= Inorganic Computational Lab =

== EX3 Section ==

=== BH3 ===

==== 1. B3LYP/3-21G Calculation Method====

''' Method and Basis Set:''' B3LYP/3-21G

[[File:Chinglam BH3table321.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM BH3OPT 321.LOG|CHINGLAM BH3OPT 321.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000174 0.000450 YES
RMS Force 0.000100 0.000300 YES
Maximum Displacement 0.000674 0.001800 YES
RMS Displacement 0.000397 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> Borane </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM BH3OPT 321.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== 2. B3LYP/6-31G(d,p)Calculation Method ====

'''Method and Basis Set:''' B3LYP/6-31G(d,p)

[[File:Chinglam BH3table631.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM BH3OPT 631.LOG|CHINGLAM BH3OPT 631.LOG]]

'''Frequency analysis log file:''' [[Media:CHINGLAM BH3OPT 631 FREQ.LOG|CHINGLAM BH3OPT 631 FREQ.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -4.8294 -1.2074 -0.0054 1.0243 9.1094 9.1890
Low frequencies --- 1162.9789 1213.1709 1213.1736
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> Borane </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM BH3OPT 631.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

====IR Vibrations====

{|border="1" cellpadding="1" cellspacing="0" align="center"
|+ IR Data of BH3
! Mode !! wavenumber (cm-1 !! Intensity (arbitrary units) !! symmetry !! IR active? !! type
|-
|1 || 1163 || 93 || A2 " ||yes ||out-of-plane bending
|-
|2 || 1213 || 14 ||E' ||very slight ||in-plane bending
|-
|3 || 1213 ||14 ||E' ||very slight ||in-plane bending
|-
|4 || 2582 ||0 ||A1' ||no ||symmetric stretch
|-
|5 || 2716 ||126 ||E' ||Yes ||asymmetric stretch
|-
|6 || 2716 ||126 ||E' ||Yes ||asymmetric stretch
|}

[[File:Chinglam BH3irspectrum.PNG|thumb|center|IR spectrum|800px]]

By the 3N-6 rule, there should be 6 different vibration modes. However, there is only three peaks found in the IR spectrum. Only one peak is observed for the in-plane bending vibration as mode 2 and 3 are degenerated in energy. The same applies to the asymmetric stretch modes (mode 5 and 6), which are also degenerated in energy. There is no change in the dipole moment of the molecule for mode 3 (the symmetrical stretching vibration) and hence it doesn't lead to infrared absorption.

==== MO of BH3 ====

[[File:ChingLam BH3MO 852.png|thumb|center|MO Diagram - LCAOs with the calculated MOs <ref name="hunt"/>|600px]]

'''Are there any significant differences between the real and LCAO MOs? '''

The real (calculated) MOs are generally more diffused than the LCAO (linear combination of atomic orbitals) MOs, especially for the unoccupied orbitals high in energy (from MO 5 to MO 8 as labelled in the above diagram). Hence, the real MO can look quite different from the LCAO prediction (e.g. MO 6 - the H3 FO is much larger than the LCAO has predicted; MO 8 - the electron density is spread across the whole molecule, unlike the prediction)

'''What does this say about the accuracy and usefulness of qualitative MO theory?'''

The qualitative MO theory are more accurate and useful for occupied MOs with low energy. Above the HOMO (highest occupied molecular orbital), the prediction are less accurate.

=== NH3 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)

[[File:ChingLam NH3 sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM NH3 6313.LOG|CHINGLAM NH3 6313.LOG]]

'''Frequency analysis log file:''' [[Media:CHINGLAM NH3 6313 FREQ.LOG|CHINGLAM NH3 6313 FREQ.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -0.2239 -0.0404 -0.0040 7.1998 7.2613 27.9769
Low frequencies --- 1089.9671 1694.2126 1694.2129
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> NH3 (B3LYP/6-31G(d,p))</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM NH3 6313.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== NH3-BH3 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)

[[File:ChingLam NH3BH3 sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM NH3BH3 OPT3.LOG|CHINGLAM NH3BH3 OPT3.LOG]]

'''Frequency analysis log file:''' [[Media:CHINGLAM NH3BH3 OPT3 FREQ2.LOG|CHINGLAM NH3BH3 OPT3 FREQ2.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000052 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000423 0.001800 YES
RMS Displacement 0.000145 0.001200 YES
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -0.1703 -0.0781 -0.0066 12.6039 12.6146 12.8091
Low frequencies --- 263.1708 632.8934 638.8999
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> NH3-BH3 (B3LYP/6-31G(d,p))</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM NH3BH3 OPT3 FREQ2.mol</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== Association energies: Ammonia-Borane ===

From the above calculation (Method: B3LYP/6-31G(d,p)) :

'''E(NH3)=''' -56.55776862 a.u.

'''E(BH3)= ''' -26.61532363 a.u.

''' E(NH3-BH3)=''' -83.22469020 a.u.

ΔE=E(NH3-BH3)-[E(NH3)+E(BH3)]

'''ΔE=''' (-83.22469020)- [(-56.55776862)+ (-26.61532363)] = -0.05159795 a.u. ≈ -0.05160 a.u. (5 d.p.)

'''ΔE=''' 2625.5 x -0.05159795 ≈ ''' -135 kJ / mol '''

ΔE is negative, implying that the reaction is overall exothermic - the bond forming process is energy releasing. The association energy of the adduct is 135 kJ/mol. The means that the B-N dative bond is quite week relative to the stronger covalent bonds (For reference, some mean bond enthalpies data <ref name="energy" /> are listed as following: C-H 420 kJ/mol, C-C 350 kJ/mol, O-H 463 kJ/mol). However, the enthalpy of B-N dative bond is quite similar to some of the weak covalent bond (O-O 146 kJ/mol, I-I 151 kJ/mol) and much higher than the enthalpy of hydrogen bonding (HO-H -- OH 2 22 kJ/mol).

Overall, B-N dative bond is consider to be weak comparing to covalent bonds, but it is much stronger than H-bonding and van der Waals interactions.

=== BBr3 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam BBr3 sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:Log 10047290 Ching BBr3.log|Log 10047290 Ching BBr3.log]]

'''Frequency analysis log file:''' [[Media:Log 10047294 Ching BBr3 freq.log|Log 10047294 Ching BBr3 freq.log]]

'''DSpace link:''' {{DOI|10042/202401}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-4.027119D-10
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Log 10047290 Ching BBr3.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

== Project Section -- Lewis Acids and Bases - Main Group Halide==

The Isomers of AlBr2Cl4:

[[File:ChingLamisomers Al2Br2Cl4.jpg|thumb|center|The Isomers of AlBr2Cl4|400px]]

=== AlBr2Cl4 (2 Bridging Br Ions) - Isomer 1 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam Al2Br2Cl4bridge sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:ChingLam Al2Br2Cl4 Brbridge.log|ChingLam Al2Br2Cl4 Brbridge.log]]

'''Frequency analysis log file:''' [[Media:ChingLam Al2Br2Cl4 Brbridge freq.log|ChingLam Al2Br2Cl4 Brbridge freq.log]]

'''DSpace link:''' {{DOI|10042/202404}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000029 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000664 0.001800 YES
RMS Displacement 0.000278 0.001200 YES
Predicted change in Energy=-1.390401D-08
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -5.1253 -5.0805 -3.1847 -0.0051 -0.0047 -0.0045
Low frequencies --- 14.8608 63.2610 86.0512
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ChingLam Al2Br2Cl4 Brbridge.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== AlBr2Cl4 (The Isomer with Trans Terminal Br and Bridging Cl Ions) - Isomer 2 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam Al2Br2Cl4trans sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:ChingLam Al2Br2Cl4 Transopt.log|ChingLam Al2Br2Cl4 Transopt.log]]

'''Frequency analysis log file:''' [[Media:ChingLam Al2Br2Cl4 Transopt freq.log|ChingLam Al2Br2Cl4 Transopt freq.log]]

'''DSpace link:''' {{DOI|10042/202406}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.001800 0.001800 YES
RMS Displacement 0.000622 0.001200 YES
Predicted change in Energy=-1.168706D-07
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>

Low frequencies --- -3.5004 -2.4150 0.0007 0.0025 0.0027 0.7437
Low frequencies --- 17.7463 49.0305 72.9456

</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ChingLam Al2Br2Cl4 Transopt.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== Relative Energy of Isomer 1 and 2 ===

'''E(Isomer 1)=''' -2352.40630796 a.u.

'''E(Isomer 2)=''' -2352.41628799 a.u.

Relative Energy = E(Isomer 1)- E(Isomer 2) = (-2352.40630796) - (-2352.41628799) = 0.00998002999 a.u.

'''Relative Energy in kJ/mol =''' 0.00998002999 x 2625.5 = 26 kJ/mol (Round to whole no.)

'''Discuss the relative stability of these conformers with respect to the bridging ions.'''

The above calculations demonstrate that isomer 2 is lower in energy comparing to isomer 1 by 26 kJ/mol. This implies that isomer 2 is more stable than isomer 1. The difference in the stability is due to the difference bridging ions of the conformer. Isomer 2 has two Cl ions as the bridging atoms, while isomer 1 has two bridging Br ions. Cl is in row 3 of the periodic table and Br is in row 4. As Cl and Al are in the same row in the periodic table, their valence orbitals would be similar in size and energy comparing to Br. In the case for isomer 2 in the bridging region of the molecule, there would be better overlaps between the fragment orbitals (FOs) and greater stabilization from smaller FOs energy difference comparing to isomer 1. Apart from the electronic perspectives, Cl ions are smaller than Br ions, which makes the Cl bridging more sterically favorable and contributes to the higher stability.

