ChemWiki - User contributions [en]

ICL:zl4817

2019-05-24T13:05:27Z

Zl4817: /* Symmetry and Energy of Al2Cl4Br2 Isomers */

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

Figure 1: Summary Table of BH3

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (a.u.) || Symmetry Point Group || IR active? || Vibrational Mode
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

Figure 2: BH3 Proposed IR Spectrum by Gaussian

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). A maximum of 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

Figure 3: BH3 LCAO and 'Real' MO Diagram 

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.<ref name="Hunt_MO" />

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

Figure 4: NH3 Summary Table

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

Figure 5: NH3BH3 Summary Table

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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 (1 kJ/mol = 0.0004 au) <ref name="conversion" />

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).<ref name="NB bond" />

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

Figure 6: NI3 Summary Table

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

Figure 7: Isomer A

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

Figure 8: Isomer A Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

Figure 9: Isomer B

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

Figure 10: Isomer B Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

Figure 11: Isomer C

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

Figure 12: Isomer C Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

Figure 13: Isomer D

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

Figure 14: Isomer D Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

Figure 15: Isomer E

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

Figure 16: Isomer E Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png| thumb |Figure 7: Isomer A]]
|D2h
|−18673857
|Very High
|-
|B
|[[File:LZY_isomer_b.png| thumb |Figure 9: Isomer B]]
|C1
|−18673850
|High
|-
|C
|[[File:LZY_isomer_c.png| thumb |Figure 11: Isomer C]]
|C2v
|−18673845
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png| thumb |Figure 13: Isomer D]]
|C2v
|−18673844
|Low
|-
|E
|[[File:LZY_isomer_e.png| thumb |Figure 15: Isomer E]]
|C2h
|−18673844
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule. <ref name="overlap" />

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

Figure 17: A General Structure of Dimer Complex

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

Figure 18: AlCl2Br Summary Table

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png| right | thumb |Figure 7: Isomer A]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy<ref name="bond break"/>, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

Atom colour label: pink - Al, green - Cl, red - Br

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front Diagram || Top Diagram || Properties
|-
|MO (1)
|[[File:LZY_MO1_FRONT.PNG| thumb |Figure 19: MO1 Front View]]
|[[File:LZY_MO1_TOP.PNG| thumb |Figure 20: MO1 Top View]]
|[[File:LZY_MO1_FRONT_ANNO.png|400px| thumb |Figure 21: MO1 Front Annotation]]
|[[File:LZY_MO1_TOP_ANNO.png|200px| thumb |Figure 22: MO1 Top Annotation]]
|Highly Antibonding
|-
|MO (2)
|[[File:LZY_MO2_FRONT.PNG| thumb |Figure 23: MO2 Front View]]
|[[File:LZY_MO2_TOP.PNG| thumb |Figure 24: MO2 Top View]]
|[[File:LZY_MO2_FRONT_ANNO.png|400px| thumb |Figure 25: MO2 Front Annotation]]
|[[File:LZY_MO2_TOP_ANNO.png|200px| thumb |Figure 26: MO2 Top Annotation]]
|Bonding
|-
|MO (3)
|[[File:LZY_MO3_FRONT.PNG| thumb |Figure 27: MO3 Front View]]
|[[File:LZY_MO3_TOP.PNG| thumb |Figure 28: MO3 Top View]]
|[[File:LZY_MO3_FRONT_ANNO.png|400px| thumb |Figure 29: MO3 Front Annotation]]
|[[File:LZY_MO1_TOP_ANNO.png|200px| thumb |Figure 30: MO3 Top Annotation]]
|Highly Bonding
|}

==References==
<references>
<ref name="Hunt_MO">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, and A.J. Thor, Quantities, Units and Symbols in Physical Chemistry, IUPAC Green Book, Third Edition, Second Printing, IUPAC & RSC Publishing, Cambridge (2008)</ref>
<ref name="overlap">C. Barnes, Inorganic Chemistry (Housecroft, Catherine E.; Sharpe, Alan G.), J. Chem. Educ., 2003, '''80''', 747.</ref>
<ref name="bond break">Peter Atkins and Julio de Paula, Physical Chemistry (8th ed., W.H. Freeman 2006), p.809 ISBN 0-7167-8759-8</ref>
</references>

ICL:zl4817

2019-05-24T11:38:56Z

Zl4817: /* Molecular Orbitals of the Lowest-Energy Conformer */

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

Figure 1: Summary Table of BH3

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (a.u.) || Symmetry Point Group || IR active? || Vibrational Mode
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

Figure 2: BH3 Proposed IR Spectrum by Gaussian

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). A maximum of 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

Figure 3: BH3 LCAO and 'Real' MO Diagram 

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.<ref name="Hunt_MO" />

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

Figure 4: NH3 Summary Table

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

Figure 5: NH3BH3 Summary Table

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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 (1 kJ/mol = 0.0004 au) <ref name="conversion" />

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).<ref name="NB bond" />

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

Figure 6: NI3 Summary Table

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

Figure 7: Isomer A

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

Figure 8: Isomer A Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

Figure 9: Isomer B

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

Figure 10: Isomer B Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

Figure 11: Isomer C

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

Figure 12: Isomer C Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

Figure 13: Isomer D

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

Figure 14: Isomer D Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

Figure 15: Isomer E

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

Figure 16: Isomer E Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png| thumb |Figure 7: Isomer A]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png| thumb |Figure 9: Isomer B]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png| thumb |Figure 11: Isomer C]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png| thumb |Figure 13: Isomer D]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png| thumb |Figure 15: Isomer E]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule. <ref name="overlap" />

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

Figure 17: A General Structure of Dimer Complex

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

Figure 18: AlCl2Br Summary Table

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png| right | thumb |Figure 7: Isomer A]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy<ref name="bond break"/>, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

Atom colour label: pink - Al, green - Cl, red - Br

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front Diagram || Top Diagram || Properties
|-
|MO (1)
|[[File:LZY_MO1_FRONT.PNG| thumb |Figure 19: MO1 Front View]]
|[[File:LZY_MO1_TOP.PNG| thumb |Figure 20: MO1 Top View]]
|[[File:LZY_MO1_FRONT_ANNO.png|400px| thumb |Figure 21: MO1 Front Annotation]]
|[[File:LZY_MO1_TOP_ANNO.png|200px| thumb |Figure 22: MO1 Top Annotation]]
|Highly Antibonding
|-
|MO (2)
|[[File:LZY_MO2_FRONT.PNG| thumb |Figure 23: MO2 Front View]]
|[[File:LZY_MO2_TOP.PNG| thumb |Figure 24: MO2 Top View]]
|[[File:LZY_MO2_FRONT_ANNO.png|400px| thumb |Figure 25: MO2 Front Annotation]]
|[[File:LZY_MO2_TOP_ANNO.png|200px| thumb |Figure 26: MO2 Top Annotation]]
|Bonding
|-
|MO (3)
|[[File:LZY_MO3_FRONT.PNG| thumb |Figure 27: MO3 Front View]]
|[[File:LZY_MO3_TOP.PNG| thumb |Figure 28: MO3 Top View]]
|[[File:LZY_MO3_FRONT_ANNO.png|400px| thumb |Figure 29: MO3 Front Annotation]]
|[[File:LZY_MO1_TOP_ANNO.png|200px| thumb |Figure 30: MO3 Top Annotation]]
|Highly Bonding
|}

==References==
<references>
<ref name="Hunt_MO">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, and A.J. Thor, Quantities, Units and Symbols in Physical Chemistry, IUPAC Green Book, Third Edition, Second Printing, IUPAC & RSC Publishing, Cambridge (2008)</ref>
<ref name="overlap">C. Barnes, Inorganic Chemistry (Housecroft, Catherine E.; Sharpe, Alan G.), J. Chem. Educ., 2003, '''80''', 747.</ref>
<ref name="bond break">Peter Atkins and Julio de Paula, Physical Chemistry (8th ed., W.H. Freeman 2006), p.809 ISBN 0-7167-8759-8</ref>
</references>

