ChemWiki - User contributions [en]

ICL:mz5717

2019-05-17T16:46:17Z

Mz5717: /* Dissociation of the Lowest-Energy Conformer into 2AlCl2Br */

==BH3==
===Borane BH3===

'''B3LYP/6-31G(d.p) level'''

[[File:mz5717_BH3_summary.JPG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000070 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

Frequency analysis log file [[Media:MZ5717_BH3_FREQT.LOG|MZ5717_BH3_FREQ.log]]

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_BH3_FREQT.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational Spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2582
|0
|A1'
|no
|symmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

|[[File:Mz5717_BH3_IR.JPG]]

First of all there are two sets of degenerate vibrations at 1213 and 2716 cm-1, therefore there should be at most 4 signals. Furthermore, the vibration mode at 2582 cm-1 is a symmetric stretch, which means that it is not IR active. Thus there are only three signals present in the IR spectrum.

===Molecular Orbital Diagram for BH3===

[[File:mz5717_bh3_mo_all.PNG|800px]]

The MO of BH3 produced by LCAO as well as the ones calculated by Gaussian. <ref name="Hunt_MO" />

Here are some minor differences between the LCAO MO diagram and the calculated 'real' diagram:

- In-phase orbitals in the 'real' diagram merge together while all difference orbitals in the LCAO diagram are separate

- The 'real' diagram accounts for orbital repulsion (shown by certain slightly bent p orbitals)

It is reasonable to say that the LCAO diagram represents the 'real' spatial distribution of electrons to a good extent.

===Association Energy of NH3BH3===

Below is the key information of NH3 and NH3BH3.

{| class="wikitable"
|+
|-
| Name || Method & Basis Set || Summary Table || 'Item' Table || Low Frequencies || Jmol Image || LOG File
|-
|NH3
|B3LYP/6-31G(d.p)
|[[File:mz5717_nh3_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
</pre>
|<pre>
Low frequencies --- -0.0129 -0.0019 0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>
|<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_NH3_FREQ.LOG|MZ5717_NH3_FREQ.LOG]]
|-
|NH3BH3
|B3LYP/6-31G(d.p)
|[[File:mz5717_nh3bh3_summary_1.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000579 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>
|<pre>
Low frequencies --- 0.0005 0.0009 0.0011 16.8742 17.0939 37.4795
Low frequencies --- 265.8773 632.2052 639.3279
</pre>
|<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_NH3BH3_FREQ_6.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_NH3BH3_FREQ_6.LOG|MZ5717_NH3BH3_FREQ.LOG]]
|}

E(NH3)= -56.55777 au

E(BH3)= -26.61532 au

E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05160 au = -0.05160 ÷ 0.0004 kJ/mol = -129 kJ/mol <ref name="conversion" />

Therefore, the energy of the N-B dative bond is -129 kJ/mol. Compared to a normal N-B sigma bond (-377.9 kJ/mol) <ref name="NB bond" />, it is rather weak.

==NI3==
===Nitrogen Triiodide NI3===

'''B3LYP/Gen level'''

[[File:mz5717_ni3_summary_final.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
</pre>

Frequency log file [[Media:MZ5717_NI3_FREQ_4.LOG|MZ5717_NI3_FREQ.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_NI3_FREQ_4.LOG</uploadedFileContents>
</jmolApplet></jmol>

N-I bond distance: 2.184 Å

==Project: Lewis Acids and Bases==

===Key Information of Isomers of Al2Cl4Br2===

{| class="wikitable"
|+
|-
| Isomer || Method & Basis Set || Summary Table || 'Item' Table || Low Frequencies || Jmol Image || LOG File
|-
|Isomer A
[[File:Mz5717_isomer_a.png]]
|B3LYP/6-31G(d.p)
|[[File:mz5717_isomer_a_summary_1.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001018 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
</pre>
|<pre>
Low frequencies --- -2.3637 -2.2675 -0.9862 -0.0060 0.0068 0.0107
Low frequencies --- 11.7171 65.3709 88.4194
</pre>
|<jmol><jmolApplet>
<title>Isomer A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_A_2.LOG|MZ5717_ISOMER_A_OPTFREQ.LOG]]
|-
|Isomer B
[[File:Mz5717_isomer_b.png]]
|B3LYP/6-31G(d.p)
|[[File:mz5717_isomer_b_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000057 0.000450 YES
RMS Force 0.000026 0.000300 YES
Maximum Displacement 0.001712 0.001800 YES
RMS Displacement 0.000699 0.001200 YES
</pre>
|<pre>
Low frequencies --- -0.0099 -0.0086 -0.0074 1.5771 1.8810 2.5290
Low frequencies --- 14.5085 58.5774 81.4258
</pre>
|<jmol><jmolApplet>
<title>Isomer B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_B_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_B_2.LOG|MZ5717_ISOMER_B_OPTFREQ.LOG]]
|-
|Isomer C
[[File:Mz5717_isomer_c.png]]
|B3LYP/6-31G(d.p)
|[[File:mz5717_isomer_c_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000452 0.001800 YES
RMS Displacement 0.000186 0.001200 YES
</pre>
|<pre>
Low frequencies --- -0.0083 -0.0073 0.0107 0.8196 1.4180 1.6409
Low frequencies --- 13.4390 54.4089 73.7274
</pre>
|<jmol><jmolApplet>
<title>Isomer C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_D.LOG|MZ5717_ISOMER_C_OPTFREQ.LOG]]
|-
|Isomer D
[[File:Mz5717_isomer_d.png]]
|B3LYP/6-31G(d.p)
|[[File:mz5717_isomer_d_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001743 0.001800 YES
RMS Displacement 0.000677 0.001200 YES
</pre>
|<pre>
Low frequencies --- -2.1170 -1.5946 -1.4299 -0.0050 0.0035 0.0086
Low frequencies --- 17.7661 54.4445 79.9169
</pre>
|<jmol><jmolApplet>
<title>Isomer D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_E.LOG|MZ5717_ISOMER_D_OPTFREQ.LOG]]
|-
|Isomer E
[[File:Mz5717_isomer_e.png]]
|B3LYP/6-31G(d.p)
|[[File:mz5717_isomer_e_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001743 0.001800 YES
RMS Displacement 0.000637 0.001200 YES
</pre>
|<pre>
Low frequencies --- -2.1765 -1.5548 -0.0043 0.0027 0.0110 0.3832
Low frequencies --- 14.8169 52.4385 73.7073
</pre>
|<jmol><jmolApplet>
<title>Isomer E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_F.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_F.LOG|MZ5717_ISOMER_E_OPTFREQ.LOG]]
|}

===Geometry and Energy of Isomers of Al2Cl4Br2===

{| class="wikitable"
|+
|-
| Isomer || Geometry || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|Isomer A
|[[File:Mz5717_isomer_a.png]]
|D2h
|−18673857
|0
|high
|-
|Isomer B
|[[File:Mz5717_isomer_b.png]]
|C1
|−18673850
|7
|medium high
|-
|Isomer C
|[[File:Mz5717_isomer_c.png]]
|C2v
|−18673845
|12
|medium
|-
|Isomer D
|[[File:Mz5717_isomer_d.png]]
|C2v
|−18673844
|13
|low
|-
|Isomer E
|[[File:Mz5717_isomer_e.png]]
|C2h
|−18673844
|13
|low
|}

When the bridging ions are both Br, the stability of the molecule is highest. The stability decreases if one of the bridging ions is replaced with Cl, and is lowest when both the bridging ions are Cl. Let the bridging ion be X, then the Al-X-Al bond consists of a normal sigma bond, and a dative bond with X as the donor (as shown in the figure below). The strength of the Al-X-Al bond, therefore the stability of the molecule, depends on the extent of orbital overlap between Al and X. Br has larger and more diffuse orbitals, making the overlap more efficient. On the other hand, Cl is highly electronegative, having a smaller radius and holding its electrons tightly towards the core. Thus the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:Mz5717_isomer_general.png]]

===Dissociation of the Lowest-Energy Conformer into 2AlCl2Br===

{| class="wikitable"
|+
|-
| Name || Method & Basis Set || Summary Table || 'Item' Table || Low Frequencies || Jmol Image || LOG File
|-
|AlCl2Br
|B3LYP/6-31G(d.p)
|[[File:mz5717alcl2br_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000166 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
</pre>
|<pre>
Low frequencies --- -0.0103 0.0079 0.0095 1.9597 1.9884 2.9284
Low frequencies --- 125.3109 137.4204 194.7945
</pre>
|<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ALCL2BR_SINGLE.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_A_2.LOG|MZ5717_ALCL2BR_FREQ.LOG]]
|}

When [[File:Mz5717_isomer_a.png]] dissociates into two molecules of AlCl2Br, we lose two Al-Br bonds.