=== AlCl2Br (Monomer) ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam Almonomer sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:ChingLam AlBrCl2optu.log|ChingLam AlBrCl2optu.log]]

'''Frequency analysis log file:''' [[Media:ChingLam AlBrCl2optu freq.log|ChingLam AlBrCl2optu freq.log]]

'''DSpace link:''' {{DOI|10042/202409}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984435D-08
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>

Low frequencies --- 0.0010 0.0029 0.0037 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ChingLam AlBrCl2optu mol.mol2</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== Dissociation energy of Isomer 2 into 2AlCl2Br ===

2AlCl2Br --> Al2Cl4Br2

From the above calculation (Method: B3LYP/6-31G(d,p)LANL2DZ):

'''E(Al2Cl4Br2, Isomer 2)=''' -2352.41628799 a.u.

'''E(AlCl2Br) =''' -1176.19013679 a.u.

Association Energy = E(Al2Cl4Br2, Isomer 2) - 2E(AlCl2Br)

Dissociation Energy = - (Association Energy)

Dissociation Energy = 2E(AlCl2Br) - E(Al2Cl4Br2, Isomer 2) = 2(-1176.19013679) - (-2352.41628799) = 0.03601441 a. u.

'''Dissociation Energy in kJ/mol =''' 0.03601441 x 2625.5 = 95 kJ/mol (Round to whole no.)

The dissociation of the dimer into monomers is positive and endothermic as bonds are broken in the reaction. Bond breaking takes in energy.

'''Is the product more or less stable than the isolated monomers?'''

As Dissociation Energy = - (Association Energy), the association of the monomers into dimers is exothermic (association energy is negative) from the above calculation. This implies that the product (the Al2Cl4Br2 dimer) is more stable than the isolated monomers.

The AlCl2Br monomer is two electron short from a full octet. Hence, the Al centre of the isolated monomer is electron deficient. By forming dimer with lone pair electron donation from the bridging Cl, the electron deficiency at Al is relief with full octet fulfilled, making the system more stable overall.

=== MO of Al2Cl4Br2, Isomer 2===

All the occupied valence MOs of Al2Cl4Br2 (isomer 2) are visualised and 3 MOs ranging from highly bonding to highly antibonding are presented below with their LCAO MO diagrams. The interactions occurring in the MOs are annotated.

'''MO31 - highly bonding MO'''

[[File:Chinglam MO31 annotated.PNG|thumb|center|MO31 - 'Real' MO calculated by Gaussview and the LCAO MO with annotations|850px]]

'''MO42 - weakly anti-bonding MO'''

[[File:ChingLam MO42 annot.PNG|thumb|center|MO42 - 'Real' MO calculated by Gaussview and the LCAO MO with annotations|850px]]

'''MO52- highly anti-bonding MO'''

[[File:ChingLam MO52pic.PNG|thumb|center|MO52 - the 'Real' MO calculated by Gaussview|850px]]

[[File:Screen Shot 2018-05-17 at 8.03.26 PMChing Lam.png|thumb|center|MO52 - the LCAO MO with annotations|850px]]

== Reference and Acknowledgement ==

=== Acknowledgement ===

The BH3 MO diagram in BH3 section of this report is created based on Fig. 5 in this online document <ref name="hunt"/>.

=== Reference ===

<references>
<ref name="hunt">Hunt, P. “Tutorial Problem MO Diagram BH3.” Hunt Research Group , www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf. </ref>
<ref name="energy">Atkins, P. W., and D. F. Shriver. Shriver and Atkins Inorganic Chemistry. Oxford University Press, 2006.</ref>

</references>

2018-05-17T18:35:05Z

Ccl216:

Rep:Mod:01181216201805

2018-05-17T18:27:10Z

Ccl216: /* Dissociation energy of Isomer 2 into 2AlCl2Br */

= Inorganic Computational Lab =

== EX3 Section ==

=== BH3 ===

==== 1. B3LYP/3-21G Calculation Method====

''' Method and Basis Set:''' B3LYP/3-21G

[[File:Chinglam BH3table321.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM BH3OPT 321.LOG|CHINGLAM BH3OPT 321.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000174 0.000450 YES
RMS Force 0.000100 0.000300 YES
Maximum Displacement 0.000674 0.001800 YES
RMS Displacement 0.000397 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> BH3(B3LYP/3-21G)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM BH3OPT 321.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== 2. B3LYP/6-31G(d,p)Calculation Method ====

'''Method and Basis Set:''' B3LYP/6-31G(d,p)

[[File:Chinglam BH3table631.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM BH3OPT 631.LOG|CHINGLAM BH3OPT 631.LOG]]

'''Frequency analysis log file:''' [[Media:CHINGLAM BH3OPT 631 FREQ.LOG|CHINGLAM BH3OPT 631 FREQ.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -4.8294 -1.2074 -0.0054 1.0243 9.1094 9.1890
Low frequencies --- 1162.9789 1213.1709 1213.1736
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> BH3(B3LYP/6-31G(d,p))</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM BH3OPT 631.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

====IR Vibrations====

{|border="1" cellpadding="1" cellspacing="0" align="center"
|+ IR Data of BH3
! Mode !! wavenumber (cm-1 !! Intensity (arbitrary units) !! symmetry !! IR active? !! type
|-
|1 || 1163 || 93 || A2 " ||yes ||out-of-plane bending
|-
|2 || 1213 || 14 ||E' ||very slight ||in-plane bending
|-
|3 || 1213 ||14 ||E' ||very slight ||in-plane bending
|-
|4 || 2582 ||0 ||A1' ||no ||symmetric stretch
|-
|5 || 2716 ||126 ||E' ||Yes ||asymmetric stretch
|-
|6 || 2716 ||126 ||E' ||Yes ||asymmetric stretch
|}

[[File:Chinglam BH3irspectrum.PNG|thumb|center|IR spectrum|800px]]

By the 3N-6 rule, there should be 6 different vibration modes. However, there is only three peaks found in the IR spectrum. Only one peak is observed for the in-plane bending vibration as mode 2 and 3 are degenerated in energy. The same applies to the asymmetric stretch modes (mode 5 and 6), which are also degenerated in energy. There is no change in the dipole moment of the molecule for mode 3 (the symmetrical stretching vibration) and hence it doesn't lead to infrared absorption.

==== MO of BH3 ====

[[File:ChingLam BH3MO 852.png|thumb|center|MO Diagram - LCAOs with the calculated MOs |600px]]

'''Are there any significant differences between the real and LCAO MOs? '''

The real (calculated) MOs are generally more diffused than the LCAO (linear combination of atomic orbitals) MOs, especially for the unoccupied orbitals high in energy (from MO 5 to MO 8 as labelled in the above diagram). Hence, the real MO can look quite different from the LCAO prediction (e.g. MO 6 - the H3 FO is much larger than the LCAO has predicted; MO 8 - the electron density is spread across the whole molecule, unlike the prediction)

'''What does this say about the accuracy and usefulness of qualitative MO theory?'''

The qualitative MO theory are more accurate and useful for occupied MOs with low energy. Above the HOMO (highest occupied molecular orbital), the prediction are less accurate.

=== NH3 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)

[[File:ChingLam NH3 sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM NH3 6313.LOG|CHINGLAM NH3 6313.LOG]]

'''Frequency analysis log file:''' [[Media:CHINGLAM NH3 6313 FREQ.LOG|CHINGLAM NH3 6313 FREQ.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -0.2239 -0.0404 -0.0040 7.1998 7.2613 27.9769
Low frequencies --- 1089.9671 1694.2126 1694.2129
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> NH3 (B3LYP/6-31G(d,p))</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM NH3 6313.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== NH3-BH3 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)

[[File:ChingLam NH3BH3 sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM NH3BH3 OPT3.LOG|CHINGLAM NH3BH3 OPT3.LOG]]

'''Frequency analysis log file:''' [[Media:CHINGLAM NH3BH3 OPT3 FREQ2.LOG|CHINGLAM NH3BH3 OPT3 FREQ2.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000052 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000423 0.001800 YES
RMS Displacement 0.000145 0.001200 YES
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -0.1703 -0.0781 -0.0066 12.6039 12.6146 12.8091
Low frequencies --- 263.1708 632.8934 638.8999
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> NH3-BH3 (B3LYP/6-31G(d,p))</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM NH3BH3 OPT3 FREQ2.mol</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== Association energies: Ammonia-Borane ===

From the above calculation (Method: B3LYP/6-31G(d,p)) :

'''E(NH3)=''' -56.55776862 a.u.

'''E(BH3)= ''' -26.61532363 a.u.

''' E(NH3-BH3)=''' -83.22469020 a.u.

ΔE=E(NH3-BH3)-[E(NH3)+E(BH3)]

'''ΔE=''' (-83.22469020)- [(-56.55776862)+ (-26.61532363)] = -0.05159795 a.u. ≈ -0.05160 a.u. (5 d.p.)

