7,8) 111.0302 -DE/DX = 0.0 !
! A7 A(1,8,2) 113.8743 -DE/DX = 0.0 !
! A8 A(1,8,3) 113.8743 -DE/DX = 0.0 !
! A9 A(1,8,7) 104.5972 -DE/DX = 0.0 !
! A10 A(2,8,3) 113.874 -DE/DX = 0.0 !
! A11 A(2,8,7) 104.5968 -DE/DX = 0.0 !
! A12 A(3,8,7) 104.5969 -DE/DX = 0.0 !
! D1 D(4,7,8,1) 179.9998 -DE/DX = 0.0 !
! D2 D(4,7,8,2) -60.0 -DE/DX = 0.0 !
! D3 D(4,7,8,3) 59.9997 -DE/DX = 0.0 !
! D4 D(5,7,8,1) -60.0003 -DE/DX = 0.0 !
! D5 D(5,7,8,2) 59.9998 -DE/DX = 0.0 !
! D6 D(5,7,8,3) 179.9995 -DE/DX = 0.0 !
! D7 D(6,7,8,1) 60.0001 -DE/DX = 0.0 !
! D8 D(6,7,8,2) -179.9998 -DE/DX = 0.0 !
! D9 D(6,7,8,3) -60.0001 -DE/DX = 0.0 !

</pre>

*Frequency calculation results:

<pre>
Low frequencies --- -0.0002 0.0004 0.0009 17.6705 28.0331 40.2175
Low frequencies --- 266.5190 632.3638 639.4914
</pre>

*The frequency log file: [[Media:FR_BH3NH3_OPT_FREQ.LOG| BH3NH3_freq.log]]

===Association Energy calculation for BH3NH3 ===

E(NH3)= -56.5778 a.u. = 148545.03 KJ/mol
E(BH3)= -26.6153 a.u. = 69878.475 KJ/mol
E(NH3BH3)= -83.2247 a.u. = 218506.47 KJ/mol

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -83.2247 -[-56.5778 -26.6153] = -0.0316 a.u. = - 82.96581 KJ/mol

The B-N bond in this molecule is a relatively weak dative bond. A covalent B-N bond has a dissociation energy of about 380 KJ/mol, while the predicted one for this molecule is much smaller, implying that the bond itself is much weaker.

http://staff.ustc.edu.cn/~luo971/2010-91-CRC-BDEs-Tables.pdf

===BBr3===

====Computational basis set: B - 6-31G and Br - LanL2DZ ====

<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>fr_Log_10047061_optmfin.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:
[[File:Fr_Summary_bf3.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000058 0.001800 YES
RMS Displacement 0.000042 0.001200 YES
Predicted change in Energy=-1.616527D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.934 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 119.9962 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0034 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0004 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -4.3208 -2.7694 -2.3007 -0.0002 -0.0001 0.0001
Low frequencies --- 155.8708 155.9431 267.6977
</pre>

*The frequency log file: [[Media:Fr_Frequency_for_br3.log| BBr3_freq.log]]

*url for the dspace file: http://hdl.handle.net/10042/202392

===Mini project - Lewis Acids and Bases===

The five isomers are shown in the following figure:

[[File:federica_5_isomers.png|center|frame|5 isomers of Al2Cl4Br2]]

====Confomer with trans-Br groups====

<jmol><jmolApplet>
<title>optimised trans confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_TRANS_LA3.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table for the trans-confomer is shown below:

[[File:fr_Project_trans_summary.png|center|frame|trans-Al2Cl4Br2]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.000424 0.001800 YES
RMS Displacement 0.000184 0.001200 YES
Predicted change in Energy=-1.664899D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.2982 -DE/DX = 0.0 !
! R2 R(1,4) 2.2982 -DE/DX = 0.0 !
! R3 R(1,5) 2.0936 -DE/DX = 0.0 !
! R4 R(1,6) 2.2746 -DE/DX = 0.0 !
! R5 R(2,3) 2.2982 -DE/DX = 0.0 !
! R6 R(2,4) 2.2982 -DE/DX = 0.0 !
! R7 R(2,7) 2.0936 -DE/DX = 0.0 !
! R8 R(2,8) 2.2746 -DE/DX = 0.0 !
! A1 A(3,1,4) 90.1483 -DE/DX = 0.0 !
! A2 A(3,1,5) 109.8461 -DE/DX = 0.0 !
! A3 A(3,1,6) 110.5133 -DE/DX = 0.0 !
! A4 A(4,1,5) 109.8462 -DE/DX = 0.0 !
! A5 A(4,1,6) 110.5135 -DE/DX = 0.0 !
! A6 A(5,1,6) 121.5158 -DE/DX = 0.0 !
! A7 A(3,2,4) 90.1483 -DE/DX = 0.0 !
! A8 A(3,2,7) 109.8462 -DE/DX = 0.0 !
! A9 A(3,2,8) 110.5135 -DE/DX = 0.0 !
! A10 A(4,2,7) 109.8461 -DE/DX = 0.0 !
! A11 A(4,2,8) 110.5133 -DE/DX = 0.0 !
! A12 A(7,2,8) 121.5158 -DE/DX = 0.0 !
! A13 A(1,3,2) 89.8517 -DE/DX = 0.0 !
! A14 A(1,4,2) 89.8517 -DE/DX = 0.0 !
! D1 D(4,1,3,2) 0.0 -DE/DX = 0.0 !
! D2 D(5,1,3,2) -111.215 -DE/DX = 0.0 !
! D3 D(6,1,3,2) 112.0319 -DE/DX = 0.0 !
! D4 D(3,1,4,2) 0.0 -DE/DX = 0.0 !
! D5 D(5,1,4,2) 111.2149 -DE/DX = 0.0 !
! D6 D(6,1,4,2) -112.0317 -DE/DX = 0.0 !
! D7 D(4,2,3,1) 0.0 -DE/DX = 0.0 !
! D8 D(7,2,3,1) -111.2149 -DE/DX = 0.0 !
! D9 D(8,2,3,1) 112.0317 -DE/DX = 0.0 !
! D10 D(3,2,4,1) 0.0 -DE/DX = 0.0 !
! D11 D(7,2,4,1) 111.215 -DE/DX = 0.0 !
! D12 D(8,2,4,1) -112.0319 -DE/DX = 0.0 !
</pre>

*Frequency analysis results:

<pre>
Low frequencies --- -5.3777 -0.0036 -0.0029 -0.0019 1.2979 2.1662
Low frequencies --- 18.1035 49.0942 72.9997
</pre>

*The frequency log file: [[Media:fr_Trans_isomer_freq.log| Trans confomer.log]]

====Confomer with bridging Br groups ====

<jmol><jmolApplet>
<title>optimised bridging Br confomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>PROJECT_BRIDGING_PERCY.LOG</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:Fr_Summary_bridging.png|center|frame|5 isomers of Al2Cl4Br2]]

*The item table is shown below:

<pre>

Item Value Threshold Converged?
Maximum Force 0.000125 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.001576 0.001800 YES
RMS Displacement 0.000754 0.001200 YES
Predicted change in Energy=-6.256738D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,3) 2.0939 -DE/DX = -0.0001 !
! R2 R(1,5) 2.489 -DE/DX = 0.0001 !
! R3 R(1,6) 2.489 -DE/DX = 0.0001 !
! R4 R(1,8) 2.0929 -DE/DX = 0.0001 !
! R5 R(2,4) 2.0939 -DE/DX = -0.0001 !
! R6 R(2,5) 2.489 -DE/DX = 0.0001 !
! R7 R(2,6) 2.489 -DE/DX = 0.0001 !
! R8 R(2,7) 2.0929 -DE/DX = 0.0001 !
! A1 A(3,1,5) 109.7021 -DE/DX = 0.0001 !
! A2 A(3,1,6) 109.7055 -DE/DX = 0.0 !
! A3 A(3,1,8) 121.7963 -DE/DX = 0.0 !
! A4 A(5,1,6) 91.668 -DE/DX = 0.0001 !
! A5 A(5,1,8) 109.9117 -DE/DX = -0.0001 !
! A6 A(6,1,8) 109.9123 -DE/DX = -0.0001 !
! A7 A(4,2,5) 109.7039 -DE/DX = 0.0001 !
! A8 A(4,2,6) 109.7033 -DE/DX = 0.0001 !
! A9 A(4,2,7) 121.7959 -DE/DX = 0.0 !
! A10 A(5,2,6) 91.6682 -DE/DX = 0.0001 !
! A11 A(5,2,7) 109.9139 -DE/DX = -0.0001 !
! A12 A(6,2,7) 109.911 -DE/DX = -0.0001 !
! A13 A(1,5,2) 88.3319 -DE/DX = -0.0001 !
! A14 A(1,6,2) 88.3319 -DE/DX = -0.0001 !
! D1 D(3,1,5,2) -111.6266 -DE/DX = -0.0001 !
! D2 D(6,1,5,2) 0.0109 -DE/DX = 0.0 !
! D3 D(8,1,5,2) 111.9078 -DE/DX = 0.0 !
! D4 D(3,1,6,2) 111.6235 -DE/DX = 0.0001 !
! D5 D(5,1,6,2) -0.0109 -DE/DX = 0.0 !
! D6 D(8,1,6,2) -111.9073 -DE/DX = 0.0 !
! D7 D(4,2,5,1) -111.6464 -DE/DX = -0.0001 !
! D8 D(6,2,5,1) -0.0109 -DE/DX = 0.0 !
! D9 D(7,2,5,1) 111.8851 -DE/DX = 0.0 !
! D10 D(4,2,6,1) 111.6469 -DE/DX = 0.0001 !
! D11 D(5,2,6,1) 0.0109 -DE/DX = 0.0 !
! D12 D(7,2,6,1) -111.8877 -DE/DX = 0.0 !
</pre>

*The frequency calculation gave the following results:

<pre>
Low frequencies --- -5.8862 -5.2899 -4.0205 0.0008 0.0011 0.0029
Low frequencies --- 14.6917 63.2414 86.0249
</pre>

*The frequency log file: [[Media:fr_Bridging_frequency.gjf| Bridge confomer_freq.log]]

====Difference in energy between confomers====

E(isomer with bridging Br groups) = -2352.4063 a.u.
E(isomer with trans Br groups) = -2352.4163 a.u.

ΔE = -2352.4063 + 2352.4163 = 0.01 a.u. = 26.255 kJ/mol

Both confomers present halogens as bridging units in the dimer. Halogens are generally speaking good bridging groups due to their high electronegativity. In the fist case (trans isomer) the bridging atoms are Cl atoms, while in the second they are Br atoms. Cl is more electronegative and less bulky, and gives therefore the more stable ligand (lower energy).

====AlCl2Br (monomer) ====

<jmol><jmolApplet>
<title>optimized monomer</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>Monomer_fede_opt.log</uploadedFileContents>
</jmolApplet></jmol>

*The summary table is shown below:

[[File:fr_Monomer_summary_table.png|center|frame]]

*The item table is shown below:

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984436D-08
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.089 -DE/DX = -0.0001 !
! R2 R(1,3) 2.089 -DE/DX = -0.0001 !
! R3 R(1,4) 2.2695 -DE/DX = -0.0001 !
! A1 A(2,1,3) 119.8353 -DE/DX = 0.0001 !
! A2 A(2,1,4) 120.0823 -DE/DX = -0.0001 !
! A3 A(3,1,4) 120.0823 -DE/DX = -0.0001 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
</pre>

*The frequency calculations results are shown below:

<pre>
Low frequencies --- 0.0023 0.0029 0.0039 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.895
</pre>

*The frequency log file: [[Media:fr_Monomer_frequency_final.log| Monomer_freq.log]]

====Dissociation energy calculations====

ΔE = E(dimer)-[2 x E(monomer)] = - 2352.4163 -[2 x (-1176.1901)] = - 0.0361 a.u. = - 94.78056 kJ/mol

Therefore, the dimer is lower in energy than the two singular monomers together and hence more stable.