The energy of one molecule of AlCl2Br is calculated to be -9336871 kJ/mol.

Therefore, the total energy of two such molecules is -18673743 kJ/mol, which is +114 kJ/mol relative to the energy of Isomer A, the lowest-energy isomer.

Each Al-Br broken means raising the total energy by 57 kJ/mol. It is evident that the dimer is considerably more stable than the separated monomers.

===Molecular Orbitals of the Lowest-Energy Conformer===

For the lowest-energy conformer, [[File:Mz5717_isomer_a.png]], there are 24 filled valence molecular orbitals in total. Below are three of them, ranked by their extent of bonding/antibonding character.

Atom colour code: pink - Al, red - Br. green - Cl.

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front View || Top View || Bonding/Antibonding Nature
|-
|MO No.1
|[[File:mz5717_antibonding.PNG]]
|[[File:Mz5717_antibonding_1.PNG]]
|[[File:mz5717_antibonding_annotation_0.png]]
|[[File:Mz5717_antibonding_1_annotation_0.png]]
|Highly ANTIBONDING
|-
|MO No.2
|[[File:Mz5717_in_between.PNG]]
|[[File:Mz5717_in_between_1.PNG]]
|[[File:Mz5717_in_between_annotation_0.png]]
|[[File:Mz5717_in_between_1_annotation_0.png]]
|Mainly BONDING
|-
|MO No.3
|[[File:Mz5717_bonding.PNG]]
|[[File:Mz5717_bonding_1.PNG]]
|[[File:Mz5717_bonding_annotation_0.png]]
|[[File:Mz5717_bonding_1_annotation_0.png]]
|Highly BONDING
|}

==References==
<references>
<ref name="Hunt_MO">LCAO MO diagram from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">1 kJ/mol = 0.0004 au conversion from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007
</references>

File:Mz5717alcl2br summary.PNG

2019-05-17T16:45:08Z

Mz5717:

File:MZ5717 ALCL2BR SINGLE.LOG

2019-05-17T16:44:59Z

Mz5717:

ICL:mz5717

2019-05-17T16:44:41Z

Mz5717: /* Dissociation of the Lowest-Energy Conformer into 2AlCl2Br */

==BH3==
===Borane BH3===

'''B3LYP/6-31G(d.p) level'''

[[File:mz5717_BH3_summary.JPG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000070 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

Frequency analysis log file [[Media:MZ5717_BH3_FREQT.LOG|MZ5717_BH3_FREQ.log]]

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_BH3_FREQT.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational Spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2582
|0
|A1'
|no
|symmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

|[[File:Mz5717_BH3_IR.JPG]]

First of all there are two sets of degenerate vibrations at 1213 and 2716 cm-1, therefore there should be at most 4 signals. Furthermore, the vibration mode at 2582 cm-1 is a symmetric stretch, which means that it is not IR active. Thus there are only three signals present in the IR spectrum.

===Molecular Orbital Diagram for BH3===

[[File:mz5717_bh3_mo_all.PNG|800px]]

The MO of BH3 produced by LCAO as well as the ones calculated by Gaussian. <ref name="Hunt_MO" />

Here are some minor differences between the LCAO MO diagram and the calculated 'real' diagram:

- In-phase orbitals in the 'real' diagram merge together while all difference orbitals in the LCAO diagram are separate

- The 'real' diagram accounts for orbital repulsion (shown by certain slightly bent p orbitals)

It is reasonable to say that the LCAO diagram represents the 'real' spatial distribution of electrons to a good extent.

===Association Energy of NH3BH3===

Below is the key information of NH3 and NH3BH3.

{| class="wikitable"
|+
|-
| Name || Method & Basis Set || Summary Table || 'Item' Table || Low Frequencies || Jmol Image || LOG File
|-
|NH3
|B3LYP/6-31G(d.p)
|[[File:mz5717_nh3_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
</pre>
|<pre>
Low frequencies --- -0.0129 -0.0019 0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>
|<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_NH3_FREQ.LOG|MZ5717_NH3_FREQ.LOG]]
|-
|NH3BH3
|B3LYP/6-31G(d.p)
|[[File:mz5717_nh3bh3_summary_1.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000579 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>
|<pre>
Low frequencies --- 0.0005 0.0009 0.0011 16.8742 17.0939 37.4795
Low frequencies --- 265.8773 632.2052 639.3279
</pre>
|<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_NH3BH3_FREQ_6.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_NH3BH3_FREQ_6.LOG|MZ5717_NH3BH3_FREQ.LOG]]
|}

E(NH3)= -56.55777 au

E(BH3)= -26.61532 au

E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05160 au = -0.05160 ÷ 0.0004 kJ/mol = -129 kJ/mol <ref name="conversion" />

Therefore, the energy of the N-B dative bond is -129 kJ/mol. Compared to a normal N-B sigma bond (-377.9 kJ/mol) <ref name="NB bond" />, it is rather weak.

==NI3==
===Nitrogen Triiodide NI3===

'''B3LYP/Gen level'''

[[File:mz5717_ni3_summary_final.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
</pre>

Frequency log file [[Media:MZ5717_NI3_FREQ_4.LOG|MZ5717_NI3_FREQ.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_NI3_FREQ_4.LOG</uploadedFileContents>
</jmolApplet></jmol>