'''ΔE=''' 2625.5 x -0.05159795 ≈ ''' -135 kJ / mol '''

ΔE is negative, implying that the reaction is overall exothermic - the bond forming process is energy releasing. The association energy of the adduct is 135 kJ/mol. The means that the B-N dative bond is quite week relative to the stronger covalent bonds (For reference, some mean bond enthalpies data <ref name="energy" /> are listed as following: C-H 420 kJ/mol, C-C 350 kJ/mol, O-H 463 kJ/mol). However, the enthalpy of B-N dative bond is quite similar to some of the weak covalent bond (O-O 146 kJ/mol, I-I 151 kJ/mol) and much higher than the enthalpy of hydrogen bonding (HO-H -- OH 2 22 kJ/mol).

Overall, B-N dative bond is consider to be weak comparing to covalent bonds, but it is much stronger than H-bonding and van der Waals interactions.

=== BBr3 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam BBr3 sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:Log 10047290 Ching BBr3.log|Log 10047290 Ching BBr3.log]]

'''Frequency analysis log file:''' [[Media:Log 10047294 Ching BBr3 freq.log|Log 10047294 Ching BBr3 freq.log]]

'''DSpace link:''' {{DOI|10042/202401}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-4.027119D-10
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Log 10047290 Ching BBr3.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

== Project Section -- Lewis Acids and Bases - Main Group Halide==

The Isomers of AlBr2Cl4:

[[File:ChingLamisomers Al2Br2Cl4.jpg|thumb|center|The Isomers of AlBr2Cl4|400px]]

=== AlBr2Cl4 (2 Bridging Br Ions) - Isomer 1 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam Al2Br2Cl4bridge sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:ChingLam Al2Br2Cl4 Brbridge.log|ChingLam Al2Br2Cl4 Brbridge.log]]

'''Frequency analysis log file:''' [[Media:ChingLam Al2Br2Cl4 Brbridge freq.log|ChingLam Al2Br2Cl4 Brbridge freq.log]]

'''DSpace link:''' {{DOI|10042/202404}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000029 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000664 0.001800 YES
RMS Displacement 0.000278 0.001200 YES
Predicted change in Energy=-1.390401D-08
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -5.1253 -5.0805 -3.1847 -0.0051 -0.0047 -0.0045
Low frequencies --- 14.8608 63.2610 86.0512
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ChingLam Al2Br2Cl4 Brbridge.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== AlBr2Cl4 (The Isomer with Trans Terminal Br and Bridging Cl Ions) - Isomer 2 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam Al2Br2Cl4trans sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:ChingLam Al2Br2Cl4 Transopt.log|ChingLam Al2Br2Cl4 Transopt.log]]

'''Frequency analysis log file:''' [[Media:ChingLam Al2Br2Cl4 Transopt freq.log|ChingLam Al2Br2Cl4 Transopt freq.log]]

'''DSpace link:''' {{DOI|10042/202406}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.001800 0.001800 YES
RMS Displacement 0.000622 0.001200 YES
Predicted change in Energy=-1.168706D-07
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>

Low frequencies --- -3.5004 -2.4150 0.0007 0.0025 0.0027 0.7437
Low frequencies --- 17.7463 49.0305 72.9456

</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ChingLam Al2Br2Cl4 Transopt.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== Relative Energy of Isomer 1 and 2 ===

'''E(Isomer 1)=''' -2352.40630796 a.u.

'''E(Isomer 2)=''' -2352.41628799 a.u.

Relative Energy = E(Isomer 1)- E(Isomer 2) = (-2352.40630796) - (-2352.41628799) = 0.00998002999 a.u.

'''Relative Energy in kJ/mol =''' 0.00998002999 x 2625.5 = 26 kJ/mol (Round to whole no.)

'''Discuss the relative stability of these conformers with respect to the bridging ions.'''

The above calculations demonstrate that isomer 2 is lower in energy comparing to isomer 1 by 26 kJ/mol. This implies that isomer 2 is more stable than isomer 1. The difference in the stability is due to the difference bridging ions of the conformer. Isomer 2 has two Cl ions as the bridging atoms, while isomer 1 has two bridging Br ions. Cl is in row 3 of the periodic table and Br is in row 4. As Cl and Al are in the same row in the periodic table, their valence orbitals would be similar in size and energy comparing to Br. In the case for isomer 2 in the bridging region of the molecule, there would be better overlaps between the fragment orbitals (FOs) and greater stabilization from smaller FOs energy difference comparing to isomer 1. Apart from the electronic perspectives, Cl ions are smaller than Br ions, which makes the Cl bridging more sterically favorable and contributes to the higher stability.

=== AlCl2Br (Monomer) ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam Almonomer sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:ChingLam AlBrCl2optu.log|ChingLam AlBrCl2optu.log]]

'''Frequency analysis log file:''' [[Media:ChingLam AlBrCl2optu freq.log|ChingLam AlBrCl2optu freq.log]]

'''DSpace link:''' {{DOI|10042/202409}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984435D-08
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>

Low frequencies --- 0.0010 0.0029 0.0037 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ChingLam AlBrCl2optu mol.mol2</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== Dissociation energy of Isomer 2 into 2AlCl2Br ===

2AlCl2Br --> Al2Cl4Br2

From the above calculation (Method: B3LYP/6-31G(d,p)LANL2DZ):

'''E(Al2Cl4Br2, Isomer 2)=''' -2352.41628799 a.u.

'''E(AlCl2Br) =''' -1176.19013679 a.u.

Association Energy = E(Al2Cl4Br2, Isomer 2) - 2E(AlCl2Br)

Dissociation Energy = - (Association Energy)

Dissociation Energy = 2E(AlCl2Br) - E(Al2Cl4Br2, Isomer 2) = 2(-1176.19013679) - (-2352.41628799) = 0.03601441 a. u.

'''Dissociation Energy in kJ/mol =''' 0.03601441 x 2625.5 = 95 kJ/mol (Round to whole no.)

The dissociation of the dimer into monomers is positive and endothermic as bonds are broken in the reaction. Bond breaking takes in energy.

'''Is the product more or less stable than the isolated monomers?'''

As Dissociation Energy = - (Association Energy), the association of the monomers into dimers is exothermic (association energy is negative) from the above calculation. This implies that the product (the Al2Cl4Br2 dimer) is more stable than the isolated monomers.

The AlCl2Br monomer is two electron short from a full octet. Hence, the Al centre of the isolated monomer is electron deficient. By forming dimer with lone pair electron donation from the bridging Cl, the electron deficiency at Al is relief with full octet fulfilled, making the system more stable overall.

== MO of Isomer 2==

All the occupied valence MOs of Al2Cl4Br2 (isomer 2) are visualised and 3 MOs ranging from highly bonding to highly antibonding are presented below with their LCAO MO diagrams. The interactions occurring in the MOs are annotated.

'''MO31 - highly bonding MO'''

[[File:Chinglam MO31 annotated.PNG|thumb|center|MO31 - 'Real' MO calculated by Gaussview and the LCAO MO with annotations|850px]]

'''MO42 - weakly anti-bonding MO'''

[[File:ChingLam MO42 annot.PNG|thumb|center|MO42 - 'Real' MO calculated by Gaussview and the LCAO MO with annotations|850px]]

'''MO52- highly anti-bonding MO'''

[[File:ChingLam MO52pic.PNG|thumb|center|MO52 - the 'Real' MO calculated by Gaussview|850px]]

[[File:Screen Shot 2018-05-17 at 7.09.32 PM Ching Lam.png|thumb|center|MO52 - the LCAO MO with annotations|850px]]

== Reference ==

<references>
<ref name="energy">Atkins, P. W., and D. F. Shriver. Shriver and Atkins Inorganic Chemistry. Oxford University Press, 2006.</ref>
</references>

Rep:Mod:01181216201805

2018-05-17T18:25:35Z

Ccl216: /* MO of Isomer 2 */

= Inorganic Computational Lab =

== EX3 Section ==

=== BH3 ===

==== 1. B3LYP/3-21G Calculation Method====

''' Method and Basis Set:''' B3LYP/3-21G

[[File:Chinglam BH3table321.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM BH3OPT 321.LOG|CHINGLAM BH3OPT 321.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000174 0.000450 YES
RMS Force 0.000100 0.000300 YES
Maximum Displacement 0.000674 0.001800 YES
RMS Displacement 0.000397 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> BH3(B3LYP/3-21G)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM BH3OPT 321.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== 2. B3LYP/6-31G(d,p)Calculation Method ====

'''Method and Basis Set:''' B3LYP/6-31G(d,p)

[[File:Chinglam BH3table631.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM BH3OPT 631.LOG|CHINGLAM BH3OPT 631.LOG]]

'''Frequency analysis log file:''' [[Media:CHINGLAM BH3OPT 631 FREQ.LOG|CHINGLAM BH3OPT 631 FREQ.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -4.8294 -1.2074 -0.0054 1.0243 9.1094 9.1890
Low frequencies --- 1162.9789 1213.1709 1213.1736
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> BH3(B3LYP/6-31G(d,p))</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM BH3OPT 631.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

====IR Vibrations====

{|border="1" cellpadding="1" cellspacing="0" align="center"
|+ IR Data of BH3
! Mode !! wavenumber (cm-1 !! Intensity (arbitrary units) !! symmetry !! IR active? !! type
|-
|1 || 1163 || 93 || A2 " ||yes ||out-of-plane bending
|-
|2 || 1213 || 14 ||E' ||very slight ||in-plane bending
|-
|3 || 1213 ||14 ||E' ||very slight ||in-plane bending
|-
|4 || 2582 ||0 ||A1' ||no ||symmetric stretch
|-
|5 || 2716 ||126 ||E' ||Yes ||asymmetric stretch
|-
|6 || 2716 ||126 ||E' ||Yes ||asymmetric stretch
|}

[[File:Chinglam BH3irspectrum.PNG|thumb|center|IR spectrum|800px]]

By the 3N-6 rule, there should be 6 different vibration modes. However, there is only three peaks found in the IR spectrum. Only one peak is observed for the in-plane bending vibration as mode 2 and 3 are degenerated in energy. The same applies to the asymmetric stretch modes (mode 5 and 6), which are also degenerated in energy. There is no change in the dipole moment of the molecule for mode 3 (the symmetrical stretching vibration) and hence it doesn't lead to infrared absorption.