ICL:zl4817

2019-05-24T11:33:33Z

Zl4817: /* Project: Lewis Acids and Bases */

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

Figure 1: Summary Table of BH3

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (a.u.) || Symmetry Point Group || IR active? || Vibrational Mode
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

Figure 2: BH3 Proposed IR Spectrum by Gaussian

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). A maximum of 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

Figure 3: BH3 LCAO and 'Real' MO Diagram 

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.<ref name="Hunt_MO" />

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

Figure 4: NH3 Summary Table

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

Figure 5: NH3BH3 Summary Table

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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 (1 kJ/mol = 0.0004 au) <ref name="conversion" />

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).<ref name="NB bond" />

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

Figure 6: NI3 Summary Table

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

Figure 7: Isomer A

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

Figure 8: Isomer A Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

Figure 9: Isomer B

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

Figure 10: Isomer B Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

Figure 11: Isomer C

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

Figure 12: Isomer C Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

Figure 13: Isomer D

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

Figure 14: Isomer D Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

Figure 15: Isomer E

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

Figure 16: Isomer E Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png| thumb |Figure 7: Isomer A]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png| thumb |Figure 9: Isomer B]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png| thumb |Figure 11: Isomer C]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png| thumb |Figure 13: Isomer D]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png| thumb |Figure 15: Isomer E]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule. <ref name="overlap" />

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

Figure 17: A General Structure of Dimer Complex

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

Figure 18: AlCl2Br Summary Table

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png| right | thumb |Figure 7: Isomer A]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy<ref name="bond break"/>, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

Atom colour label: pink - Al, green - Cl, red - Br

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front Diagram || Top Diagram || Properties
|-
|MO (1)
|[[File:LZY_MO1_FRONT.PNG| thumb |Figure 19: MO1 Front View]]
|[[File:LZY_MO1_TOP.PNG| thumb |Figure 20: MO1 Top View]]
|[[File:LZY_MO1_FRONT_ANNO.png|400px| thumb |Figure 21: MO1 Front Annotation]]
|[[File:LZY_MO1_TOP_ANNO.png|200px| thumb |Figure 22: MO1 Top Annotation]]
|Highly Antibonding
|-
|MO (2)
|[[File:LZY_MO2_FRONT.PNG| thumb |Figure 23: MO2 Front View]]
|[[File:LZY_MO2_TOP.PNG| thumb |Figure 24: MO2 Top View]]
|[[File:LZY_MO2_FRONT_ANNO.png|400px| thumb |Figure 25: MO2 Front Annotation]]
|[[File:LZY_MO2_TOP_ANNO.png|200px| thumb |Figure 26: MO2 Top Annotation]]
|Bonding
|-
|MO (3)
|[[File:LZY_MO3_FRONT.PNG| thumb |Figure 27: MO3 Front View]]
|[[File:LZY_MO3_TOP.PNG| thumb |Figure 28: MO3 Top View]]
|[[File:LZY_MO3_FRONT_ANNO.png|400px| thumb |Figure 29: MO3 Front Annotation]]
|[[File:LZY_MO1_TOP_ANNO.png|200px| thumb |Figure 30: MO3 Top Annotation]]
|Highly Bonding
|}

==References==
<references>
<ref name="Hunt_MO">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, and A.J. Thor, Quantities, Units and Symbols in Physical Chemistry, IUPAC Green Book, Third Edition, Second Printing, IUPAC & RSC Publishing, Cambridge (2008)</ref>
<ref name="overlap">C. Barnes, Inorganic Chemistry (Housecroft, Catherine E.; Sharpe, Alan G.), J. Chem. Educ., 2003, '''80''', 747.</ref>
<ref name="bond break">Peter Atkins and Julio de Paula, Physical Chemistry (8th ed., W.H. Freeman 2006), p.809 ISBN 0-7167-8759-8</ref>
</references>

ICL:zl4817

2019-05-24T11:27:30Z

Zl4817: /* Project: Lewis Acids and Bases */

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

Figure 1: Summary Table of BH3

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (a.u.) || Symmetry Point Group || IR active? || Vibrational Mode
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

Figure 2: BH3 Proposed IR Spectrum by Gaussian

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). A maximum of 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

Figure 3: BH3 LCAO and 'Real' MO Diagram 

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.<ref name="Hunt_MO" />

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

Figure 4: NH3 Summary Table

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

Figure 5: NH3BH3 Summary Table

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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 (1 kJ/mol = 0.0004 au) <ref name="conversion" />

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).<ref name="NB bond" />

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

Figure 6: NI3 Summary Table

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

Figure 7: Isomer A

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

Figure 8: Isomer A Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

Figure 9: Isomer B

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

Figure 10: Isomer B Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

Figure 11: Isomer C

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

Figure 12: Isomer C Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

Figure 13: Isomer D

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

Figure 14: Isomer D Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

Figure 15: Isomer E

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

Figure 16: Isomer E Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png| thumb |Figure 7: Isomer A]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png| thumb |Figure 9: Isomer B]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png| thumb |Figure 11: Isomer C]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png| thumb |Figure 13: Isomer D]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png| thumb |Figure 15: Isomer E]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule. <ref name="overlap" />

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

Figure 17: A General Structure of Dimer Complex

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

Figure 18: AlCl2Br Summary Table

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png| right | thumb |Figure 7: Isomer A]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy<ref name="bond break"/>, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

Atom colour label: pink - Al, green - Cl, red - Br

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front Diagram || Top Diagram || Properties
|-
|MO (1)
|[[File:LZY_MO1_FRONT.PNG| thumb |Figure 19: MO1 Front View]]
|[[File:LZY_MO1_TOP.PNG| thumb |Figure 20: MO1 Top View]]
|[[File:LZY_MO1_FRONT_ANNO.png|400px| thumb |Figure 21: MO1 Front Annotation]]
|[[File:LZY_MO1_TOP_ANNO.png|200px| thumb |Figure 22: MO1 Top Annotation]]
|Highly Antibonding
|-
|MO (2)
|[[File:LZY_MO2_FRONT.PNG| thumb |Figure 23: MO2 Front View]]
|[[File:LZY_MO2_TOP.PNG| thumb |Figure 24: MO2 Top View]]
|[[File:LZY_MO2_FRONT_ANNO.png|400px| thumb |Figure 25: MO2 Front Annotation]]
|[[File:LZY_MO2_TOP_ANNO.png|200px| thumb |Figure 26: MO2 Top Annotation]]
|Bonding
|-
|MO (3)
|[[File:LZY_MO3_FRONT.PNG| thumb |Figure 27: MO3 Front View]]
|[[File:LZY_MO3_TOP.PNG| thumb |Figure 28: MO3 Top View]]
|[[File:LZY_MO3_FRONT_ANNO.png|400px| thumb |Figure 29: MO3 Front Annotation]]
|[[File:LZY_MO1_TOP_ANNO.png|200px| thumb |Figure 30: MO3 Top Annotation]]
|Highly Bonding
|}

==References==
<references>
<ref name="Hunt_MO">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, and A.J. Thor, Quantities, Units and Symbols in Physical Chemistry, IUPAC Green Book, Third Edition, Second Printing, IUPAC & RSC Publishing, Cambridge (2008)</ref>
<ref name="overlap">C. Barnes, Inorganic Chemistry (Housecroft, Catherine E.; Sharpe, Alan G.), J. Chem. Educ., 2003, '''80''', 747.</ref>
<ref name="bond break">Peter Atkins and Julio de Paula, Physical Chemistry (8th ed., W.H. Freeman 2006), p.809 ISBN 0-7167-8759-8</ref>
</references>

ICL:zl4817

2019-05-24T11:21:40Z

Zl4817:

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

Figure 1: Summary Table of BH3

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (a.u.) || Symmetry Point Group || IR active? || Vibrational Mode
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

Figure 2: BH3 Proposed IR Spectrum by Gaussian

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). A maximum of 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

Figure 3: BH3 LCAO and 'Real' MO Diagram 

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.<ref name="Hunt_MO" />

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

Figure 4: NH3 Summary Table

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

Figure 5: NH3BH3 Summary Table

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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 (1 kJ/mol = 0.0004 au) <ref name="conversion" />

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).<ref name="NB bond" />

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

Figure 6: NI3 Summary Table

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

Figure 7: Isomer A

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

Figure 8: Isomer A Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

Figure 9: Isomer B

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

Figure 10: Isomer B Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

Figure 11: Isomer C

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

Figure 12: Isomer C Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

Figure 13: Isomer D

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

Figure 14: Isomer D Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

Figure 15: Isomer E

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

Figure 16: Isomer E Summary Table

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule. <ref name="overlap" />

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

Figure 17: A General Structure of Dimer Complex

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

Figure 18: AlCl2Br Summary Table

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy<ref name="bond break"/>, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

Atom colour label: pink - Al, green - Cl, red - Br

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front Diagram || Top Diagram || Properties
|-
|MO (1)
|[[File:LZY_MO1_FRONT.PNG| thumb |Figure 19: MO1 Front View]]
|[[File:LZY_MO1_TOP.PNG| thumb |Figure 20: MO1 Top View]]
|[[File:LZY_MO1_FRONT_ANNO.png|400px| thumb |Figure 21: MO1 Front Annotation]]
|[[File:LZY_MO1_TOP_ANNO.png|200px| thumb |Figure 22: MO1 Top Annotation]]
|Highly Antibonding
|-
|MO (2)
|[[File:LZY_MO2_FRONT.PNG| thumb |Figure 23: MO2 Front View]]
|[[File:LZY_MO2_TOP.PNG| thumb |Figure 24: MO2 Top View]]
|[[File:LZY_MO2_FRONT_ANNO.png|400px| thumb |Figure 25: MO2 Front Annotation]]
|[[File:LZY_MO2_TOP_ANNO.png|200px| thumb |Figure 26: MO2 Top Annotation]]
|Bonding
|-
|MO (3)
|[[File:LZY_MO3_FRONT.PNG| thumb |Figure 27: MO3 Front View]]
|[[File:LZY_MO3_TOP.PNG| thumb |Figure 28: MO3 Top View]]
|[[File:LZY_MO3_FRONT_ANNO.png|400px| thumb |Figure 29: MO3 Front Annotation]]
|[[File:LZY_MO1_TOP_ANNO.png|200px| thumb |Figure 30: MO3 Top Annotation]]
|Highly Bonding
|}

==References==
<references>
<ref name="Hunt_MO">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, and A.J. Thor, Quantities, Units and Symbols in Physical Chemistry, IUPAC Green Book, Third Edition, Second Printing, IUPAC & RSC Publishing, Cambridge (2008)</ref>
<ref name="overlap">C. Barnes, Inorganic Chemistry (Housecroft, Catherine E.; Sharpe, Alan G.), J. Chem. Educ., 2003, '''80''', 747.</ref>
<ref name="bond break">Peter Atkins and Julio de Paula, Physical Chemistry (8th ed., W.H. Freeman 2006), p.809 ISBN 0-7167-8759-8</ref>
</references>

ICL:zl4817

2019-05-24T10:54:49Z

Zl4817: /* Summary Table */

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]
Figure 1: Summary Table

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (a.u.) || Symmetry Point Group || IR active? || Vibrational Mode
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). A maximum of 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.<ref name="Hunt_MO" />

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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 (1 kJ/mol = 0.0004 au) <ref name="conversion" />

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).<ref name="NB bond" />

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule. <ref name="overlap" />

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy<ref name="bond break"/>, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

Atom colour label: pink - Al, green - Cl, red - Br

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front Diagram || Top Diagram || Properties
|-
|MO (1)
|[[File:LZY_MO1_FRONT.PNG]]
|[[File:LZY_MO1_TOP.PNG]]
|[[File:LZY_MO1_FRONT_ANNO.png|400px]]
|[[File:LZY_MO1_TOP_ANNO.png|200px]]
|Highly Antibonding
|-
|MO (2)
|[[File:LZY_MO2_FRONT.PNG]]
|[[File:LZY_MO2_TOP.PNG]]
|[[File:LZY_MO2_FRONT_ANNO.png|400px]]
|[[File:LZY_MO2_TOP_ANNO.png|200px]]
|Bonding
|-
|MO (3)
|[[File:LZY_MO3_FRONT.PNG]]
|[[File:LZY_MO3_TOP.PNG]]
|[[File:LZY_MO3_FRONT_ANNO.png|400px]]
|[[File:LZY_MO1_TOP_ANNO.png|200px]]
|Highly Bonding
|}

==References==
<references>
<ref name="Hunt_MO">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, and A.J. Thor, Quantities, Units and Symbols in Physical Chemistry, IUPAC Green Book, Third Edition, Second Printing, IUPAC & RSC Publishing, Cambridge (2008)</ref>
<ref name="overlap">C. Barnes, Inorganic Chemistry (Housecroft, Catherine E.; Sharpe, Alan G.), J. Chem. Educ., 2003, '''80''', 747.</ref>
<ref name="bond break">Peter Atkins and Julio de Paula, Physical Chemistry (8th ed., W.H. Freeman 2006), p.809 ISBN 0-7167-8759-8</ref>
</references>

ICL:zl4817

2019-05-24T10:52:55Z

Zl4817: /* BH3 Molecule */

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (a.u.) || Symmetry Point Group || IR active? || Vibrational Mode
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). A maximum of 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.<ref name="Hunt_MO" />

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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 (1 kJ/mol = 0.0004 au) <ref name="conversion" />

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).<ref name="NB bond" />

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule. <ref name="overlap" />

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy<ref name="bond break"/>, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

Atom colour label: pink - Al, green - Cl, red - Br

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front Diagram || Top Diagram || Properties
|-
|MO (1)
|[[File:LZY_MO1_FRONT.PNG]]
|[[File:LZY_MO1_TOP.PNG]]
|[[File:LZY_MO1_FRONT_ANNO.png|400px]]
|[[File:LZY_MO1_TOP_ANNO.png|200px]]
|Highly Antibonding
|-
|MO (2)
|[[File:LZY_MO2_FRONT.PNG]]
|[[File:LZY_MO2_TOP.PNG]]
|[[File:LZY_MO2_FRONT_ANNO.png|400px]]
|[[File:LZY_MO2_TOP_ANNO.png|200px]]
|Bonding
|-
|MO (3)
|[[File:LZY_MO3_FRONT.PNG]]
|[[File:LZY_MO3_TOP.PNG]]
|[[File:LZY_MO3_FRONT_ANNO.png|400px]]
|[[File:LZY_MO1_TOP_ANNO.png|200px]]
|Highly Bonding
|}

==References==
<references>
<ref name="Hunt_MO">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, and A.J. Thor, Quantities, Units and Symbols in Physical Chemistry, IUPAC Green Book, Third Edition, Second Printing, IUPAC & RSC Publishing, Cambridge (2008)</ref>
<ref name="overlap">C. Barnes, Inorganic Chemistry (Housecroft, Catherine E.; Sharpe, Alan G.), J. Chem. Educ., 2003, '''80''', 747.</ref>
<ref name="bond break">Peter Atkins and Julio de Paula, Physical Chemistry (8th ed., W.H. Freeman 2006), p.809 ISBN 0-7167-8759-8</ref>
</references>