N-I bond distance: 2.184 Å

==Project: Lewis Acids and Bases==

===Key Information of Isomers of Al2Cl4Br2===

{| class="wikitable"
|+
|-
| Isomer || Method & Basis Set || Summary Table || 'Item' Table || Low Frequencies || Jmol Image || LOG File
|-
|Isomer A
[[File:Mz5717_isomer_a.png]]
|B3LYP/6-31G(d.p)
|[[File:mz5717_isomer_a_summary_1.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001018 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
</pre>
|<pre>
Low frequencies --- -2.3637 -2.2675 -0.9862 -0.0060 0.0068 0.0107
Low frequencies --- 11.7171 65.3709 88.4194
</pre>
|<jmol><jmolApplet>
<title>Isomer A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_A_2.LOG|MZ5717_ISOMER_A_OPTFREQ.LOG]]
|-
|Isomer B
[[File:Mz5717_isomer_b.png]]
|B3LYP/6-31G(d.p)
|[[File:mz5717_isomer_b_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000057 0.000450 YES
RMS Force 0.000026 0.000300 YES
Maximum Displacement 0.001712 0.001800 YES
RMS Displacement 0.000699 0.001200 YES
</pre>
|<pre>
Low frequencies --- -0.0099 -0.0086 -0.0074 1.5771 1.8810 2.5290
Low frequencies --- 14.5085 58.5774 81.4258
</pre>
|<jmol><jmolApplet>
<title>Isomer B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_B_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_B_2.LOG|MZ5717_ISOMER_B_OPTFREQ.LOG]]
|-
|Isomer C
[[File:Mz5717_isomer_c.png]]
|B3LYP/6-31G(d.p)
|[[File:mz5717_isomer_c_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000452 0.001800 YES
RMS Displacement 0.000186 0.001200 YES
</pre>
|<pre>
Low frequencies --- -0.0083 -0.0073 0.0107 0.8196 1.4180 1.6409
Low frequencies --- 13.4390 54.4089 73.7274
</pre>
|<jmol><jmolApplet>
<title>Isomer C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_D.LOG|MZ5717_ISOMER_C_OPTFREQ.LOG]]
|-
|Isomer D
[[File:Mz5717_isomer_d.png]]
|B3LYP/6-31G(d.p)
|[[File:mz5717_isomer_d_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001743 0.001800 YES
RMS Displacement 0.000677 0.001200 YES
</pre>
|<pre>
Low frequencies --- -2.1170 -1.5946 -1.4299 -0.0050 0.0035 0.0086
Low frequencies --- 17.7661 54.4445 79.9169
</pre>
|<jmol><jmolApplet>
<title>Isomer D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_E.LOG|MZ5717_ISOMER_D_OPTFREQ.LOG]]
|-
|Isomer E
[[File:Mz5717_isomer_e.png]]
|B3LYP/6-31G(d.p)
|[[File:mz5717_isomer_e_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001743 0.001800 YES
RMS Displacement 0.000637 0.001200 YES
</pre>
|<pre>
Low frequencies --- -2.1765 -1.5548 -0.0043 0.0027 0.0110 0.3832
Low frequencies --- 14.8169 52.4385 73.7073
</pre>
|<jmol><jmolApplet>
<title>Isomer E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_F.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_F.LOG|MZ5717_ISOMER_E_OPTFREQ.LOG]]
|}

===Geometry and Energy of Isomers of Al2Cl4Br2===

{| class="wikitable"
|+
|-
| Isomer || Geometry || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|Isomer A
|[[File:Mz5717_isomer_a.png]]
|D2h
|−18673857
|0
|high
|-
|Isomer B
|[[File:Mz5717_isomer_b.png]]
|C1
|−18673850
|7
|medium high
|-
|Isomer C
|[[File:Mz5717_isomer_c.png]]
|C2v
|−18673845
|12
|medium
|-
|Isomer D
|[[File:Mz5717_isomer_d.png]]
|C2v
|−18673844
|13
|low
|-
|Isomer E
|[[File:Mz5717_isomer_e.png]]
|C2h
|−18673844
|13
|low
|}

When the bridging ions are both Br, the stability of the molecule is highest. The stability decreases if one of the bridging ions is replaced with Cl, and is lowest when both the bridging ions are Cl. Let the bridging ion be X, then the Al-X-Al bond consists of a normal sigma bond, and a dative bond with X as the donor (as shown in the figure below). The strength of the Al-X-Al bond, therefore the stability of the molecule, depends on the extent of orbital overlap between Al and X. Br has larger and more diffuse orbitals, making the overlap more efficient. On the other hand, Cl is highly electronegative, having a smaller radius and holding its electrons tightly towards the core. Thus the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:Mz5717_isomer_general.png]]

===Dissociation of the Lowest-Energy Conformer into 2AlCl2Br===

{| class="wikitable"
|+
|-
| Name || Method & Basis Set || Summary Table || 'Item' Table || Low Frequencies || Jmol Image || LOG File
|-
|AlCl2Br
|B3LYP/6-31G(d.p)
|[[File:mz5717alcl2br_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000166 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
</pre>
|<pre>
Low frequencies --- -0.0103 0.0079 0.0095 1.9597 1.9884 2.9284
Low frequencies --- 125.3109 137.4204 194.7945
</pre>
|<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ALCL2BR_SINGLE.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_A_2.LOG|MZ5717_ISOMER_A_OPTFREQ.LOG]]
|}

When [[File:Mz5717_isomer_a.png]] dissociates into two molecules of AlCl2Br, we lose two Al-Br bonds.

The energy of one molecule of AlCl2Br is calculated to be -9336871 kJ/mol.

Therefore, the total energy of two such molecules is -18673743 kJ/mol, which is +114 kJ/mol relative to the energy of Isomer A, the lowest-energy isomer.

Each Al-Br broken means raising the total energy by 57 kJ/mol. It is evident that the dimer is considerably more stable than the separated monomers.

===Molecular Orbitals of the Lowest-Energy Conformer===

For the lowest-energy conformer, [[File:Mz5717_isomer_a.png]], there are 24 filled valence molecular orbitals in total. Below are three of them, ranked by their extent of bonding/antibonding character.

Atom colour code: pink - Al, red - Br. green - Cl.

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front View || Top View || Bonding/Antibonding Nature
|-
|MO No.1
|[[File:mz5717_antibonding.PNG]]
|[[File:Mz5717_antibonding_1.PNG]]
|[[File:mz5717_antibonding_annotation_0.png]]
|[[File:Mz5717_antibonding_1_annotation_0.png]]
|Highly ANTIBONDING
|-
|MO No.2
|[[File:Mz5717_in_between.PNG]]
|[[File:Mz5717_in_between_1.PNG]]
|[[File:Mz5717_in_between_annotation_0.png]]
|[[File:Mz5717_in_between_1_annotation_0.png]]
|Mainly BONDING
|-
|MO No.3
|[[File:Mz5717_bonding.PNG]]
|[[File:Mz5717_bonding_1.PNG]]
|[[File:Mz5717_bonding_annotation_0.png]]
|[[File:Mz5717_bonding_1_annotation_0.png]]
|Highly BONDING
|}

==References==
<references>
<ref name="Hunt_MO">LCAO MO diagram from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">1 kJ/mol = 0.0004 au conversion from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007
</references>

ICL:mz5717

2019-05-17T16:25:54Z

Mz5717: /* Key Information of Isomers of Al2Cl4Br2 */

==BH3==
===Borane BH3===

'''B3LYP/6-31G(d.p) level'''

[[File:mz5717_BH3_summary.JPG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000070 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

Frequency analysis log file [[Media:MZ5717_BH3_FREQT.LOG|MZ5717_BH3_FREQ.log]]

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_BH3_FREQT.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational Spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2582
|0
|A1'
|no
|symmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

|[[File:Mz5717_BH3_IR.JPG]]

First of all there are two sets of degenerate vibrations at 1213 and 2716 cm-1, therefore there should be at most 4 signals. Furthermore, the vibration mode at 2582 cm-1 is a symmetric stretch, which means that it is not IR active. Thus there are only three signals present in the IR spectrum.

===Molecular Orbital Diagram for BH3===

[[File:mz5717_bh3_mo_all.PNG|800px]]

The MO of BH3 produced by LCAO as well as the ones calculated by Gaussian. <ref name="Hunt_MO" />

Here are some minor differences between the LCAO MO diagram and the calculated 'real' diagram:

- In-phase orbitals in the 'real' diagram merge together while all difference orbitals in the LCAO diagram are separate

- The 'real' diagram accounts for orbital repulsion (shown by certain slightly bent p orbitals)

It is reasonable to say that the LCAO diagram represents the 'real' spatial distribution of electrons to a good extent.

===Association Energy of NH3BH3===

Below is the key information of NH3 and NH3BH3.