==== MO of BH3 ====

[[File:ChingLam BH3MO 852.png|thumb|center|MO Diagram - LCAOs with the calculated MOs |600px]]

'''Are there any significant differences between the real and LCAO MOs? '''

The real (calculated) MOs are generally more diffused than the LCAO (linear combination of atomic orbitals) MOs, especially for the unoccupied orbitals high in energy (from MO 5 to MO 8 as labelled in the above diagram). Hence, the real MO can look quite different from the LCAO prediction (e.g. MO 6 - the H3 FO is much larger than the LCAO has predicted; MO 8 - the electron density is spread across the whole molecule, unlike the prediction)

'''What does this say about the accuracy and usefulness of qualitative MO theory?'''

The qualitative MO theory are more accurate and useful for occupied MOs with low energy. Above the HOMO (highest occupied molecular orbital), the prediction are less accurate.

=== NH3 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)

[[File:ChingLam NH3 sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM NH3 6313.LOG|CHINGLAM NH3 6313.LOG]]

'''Frequency analysis log file:''' [[Media:CHINGLAM NH3 6313 FREQ.LOG|CHINGLAM NH3 6313 FREQ.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -0.2239 -0.0404 -0.0040 7.1998 7.2613 27.9769
Low frequencies --- 1089.9671 1694.2126 1694.2129
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> NH3 (B3LYP/6-31G(d,p))</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM NH3 6313.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== NH3-BH3 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)

[[File:ChingLam NH3BH3 sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM NH3BH3 OPT3.LOG|CHINGLAM NH3BH3 OPT3.LOG]]

'''Frequency analysis log file:''' [[Media:CHINGLAM NH3BH3 OPT3 FREQ2.LOG|CHINGLAM NH3BH3 OPT3 FREQ2.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000052 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000423 0.001800 YES
RMS Displacement 0.000145 0.001200 YES
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -0.1703 -0.0781 -0.0066 12.6039 12.6146 12.8091
Low frequencies --- 263.1708 632.8934 638.8999
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> NH3-BH3 (B3LYP/6-31G(d,p))</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM NH3BH3 OPT3 FREQ2.mol</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== Association energies: Ammonia-Borane ===

From the above calculation (Method: B3LYP/6-31G(d,p)) :

'''E(NH3)=''' -56.55776862 a.u.

'''E(BH3)= ''' -26.61532363 a.u.

''' E(NH3-BH3)=''' -83.22469020 a.u.

ΔE=E(NH3-BH3)-[E(NH3)+E(BH3)]

'''ΔE=''' (-83.22469020)- [(-56.55776862)+ (-26.61532363)] = -0.05159795 a.u. ≈ -0.05160 a.u. (5 d.p.)

'''ΔE=''' 2625.5 x -0.05159795 ≈ ''' -135 kJ / mol '''

ΔE is negative, implying that the reaction is overall exothermic - the bond forming process is energy releasing. The association energy of the adduct is 135 kJ/mol. The means that the B-N dative bond is quite week relative to the stronger covalent bonds (For reference, some mean bond enthalpies data <ref name="energy" /> are listed as following: C-H 420 kJ/mol, C-C 350 kJ/mol, O-H 463 kJ/mol). However, the enthalpy of B-N dative bond is quite similar to some of the weak covalent bond (O-O 146 kJ/mol, I-I 151 kJ/mol) and much higher than the enthalpy of hydrogen bonding (HO-H -- OH 2 22 kJ/mol).

Overall, B-N dative bond is consider to be weak comparing to covalent bonds, but it is much stronger than H-bonding and van der Waals interactions.

=== BBr3 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam BBr3 sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:Log 10047290 Ching BBr3.log|Log 10047290 Ching BBr3.log]]

'''Frequency analysis log file:''' [[Media:Log 10047294 Ching BBr3 freq.log|Log 10047294 Ching BBr3 freq.log]]

'''DSpace link:''' {{DOI|10042/202401}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-4.027119D-10
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Log 10047290 Ching BBr3.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

== Project Section -- Lewis Acids and Bases - Main Group Halide==

The Isomers of AlBr2Cl4:

[[File:ChingLamisomers Al2Br2Cl4.jpg|thumb|center|The Isomers of AlBr2Cl4|400px]]

=== AlBr2Cl4 (2 Bridging Br Ions) - Isomer 1 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam Al2Br2Cl4bridge sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:ChingLam Al2Br2Cl4 Brbridge.log|ChingLam Al2Br2Cl4 Brbridge.log]]

'''Frequency analysis log file:''' [[Media:ChingLam Al2Br2Cl4 Brbridge freq.log|ChingLam Al2Br2Cl4 Brbridge freq.log]]

'''DSpace link:''' {{DOI|10042/202404}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000029 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000664 0.001800 YES
RMS Displacement 0.000278 0.001200 YES
Predicted change in Energy=-1.390401D-08
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -5.1253 -5.0805 -3.1847 -0.0051 -0.0047 -0.0045
Low frequencies --- 14.8608 63.2610 86.0512
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ChingLam Al2Br2Cl4 Brbridge.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== AlBr2Cl4 (The Isomer with Trans Terminal Br and Bridging Cl Ions) - Isomer 2 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam Al2Br2Cl4trans sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:ChingLam Al2Br2Cl4 Transopt.log|ChingLam Al2Br2Cl4 Transopt.log]]

'''Frequency analysis log file:''' [[Media:ChingLam Al2Br2Cl4 Transopt freq.log|ChingLam Al2Br2Cl4 Transopt freq.log]]

'''DSpace link:''' {{DOI|10042/202406}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.001800 0.001800 YES
RMS Displacement 0.000622 0.001200 YES
Predicted change in Energy=-1.168706D-07
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>

Low frequencies --- -3.5004 -2.4150 0.0007 0.0025 0.0027 0.7437
Low frequencies --- 17.7463 49.0305 72.9456

</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ChingLam Al2Br2Cl4 Transopt.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== Relative Energy of Isomer 1 and 2 ===

'''E(Isomer 1)=''' -2352.40630796 a.u.

'''E(Isomer 2)=''' -2352.41628799 a.u.

Relative Energy = E(Isomer 1)- E(Isomer 2) = (-2352.40630796) - (-2352.41628799) = 0.00998002999 a.u.

'''Relative Energy in kJ/mol =''' 0.00998002999 x 2625.5 = 26 kJ/mol (Round to whole no.)

'''Discuss the relative stability of these conformers with respect to the bridging ions.'''

The above calculations demonstrate that isomer 2 is lower in energy comparing to isomer 1 by 26 kJ/mol. This implies that isomer 2 is more stable than isomer 1. The difference in the stability is due to the difference bridging ions of the conformer. Isomer 2 has two Cl ions as the bridging atoms, while isomer 1 has two bridging Br ions. Cl is in row 3 of the periodic table and Br is in row 4. As Cl and Al are in the same row in the periodic table, their valence orbitals would be similar in size and energy comparing to Br. In the case for isomer 2 in the bridging region of the molecule, there would be better overlaps between the fragment orbitals (FOs) and greater stabilization from smaller FOs energy difference comparing to isomer 1. Apart from the electronic perspectives, Cl ions are smaller than Br ions, which makes the Cl bridging more sterically favorable and contributes to the higher stability.

=== AlCl2Br (Monomer) ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam Almonomer sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:ChingLam AlBrCl2optu.log|ChingLam AlBrCl2optu.log]]

'''Frequency analysis log file:''' [[Media:ChingLam AlBrCl2optu freq.log|ChingLam AlBrCl2optu freq.log]]

'''DSpace link:''' {{DOI|10042/202409}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984435D-08
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>

Low frequencies --- 0.0010 0.0029 0.0037 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ChingLam AlBrCl2optu mol.mol2</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== Dissociation energy of Isomer 2 into 2AlCl2Br ===

2AlCl2Br --> Al2Cl4Br2

From the above calculation (Method: B3LYP/6-31G(d,p)LANL2DZ):

'''E(Al2Cl4Br2, Isomer 2)=''' -2352.41628799 a.u.

'''E(AlCl2Br) =''' -1176.19013679 a.u.

Association Energy = E(Al2Cl4Br2, Isomer 2) - 2E(AlCl2Br)

Dissociation Energy = - (Association Energy)

Dissociation Energy = 2E(AlCl2Br) - E(Al2Cl4Br2, Isomer 2) = 2(-1176.19013679) - (-2352.41628799) = 0.03601441 a. u.

'''Dissociation Energy in kJ/mol =''' 0.03601441 x 2625.5 = 95 kJ/mol (Round to whole no.)

The dissociation of the dimer into monomers is positive and endothermic as bonds are broken in the reaction. Bond breaking takes in energy.