ICL:zl4817

2019-05-24T10:52:17Z

Zl4817: /* Table of Vibrational Modes */

ICL:zl4817

2019-05-24T10:51:53Z

Zl4817: /* Table of Vibrational Modes */

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|Wavenumber (cm-1 || Intensity (arbitrary units) || Symmetry Point Group || IR active? || Vibrational Mode
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). A maximum of 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.<ref name="Hunt_MO" />

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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 (1 kJ/mol = 0.0004 au) <ref name="conversion" />

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).<ref name="NB bond" />

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule. <ref name="overlap" />

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy<ref name="bond break"/>, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

Atom colour label: pink - Al, green - Cl, red - Br

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front Diagram || Top Diagram || Properties
|-
|MO (1)
|[[File:LZY_MO1_FRONT.PNG]]
|[[File:LZY_MO1_TOP.PNG]]
|[[File:LZY_MO1_FRONT_ANNO.png|400px]]
|[[File:LZY_MO1_TOP_ANNO.png|200px]]
|Highly Antibonding
|-
|MO (2)
|[[File:LZY_MO2_FRONT.PNG]]
|[[File:LZY_MO2_TOP.PNG]]
|[[File:LZY_MO2_FRONT_ANNO.png|400px]]
|[[File:LZY_MO2_TOP_ANNO.png|200px]]
|Bonding
|-
|MO (3)
|[[File:LZY_MO3_FRONT.PNG]]
|[[File:LZY_MO3_TOP.PNG]]
|[[File:LZY_MO3_FRONT_ANNO.png|400px]]
|[[File:LZY_MO1_TOP_ANNO.png|200px]]
|Highly Bonding
|}

==References==
<references>
<ref name="Hunt_MO">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, and A.J. Thor, Quantities, Units and Symbols in Physical Chemistry, IUPAC Green Book, Third Edition, Second Printing, IUPAC & RSC Publishing, Cambridge (2008)</ref>
<ref name="overlap">C. Barnes, Inorganic Chemistry (Housecroft, Catherine E.; Sharpe, Alan G.), J. Chem. Educ., 2003, '''80''', 747.</ref>
<ref name="bond break">Peter Atkins and Julio de Paula, Physical Chemistry (8th ed., W.H. Freeman 2006), p.809 ISBN 0-7167-8759-8</ref>
</references>

ICL:zl4817

2019-05-24T10:49:04Z

Zl4817: /* BH3 Molecule */

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). A maximum of 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.<ref name="Hunt_MO" />

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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 (1 kJ/mol = 0.0004 au) <ref name="conversion" />

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).<ref name="NB bond" />

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule. <ref name="overlap" />

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy<ref name="bond break"/>, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

Atom colour label: pink - Al, green - Cl, red - Br

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front Diagram || Top Diagram || Properties
|-
|MO (1)
|[[File:LZY_MO1_FRONT.PNG]]
|[[File:LZY_MO1_TOP.PNG]]
|[[File:LZY_MO1_FRONT_ANNO.png|400px]]
|[[File:LZY_MO1_TOP_ANNO.png|200px]]
|Highly Antibonding
|-
|MO (2)
|[[File:LZY_MO2_FRONT.PNG]]
|[[File:LZY_MO2_TOP.PNG]]
|[[File:LZY_MO2_FRONT_ANNO.png|400px]]
|[[File:LZY_MO2_TOP_ANNO.png|200px]]
|Bonding
|-
|MO (3)
|[[File:LZY_MO3_FRONT.PNG]]
|[[File:LZY_MO3_TOP.PNG]]
|[[File:LZY_MO3_FRONT_ANNO.png|400px]]
|[[File:LZY_MO1_TOP_ANNO.png|200px]]
|Highly Bonding
|}

==References==
<references>
<ref name="Hunt_MO">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, and A.J. Thor, Quantities, Units and Symbols in Physical Chemistry, IUPAC Green Book, Third Edition, Second Printing, IUPAC & RSC Publishing, Cambridge (2008)</ref>
<ref name="overlap">C. Barnes, Inorganic Chemistry (Housecroft, Catherine E.; Sharpe, Alan G.), J. Chem. Educ., 2003, '''80''', 747.</ref>
<ref name="bond break">Peter Atkins and Julio de Paula, Physical Chemistry (8th ed., W.H. Freeman 2006), p.809 ISBN 0-7167-8759-8</ref>
</references>

ICL:zl4817

2019-05-24T10:43:36Z

Zl4817: /* Summary Table */

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG|Figure 1:]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). A maximum of 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.<ref name="Hunt_MO" />

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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 (1 kJ/mol = 0.0004 au) <ref name="conversion" />

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).<ref name="NB bond" />

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule. <ref name="overlap" />

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy<ref name="bond break"/>, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

Atom colour label: pink - Al, green - Cl, red - Br

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front Diagram || Top Diagram || Properties
|-
|MO (1)
|[[File:LZY_MO1_FRONT.PNG]]
|[[File:LZY_MO1_TOP.PNG]]
|[[File:LZY_MO1_FRONT_ANNO.png|400px]]
|[[File:LZY_MO1_TOP_ANNO.png|200px]]
|Highly Antibonding
|-
|MO (2)
|[[File:LZY_MO2_FRONT.PNG]]
|[[File:LZY_MO2_TOP.PNG]]
|[[File:LZY_MO2_FRONT_ANNO.png|400px]]
|[[File:LZY_MO2_TOP_ANNO.png|200px]]
|Bonding
|-
|MO (3)
|[[File:LZY_MO3_FRONT.PNG]]
|[[File:LZY_MO3_TOP.PNG]]
|[[File:LZY_MO3_FRONT_ANNO.png|400px]]
|[[File:LZY_MO1_TOP_ANNO.png|200px]]
|Highly Bonding
|}

==References==
<references>
<ref name="Hunt_MO">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, and A.J. Thor, Quantities, Units and Symbols in Physical Chemistry, IUPAC Green Book, Third Edition, Second Printing, IUPAC & RSC Publishing, Cambridge (2008)</ref>
<ref name="overlap">C. Barnes, Inorganic Chemistry (Housecroft, Catherine E.; Sharpe, Alan G.), J. Chem. Educ., 2003, '''80''', 747.</ref>
<ref name="bond break">Peter Atkins and Julio de Paula, Physical Chemistry (8th ed., W.H. Freeman 2006), p.809 ISBN 0-7167-8759-8</ref>
</references>

ICL:zl4817

2019-05-24T10:42:28Z

Zl4817: /* Explanation for Number of Peaks in Spectrum */

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). A maximum of 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.<ref name="Hunt_MO" />

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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 (1 kJ/mol = 0.0004 au) <ref name="conversion" />

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).<ref name="NB bond" />

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule. <ref name="overlap" />

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy<ref name="bond break"/>, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

Atom colour label: pink - Al, green - Cl, red - Br

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front Diagram || Top Diagram || Properties
|-
|MO (1)
|[[File:LZY_MO1_FRONT.PNG]]
|[[File:LZY_MO1_TOP.PNG]]
|[[File:LZY_MO1_FRONT_ANNO.png|400px]]
|[[File:LZY_MO1_TOP_ANNO.png|200px]]
|Highly Antibonding
|-
|MO (2)
|[[File:LZY_MO2_FRONT.PNG]]
|[[File:LZY_MO2_TOP.PNG]]
|[[File:LZY_MO2_FRONT_ANNO.png|400px]]
|[[File:LZY_MO2_TOP_ANNO.png|200px]]
|Bonding
|-
|MO (3)
|[[File:LZY_MO3_FRONT.PNG]]
|[[File:LZY_MO3_TOP.PNG]]
|[[File:LZY_MO3_FRONT_ANNO.png|400px]]
|[[File:LZY_MO1_TOP_ANNO.png|200px]]
|Highly Bonding
|}