{| class="wikitable"
|+
|-
| Name || Method & Basis Set || Summary Table || 'Item' Table || Low Frequencies || Jmol Image || LOG File
|-
|NH3
|B3LYP/6-31G(d.p)
|[[File:mz5717_nh3_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
</pre>
|<pre>
Low frequencies --- -0.0129 -0.0019 0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>
|<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_NH3_FREQ.LOG|MZ5717_NH3_FREQ.LOG]]
|-
|NH3BH3
|B3LYP/6-31G(d.p)
|[[File:mz5717_nh3bh3_summary_1.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000579 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>
|<pre>
Low frequencies --- 0.0005 0.0009 0.0011 16.8742 17.0939 37.4795
Low frequencies --- 265.8773 632.2052 639.3279
</pre>
|<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_NH3BH3_FREQ_6.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_NH3BH3_FREQ_6.LOG|MZ5717_NH3BH3_FREQ.LOG]]
|}

E(NH3)= -56.55777 au

E(BH3)= -26.61532 au

E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05160 au = -0.05160 ÷ 0.0004 kJ/mol = -129 kJ/mol <ref name="conversion" />

Therefore, the energy of the N-B dative bond is -129 kJ/mol. Compared to a normal N-B sigma bond (-377.9 kJ/mol) <ref name="NB bond" />, it is rather weak.

==NI3==
===Nitrogen Triiodide NI3===

'''B3LYP/Gen level'''

[[File:mz5717_ni3_summary_final.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
</pre>

Frequency log file [[Media:MZ5717_NI3_FREQ_4.LOG|MZ5717_NI3_FREQ.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_NI3_FREQ_4.LOG</uploadedFileContents>
</jmolApplet></jmol>

N-I bond distance: 2.184 Å

==Project: Lewis Acids and Bases==

===Key Information of Isomers of Al2Cl4Br2===

{| class="wikitable"
|+
|-
| Isomer || Method & Basis Set || Summary Table || 'Item' Table || Low Frequencies || Jmol Image || LOG File
|-
|Isomer A
[[File:Mz5717_isomer_a.png]]
|B3LYP/6-31G(d.p)
|[[File:mz5717_isomer_a_summary_1.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001018 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
</pre>
|<pre>
Low frequencies --- -2.3637 -2.2675 -0.9862 -0.0060 0.0068 0.0107
Low frequencies --- 11.7171 65.3709 88.4194
</pre>
|<jmol><jmolApplet>
<title>Isomer A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_A_2.LOG|MZ5717_ISOMER_A_OPTFREQ.LOG]]
|-
|Isomer B
[[File:Mz5717_isomer_b.png]]
|B3LYP/6-31G(d.p)
|[[File:mz5717_isomer_b_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000057 0.000450 YES
RMS Force 0.000026 0.000300 YES
Maximum Displacement 0.001712 0.001800 YES
RMS Displacement 0.000699 0.001200 YES
</pre>
|<pre>
Low frequencies --- -0.0099 -0.0086 -0.0074 1.5771 1.8810 2.5290
Low frequencies --- 14.5085 58.5774 81.4258
</pre>
|<jmol><jmolApplet>
<title>Isomer B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_B_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_B_2.LOG|MZ5717_ISOMER_B_OPTFREQ.LOG]]
|-
|Isomer C
[[File:Mz5717_isomer_c.png]]
|B3LYP/6-31G(d.p)
|[[File:mz5717_isomer_c_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000452 0.001800 YES
RMS Displacement 0.000186 0.001200 YES
</pre>
|<pre>
Low frequencies --- -0.0083 -0.0073 0.0107 0.8196 1.4180 1.6409
Low frequencies --- 13.4390 54.4089 73.7274
</pre>
|<jmol><jmolApplet>
<title>Isomer C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_D.LOG|MZ5717_ISOMER_C_OPTFREQ.LOG]]
|-
|Isomer D
[[File:Mz5717_isomer_d.png]]
|B3LYP/6-31G(d.p)
|[[File:mz5717_isomer_d_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001743 0.001800 YES
RMS Displacement 0.000677 0.001200 YES
</pre>
|<pre>
Low frequencies --- -2.1170 -1.5946 -1.4299 -0.0050 0.0035 0.0086
Low frequencies --- 17.7661 54.4445 79.9169
</pre>
|<jmol><jmolApplet>
<title>Isomer D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_E.LOG|MZ5717_ISOMER_D_OPTFREQ.LOG]]
|-
|Isomer E
[[File:Mz5717_isomer_e.png]]
|B3LYP/6-31G(d.p)
|[[File:mz5717_isomer_e_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001743 0.001800 YES
RMS Displacement 0.000637 0.001200 YES
</pre>
|<pre>
Low frequencies --- -2.1765 -1.5548 -0.0043 0.0027 0.0110 0.3832
Low frequencies --- 14.8169 52.4385 73.7073
</pre>
|<jmol><jmolApplet>
<title>Isomer E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_F.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_F.LOG|MZ5717_ISOMER_E_OPTFREQ.LOG]]
|}

===Geometry and Energy of Isomers of Al2Cl4Br2===

{| class="wikitable"
|+
|-
| Isomer || Geometry || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|Isomer A
|[[File:Mz5717_isomer_a.png]]
|D2h
|−18673857
|0
|high
|-
|Isomer B
|[[File:Mz5717_isomer_b.png]]
|C1
|−18673850
|7
|medium high
|-
|Isomer C
|[[File:Mz5717_isomer_c.png]]
|C2v
|−18673845
|12
|medium
|-
|Isomer D
|[[File:Mz5717_isomer_d.png]]
|C2v
|−18673844
|13
|low
|-
|Isomer E
|[[File:Mz5717_isomer_e.png]]
|C2h
|−18673844
|13
|low
|}

When the bridging ions are both Br, the stability of the molecule is highest. The stability decreases if one of the bridging ions is replaced with Cl, and is lowest when both the bridging ions are Cl. Let the bridging ion be X, then the Al-X-Al bond consists of a normal sigma bond, and a dative bond with X as the donor (as shown in the figure below). The strength of the Al-X-Al bond, therefore the stability of the molecule, depends on the extent of orbital overlap between Al and X. Br has larger and more diffuse orbitals, making the overlap more efficient. On the other hand, Cl is highly electronegative, having a smaller radius and holding its electrons tightly towards the core. Thus the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:Mz5717_isomer_general.png]]

===Dissociation of the Lowest-Energy Conformer into 2AlCl2Br===

When [[File:Mz5717_isomer_a.png]] dissociates into two molecules of AlCl2Br, we lose two Al-Br bonds.

The energy of one molecule of AlCl2Br is calculated to be -9336871 kJ/mol.

Therefore, the total energy of two such molecules is -18673743 kJ/mol, which is +114 kJ/mol relative to the energy of Isomer A, the lowest-energy isomer.

Each Al-Br broken means raising the total energy by 57 kJ/mol. It is evident that the dimer is considerably more stable than the separated monomers.

===Molecular Orbitals of the Lowest-Energy Conformer===

For the lowest-energy conformer, [[File:Mz5717_isomer_a.png]], there are 24 filled valence molecular orbitals in total. Below are three of them, ranked by their extent of bonding/antibonding character.

Atom colour code: pink - Al, red - Br. green - Cl.