'''Is the product more or less stable than the isolated monomers?'''

As Dissociation Energy = - (Association Energy), the association of the monomers into dimers is exothermic (association energy is negative) from the above calculation. This implies that the product (the Al2Cl4Br2 dimer) is more stable than the isolated monomers.

The AlCl2Br monomer is two electron short from a full octet. Hence, the Al centre is electron deficient. By forming dimer with lone pair electron donation from the bridging Cl, the electron deficiency at Al is relief with full octet fulfilled, making the system more stable overall.

== MO of Isomer 2==

All the occupied valence MOs of Al2Cl4Br2 (isomer 2) are visualised and 3 MOs ranging from highly bonding to highly antibonding are presented below with their LCAO MO diagrams. The interactions occurring in the MOs are annotated.

'''MO31 - highly bonding MO'''

[[File:Chinglam MO31 annotated.PNG|thumb|center|MO31 - 'Real' MO calculated by Gaussview and the LCAO MO with annotations|850px]]

'''MO42 - weakly anti-bonding MO'''

[[File:ChingLam MO42 annot.PNG|thumb|center|MO42 - 'Real' MO calculated by Gaussview and the LCAO MO with annotations|850px]]

'''MO52- highly anti-bonding MO'''

[[File:ChingLam MO52pic.PNG|thumb|center|MO52 - the 'Real' MO calculated by Gaussview|850px]]

[[File:Screen Shot 2018-05-17 at 7.09.32 PM Ching Lam.png|thumb|center|MO52 - the LCAO MO with annotations|850px]]

== Reference ==

<references>
<ref name="energy">Atkins, P. W., and D. F. Shriver. Shriver and Atkins Inorganic Chemistry. Oxford University Press, 2006.</ref>
</references>

Rep:Mod:01181216201805

2018-05-17T18:19:11Z

Ccl216: /* Dissociation energy of Isomer 2 into 2AlCl2Br */

= Inorganic Computational Lab =

== EX3 Section ==

=== BH3 ===

==== 1. B3LYP/3-21G Calculation Method====

''' Method and Basis Set:''' B3LYP/3-21G

[[File:Chinglam BH3table321.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM BH3OPT 321.LOG|CHINGLAM BH3OPT 321.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000174 0.000450 YES
RMS Force 0.000100 0.000300 YES
Maximum Displacement 0.000674 0.001800 YES
RMS Displacement 0.000397 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> BH3(B3LYP/3-21G)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM BH3OPT 321.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== 2. B3LYP/6-31G(d,p)Calculation Method ====

'''Method and Basis Set:''' B3LYP/6-31G(d,p)

[[File:Chinglam BH3table631.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM BH3OPT 631.LOG|CHINGLAM BH3OPT 631.LOG]]

'''Frequency analysis log file:''' [[Media:CHINGLAM BH3OPT 631 FREQ.LOG|CHINGLAM BH3OPT 631 FREQ.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -4.8294 -1.2074 -0.0054 1.0243 9.1094 9.1890
Low frequencies --- 1162.9789 1213.1709 1213.1736
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> BH3(B3LYP/6-31G(d,p))</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM BH3OPT 631.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

====IR Vibrations====

{|border="1" cellpadding="1" cellspacing="0" align="center"
|+ IR Data of BH3
! Mode !! wavenumber (cm-1 !! Intensity (arbitrary units) !! symmetry !! IR active? !! type
|-
|1 || 1163 || 93 || A2 " ||yes ||out-of-plane bending
|-
|2 || 1213 || 14 ||E' ||very slight ||in-plane bending
|-
|3 || 1213 ||14 ||E' ||very slight ||in-plane bending
|-
|4 || 2582 ||0 ||A1' ||no ||symmetric stretch
|-
|5 || 2716 ||126 ||E' ||Yes ||asymmetric stretch
|-
|6 || 2716 ||126 ||E' ||Yes ||asymmetric stretch
|}

[[File:Chinglam BH3irspectrum.PNG|thumb|center|IR spectrum|800px]]

By the 3N-6 rule, there should be 6 different vibration modes. However, there is only three peaks found in the IR spectrum. Only one peak is observed for the in-plane bending vibration as mode 2 and 3 are degenerated in energy. The same applies to the asymmetric stretch modes (mode 5 and 6), which are also degenerated in energy. There is no change in the dipole moment of the molecule for mode 3 (the symmetrical stretching vibration) and hence it doesn't lead to infrared absorption.

==== MO of BH3 ====

[[File:ChingLam BH3MO 852.png|thumb|center|MO Diagram - LCAOs with the calculated MOs |600px]]

'''Are there any significant differences between the real and LCAO MOs? '''

The real (calculated) MOs are generally more diffused than the LCAO (linear combination of atomic orbitals) MOs, especially for the unoccupied orbitals high in energy (from MO 5 to MO 8 as labelled in the above diagram). Hence, the real MO can look quite different from the LCAO prediction (e.g. MO 6 - the H3 FO is much larger than the LCAO has predicted; MO 8 - the electron density is spread across the whole molecule, unlike the prediction)

'''What does this say about the accuracy and usefulness of qualitative MO theory?'''

The qualitative MO theory are more accurate and useful for occupied MOs with low energy. Above the HOMO (highest occupied molecular orbital), the prediction are less accurate.

=== NH3 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)

[[File:ChingLam NH3 sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM NH3 6313.LOG|CHINGLAM NH3 6313.LOG]]

'''Frequency analysis log file:''' [[Media:CHINGLAM NH3 6313 FREQ.LOG|CHINGLAM NH3 6313 FREQ.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -0.2239 -0.0404 -0.0040 7.1998 7.2613 27.9769
Low frequencies --- 1089.9671 1694.2126 1694.2129
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> NH3 (B3LYP/6-31G(d,p))</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM NH3 6313.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== NH3-BH3 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)

[[File:ChingLam NH3BH3 sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM NH3BH3 OPT3.LOG|CHINGLAM NH3BH3 OPT3.LOG]]

'''Frequency analysis log file:''' [[Media:CHINGLAM NH3BH3 OPT3 FREQ2.LOG|CHINGLAM NH3BH3 OPT3 FREQ2.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000052 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000423 0.001800 YES
RMS Displacement 0.000145 0.001200 YES
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -0.1703 -0.0781 -0.0066 12.6039 12.6146 12.8091
Low frequencies --- 263.1708 632.8934 638.8999
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> NH3-BH3 (B3LYP/6-31G(d,p))</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM NH3BH3 OPT3 FREQ2.mol</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== Association energies: Ammonia-Borane ===

From the above calculation (Method: B3LYP/6-31G(d,p)) :

'''E(NH3)=''' -56.55776862 a.u.

'''E(BH3)= ''' -26.61532363 a.u.

''' E(NH3-BH3)=''' -83.22469020 a.u.

ΔE=E(NH3-BH3)-[E(NH3)+E(BH3)]

'''ΔE=''' (-83.22469020)- [(-56.55776862)+ (-26.61532363)] = -0.05159795 a.u. ≈ -0.05160 a.u. (5 d.p.)

'''ΔE=''' 2625.5 x -0.05159795 ≈ ''' -135 kJ / mol '''

ΔE is negative, implying that the reaction is overall exothermic - the bond forming process is energy releasing. The association energy of the adduct is 135 kJ/mol. The means that the B-N dative bond is quite week relative to the stronger covalent bonds (For reference, some mean bond enthalpies data <ref name="energy" /> are listed as following: C-H 420 kJ/mol, C-C 350 kJ/mol, O-H 463 kJ/mol). However, the enthalpy of B-N dative bond is quite similar to some of the weak covalent bond (O-O 146 kJ/mol, I-I 151 kJ/mol) and much higher than the enthalpy of hydrogen bonding (HO-H -- OH 2 22 kJ/mol).

Overall, B-N dative bond is consider to be weak comparing to covalent bonds, but it is much stronger than H-bonding and van der Waals interactions.

=== BBr3 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam BBr3 sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:Log 10047290 Ching BBr3.log|Log 10047290 Ching BBr3.log]]

'''Frequency analysis log file:''' [[Media:Log 10047294 Ching BBr3 freq.log|Log 10047294 Ching BBr3 freq.log]]

'''DSpace link:''' {{DOI|10042/202401}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-4.027119D-10
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Log 10047290 Ching BBr3.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

== Project Section -- Lewis Acids and Bases - Main Group Halide==

The Isomers of AlBr2Cl4:

[[File:ChingLamisomers Al2Br2Cl4.jpg|thumb|center|The Isomers of AlBr2Cl4|400px]]

=== AlBr2Cl4 (2 Bridging Br Ions) - Isomer 1 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam Al2Br2Cl4bridge sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:ChingLam Al2Br2Cl4 Brbridge.log|ChingLam Al2Br2Cl4 Brbridge.log]]

'''Frequency analysis log file:''' [[Media:ChingLam Al2Br2Cl4 Brbridge freq.log|ChingLam Al2Br2Cl4 Brbridge freq.log]]

'''DSpace link:''' {{DOI|10042/202404}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000029 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000664 0.001800 YES
RMS Displacement 0.000278 0.001200 YES
Predicted change in Energy=-1.390401D-08
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -5.1253 -5.0805 -3.1847 -0.0051 -0.0047 -0.0045
Low frequencies --- 14.8608 63.2610 86.0512
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ChingLam Al2Br2Cl4 Brbridge.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== AlBr2Cl4 (The Isomer with Trans Terminal Br and Bridging Cl Ions) - Isomer 2 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam Al2Br2Cl4trans sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:ChingLam Al2Br2Cl4 Transopt.log|ChingLam Al2Br2Cl4 Transopt.log]]

'''Frequency analysis log file:''' [[Media:ChingLam Al2Br2Cl4 Transopt freq.log|ChingLam Al2Br2Cl4 Transopt freq.log]]

'''DSpace link:''' {{DOI|10042/202406}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.001800 0.001800 YES
RMS Displacement 0.000622 0.001200 YES
Predicted change in Energy=-1.168706D-07
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>

Low frequencies --- -3.5004 -2.4150 0.0007 0.0025 0.0027 0.7437
Low frequencies --- 17.7463 49.0305 72.9456

</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ChingLam Al2Br2Cl4 Transopt.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== Relative Energy of Isomer 1 and 2 ===

'''E(Isomer 1)=''' -2352.40630796 a.u.