==References==
<references>
<ref name="Hunt_MO">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, and A.J. Thor, Quantities, Units and Symbols in Physical Chemistry, IUPAC Green Book, Third Edition, Second Printing, IUPAC & RSC Publishing, Cambridge (2008)</ref>
<ref name="overlap">C. Barnes, Inorganic Chemistry (Housecroft, Catherine E.; Sharpe, Alan G.), J. Chem. Educ., 2003, '''80''', 747.</ref>
<ref name="bond break">Peter Atkins and Julio de Paula, Physical Chemistry (8th ed., W.H. Freeman 2006), p.809 ISBN 0-7167-8759-8</ref>
</references>

ICL:zl4817

2019-05-24T10:40:03Z

Zl4817: /* Molecular Orbitals of the Lowest-Energy Conformer */

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). At most 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.<ref name="Hunt_MO" />

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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 (1 kJ/mol = 0.0004 au) <ref name="conversion" />

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).<ref name="NB bond" />

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule. <ref name="overlap" />

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy<ref name="bond break"/>, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

Atom colour label: pink - Al, green - Cl, red - Br

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front Diagram || Top Diagram || Properties
|-
|MO (1)
|[[File:LZY_MO1_FRONT.PNG]]
|[[File:LZY_MO1_TOP.PNG]]
|[[File:LZY_MO1_FRONT_ANNO.png|400px]]
|[[File:LZY_MO1_TOP_ANNO.png|200px]]
|Highly Antibonding
|-
|MO (2)
|[[File:LZY_MO2_FRONT.PNG]]
|[[File:LZY_MO2_TOP.PNG]]
|[[File:LZY_MO2_FRONT_ANNO.png|400px]]
|[[File:LZY_MO2_TOP_ANNO.png|200px]]
|Bonding
|-
|MO (3)
|[[File:LZY_MO3_FRONT.PNG]]
|[[File:LZY_MO3_TOP.PNG]]
|[[File:LZY_MO3_FRONT_ANNO.png|400px]]
|[[File:LZY_MO1_TOP_ANNO.png|200px]]
|Highly Bonding
|}

==References==
<references>
<ref name="Hunt_MO">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, and A.J. Thor, Quantities, Units and Symbols in Physical Chemistry, IUPAC Green Book, Third Edition, Second Printing, IUPAC & RSC Publishing, Cambridge (2008)</ref>
<ref name="overlap">C. Barnes, Inorganic Chemistry (Housecroft, Catherine E.; Sharpe, Alan G.), J. Chem. Educ., 2003, '''80''', 747.</ref>
<ref name="bond break">Peter Atkins and Julio de Paula, Physical Chemistry (8th ed., W.H. Freeman 2006), p.809 ISBN 0-7167-8759-8</ref>
</references>

ICL:zl4817

2019-05-23T23:20:45Z

Zl4817: /* Comparison of Energy */

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). At most 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.<ref name="Hunt_MO" />

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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 (1 kJ/mol = 0.0004 au) <ref name="conversion" />

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).<ref name="NB bond" />

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule. <ref name="overlap" />

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy<ref name="bond break"/>, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

Atom colour label: pink - Al, green - Cl, red - Br

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front Diagram || Top Diagram || Properties
|-
|MO (1)
|[[File:LZY_MO1_FRONT.PNG]]
|[[File:LZY_MO1_TOP.PNG]]
|[[File:LZY_MO1_FRONT_ANNO.png]]
|[[File:LZY_MO1_TOP_ANNO.png]]
|Highly Antibonding
|-
|MO (2)
|[[File:LZY_MO2_FRONT.PNG]]
|[[File:LZY_MO2_TOP.PNG]]
|[[File:LZY_MO2_FRONT_ANNO.png]]
|[[File:LZY_MO2_TOP_ANNO.png]]
|BONDING
|-
|MO (3)
|[[File:LZY_MO3_FRONT.PNG]]
|[[File:LZY_MO3_TOP.PNG]]
|[[File:LZY_MO3_FRONT_ANNO.png]]
|[[File:LZY_MO1_TOP_ANNO.png]]
|Highly BONDING
|}

==References==
<references>
<ref name="Hunt_MO">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, and A.J. Thor, Quantities, Units and Symbols in Physical Chemistry, IUPAC Green Book, Third Edition, Second Printing, IUPAC & RSC Publishing, Cambridge (2008)</ref>
<ref name="overlap">C. Barnes, Inorganic Chemistry (Housecroft, Catherine E.; Sharpe, Alan G.), J. Chem. Educ., 2003, '''80''', 747.</ref>
<ref name="bond break">Peter Atkins and Julio de Paula, Physical Chemistry (8th ed., W.H. Freeman 2006), p.809 ISBN 0-7167-8759-8</ref>
</references>

ICL:zl4817

2019-05-23T23:19:48Z

Zl4817: /* Comparison of Energy */

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). At most 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.<ref name="Hunt_MO" />

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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 (1 kJ/mol = 0.0004 au) <ref name="conversion" />

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).<ref name="NB bond" />

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule. <ref name="overlap" />

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy<ref name="bond break">, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

Atom colour label: pink - Al, green - Cl, red - Br

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front Diagram || Top Diagram || Properties
|-
|MO (1)
|[[File:LZY_MO1_FRONT.PNG]]
|[[File:LZY_MO1_TOP.PNG]]
|[[File:LZY_MO1_FRONT_ANNO.png]]
|[[File:LZY_MO1_TOP_ANNO.png]]
|Highly Antibonding
|-
|MO (2)
|[[File:LZY_MO2_FRONT.PNG]]
|[[File:LZY_MO2_TOP.PNG]]
|[[File:LZY_MO2_FRONT_ANNO.png]]
|[[File:LZY_MO2_TOP_ANNO.png]]
|BONDING
|-
|MO (3)
|[[File:LZY_MO3_FRONT.PNG]]
|[[File:LZY_MO3_TOP.PNG]]
|[[File:LZY_MO3_FRONT_ANNO.png]]
|[[File:LZY_MO1_TOP_ANNO.png]]
|Highly BONDING
|}

==References==
<references>
<ref name="Hunt_MO">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, and A.J. Thor, Quantities, Units and Symbols in Physical Chemistry, IUPAC Green Book, Third Edition, Second Printing, IUPAC & RSC Publishing, Cambridge (2008)</ref>
<ref name="overlap">C. Barnes, Inorganic Chemistry (Housecroft, Catherine E.; Sharpe, Alan G.), J. Chem. Educ., 2003, '''80''', 747.</ref>
<ref name="bond break">Peter Atkins and Julio de Paula, Physical Chemistry (8th ed., W.H. Freeman 2006), p.809 ISBN 0-7167-8759-8</ref>
</references>

ICL:zl4817

2019-05-23T23:19:12Z

Zl4817: /* References */

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). At most 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.<ref name="Hunt_MO" />

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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 (1 kJ/mol = 0.0004 au) <ref name="conversion" />

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).<ref name="NB bond" />

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule. <ref name="overlap" />

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

Atom colour label: pink - Al, green - Cl, red - Br

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front Diagram || Top Diagram || Properties
|-
|MO (1)
|[[File:LZY_MO1_FRONT.PNG]]
|[[File:LZY_MO1_TOP.PNG]]
|[[File:LZY_MO1_FRONT_ANNO.png]]
|[[File:LZY_MO1_TOP_ANNO.png]]
|Highly Antibonding
|-
|MO (2)
|[[File:LZY_MO2_FRONT.PNG]]
|[[File:LZY_MO2_TOP.PNG]]
|[[File:LZY_MO2_FRONT_ANNO.png]]
|[[File:LZY_MO2_TOP_ANNO.png]]
|BONDING
|-
|MO (3)
|[[File:LZY_MO3_FRONT.PNG]]
|[[File:LZY_MO3_TOP.PNG]]
|[[File:LZY_MO3_FRONT_ANNO.png]]
|[[File:LZY_MO1_TOP_ANNO.png]]
|Highly BONDING
|}