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front View || Top View || Bonding/Antibonding Nature
|-
|MO No.1
|[[File:mz5717_antibonding.PNG]]
|[[File:Mz5717_antibonding_1.PNG]]
|[[File:mz5717_antibonding_annotation_0.png]]
|[[File:Mz5717_antibonding_1_annotation_0.png]]
|Highly ANTIBONDING
|-
|MO No.2
|[[File:Mz5717_in_between.PNG]]
|[[File:Mz5717_in_between_1.PNG]]
|[[File:Mz5717_in_between_annotation_0.png]]
|[[File:Mz5717_in_between_1_annotation_0.png]]
|Mainly BONDING
|-
|MO No.3
|[[File:Mz5717_bonding.PNG]]
|[[File:Mz5717_bonding_1.PNG]]
|[[File:Mz5717_bonding_annotation_0.png]]
|[[File:Mz5717_bonding_1_annotation_0.png]]
|Highly BONDING
|}

==References==
<references>
<ref name="Hunt_MO">LCAO MO diagram from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">1 kJ/mol = 0.0004 au conversion from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007
</references>

ICL:mz5717

2019-05-17T16:24:55Z

Mz5717: /* Association Energy of NH3BH3 */

==BH3==
===Borane BH3===

'''B3LYP/6-31G(d.p) level'''

[[File:mz5717_BH3_summary.JPG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000070 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

Frequency analysis log file [[Media:MZ5717_BH3_FREQT.LOG|MZ5717_BH3_FREQ.log]]

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_BH3_FREQT.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational Spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2582
|0
|A1'
|no
|symmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

|[[File:Mz5717_BH3_IR.JPG]]

First of all there are two sets of degenerate vibrations at 1213 and 2716 cm-1, therefore there should be at most 4 signals. Furthermore, the vibration mode at 2582 cm-1 is a symmetric stretch, which means that it is not IR active. Thus there are only three signals present in the IR spectrum.

===Molecular Orbital Diagram for BH3===

[[File:mz5717_bh3_mo_all.PNG|800px]]

The MO of BH3 produced by LCAO as well as the ones calculated by Gaussian. <ref name="Hunt_MO" />

Here are some minor differences between the LCAO MO diagram and the calculated 'real' diagram:

- In-phase orbitals in the 'real' diagram merge together while all difference orbitals in the LCAO diagram are separate

- The 'real' diagram accounts for orbital repulsion (shown by certain slightly bent p orbitals)

It is reasonable to say that the LCAO diagram represents the 'real' spatial distribution of electrons to a good extent.

===Association Energy of NH3BH3===

Below is the key information of NH3 and NH3BH3.

{| class="wikitable"
|+
|-
| Name || Method & Basis Set || Summary Table || 'Item' Table || Low Frequencies || Jmol Image || LOG File
|-
|NH3
|B3LYP/6-31G(d.p)
|[[File:mz5717_nh3_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
</pre>
|<pre>
Low frequencies --- -0.0129 -0.0019 0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>
|<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_NH3_FREQ.LOG|MZ5717_NH3_FREQ.LOG]]
|-
|NH3BH3
|B3LYP/6-31G(d.p)
|[[File:mz5717_nh3bh3_summary_1.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000579 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>
|<pre>
Low frequencies --- 0.0005 0.0009 0.0011 16.8742 17.0939 37.4795
Low frequencies --- 265.8773 632.2052 639.3279
</pre>
|<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_NH3BH3_FREQ_6.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_NH3BH3_FREQ_6.LOG|MZ5717_NH3BH3_FREQ.LOG]]
|}

E(NH3)= -56.55777 au

E(BH3)= -26.61532 au

E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05160 au = -0.05160 ÷ 0.0004 kJ/mol = -129 kJ/mol <ref name="conversion" />

Therefore, the energy of the N-B dative bond is -129 kJ/mol. Compared to a normal N-B sigma bond (-377.9 kJ/mol) <ref name="NB bond" />, it is rather weak.

==NI3==
===Nitrogen Triiodide NI3===

'''B3LYP/Gen level'''

[[File:mz5717_ni3_summary_final.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
</pre>

Frequency log file [[Media:MZ5717_NI3_FREQ_4.LOG|MZ5717_NI3_FREQ.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_NI3_FREQ_4.LOG</uploadedFileContents>
</jmolApplet></jmol>

N-I bond distance: 2.184 Å

==Project: Lewis Acids and Bases==

===Key Information of Isomers of Al2Cl4Br2===

{| class="wikitable"
|+
|-
| Isomer || Method & Basis Set || Summary Table || 'Item' Table || Low Frequencies || Jmol Image || LOG File
|-
|Isomer A
[[File:Mz5717_isomer_a.png]]
|B3LYP/6-31G
|[[File:mz5717_isomer_a_summary_1.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001018 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
</pre>
|<pre>
Low frequencies --- -2.3637 -2.2675 -0.9862 -0.0060 0.0068 0.0107
Low frequencies --- 11.7171 65.3709 88.4194
</pre>
|<jmol><jmolApplet>
<title>Isomer A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_A_2.LOG|MZ5717_ISOMER_A_OPTFREQ.LOG]]
|-
|Isomer B
[[File:Mz5717_isomer_b.png]]
|B3LYP/6-31G
|[[File:mz5717_isomer_b_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000057 0.000450 YES
RMS Force 0.000026 0.000300 YES
Maximum Displacement 0.001712 0.001800 YES
RMS Displacement 0.000699 0.001200 YES
</pre>
|<pre>
Low frequencies --- -0.0099 -0.0086 -0.0074 1.5771 1.8810 2.5290
Low frequencies --- 14.5085 58.5774 81.4258
</pre>
|<jmol><jmolApplet>
<title>Isomer B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_B_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_B_2.LOG|MZ5717_ISOMER_B_OPTFREQ.LOG]]
|-
|Isomer C
[[File:Mz5717_isomer_c.png]]
|B3LYP/6-31G
|[[File:mz5717_isomer_c_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000452 0.001800 YES
RMS Displacement 0.000186 0.001200 YES
</pre>
|<pre>
Low frequencies --- -0.0083 -0.0073 0.0107 0.8196 1.4180 1.6409
Low frequencies --- 13.4390 54.4089 73.7274
</pre>
|<jmol><jmolApplet>
<title>Isomer C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_D.LOG|MZ5717_ISOMER_C_OPTFREQ.LOG]]
|-
|Isomer D
[[File:Mz5717_isomer_d.png]]
|B3LYP/6-31G
|[[File:mz5717_isomer_d_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001743 0.001800 YES
RMS Displacement 0.000677 0.001200 YES
</pre>
|<pre>
Low frequencies --- -2.1170 -1.5946 -1.4299 -0.0050 0.0035 0.0086
Low frequencies --- 17.7661 54.4445 79.9169
</pre>
|<jmol><jmolApplet>
<title>Isomer D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_E.LOG|MZ5717_ISOMER_D_OPTFREQ.LOG]]
|-
|Isomer E
[[File:Mz5717_isomer_e.png]]
|B3LYP/6-31G
|[[File:mz5717_isomer_e_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001743 0.001800 YES
RMS Displacement 0.000637 0.001200 YES
</pre>
|<pre>
Low frequencies --- -2.1765 -1.5548 -0.0043 0.0027 0.0110 0.3832
Low frequencies --- 14.8169 52.4385 73.7073
</pre>
|<jmol><jmolApplet>
<title>Isomer E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_F.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_F.LOG|MZ5717_ISOMER_E_OPTFREQ.LOG]]
|}

===Geometry and Energy of Isomers of Al2Cl4Br2===

{| class="wikitable"
|+
|-
| Isomer || Geometry || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|Isomer A
|[[File:Mz5717_isomer_a.png]]
|D2h
|−18673857
|0
|high
|-
|Isomer B
|[[File:Mz5717_isomer_b.png]]
|C1
|−18673850
|7
|medium high
|-
|Isomer C
|[[File:Mz5717_isomer_c.png]]
|C2v
|−18673845
|12
|medium
|-
|Isomer D
|[[File:Mz5717_isomer_d.png]]
|C2v
|−18673844
|13
|low
|-
|Isomer E
|[[File:Mz5717_isomer_e.png]]
|C2h
|−18673844
|13
|low
|}

When the bridging ions are both Br, the stability of the molecule is highest. The stability decreases if one of the bridging ions is replaced with Cl, and is lowest when both the bridging ions are Cl. Let the bridging ion be X, then the Al-X-Al bond consists of a normal sigma bond, and a dative bond with X as the donor (as shown in the figure below). The strength of the Al-X-Al bond, therefore the stability of the molecule, depends on the extent of orbital overlap between Al and X. Br has larger and more diffuse orbitals, making the overlap more efficient. On the other hand, Cl is highly electronegative, having a smaller radius and holding its electrons tightly towards the core. Thus the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:Mz5717_isomer_general.png]]

===Dissociation of the Lowest-Energy Conformer into 2AlCl2Br===

When [[File:Mz5717_isomer_a.png]] dissociates into two molecules of AlCl2Br, we lose two Al-Br bonds.