'''E(Isomer 2)=''' -2352.41628799 a.u.

Relative Energy = E(Isomer 1)- E(Isomer 2) = (-2352.40630796) - (-2352.41628799) = 0.00998002999 a.u.

'''Relative Energy in kJ/mol =''' 0.00998002999 x 2625.5 = 26 kJ/mol (Round to whole no.)

'''Discuss the relative stability of these conformers with respect to the bridging ions.'''

The above calculations demonstrate that isomer 2 is lower in energy comparing to isomer 1 by 26 kJ/mol. This implies that isomer 2 is more stable than isomer 1. The difference in the stability is due to the difference bridging ions of the conformer. Isomer 2 has two Cl ions as the bridging atoms, while isomer 1 has two bridging Br ions. Cl is in row 3 of the periodic table and Br is in row 4. As Cl and Al are in the same row in the periodic table, their valence orbitals would be similar in size and energy comparing to Br. In the case for isomer 2 in the bridging region of the molecule, there would be better overlaps between the fragment orbitals (FOs) and greater stabilization from smaller FOs energy difference comparing to isomer 1. Apart from the electronic perspectives, Cl ions are smaller than Br ions, which makes the Cl bridging more sterically favorable and contributes to the higher stability.

=== AlCl2Br (Monomer) ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam Almonomer sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:ChingLam AlBrCl2optu.log|ChingLam AlBrCl2optu.log]]

'''Frequency analysis log file:''' [[Media:ChingLam AlBrCl2optu freq.log|ChingLam AlBrCl2optu freq.log]]

'''DSpace link:''' {{DOI|10042/202409}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984435D-08
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>

Low frequencies --- 0.0010 0.0029 0.0037 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ChingLam AlBrCl2optu mol.mol2</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== Dissociation energy of Isomer 2 into 2AlCl2Br ===

2AlCl2Br --> Al2Cl4Br2

From the above calculation (Method: B3LYP/6-31G(d,p)LANL2DZ):

'''E(Al2Cl4Br2, Isomer 2)=''' -2352.41628799 a.u.

'''E(AlCl2Br) =''' -1176.19013679 a.u.

Association Energy = E(Al2Cl4Br2, Isomer 2) - 2E(AlCl2Br)

Dissociation Energy = - (Association Energy)

Dissociation Energy = 2E(AlCl2Br) - E(Al2Cl4Br2, Isomer 2) = 2(-1176.19013679) - (-2352.41628799) = 0.03601441 a. u.

'''Dissociation Energy in kJ/mol =''' 0.03601441 x 2625.5 = 95 kJ/mol (Round to whole no.)

The dissociation of the dimer into monomers is positive and endothermic as bonds are broken in the reaction. Bond breaking takes in energy.

'''Is the product more or less stable than the isolated monomers?'''

As Dissociation Energy = - (Association Energy), the association of the monomers into dimers is exothermic (association energy is negative) from the above calculation. This implies that the product (the Al2Cl4Br2 dimer) is more stable than the isolated monomers.

The AlCl2Br monomer is two electron short from a full octet. Hence, the Al centre is electron deficient. By forming dimer with lone pair electron donation from the bridging Cl, the electron deficiency at Al is relief with full octet fulfilled, making the system more stable overall.

== MO of Isomer 2==

The MO of

[[File:Chinglam MO31 annotated.PNG|thumb|center|MO31 - 'Real' MO calculated by Gaussview and the LCAO MO with annotations|850px]]

[[File:ChingLam MO42 annot.PNG|thumb|center|MO42 - 'Real' MO calculated by Gaussview and the LCAO MO with annotations|850px]]

[[File:ChingLam MO52pic.PNG|thumb|center|MO52 - the 'Real' MO calculated by Gaussview|850px]]

[[File:Screen Shot 2018-05-17 at 7.09.32 PM Ching Lam.png|thumb|center|MO52 - the LCAO MO with annotations|850px]]

== Reference ==

<references>
<ref name="energy">Atkins, P. W., and D. F. Shriver. Shriver and Atkins Inorganic Chemistry. Oxford University Press, 2006.</ref>
</references>

Rep:Mod:01181216201805

2018-05-17T18:18:56Z

Ccl216: /* MO of Isomer 2 */

= Inorganic Computational Lab =

== EX3 Section ==

=== BH3 ===

==== 1. B3LYP/3-21G Calculation Method====

''' Method and Basis Set:''' B3LYP/3-21G

[[File:Chinglam BH3table321.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM BH3OPT 321.LOG|CHINGLAM BH3OPT 321.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000174 0.000450 YES
RMS Force 0.000100 0.000300 YES
Maximum Displacement 0.000674 0.001800 YES
RMS Displacement 0.000397 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> BH3(B3LYP/3-21G)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM BH3OPT 321.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== 2. B3LYP/6-31G(d,p)Calculation Method ====

'''Method and Basis Set:''' B3LYP/6-31G(d,p)

[[File:Chinglam BH3table631.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM BH3OPT 631.LOG|CHINGLAM BH3OPT 631.LOG]]

'''Frequency analysis log file:''' [[Media:CHINGLAM BH3OPT 631 FREQ.LOG|CHINGLAM BH3OPT 631 FREQ.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -4.8294 -1.2074 -0.0054 1.0243 9.1094 9.1890
Low frequencies --- 1162.9789 1213.1709 1213.1736
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> BH3(B3LYP/6-31G(d,p))</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM BH3OPT 631.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

====IR Vibrations====

{|border="1" cellpadding="1" cellspacing="0" align="center"
|+ IR Data of BH3
! Mode !! wavenumber (cm-1 !! Intensity (arbitrary units) !! symmetry !! IR active? !! type
|-
|1 || 1163 || 93 || A2 " ||yes ||out-of-plane bending
|-
|2 || 1213 || 14 ||E' ||very slight ||in-plane bending
|-
|3 || 1213 ||14 ||E' ||very slight ||in-plane bending
|-
|4 || 2582 ||0 ||A1' ||no ||symmetric stretch
|-
|5 || 2716 ||126 ||E' ||Yes ||asymmetric stretch
|-
|6 || 2716 ||126 ||E' ||Yes ||asymmetric stretch
|}

[[File:Chinglam BH3irspectrum.PNG|thumb|center|IR spectrum|800px]]

By the 3N-6 rule, there should be 6 different vibration modes. However, there is only three peaks found in the IR spectrum. Only one peak is observed for the in-plane bending vibration as mode 2 and 3 are degenerated in energy. The same applies to the asymmetric stretch modes (mode 5 and 6), which are also degenerated in energy. There is no change in the dipole moment of the molecule for mode 3 (the symmetrical stretching vibration) and hence it doesn't lead to infrared absorption.

==== MO of BH3 ====

[[File:ChingLam BH3MO 852.png|thumb|center|MO Diagram - LCAOs with the calculated MOs |600px]]

'''Are there any significant differences between the real and LCAO MOs? '''

The real (calculated) MOs are generally more diffused than the LCAO (linear combination of atomic orbitals) MOs, especially for the unoccupied orbitals high in energy (from MO 5 to MO 8 as labelled in the above diagram). Hence, the real MO can look quite different from the LCAO prediction (e.g. MO 6 - the H3 FO is much larger than the LCAO has predicted; MO 8 - the electron density is spread across the whole molecule, unlike the prediction)

'''What does this say about the accuracy and usefulness of qualitative MO theory?'''

The qualitative MO theory are more accurate and useful for occupied MOs with low energy. Above the HOMO (highest occupied molecular orbital), the prediction are less accurate.

=== NH3 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)

[[File:ChingLam NH3 sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM NH3 6313.LOG|CHINGLAM NH3 6313.LOG]]

'''Frequency analysis log file:''' [[Media:CHINGLAM NH3 6313 FREQ.LOG|CHINGLAM NH3 6313 FREQ.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -0.2239 -0.0404 -0.0040 7.1998 7.2613 27.9769
Low frequencies --- 1089.9671 1694.2126 1694.2129
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> NH3 (B3LYP/6-31G(d,p))</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM NH3 6313.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== NH3-BH3 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)

[[File:ChingLam NH3BH3 sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM NH3BH3 OPT3.LOG|CHINGLAM NH3BH3 OPT3.LOG]]

'''Frequency analysis log file:''' [[Media:CHINGLAM NH3BH3 OPT3 FREQ2.LOG|CHINGLAM NH3BH3 OPT3 FREQ2.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000052 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000423 0.001800 YES
RMS Displacement 0.000145 0.001200 YES
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -0.1703 -0.0781 -0.0066 12.6039 12.6146 12.8091
Low frequencies --- 263.1708 632.8934 638.8999
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> NH3-BH3 (B3LYP/6-31G(d,p))</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM NH3BH3 OPT3 FREQ2.mol</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== Association energies: Ammonia-Borane ===

From the above calculation (Method: B3LYP/6-31G(d,p)) :

'''E(NH3)=''' -56.55776862 a.u.