==References==
<references>
<ref name="Hunt_MO">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, and A.J. Thor, Quantities, Units and Symbols in Physical Chemistry, IUPAC Green Book, Third Edition, Second Printing, IUPAC & RSC Publishing, Cambridge (2008)</ref>
<ref name="overlap">C. Barnes, Inorganic Chemistry (Housecroft, Catherine E.; Sharpe, Alan G.), J. Chem. Educ., 2003, '''80''', 747.</ref>
<ref name="bond break">Peter Atkins and Julio de Paula, Physical Chemistry (8th ed., W.H. Freeman 2006), p.809 ISBN 0-7167-8759-8</ref>
</references>

ICL:zl4817

2019-05-23T23:17:04Z

Zl4817: /* References */

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). At most 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.<ref name="Hunt_MO" />

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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 (1 kJ/mol = 0.0004 au) <ref name="conversion" />

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).<ref name="NB bond" />

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule. <ref name="overlap" />

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

Atom colour label: pink - Al, green - Cl, red - Br

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front Diagram || Top Diagram || Properties
|-
|MO (1)
|[[File:LZY_MO1_FRONT.PNG]]
|[[File:LZY_MO1_TOP.PNG]]
|[[File:LZY_MO1_FRONT_ANNO.png]]
|[[File:LZY_MO1_TOP_ANNO.png]]
|Highly Antibonding
|-
|MO (2)
|[[File:LZY_MO2_FRONT.PNG]]
|[[File:LZY_MO2_TOP.PNG]]
|[[File:LZY_MO2_FRONT_ANNO.png]]
|[[File:LZY_MO2_TOP_ANNO.png]]
|BONDING
|-
|MO (3)
|[[File:LZY_MO3_FRONT.PNG]]
|[[File:LZY_MO3_TOP.PNG]]
|[[File:LZY_MO3_FRONT_ANNO.png]]
|[[File:LZY_MO1_TOP_ANNO.png]]
|Highly BONDING
|}

==References==
<references>
<ref name="Hunt_MO">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, and A.J. Thor, Quantities, Units and Symbols in Physical Chemistry, IUPAC Green Book, Third Edition, Second Printing, IUPAC & RSC Publishing, Cambridge (2008)</ref>
<ref name="overlap">C. Barnes, Inorganic Chemistry (Housecroft, Catherine E.; Sharpe, Alan G.), J. Chem. Educ., 2003, '''80''', 747.</ref>
</references>

ICL:zl4817

2019-05-23T23:16:03Z

Zl4817:

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). At most 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.<ref name="Hunt_MO" />

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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 (1 kJ/mol = 0.0004 au) <ref name="conversion" />

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).<ref name="NB bond" />

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule. <ref name="overlap" />

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

Atom colour label: pink - Al, green - Cl, red - Br

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front Diagram || Top Diagram || Properties
|-
|MO (1)
|[[File:LZY_MO1_FRONT.PNG]]
|[[File:LZY_MO1_TOP.PNG]]
|[[File:LZY_MO1_FRONT_ANNO.png]]
|[[File:LZY_MO1_TOP_ANNO.png]]
|Highly Antibonding
|-
|MO (2)
|[[File:LZY_MO2_FRONT.PNG]]
|[[File:LZY_MO2_TOP.PNG]]
|[[File:LZY_MO2_FRONT_ANNO.png]]
|[[File:LZY_MO2_TOP_ANNO.png]]
|BONDING
|-
|MO (3)
|[[File:LZY_MO3_FRONT.PNG]]
|[[File:LZY_MO3_TOP.PNG]]
|[[File:LZY_MO3_FRONT_ANNO.png]]
|[[File:LZY_MO1_TOP_ANNO.png]]
|Highly BONDING
|}

==References==
<references>
<ref name="Hunt_MO">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, and A.J. Thor, Quantities, Units and Symbols in Physical Chemistry, IUPAC Green Book, Third Edition, Second Printing, IUPAC & RSC Publishing, Cambridge (2008)</ref>
<ref name="overlap">1 C. Barnes, Inorganic Chemistry (Housecroft, Catherine E.; Sharpe, Alan G.), J. Chem. Educ., 2003, '''80''', 747.</ref>
</references>

ICL:zl4817

2019-05-23T23:03:29Z

Zl4817: /* References */

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). At most 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.<ref name="Hunt_MO" />

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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 (1 kJ/mol = 0.0004 au) <ref name="conversion" />

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).<ref name="NB bond" />

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule.

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

Atom colour label: pink - Al, green - Cl, red - Br

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front Diagram || Top Diagram || Properties
|-
|MO (1)
|[[File:LZY_MO1_FRONT.PNG]]
|[[File:LZY_MO1_TOP.PNG]]
|[[File:LZY_MO1_FRONT_ANNO.png]]
|[[File:LZY_MO1_TOP_ANNO.png]]
|Highly Antibonding
|-
|MO (2)
|[[File:LZY_MO2_FRONT.PNG]]
|[[File:LZY_MO2_TOP.PNG]]
|[[File:LZY_MO2_FRONT_ANNO.png]]
|[[File:LZY_MO2_TOP_ANNO.png]]
|BONDING
|-
|MO (3)
|[[File:LZY_MO3_FRONT.PNG]]
|[[File:LZY_MO3_TOP.PNG]]
|[[File:LZY_MO3_FRONT_ANNO.png]]
|[[File:LZY_MO1_TOP_ANNO.png]]
|Highly BONDING
|}

==References==
<references>
<ref name="Hunt_MO">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/4b_better_basis.html .</ref>
<ref name="NB bond">E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H.L. Strauss, M. Takami, and A.J. Thor, Quantities, Units and Symbols in Physical Chemistry, IUPAC Green Book, Third Edition, Second Printing, IUPAC & RSC Publishing, Cambridge (2008)
</references>

ICL:zl4817

2019-05-23T23:01:51Z

Zl4817: /* Association Energy Analysis */

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). At most 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.<ref name="Hunt_MO" />

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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 (1 kJ/mol = 0.0004 au) <ref name="conversion" />

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).<ref name="NB bond" />

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule.

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

Atom colour label: pink - Al, green - Cl, red - Br

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front Diagram || Top Diagram || Properties
|-
|MO (1)
|[[File:LZY_MO1_FRONT.PNG]]
|[[File:LZY_MO1_TOP.PNG]]
|[[File:LZY_MO1_FRONT_ANNO.png]]
|[[File:LZY_MO1_TOP_ANNO.png]]
|Highly Antibonding
|-
|MO (2)
|[[File:LZY_MO2_FRONT.PNG]]
|[[File:LZY_MO2_TOP.PNG]]
|[[File:LZY_MO2_FRONT_ANNO.png]]
|[[File:LZY_MO2_TOP_ANNO.png]]
|BONDING
|-
|MO (3)
|[[File:LZY_MO3_FRONT.PNG]]
|[[File:LZY_MO3_TOP.PNG]]
|[[File:LZY_MO3_FRONT_ANNO.png]]
|[[File:LZY_MO1_TOP_ANNO.png]]
|Highly BONDING
|}

==References==
<references>
<ref name="Hunt_MO">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">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:zl4817

2019-05-23T23:01:05Z

Zl4817:

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). At most 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.<ref name="Hunt_MO" />

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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" />

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).<ref name="NB bond" />

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule.