The energy of one molecule of AlCl2Br is calculated to be -9336871 kJ/mol.

Therefore, the total energy of two such molecules is -18673743 kJ/mol, which is +114 kJ/mol relative to the energy of Isomer A, the lowest-energy isomer.

Each Al-Br broken means raising the total energy by 57 kJ/mol. It is evident that the dimer is considerably more stable than the separated monomers.

===Molecular Orbitals of the Lowest-Energy Conformer===

For the lowest-energy conformer, [[File:Mz5717_isomer_a.png]], there are 24 filled valence molecular orbitals in total. Below are three of them, ranked by their extent of bonding/antibonding character.

Atom colour code: pink - Al, red - Br. green - Cl.

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front View || Top View || Bonding/Antibonding Nature
|-
|MO No.1
|[[File:mz5717_antibonding.PNG]]
|[[File:Mz5717_antibonding_1.PNG]]
|[[File:mz5717_antibonding_annotation_0.png]]
|[[File:Mz5717_antibonding_1_annotation_0.png]]
|Highly ANTIBONDING
|-
|MO No.2
|[[File:Mz5717_in_between.PNG]]
|[[File:Mz5717_in_between_1.PNG]]
|[[File:Mz5717_in_between_annotation_0.png]]
|[[File:Mz5717_in_between_1_annotation_0.png]]
|Mainly BONDING
|-
|MO No.3
|[[File:Mz5717_bonding.PNG]]
|[[File:Mz5717_bonding_1.PNG]]
|[[File:Mz5717_bonding_annotation_0.png]]
|[[File:Mz5717_bonding_1_annotation_0.png]]
|Highly BONDING
|}

==References==
<references>
<ref name="Hunt_MO">LCAO MO diagram from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">1 kJ/mol = 0.0004 au conversion from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007
</references>

File:MZ5717 ISOMER F.LOG

2019-05-17T16:22:18Z

Mz5717:

File:Mz5717 isomer e summary.PNG

2019-05-17T16:22:08Z

Mz5717:

ICL:mz5717

2019-05-17T16:21:54Z

Mz5717: /* Key Information of Isomers of Al2Cl4Br2 */

==BH3==
===Borane BH3===

'''B3LYP/6-31G(d.p) level'''

[[File:mz5717_BH3_summary.JPG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000070 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

Frequency analysis log file [[Media:MZ5717_BH3_FREQT.LOG|MZ5717_BH3_FREQ.log]]

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_BH3_FREQT.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational Spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2582
|0
|A1'
|no
|symmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

|[[File:Mz5717_BH3_IR.JPG]]

First of all there are two sets of degenerate vibrations at 1213 and 2716 cm-1, therefore there should be at most 4 signals. Furthermore, the vibration mode at 2582 cm-1 is a symmetric stretch, which means that it is not IR active. Thus there are only three signals present in the IR spectrum.

===Molecular Orbital Diagram for BH3===

[[File:mz5717_bh3_mo_all.PNG|800px]]

The MO of BH3 produced by LCAO as well as the ones calculated by Gaussian. <ref name="Hunt_MO" />

Here are some minor differences between the LCAO MO diagram and the calculated 'real' diagram:

- In-phase orbitals in the 'real' diagram merge together while all difference orbitals in the LCAO diagram are separate

- The 'real' diagram accounts for orbital repulsion (shown by certain slightly bent p orbitals)

It is reasonable to say that the LCAO diagram represents the 'real' spatial distribution of electrons to a good extent.

===Association Energy of NH3BH3===

Below is the key information of NH3 and NH3BH3.

{| class="wikitable"
|+
|-
| Name || Method & Basis Set || Summary Table || 'Item' Table || Low Frequencies || Jmol Image || LOG File
|-
|NH3
|B3LYP/6-31G
|[[File:mz5717_nh3_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
</pre>
|<pre>
Low frequencies --- -0.0129 -0.0019 0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>
|<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_NH3_FREQ.LOG|MZ5717_NH3_FREQ.LOG]]
|-
|NH3BH3
|B3LYP/6-31G
|[[File:mz5717_nh3bh3_summary_1.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000579 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>
|<pre>
Low frequencies --- 0.0005 0.0009 0.0011 16.8742 17.0939 37.4795
Low frequencies --- 265.8773 632.2052 639.3279
</pre>
|<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_NH3BH3_FREQ_6.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_NH3BH3_FREQ_6.LOG|MZ5717_NH3BH3_FREQ.LOG]]
|}

E(NH3)= -56.55777 au

E(BH3)= -26.61532 au

E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05160 au = -0.05160 ÷ 0.0004 kJ/mol = -129 kJ/mol <ref name="conversion" />

Therefore, the energy of the N-B dative bond is -129 kJ/mol. Compared to a normal N-B sigma bond (-377.9 kJ/mol) <ref name="NB bond" />, it is rather weak.

==NI3==
===Nitrogen Triiodide NI3===

'''B3LYP/Gen level'''

[[File:mz5717_ni3_summary_final.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
</pre>

Frequency log file [[Media:MZ5717_NI3_FREQ_4.LOG|MZ5717_NI3_FREQ.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_NI3_FREQ_4.LOG</uploadedFileContents>
</jmolApplet></jmol>

N-I bond distance: 2.184 Å

==Project: Lewis Acids and Bases==

===Key Information of Isomers of Al2Cl4Br2===

{| class="wikitable"
|+
|-
| Isomer || Method & Basis Set || Summary Table || 'Item' Table || Low Frequencies || Jmol Image || LOG File
|-
|Isomer A
[[File:Mz5717_isomer_a.png]]
|B3LYP/6-31G
|[[File:mz5717_isomer_a_summary_1.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001018 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
</pre>
|<pre>
Low frequencies --- -2.3637 -2.2675 -0.9862 -0.0060 0.0068 0.0107
Low frequencies --- 11.7171 65.3709 88.4194
</pre>
|<jmol><jmolApplet>
<title>Isomer A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_A_2.LOG|MZ5717_ISOMER_A_OPTFREQ.LOG]]
|-
|Isomer B
[[File:Mz5717_isomer_b.png]]
|B3LYP/6-31G
|[[File:mz5717_isomer_b_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000057 0.000450 YES
RMS Force 0.000026 0.000300 YES
Maximum Displacement 0.001712 0.001800 YES
RMS Displacement 0.000699 0.001200 YES
</pre>
|<pre>
Low frequencies --- -0.0099 -0.0086 -0.0074 1.5771 1.8810 2.5290
Low frequencies --- 14.5085 58.5774 81.4258
</pre>
|<jmol><jmolApplet>
<title>Isomer B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_B_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_B_2.LOG|MZ5717_ISOMER_B_OPTFREQ.LOG]]
|-
|Isomer C
[[File:Mz5717_isomer_c.png]]
|B3LYP/6-31G
|[[File:mz5717_isomer_c_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000013 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000452 0.001800 YES
RMS Displacement 0.000186 0.001200 YES
</pre>
|<pre>
Low frequencies --- -0.0083 -0.0073 0.0107 0.8196 1.4180 1.6409
Low frequencies --- 13.4390 54.4089 73.7274
</pre>
|<jmol><jmolApplet>
<title>Isomer C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_D.LOG|MZ5717_ISOMER_C_OPTFREQ.LOG]]
|-
|Isomer D
[[File:Mz5717_isomer_d.png]]
|B3LYP/6-31G
|[[File:mz5717_isomer_d_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001743 0.001800 YES
RMS Displacement 0.000677 0.001200 YES
</pre>
|<pre>
Low frequencies --- -2.1170 -1.5946 -1.4299 -0.0050 0.0035 0.0086
Low frequencies --- 17.7661 54.4445 79.9169
</pre>
|<jmol><jmolApplet>
<title>Isomer D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_E.LOG|MZ5717_ISOMER_D_OPTFREQ.LOG]]
|-
|Isomer E
[[File:Mz5717_isomer_e.png]]
|B3LYP/6-31G
|[[File:mz5717_isomer_e_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001743 0.001800 YES
RMS Displacement 0.000637 0.001200 YES
</pre>
|<pre>
Low frequencies --- -2.1765 -1.5548 -0.0043 0.0027 0.0110 0.3832
Low frequencies --- 14.8169 52.4385 73.7073
</pre>
|<jmol><jmolApplet>
<title>Isomer E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_F.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_F.LOG|MZ5717_ISOMER_E_OPTFREQ.LOG]]
|}