'''E(BH3)= ''' -26.61532363 a.u.

''' E(NH3-BH3)=''' -83.22469020 a.u.

ΔE=E(NH3-BH3)-[E(NH3)+E(BH3)]

'''ΔE=''' (-83.22469020)- [(-56.55776862)+ (-26.61532363)] = -0.05159795 a.u. ≈ -0.05160 a.u. (5 d.p.)

'''ΔE=''' 2625.5 x -0.05159795 ≈ ''' -135 kJ / mol '''

ΔE is negative, implying that the reaction is overall exothermic - the bond forming process is energy releasing. The association energy of the adduct is 135 kJ/mol. The means that the B-N dative bond is quite week relative to the stronger covalent bonds (For reference, some mean bond enthalpies data <ref name="energy" /> are listed as following: C-H 420 kJ/mol, C-C 350 kJ/mol, O-H 463 kJ/mol). However, the enthalpy of B-N dative bond is quite similar to some of the weak covalent bond (O-O 146 kJ/mol, I-I 151 kJ/mol) and much higher than the enthalpy of hydrogen bonding (HO-H -- OH 2 22 kJ/mol).

Overall, B-N dative bond is consider to be weak comparing to covalent bonds, but it is much stronger than H-bonding and van der Waals interactions.

=== BBr3 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam BBr3 sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:Log 10047290 Ching BBr3.log|Log 10047290 Ching BBr3.log]]

'''Frequency analysis log file:''' [[Media:Log 10047294 Ching BBr3 freq.log|Log 10047294 Ching BBr3 freq.log]]

'''DSpace link:''' {{DOI|10042/202401}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-4.027119D-10
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Log 10047290 Ching BBr3.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

== Project Section -- Lewis Acids and Bases - Main Group Halide==

The Isomers of AlBr2Cl4:

[[File:ChingLamisomers Al2Br2Cl4.jpg|thumb|center|The Isomers of AlBr2Cl4|400px]]

=== AlBr2Cl4 (2 Bridging Br Ions) - Isomer 1 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam Al2Br2Cl4bridge sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:ChingLam Al2Br2Cl4 Brbridge.log|ChingLam Al2Br2Cl4 Brbridge.log]]

'''Frequency analysis log file:''' [[Media:ChingLam Al2Br2Cl4 Brbridge freq.log|ChingLam Al2Br2Cl4 Brbridge freq.log]]

'''DSpace link:''' {{DOI|10042/202404}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000029 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000664 0.001800 YES
RMS Displacement 0.000278 0.001200 YES
Predicted change in Energy=-1.390401D-08
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -5.1253 -5.0805 -3.1847 -0.0051 -0.0047 -0.0045
Low frequencies --- 14.8608 63.2610 86.0512
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ChingLam Al2Br2Cl4 Brbridge.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== AlBr2Cl4 (The Isomer with Trans Terminal Br and Bridging Cl Ions) - Isomer 2 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam Al2Br2Cl4trans sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:ChingLam Al2Br2Cl4 Transopt.log|ChingLam Al2Br2Cl4 Transopt.log]]

'''Frequency analysis log file:''' [[Media:ChingLam Al2Br2Cl4 Transopt freq.log|ChingLam Al2Br2Cl4 Transopt freq.log]]

'''DSpace link:''' {{DOI|10042/202406}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.001800 0.001800 YES
RMS Displacement 0.000622 0.001200 YES
Predicted change in Energy=-1.168706D-07
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>

Low frequencies --- -3.5004 -2.4150 0.0007 0.0025 0.0027 0.7437
Low frequencies --- 17.7463 49.0305 72.9456

</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ChingLam Al2Br2Cl4 Transopt.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== Relative Energy of Isomer 1 and 2 ===

'''E(Isomer 1)=''' -2352.40630796 a.u.

'''E(Isomer 2)=''' -2352.41628799 a.u.

Relative Energy = E(Isomer 1)- E(Isomer 2) = (-2352.40630796) - (-2352.41628799) = 0.00998002999 a.u.

'''Relative Energy in kJ/mol =''' 0.00998002999 x 2625.5 = 26 kJ/mol (Round to whole no.)

'''Discuss the relative stability of these conformers with respect to the bridging ions.'''

The above calculations demonstrate that isomer 2 is lower in energy comparing to isomer 1 by 26 kJ/mol. This implies that isomer 2 is more stable than isomer 1. The difference in the stability is due to the difference bridging ions of the conformer. Isomer 2 has two Cl ions as the bridging atoms, while isomer 1 has two bridging Br ions. Cl is in row 3 of the periodic table and Br is in row 4. As Cl and Al are in the same row in the periodic table, their valence orbitals would be similar in size and energy comparing to Br. In the case for isomer 2 in the bridging region of the molecule, there would be better overlaps between the fragment orbitals (FOs) and greater stabilization from smaller FOs energy difference comparing to isomer 1. Apart from the electronic perspectives, Cl ions are smaller than Br ions, which makes the Cl bridging more sterically favorable and contributes to the higher stability.

=== AlCl2Br (Monomer) ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam Almonomer sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:ChingLam AlBrCl2optu.log|ChingLam AlBrCl2optu.log]]

'''Frequency analysis log file:''' [[Media:ChingLam AlBrCl2optu freq.log|ChingLam AlBrCl2optu freq.log]]

'''DSpace link:''' {{DOI|10042/202409}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984435D-08
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>

Low frequencies --- 0.0010 0.0029 0.0037 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ChingLam AlBrCl2optu mol.mol2</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== Dissociation energy of Isomer 2 into 2AlCl2Br ===

2AlCl2Br --> Al2Cl4Br2

From the above calculation (Method: B3LYP/6-31G(d,p)LANL2DZ):

'''E(Al2Cl4Br2, Isomer 2)=''' -2352.41628799 a.u.

'''E(AlCl2Br) =''' -1176.19013679 a.u.

Association Energy = E(Al2Cl4Br2, Isomer 2) - 2E(AlCl2Br)

Dissociation Energy = - (Association Energy)

Dissociation Energy = 2E(AlCl2Br) - E(Al2Cl4Br2, Isomer 2) = 2(-1176.19013679) - (-2352.41628799) = 0.03601441 a. u.

'''Dissociation Energy in kJ/mol =''' 0.03601441 x 2625.5 = 95 kJ/mol (Round to whole no.)

The dissociation of the dimer into monomers is positive and endothermic as bonds are broken in the reaction. Bond breaking takes in energy.

'''Is the product more or less stable than the isolated monomers?'''

As Dissociation Energy = - (Association Energy), the association of the monomers into dimers is exothermic (association energy is negative) from the above calculation. This implies that the product (the Al2Cl4Br2 dimer) is more stable than the isolated monomers.

The AlCl2Br monomer is two electron short from a full octet. Hence, the Al centre is electron deficient. By forming dimer with lone pair electron donation from the bridging Cl, the electron deficiency at Al is relief with full octet fulfilled, making the system more stable overall.

== MO of Isomer 2==

The MO of

[[File:Chinglam MO31 annotated.PNG|thumb|center|MO31 - 'Real' MO calculated by Gaussview and the LCAO MO with annotations|850px]]

[[File:ChingLam MO42 annot.PNG|thumb|center|MO42 - 'Real' MO calculated by Gaussview and the LCAO MO with annotations|850px]]

[[File:ChingLam MO52pic.PNG|thumb|center|MO52 - the 'Real' MO calculated by Gaussview|850px]]

[[File:Screen Shot 2018-05-17 at 7.09.32 PM Ching Lam.png|thumb|center|MO52 - the LCAO MO with annotations|850px]]

== Reference ==

<references>
<ref name="energy">Atkins, P. W., and D. F. Shriver. Shriver and Atkins Inorganic Chemistry. Oxford University Press, 2006.</ref>
</references>

2018-05-17T16:06:11Z

File:ChingLam AlBrCl2optu mol.mol2

2018-05-17T11:39:27Z

Ccl216:

Rep:Mod:01181216201805

2018-05-16T14:13:06Z

Ccl216: /* Dissociation energy of Isomer 2 into 2AlCl2Br */

= Inorganic Computational Lab =

== EX3 Section ==

=== BH3 ===

==== 1. B3LYP/3-21G Calculation Method====

''' Method and Basis Set:''' B3LYP/3-21G

[[File:Chinglam BH3table321.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM BH3OPT 321.LOG|CHINGLAM BH3OPT 321.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000174 0.000450 YES
RMS Force 0.000100 0.000300 YES
Maximum Displacement 0.000674 0.001800 YES
RMS Displacement 0.000397 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> BH3(B3LYP/3-21G)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM BH3OPT 321.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== 2. B3LYP/6-31G(d,p)Calculation Method ====

'''Method and Basis Set:''' B3LYP/6-31G(d,p)

[[File:Chinglam BH3table631.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM BH3OPT 631.LOG|CHINGLAM BH3OPT 631.LOG]]