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

Atom colour label: pink - Al, green - Cl, red - Br

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front Diagram || Top Diagram || Properties
|-
|MO (1)
|[[File:LZY_MO1_FRONT.PNG]]
|[[File:LZY_MO1_TOP.PNG]]
|[[File:LZY_MO1_FRONT_ANNO.png]]
|[[File:LZY_MO1_TOP_ANNO.png]]
|Highly Antibonding
|-
|MO (2)
|[[File:LZY_MO2_FRONT.PNG]]
|[[File:LZY_MO2_TOP.PNG]]
|[[File:LZY_MO2_FRONT_ANNO.png]]
|[[File:LZY_MO2_TOP_ANNO.png]]
|BONDING
|-
|MO (3)
|[[File:LZY_MO3_FRONT.PNG]]
|[[File:LZY_MO3_TOP.PNG]]
|[[File:LZY_MO3_FRONT_ANNO.png]]
|[[File:LZY_MO1_TOP_ANNO.png]]
|Highly BONDING
|}

==References==
<references>
<ref name="Hunt_MO">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf .</ref>
<ref name="conversion">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:zl4817

2019-05-23T22:59:52Z

Zl4817: /* Association Energy Analysis */

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). At most 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.<ref name="Hunt_MO" />

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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" />

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).<ref name="NB bond" />

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule.

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

Atom colour label: pink - Al, green - Cl, red - Br

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front Diagram || Top Diagram || Properties
|-
|MO (1)
|[[File:LZY_MO1_FRONT.PNG]]
|[[File:LZY_MO1_TOP.PNG]]
|[[File:LZY_MO1_FRONT_ANNO.png]]
|[[File:LZY_MO1_TOP_ANNO.png]]
|Highly Antibonding
|-
|MO (2)
|[[File:LZY_MO2_FRONT.PNG]]
|[[File:LZY_MO2_TOP.PNG]]
|[[File:LZY_MO2_FRONT_ANNO.png]]
|[[File:LZY_MO2_TOP_ANNO.png]]
|BONDING
|-
|MO (3)
|[[File:LZY_MO3_FRONT.PNG]]
|[[File:LZY_MO3_TOP.PNG]]
|[[File:LZY_MO3_FRONT_ANNO.png]]
|[[File:LZY_MO1_TOP_ANNO.png]]
|Highly BONDING
|}

ICL:zl4817

2019-05-23T22:58:32Z

Zl4817: /* MO Diagram of BH3 */

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). At most 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.<ref name="Hunt_MO" />

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule.

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

Atom colour label: pink - Al, green - Cl, red - Br

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front Diagram || Top Diagram || Properties
|-
|MO (1)
|[[File:LZY_MO1_FRONT.PNG]]
|[[File:LZY_MO1_TOP.PNG]]
|[[File:LZY_MO1_FRONT_ANNO.png]]
|[[File:LZY_MO1_TOP_ANNO.png]]
|Highly Antibonding
|-
|MO (2)
|[[File:LZY_MO2_FRONT.PNG]]
|[[File:LZY_MO2_TOP.PNG]]
|[[File:LZY_MO2_FRONT_ANNO.png]]
|[[File:LZY_MO2_TOP_ANNO.png]]
|BONDING
|-
|MO (3)
|[[File:LZY_MO3_FRONT.PNG]]
|[[File:LZY_MO3_TOP.PNG]]
|[[File:LZY_MO3_FRONT_ANNO.png]]
|[[File:LZY_MO1_TOP_ANNO.png]]
|Highly BONDING
|}

ICL:zl4817

2019-05-23T22:56:25Z

Zl4817: /* Molecular Orbitals of the Lowest-Energy Conformer */

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). At most 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule.

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

Atom colour label: pink - Al, green - Cl, red - Br

{| class="wikitable"
|+
|-
| MO || Front View || Top View || Front Diagram || Top Diagram || Properties
|-
|MO (1)
|[[File:LZY_MO1_FRONT.PNG]]
|[[File:LZY_MO1_TOP.PNG]]
|[[File:LZY_MO1_FRONT_ANNO.png]]
|[[File:LZY_MO1_TOP_ANNO.png]]
|Highly Antibonding
|-
|MO (2)
|[[File:LZY_MO2_FRONT.PNG]]
|[[File:LZY_MO2_TOP.PNG]]
|[[File:LZY_MO2_FRONT_ANNO.png]]
|[[File:LZY_MO2_TOP_ANNO.png]]
|BONDING
|-
|MO (3)
|[[File:LZY_MO3_FRONT.PNG]]
|[[File:LZY_MO3_TOP.PNG]]
|[[File:LZY_MO3_FRONT_ANNO.png]]
|[[File:LZY_MO1_TOP_ANNO.png]]
|Highly BONDING
|}

File:LZY MO1 TOP ANNO.png

2019-05-23T22:55:49Z

Zl4817: Zl4817 uploaded a new version of File:LZY MO1 TOP ANNO.png

File:LZY MO3 FRONT ANNO.png

2019-05-23T22:54:25Z

Zl4817:

File:LZY MO3 TOP.PNG

2019-05-23T22:54:03Z

Zl4817:

File:LZY MO3 FRONT.PNG

2019-05-23T22:53:41Z

Zl4817:

File:LZY MO2 TOP ANNO.png

2019-05-23T22:52:53Z

Zl4817:

File:LZY MO2 FRONT ANNO.png

2019-05-23T22:52:27Z

Zl4817:

File:LZY MO2 TOP.PNG

2019-05-23T22:52:03Z

Zl4817:

File:LZY MO2 FRONT.PNG

2019-05-23T22:51:40Z

Zl4817:

File:LZY MO1 TOP ANNO.png

2019-05-23T22:50:20Z

Zl4817:

File:LZY MO1 FRONT ANNO.png

2019-05-23T22:49:56Z

Zl4817:

File:LZY MO1 TOP.PNG

2019-05-23T22:49:29Z

Zl4817:

File:LZY MO1 FRONT.PNG

2019-05-23T22:48:53Z

Zl4817:

ICL:zl4817

2019-05-23T16:20:46Z

Zl4817:

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). At most 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule.

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

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

The lowest-energy conformer is Isomer A. There are 24 occupied valence molecular orbitals in total.

Three among them are selected, analysed and arranged in order by their extent of bonding/antibonding character.

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

ICL:zl4817

2019-05-23T15:43:21Z

Zl4817:

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). At most 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule.

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Comparison of Energy ====

Isomer A is the conformer with the lowest energy.

[[File:LZY_isomer_a.png]]

When the dimer dissociates into two molecules of AlCl2Br, 2 Al-Br bonds are lost.

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

Hence, the sum of energy of two AlCl2Br molecules is -18673743 kJ/mol which is 114 kJ/mol higher relative to the energy of Isomer A.

As breaking bonds involves absorption of energy, each Al-Br bond broken increases total energy by 57 kJ/mol.

This explains why the dimer is more stable than the dissociated monomers.

ICL:zl4817

2019-05-23T14:20:16Z

Zl4817:

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). At most 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule.

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

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

Link: [[Media:LZY_ISOMER_HALF_1.LOG|LZY_ISOMER_HALF_1.LOG]]

====Summary Table====

B3LYP/6-31G(d.p)

[[file:LZY_isomer_half_sum_1.PNG]]

====Item Table====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000028 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000083 0.001800 YES
RMS Displacement 0.000048 0.001200 YES
</pre>

====Frequency Analysis====

<pre>
Low frequencies --- -3.3374 -1.9339 0.0130 0.0138 0.0142 4.7835
Low frequencies --- 125.0015 137.4966 194.8482
</pre>

====Jmol Dynamic Image====

<jmol><jmolApplet>
<title>AlCl2Br</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_HALF_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

File:LZY isomer half sum 1.PNG

2019-05-23T14:16:54Z

Zl4817:

File:LZY ISOMER HALF 1.LOG

2019-05-23T14:14:06Z

Zl4817:

File:LZY isomer half sum.PNG

2019-05-23T14:06:55Z

Zl4817:

File:LZY ISOMER HALF.LOG

2019-05-23T14:02:46Z

Zl4817:

ICL:zl4817

2019-05-23T13:48:20Z

Zl4817:

== BH3 Molecule ==

Link: [[Media:LZY_BH3_OPT_FREQ.LOG|LZY_BH3_OPT_FREQ.LOG]]

=== Summary Table ===

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

[[file:LZY_BH3_sum.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000190 0.000450 YES
RMS Force 0.000095 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000374 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0331 49.0927 49.0932
Low frequencies --- 1163.7226 1213.6716 1213.6743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_BH3_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Table of Vibrational Modes ===

{| class="wikitable"
|+
|-
|wavenumber (cm-1 || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163
|92
|A2''
|yes
|out-of-plane bend
|-
|1213
|14
|E'
|yes
|bend
|-
|1213
|14
|E'
|yes
|bend
|-
|2580
|0
|A1'
|no
|symmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|-
|2713
|126
|E'
|yes
|asymmetric stretch
|}

=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

=== Explanation for Number of Peaks in Spectrum ===

There are two sets of degenerate vibrations at 1213 cm-1 (bend) and 2713 cm-1 (asymmetric stretch). At most 4 signals will appear on the spectrum.

