View source for ICL:zl4817

== BH<sub>3</sub> 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]]

<u>Figure 1: Summary Table of BH<sub>3</sub></u>


=== 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<sup>-1</sup> || Intensity (a.u.) || Symmetry Point Group || IR active? || Vibrational Mode
|-
|1163
|92
|A<sub>2</sub><sup>'</sup><sup>'</sup>
|yes
|out-of-plane bend
|-
|1213
|14
|E<sup>'</sup>
|yes
|bend
|-
|1213
|14
|E<sup>'</sup>
|yes
|bend
|-
|2580
|0
|A<sub>1</sub><sup>'</sup>
|no
|symmetric stretch
|-
|2713
|126
|E<sup>'</sup>
|yes
|asymmetric stretch
|-
|2713
|126
|E<sup>'</sup>
|yes
|asymmetric stretch
|}



=== IR Spectrum ===

[[file:LZY_BH3_spec.PNG]]

<u>Figure 2: BH<sub>3</sub> Proposed IR Spectrum by Gaussian</u>



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

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

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

Hence only three signals are found in the IR spectrum.



=== MO Diagram of BH<sub>3</sub> ===

[[file:LZY_BH3_MO.PNG]]


<u>Figure 3: BH<sub>3</sub> LCAO and 'Real' MO Diagram </u>


The MOs of BH<sub>3</sub> 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.

[[User:Ng611|Ng611]] ([[User talk:Ng611|talk]]) 21:12, 5 June 2019 (BST) How significant do you think this is?

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

[[User:Ng611|Ng611]] ([[User talk:Ng611|talk]]) 21:12, 5 June 2019 (BST) Yes although we sometimes mark orbitals as being 'polarised' off atomic centres.

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

== NH<sub>3</sub> Molecule ==

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

[[User:Ng611|Ng611]] ([[User talk:Ng611|talk]]) 21:13, 5 June 2019 (BST) This is your opt+freq file, not your freq .log file. 


=== Summary Table  ===

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

[[File:LZY_NH3_sum_2.PNG]]


<u>Figure 4: NH<sub>3</sub> Summary Table</u>


=== 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>

== NH<sub>3</sub>BH<sub>3</sub> 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 ‎]]

<u>Figure 5: NH<sub>3</sub>BH<sub>3</sub> Summary Table</u>

=== 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(NH<sub>3</sub>)= -56.55777 au

E(BH<sub>3</sub>)= -26.61532 au

E(NH<sub>3</sub>BH<sub>3</sub>)= -83.22469 au

ΔE=E(NH<sub>3</sub>BH<sub>3</sub>)-[E(NH<sub>3</sub>)+E(BH<sub>3</sub>)] = -0.05160 au = -0.05160 ÷ 0.0004 kJ/mol = -129 kJ/mol (1 kJ/mol = 0.0004 au) <ref name="conversion" />

[[User:Ng611|Ng611]] ([[User talk:Ng611|talk]]) 21:14, 5 June 2019 (BST) You've used the wrong conversion factor (1 kJ/mol = 0.00038 a.u.) and your final answer is off by a few kJ/mol. Otherwise, great calculation. 

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" />

== NI<sub>3</sub> Molecule ==

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


=== Summary Table  ===

B3LYP/Gen level 

[[file: LZY_NI3_freq.PNG]]

<u>Figure 6: NI<sub>3</sub> Summary Table</u>

=== 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 Al<sub>2</sub>Cl<sub>4</sub>Br<sub>2</sub> Isomers ===


==== Isomer A ====

[[User:Ng611|Ng611]] ([[User talk:Ng611|talk]]) 21:17, 5 June 2019 (BST) You've forgotten to use pseudopotentials in all of you calculations in this section. 

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

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

[[file:LZY_isomer_a.png]]

<u>Figure 7: Isomer A</u>


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

B3LYP/6-31G(d.p) 

[[file:LZY_isomer_A_sum_2.PNG]]

<u>Figure 8: Isomer A Summary Table</u>


'''''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]]

<u>Figure 9: Isomer B</u>


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

B3LYP/6-31G(d.p) 

[[file:LZY_isomer_B_sum.PNG]]

<u>Figure 10: Isomer B Summary Table</u>


'''''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]]

<u>Figure 11: Isomer C</u>


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

B3LYP/6-31G(d.p) 

[[file:LZY_isomer_C_sum_1.PNG]]

<u>Figure 12: Isomer C Summary Table</u>


'''''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]]

<u>Figure 13: Isomer D</u>


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

B3LYP/6-31G(d.p) 

[[file:LZY_isomer_D_sum.PNG]]

<u>Figure 14: Isomer D Summary Table</u>


'''''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]]

<u>Figure 15: Isomer E</u>


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

B3LYP/6-31G(d.p) 

[[file:LZY_isomer_E_sum.PNG]]

<u>Figure 16: Isomer E Summary Table</u>


'''''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 Al<sub>2</sub>Cl<sub>4</sub>Br<sub>2</sub> Isomers ===

{| class="wikitable"
|+ 
|-
| Isomer || Structure || Symmetry || Energy (kJ/mol) || Relative Stability
|-
|A
|[[File:LZY_isomer_a.png| thumb |Figure 7: Isomer A]]
|D<sub>2h</sub>
|−18673857
|Very High
|-
|B
|[[File:LZY_isomer_b.png| thumb |Figure 9: Isomer B]]
|C<sub>1</sub>
|−18673850
|High
|-
|C
|[[File:LZY_isomer_c.png| thumb |Figure 11: Isomer C]]
|C<sub>2v</sub>
|−18673845
|Intermediate
|-
|D
|[[File:LZY_isomer_d.png| thumb |Figure 13: Isomer D]]
|C<sub>2v</sub>
|−18673844
|Low
|-
|E
|[[File:LZY_isomer_e.png| thumb |Figure 15: Isomer E]]
|C<sub>2h</sub>
|−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. 

[[User:Ng611|Ng611]] ([[User talk:Ng611|talk]]) 21:22, 5 June 2019 (BST) Because of your incorrect pseudopotential input, you've (incorrectly) calculated that the D2h (bridging Br) structure is more stable. In fact, the opposite is true. 


[[File:LZY_isomer_gen.png]]

<u>Figure 17: A General Structure of Dimer Complex</u>

=== Dissociation of the Lowest-Energy Conformer into 2 AlCl<sub>2</sub>Br ===

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]]

<u>Figure 18: AlCl<sub>2</sub>Br Summary Table</u>


====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 AlCl<sub>2</sub>Br, 2 Al-Br bonds are lost.

The energy of one molecule of AlCl<sub>2</sub>Br is calculated to be -9336871 kJ/mol by Gaussian.

Hence, the sum of energy of two AlCl<sub>2</sub>Br 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.

[[User:Ng611|Ng611]] ([[User talk:Ng611|talk]]) 21:23, 5 June 2019 (BST) e.c.f for calculation.

=== 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
|}

[[User:Ng611|Ng611]] ([[User talk:Ng611|talk]]) 21:25, 5 June 2019 (BST) Excellent LCAO analysis! Very neatly laid-out and well annontated. Well done!

==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, <i>Quantities, Units and Symbols in Physical Chemistry</i>, 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.), <i>J. Chem</i>. Educ., 2003, '''80''', 747.</ref>
<ref name="bond break">Peter Atkins and Julio de Paula, <i>Physical Chemistry</i> (8th ed., W.H. Freeman 2006), p.809 ISBN 0-7167-8759-8</ref>
</references>