===Geometry and Energy of Isomers of Al2Cl4Br2===

{| class="wikitable"
|+
|-
| Isomer || Geometry || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|Isomer A
|[[File:Mz5717_isomer_a.png]]
|D2h
|−18673857
|0
|high
|-
|Isomer B
|[[File:Mz5717_isomer_b.png]]
|C1
|−18673850
|7
|medium high
|-
|Isomer C
|[[File:Mz5717_isomer_c.png]]
|C2v
|−18673845
|12
|medium
|-
|Isomer D
|[[File:Mz5717_isomer_d.png]]
|C2v
|−18673844
|13
|low
|-
|Isomer E
|[[File:Mz5717_isomer_e.png]]
|C2h
|−18673844
|13
|low
|}

When the bridging ions are both Br, the stability of the molecule is highest. The stability decreases if one of the bridging ions is replaced with Cl, and is lowest when both the bridging ions are Cl. Let the bridging ion be X, then the Al-X-Al bond consists of a normal sigma bond, and a dative bond with X as the donor (as shown in the figure below). The strength of the Al-X-Al bond, therefore the stability of the molecule, depends on the extent of orbital overlap between Al and X. Br has larger and more diffuse orbitals, making the overlap more efficient. On the other hand, Cl is highly electronegative, having a smaller radius and holding its electrons tightly towards the core. Thus the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:Mz5717_isomer_general.png]]

===Dissociation of the Lowest-Energy Conformer into 2AlCl2Br===

When [[File:Mz5717_isomer_a.png]] dissociates into two molecules of AlCl2Br, we lose two Al-Br bonds.

The energy of one molecule of AlCl2Br is calculated to be -9336871 kJ/mol.

Therefore, the total energy of two such molecules is -18673743 kJ/mol, which is +114 kJ/mol relative to the energy of Isomer A, the lowest-energy isomer.

Each Al-Br broken means raising the total energy by 57 kJ/mol. It is evident that the dimer is considerably more stable than the separated monomers.

===Molecular Orbitals of the Lowest-Energy Conformer===

For the lowest-energy conformer, [[File:Mz5717_isomer_a.png]], there are 24 filled valence molecular orbitals in total. Below are three of them, ranked by their extent of bonding/antibonding character.

Atom colour code: pink - Al, red - Br. green - Cl.

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front View || Top View || Bonding/Antibonding Nature
|-
|MO No.1
|[[File:mz5717_antibonding.PNG]]
|[[File:Mz5717_antibonding_1.PNG]]
|[[File:mz5717_antibonding_annotation_0.png]]
|[[File:Mz5717_antibonding_1_annotation_0.png]]
|Highly ANTIBONDING
|-
|MO No.2
|[[File:Mz5717_in_between.PNG]]
|[[File:Mz5717_in_between_1.PNG]]
|[[File:Mz5717_in_between_annotation_0.png]]
|[[File:Mz5717_in_between_1_annotation_0.png]]
|Mainly BONDING
|-
|MO No.3
|[[File:Mz5717_bonding.PNG]]
|[[File:Mz5717_bonding_1.PNG]]
|[[File:Mz5717_bonding_annotation_0.png]]
|[[File:Mz5717_bonding_1_annotation_0.png]]
|Highly BONDING
|}

==References==
<references>
<ref name="Hunt_MO">LCAO MO diagram from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">1 kJ/mol = 0.0004 au conversion from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007
</references>

File:MZ5717 ISOMER E.LOG

2019-05-17T16:18:14Z

Mz5717:

2019-05-17T16:01:20Z

Mz5717: /* Key Information of Isomers of Al2Cl4Br2 */

==BH3==
===Borane BH3===

'''B3LYP/6-31G(d.p) level'''

[[File:mz5717_BH3_summary.JPG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000070 0.001800 YES
RMS Displacement 0.000035 0.001200 YES
</pre>

Frequency analysis log file [[Media:MZ5717_BH3_FREQT.LOG|MZ5717_BH3_FREQ.log]]

<pre>
Low frequencies --- -10.3498 -3.4492 -1.2454 -0.0055 0.4779 3.2165
Low frequencies --- 1162.9519 1213.1527 1213.1554
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_BH3_FREQT.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational Spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|93
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2582
|0
|A1'
|no
|symmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

|[[File:Mz5717_BH3_IR.JPG]]

First of all there are two sets of degenerate vibrations at 1213 and 2716 cm-1, therefore there should be at most 4 signals. Furthermore, the vibration mode at 2582 cm-1 is a symmetric stretch, which means that it is not IR active. Thus there are only three signals present in the IR spectrum.

===Molecular Orbital Diagram for BH3===

[[File:mz5717_bh3_mo_all.PNG|800px]]

The MO of BH3 produced by LCAO as well as the ones calculated by Gaussian. <ref name="Hunt_MO" />

Here are some minor differences between the LCAO MO diagram and the calculated 'real' diagram:

- In-phase orbitals in the 'real' diagram merge together while all difference orbitals in the LCAO diagram are separate

- The 'real' diagram accounts for orbital repulsion (shown by certain slightly bent p orbitals)

It is reasonable to say that the LCAO diagram represents the 'real' spatial distribution of electrons to a good extent.

===Association Energy of NH3BH3===

Below is the key information of NH3 and NH3BH3.

{| class="wikitable"
|+
|-
| Name || Method & Basis Set || Summary Table || 'Item' Table || Low Frequencies || Jmol Image || LOG File
|-
|NH3
|B3LYP/6-31G
|[[File:mz5717_nh3_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
</pre>
|<pre>
Low frequencies --- -0.0129 -0.0019 0.0014 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368
</pre>
|<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_NH3_FREQ.LOG|MZ5717_NH3_FREQ.LOG]]
|-
|NH3BH3
|B3LYP/6-31G
|[[File:mz5717_nh3bh3_summary_1.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000115 0.000450 YES
RMS Force 0.000060 0.000300 YES
Maximum Displacement 0.000579 0.001800 YES
RMS Displacement 0.000345 0.001200 YES
</pre>
|<pre>
Low frequencies --- 0.0005 0.0009 0.0011 16.8742 17.0939 37.4795
Low frequencies --- 265.8773 632.2052 639.3279
</pre>
|<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_NH3BH3_FREQ_6.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_NH3BH3_FREQ_6.LOG|MZ5717_NH3BH3_FREQ.LOG]]
|}

E(NH3)= -56.55777 au

E(BH3)= -26.61532 au

E(NH3BH3)= -83.22469 au

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05160 au = -0.05160 ÷ 0.0004 kJ/mol = -129 kJ/mol <ref name="conversion" />

Therefore, the energy of the N-B dative bond is -129 kJ/mol. Compared to a normal N-B sigma bond (-377.9 kJ/mol) <ref name="NB bond" />, it is rather weak.