Moreover, the vibration mode at 2580 cm-1 is a symmetric stretch, which is IR inactive.

Hence only three signals are found in the IR spectrum.

=== MO Diagram of BH3 ===

[[file:LZY_BH3_MO.PNG]]

The MOs of BH3 produced by LCAO (black and white) and MOs produced by Gaussian Calculation (coloured) are shown in the above diagram.

There are some small differences between the LCAO MO diagram and the 'real' diagrams performed by Gaussian.

* In-phase orbitals in 'real' MOs merge together to form a joint orbital. However, individual orbitals in the LCAO diagram remain separate.

* The 'real' MOs accounts for repulsion between orbital, which are shown by slightly bent p orbitals.

Comparing the results, we may conclude that the LCAO diagram shows the 'real' spatial electron density distribution in a relatively accurate manner.

== NH3 Molecule ==

Link: [[Media:LZY_NH3_FREQ_2.LOG|LZY_NH3_FREQ_2.LOG]]

=== Summary Table ===

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

[[File:LZY_NH3_sum_2.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -11.3135 -11.2772 -0.0036 0.0250 0.1442 25.7141
Low frequencies --- 1089.6627 1694.1740 1694.1743
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3_FREQ_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

== NH3BH3 Molecule ==

Link: [[Media:LZY_NH3BH3_FREQ.LOG|LZY_NH3BH3_FREQ.LOG]]

=== Summary Table ===

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

[[file: LZY_NH3BH3_SUM_1.PNG ‎]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000113 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000616 0.001800 YES
RMS Displacement 0.000354 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -0.0615 -0.0457 -0.0066 21.6949 21.7008 40.5895
Low frequencies --- 266.0361 632.3691 640.1428
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NH3BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Association Energy Analysis ===

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

Hence, N-B dative bond energy is -129 kJ/mol.

It is much weaker than a normal N-B sigma bond (-377.9 kJ/mol).

== NI3 Molecule ==

Link: [[Media:LZY_NI3_FREQ.LOG|LZY_NI3_FREQ.LOG]]

=== Summary Table ===

B3LYP/Gen level

[[file: LZY_NI3_freq.PNG]]

=== Item Table ===

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000486 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
</pre>

=== Frequency Analysis ===

<pre>
Low frequencies --- -12.7375 -12.7314 -6.2899 -0.0039 0.0188 0.0633
Low frequencies --- 101.0325 101.0332 147.4122
</pre>

=== Jmol Dynamic Image ===

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

* N-I bond distance: 2.184 Å

== Project: Lewis Acids and Bases ==

=== Different Al2Cl4Br2 Isomers ===

==== Isomer A ====

Link: [[Media:LZY_ISOMER_A_2.LOG|LZY_ISOMER_A_2.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_a.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_A_sum_2.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000200 0.000450 YES
RMS Force 0.000094 0.000300 YES
Maximum Displacement 0.000826 0.001800 YES
RMS Displacement 0.000375 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -2.7897 -2.7222 -0.0167 0.0065 0.0076 3.3444
Low frequencies --- 11.5302 65.3796 88.6180
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER A</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_A_2.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer B ====

Link: [[Media:LZY_ISOMER_B.LOG|LZY_ISOMER_B.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_b.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_B_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000080 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.000744 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -3.7545 -0.0084 -0.0076 0.0055 2.9743 5.3976
Low frequencies --- 15.0735 58.8033 81.4340
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER B</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_B.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer C ====

Link: [[Media:LZY_ISOMER_C_1.LOG|LZY_ISOMER_C_1.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_c.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_C_sum_1.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000085 0.000450 YES
RMS Force 0.000030 0.000300 YES
Maximum Displacement 0.000753 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -1.8103 -0.0157 -0.0134 -0.0124 3.1304 3.1724
Low frequencies --- 13.1236 54.3351 73.8370
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER C</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_C_1.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer D ====

Link: [[Media:LZY_ISOMER_D.LOG|LZY_ISOMER_D.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_d.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_D_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000096 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.001637 0.001800 YES
RMS Displacement 0.000724 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -8.9580 -3.9751 -3.5921 -0.0122 -0.0093 -0.0075
Low frequencies --- 16.2873 53.6939 79.7829
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER D</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_D.LOG</uploadedFileContents>
</jmolApplet></jmol>

==== Isomer E ====

Link: [[Media:LZY_ISOMER_E.LOG|LZY_ISOMER_E.LOG]]

'''''Molecular Diagram'''''

[[file:LZY_isomer_e.png]]

'''''Summary Table'''''

B3LYP/6-31G(d.p)

[[file:LZY_isomer_E_sum.PNG]]

'''''Item Table'''''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000208 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000265 0.001200 YES
</pre>

'''''Frequency Analysis'''''

<pre>
Low frequencies --- -4.5056 -2.1615 0.0048 0.0063 0.0067 3.1231
Low frequencies --- 15.1154 52.1657 73.8402
</pre>

'''''Jmol Dynamic Image'''''

<jmol><jmolApplet>
<title>ISOMER E</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>LZY_ISOMER_E.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Symmetry and Energy of Al2Cl4Br2 Isomers ===

{| class="wikitable"
|+
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png]]
|D2h
|−18673857
|0
|Very High
|-
|B
|[[File:LZY_isomer_b.png]]
|C1
|−18673850
|7
|High
|-
|C
|[[File:LZY_isomer_c.png]]
|C2v
|−18673845
|12
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png]]
|C2v
|−18673844
|13
|Low
|-
|E
|[[File:LZY_isomer_e.png]]
|C2h
|−18673844
|13
|Low
|}

'''''Observations'''''

When both bridging ions are Br, the molecule has highest stability.

The stability decreases when one of the bridging ions is replaced by Cl, and is lowest when both of the bridging ions are Cl.

'''''Explanations'''''

The Al-X-Al bridging bond (X = Br or Cl) consists of a σ-type bond, and a dative bond with X as the electron donor (as shown in the figure below).

The strength of the Al-X-Al bond is proportional to the orbital overlap efficiency between Al and X, and the bond strength is in turn proportional to the relative stability of the complex molecule.

Br is lower in Group 17, hence it has larger and more diffuse orbitals, making the orbital overlap with Al more efficient. In contrast, Cl is higher in Group 17 and it is very electronegative. Hence, it has a smaller radius and its nucleus holds its electrons tightly.

Therefore, we may conclude the Al-Br-Al bonding provides greater stability than the Al-Cl-Al one.

[[File:LZY_isomer_gen.png]]

File:LZY isomer gen.png

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ICL:zl4817

2019-05-23T13:17:12Z

Zl4817: /* Project: Lewis Acids and Bases */

File:LZY isomer E sum.PNG

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File:LZY ISOMER E.LOG

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ICL:zl4817

2019-05-23T13:09:08Z

Zl4817: /* Project: Lewis Acids and Bases */

File:LZY isomer D sum.PNG

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