==NI3==
===Nitrogen Triiodide NI3===

'''B3LYP/Gen level'''

[[File:mz5717_ni3_summary_final.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000088 0.000450 YES
RMS Force 0.000044 0.000300 YES
Maximum Displacement 0.000858 0.001800 YES
RMS Displacement 0.000481 0.001200 YES
</pre>

Frequency log file [[Media:MZ5717_NI3_FREQ_4.LOG|MZ5717_NI3_FREQ.log]]

<pre>
Low frequencies --- -12.3847 -12.3783 -5.6131 -0.0040 0.0194 0.0711
Low frequencies --- 100.9307 100.9314 147.2333
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_NI3_FREQ_4.LOG</uploadedFileContents>
</jmolApplet></jmol>

N-I bond distance: 2.184 Å

==Project: Lewis Acids and Bases==

===Key Information of Isomers of Al2Cl4Br2===

{| class="wikitable"
|+
|-
| Isomer || Method & Basis Set || Summary Table || 'Item' Table || Low Frequencies || Jmol Image || LOG File
|-
|Isomer A
[[File:Mz5717_isomer_a.png]]
|B3LYP/6-31G
|[[File:mz5717_isomer_a_summary_1.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001018 0.001800 YES
RMS Displacement 0.000411 0.001200 YES
</pre>
|<pre>
Low frequencies --- -2.3637 -2.2675 -0.9862 -0.0060 0.0068 0.0107
Low frequencies --- 11.7171 65.3709 88.4194
</pre>
|<jmol><jmolApplet>
<title>Isomer A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_A_2.LOG|MZ5717_ISOMER_A_OPTFREQ.LOG]]
|-
|Isomer B
[[File:Mz5717_isomer_b.png]]
|B3LYP/6-31G
|[[File:mz5717_isomer_b_summary.PNG]]
|<pre>
Item Value Threshold Converged?
Maximum Force 0.000057 0.000450 YES
RMS Force 0.000026 0.000300 YES
Maximum Displacement 0.001712 0.001800 YES
RMS Displacement 0.000699 0.001200 YES
</pre>
|<pre>
Low frequencies --- -0.0099 -0.0086 -0.0074 1.5771 1.8810 2.5290
Low frequencies --- 14.5085 58.5774 81.4258
</pre>
|<jmol><jmolApplet>
<title>Isomer B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_ISOMER_B_2.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_ISOMER_B_2.LOG|MZ5717_ISOMER_B_OPTFREQ.LOG]]
|-
|Isomer C
[[File:Mz5717_isomer_a.png]]
|B3LYP/6-31G
|[[File:mz5717_isomer_a_summary.PNG]]
|<pre>

</pre>
|<pre>

</pre>
|<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_Q.LOG|MZ5717_NH3_FREQ.LOG]]
|-
|Isomer D
[[File:Mz5717_isomer_a.png]]
|B3LYP/6-31G
|[[File:mz5717_isomer_a_summary.PNG]]
|<pre>

</pre>
|<pre>

</pre>
|<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_Q.LOG|MZ5717_NH3_FREQ.LOG]]
|-
|Isomer E
[[File:Mz5717_isomer_a.png]]
|B3LYP/6-31G
|[[File:mz5717_isomer_a_summary.PNG]]
|<pre>

</pre>
|<pre>

</pre>
|<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_Q.LOG|MZ5717_NH3_FREQ.LOG]]
|-
|Isomer F
[[File:Mz5717_isomer_a.png]]
|B3LYP/6-31G
|[[File:mz5717_isomer_a_summary.PNG]]
|<pre>

</pre>
|<pre>

</pre>
|<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MZ5717_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>
|[[Media:MZ5717_Q.LOG|MZ5717_NH3_FREQ.LOG]]
|}

===Geometry and Energy of Isomers of Al2Cl4Br2===

{| class="wikitable"
|+
|-
| Isomer || Geometry || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|Isomer A
|[[File:Mz5717_isomer_a.png]]
|D2h
|−18673857
|0
|high
|-
|Isomer B
|[[File:Mz5717_isomer_b.png]]
|C1
|−18673850
|7
|medium high
|-
|Isomer C
|[[File:Mz5717_isomer_c.png]]
|C2v
|−18673845
|12
|medium
|-
|Isomer D
|[[File:Mz5717_isomer_d.png]]
|C2v
|−18673844
|13
|low
|-
|Isomer E
|[[File:Mz5717_isomer_e.png]]
|C2h
|−18673844
|13
|low
|}

When the bridging ions are both Br, the stability of the molecule is highest. The stability decreases if one of the bridging ions is replaced with Cl, and is lowest when both the bridging ions are Cl. Let the bridging ion be X, then the Al-X-Al bond consists of a normal sigma bond, and a dative bond with X as the donor (as shown in the figure below). The strength of the Al-X-Al bond, therefore the stability of the molecule, depends on the extent of orbital overlap between Al and X. Br has larger and more diffuse orbitals, making the overlap more efficient. On the other hand, Cl is highly electronegative, having a smaller radius and holding its electrons tightly towards the core. Thus the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:Mz5717_isomer_general.png]]

===Dissociation of the Lowest-Energy Conformer into 2AlCl2Br===

When [[File:Mz5717_isomer_a.png]] dissociates into two molecules of AlCl2Br, we lose two Al-Br bonds.

The energy of one molecule of AlCl2Br is calculated to be -9336871 kJ/mol.

Therefore, the total energy of two such molecules is -18673743 kJ/mol, which is +114 kJ/mol relative to the energy of Isomer A, the lowest-energy isomer.

Each Al-Br broken means raising the total energy by 57 kJ/mol. It is evident that the dimer is considerably more stable than the separated monomers.

===Molecular Orbitals of the Lowest-Energy Conformer===

For the lowest-energy conformer, [[File:Mz5717_isomer_a.png]], there are 24 filled valence molecular orbitals in total. Below are three of them, ranked by their extent of bonding/antibonding character.

Atom colour code: pink - Al, red - Br. green - Cl.

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front View || Top View || Bonding/Antibonding Nature
|-
|MO No.1
|[[File:mz5717_antibonding.PNG]]
|[[File:Mz5717_antibonding_1.PNG]]
|[[File:mz5717_antibonding_annotation_0.png]]
|[[File:Mz5717_antibonding_1_annotation_0.png]]
|Highly ANTIBONDING
|-
|MO No.2
|[[File:Mz5717_in_between.PNG]]
|[[File:Mz5717_in_between_1.PNG]]
|[[File:Mz5717_in_between_annotation_0.png]]
|[[File:Mz5717_in_between_1_annotation_0.png]]
|Mainly BONDING
|-
|MO No.3
|[[File:Mz5717_bonding.PNG]]
|[[File:Mz5717_bonding_1.PNG]]
|[[File:Mz5717_bonding_annotation_0.png]]
|[[File:Mz5717_bonding_1_annotation_0.png]]
|Highly BONDING
|}

==References==
<references>
<ref name="Hunt_MO">LCAO MO diagram from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">1 kJ/mol = 0.0004 au conversion from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">Luo, Y. R., Comprehensive Handbook of Chemical Bond Energies, CRC Press, Boca Raton, FL, 2007
</references>

File:MZ5717 ISOMER A 2.LOG

2019-05-17T15:53:44Z

Mz5717:

ICL:mz5717

2019-05-17T13:25:22Z

Mz5717: /* Vibrational Spectrum for BH3 */