'''Frequency analysis log file:''' [[Media:CHINGLAM BH3OPT 631 FREQ.LOG|CHINGLAM BH3OPT 631 FREQ.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -4.8294 -1.2074 -0.0054 1.0243 9.1094 9.1890
Low frequencies --- 1162.9789 1213.1709 1213.1736
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> BH3(B3LYP/6-31G(d,p))</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM BH3OPT 631.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

====IR Vibrations====

{|border="1" cellpadding="1" cellspacing="0" align="center"
|+ IR Data of BH3
! Mode !! wavenumber (cm-1 !! Intensity (arbitrary units) !! symmetry !! IR active? !! type
|-
|1 || 1163 || 93 || A2 " ||yes ||out-of-plane bending
|-
|2 || 1213 || 14 ||E' ||very slight ||in-plane bending
|-
|3 || 1213 ||14 ||E' ||very slight ||in-plane bending
|-
|4 || 2582 ||0 ||A1' ||no ||symmetric stretch
|-
|5 || 2716 ||126 ||E' ||Yes ||asymmetric stretch
|-
|6 || 2716 ||126 ||E' ||Yes ||asymmetric stretch
|}

[[File:Chinglam BH3irspectrum.PNG|thumb|center|IR spectrum|800px]]

By the 3N-6 rule, there should be 6 different vibration modes. However, there is only three peaks found in the IR spectrum. Only one peak is observed for the in-plane bending vibration as mode 2 and 3 are degenerated in energy. The same applies to the asymmetric stretch modes (mode 5 and 6), which are also degenerated in energy. There is no change in the dipole moment of the molecule for mode 3 (the symmetrical stretching vibration) and hence it doesn't lead to infrared absorption.

==== MO of BH3 ====

[[File:ChingLam BH3MO 852.png|thumb|center|MO Diagram - LCAOs with the calculated MOs |600px]]

'''Are there any significant differences between the real and LCAO MOs? '''

The real (calculated) MOs are generally more diffused than the LCAO (linear combination of atomic orbitals) MOs, especially for the unoccupied orbitals high in energy (from MO 5 to MO 8 as labelled in the above diagram). Hence, the real MO can look quite different from the LCAO prediction (e.g. MO 6 - the H3 FO is much larger than the LCAO has predicted; MO 8 - the electron density is spread across the whole molecule, unlike the prediction)

'''What does this say about the accuracy and usefulness of qualitative MO theory?'''

The qualitative MO theory are more accurate and useful for occupied MOs with low energy. Above the HOMO (highest occupied molecular orbital), the prediction are less accurate.

=== NH3 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)

[[File:ChingLam NH3 sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM NH3 6313.LOG|CHINGLAM NH3 6313.LOG]]

'''Frequency analysis log file:''' [[Media:CHINGLAM NH3 6313 FREQ.LOG|CHINGLAM NH3 6313 FREQ.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -0.2239 -0.0404 -0.0040 7.1998 7.2613 27.9769
Low frequencies --- 1089.9671 1694.2126 1694.2129
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> NH3 (B3LYP/6-31G(d,p))</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM NH3 6313.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== NH3-BH3 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)

[[File:ChingLam NH3BH3 sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM NH3BH3 OPT3.LOG|CHINGLAM NH3BH3 OPT3.LOG]]

'''Frequency analysis log file:''' [[Media:CHINGLAM NH3BH3 OPT3 FREQ2.LOG|CHINGLAM NH3BH3 OPT3 FREQ2.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000052 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000423 0.001800 YES
RMS Displacement 0.000145 0.001200 YES
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -0.1703 -0.0781 -0.0066 12.6039 12.6146 12.8091
Low frequencies --- 263.1708 632.8934 638.8999
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> NH3-BH3 (B3LYP/6-31G(d,p))</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM NH3BH3 OPT3 FREQ2.mol</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== Association energies: Ammonia-Borane ===

From the above calculation (Method: B3LYP/6-31G(d,p)) :

'''E(NH3)=''' -56.55776862 a.u.

'''E(BH3)= ''' -26.61532363 a.u.

''' E(NH3-BH3)=''' -83.22469020 a.u.

ΔE=E(NH3-BH3)-[E(NH3)+E(BH3)]

'''ΔE=''' (-83.22469020)- [(-56.55776862)+ (-26.61532363)] = -0.05159795 a.u. ≈ -0.05160 a.u. (5 d.p.)

'''ΔE=''' 2625.5 x -0.05159795 ≈ ''' -135 kJ / mol '''

ΔE is negative, implying that the reaction is overall exothermic - the bond forming process is energy releasing. The association energy of the adduct is 135 kJ/mol. The means that the B-N dative bond is quite week relative to the stronger covalent bonds (For reference, some mean bond enthalpies data <ref name="energy" /> are listed as following: C-H 420 kJ/mol, C-C 350 kJ/mol, O-H 463 kJ/mol). However, the enthalpy of B-N dative bond is quite similar to some of the weak covalent bond (O-O 146 kJ/mol, I-I 151 kJ/mol) and much higher than the enthalpy of hydrogen bonding (HO-H -- OH 2 22 kJ/mol).

Overall, B-N dative bond is consider to be weak comparing to covalent bonds, but it is much stronger than H-bonding and van der Waals interactions.

=== BBr3 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam BBr3 sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:Log 10047290 Ching BBr3.log|Log 10047290 Ching BBr3.log]]

'''Frequency analysis log file:''' [[Media:Log 10047294 Ching BBr3 freq.log|Log 10047294 Ching BBr3 freq.log]]

'''DSpace link:''' {{DOI|10042/202401}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-4.027119D-10
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Log 10047290 Ching BBr3.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

== Project Section -- Lewis Acids and Bases - Main Group Halide==

The Isomers of AlBr2Cl4:

[[File:ChingLamisomers Al2Br2Cl4.jpg|thumb|center|The Isomers of AlBr2Cl4|400px]]

=== AlBr2Cl4 (2 Bridging Br Ions) - Isomer 1 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam Al2Br2Cl4bridge sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:ChingLam Al2Br2Cl4 Brbridge.log|ChingLam Al2Br2Cl4 Brbridge.log]]

'''Frequency analysis log file:''' [[Media:ChingLam Al2Br2Cl4 Brbridge freq.log|ChingLam Al2Br2Cl4 Brbridge freq.log]]

'''DSpace link:''' {{DOI|10042/202404}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000029 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000664 0.001800 YES
RMS Displacement 0.000278 0.001200 YES
Predicted change in Energy=-1.390401D-08
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -5.1253 -5.0805 -3.1847 -0.0051 -0.0047 -0.0045
Low frequencies --- 14.8608 63.2610 86.0512
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ChingLam Al2Br2Cl4 Brbridge.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== AlBr2Cl4 (The Isomer with Trans Terminal Br and Bridging Cl Ions) - Isomer 2 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam Al2Br2Cl4trans sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:ChingLam Al2Br2Cl4 Transopt.log|ChingLam Al2Br2Cl4 Transopt.log]]

'''Frequency analysis log file:''' [[Media:ChingLam Al2Br2Cl4 Transopt freq.log|ChingLam Al2Br2Cl4 Transopt freq.log]]

'''DSpace link:''' {{DOI|10042/202406}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.001800 0.001800 YES
RMS Displacement 0.000622 0.001200 YES
Predicted change in Energy=-1.168706D-07
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>

Low frequencies --- -3.5004 -2.4150 0.0007 0.0025 0.0027 0.7437
Low frequencies --- 17.7463 49.0305 72.9456

</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ChingLam Al2Br2Cl4 Transopt.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== Relative Energy of Isomer 1 and 2 ===

'''E(Isomer 1)=''' -2352.40630796 a.u.

'''E(Isomer 2)=''' -2352.41628799 a.u.

Relative Energy = E(Isomer 1)- E(Isomer 2) = (-2352.40630796) - (-2352.41628799) = 0.00998002999 a.u.

'''Relative Energy in kJ/mol =''' 0.00998002999 x 2625.5 = 26 kJ/mol (Round to whole no.)

'''Discuss the relative stability of these conformers with respect to the bridging ions.'''

The above calculations demonstrate that isomer 2 is lower in energy comparing to isomer 1 by 26 kJ/mol. This implies that isomer 2 is more stable than isomer 1. The difference in the stability is due to the difference bridging ions of the conformer. Isomer 2 has two Cl ions as the bridging atoms, while isomer 1 has two bridging Br ions. Cl is in row 3 of the periodic table and Br is in row 4. As Cl and Al are in the same row in the periodic table, their valence orbitals would be similar in size and energy comparing to Br. In the case for isomer 2 in the bridging region of the molecule, there would be better overlaps between the fragment orbitals (FOs) and greater stabilization from smaller FOs energy difference comparing to isomer 1. Apart from the electronic perspectives, Cl ions are smaller than Br ions, which makes the Cl bridging more sterically favorable and contributes to the higher stability.

=== AlCl2Br (Monomer) ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam Almonomer sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:ChingLam AlBrCl2optu.log|ChingLam AlBrCl2optu.log]]

'''Frequency analysis log file:''' [[Media:ChingLam AlBrCl2optu freq.log|ChingLam AlBrCl2optu freq.log]]

'''DSpace link:''' {{DOI|10042/202409}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984435D-08
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>

Low frequencies --- 0.0010 0.0029 0.0037 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ChingLam AlBrCl2optu.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== Dissociation energy of Isomer 2 into 2AlCl2Br ===

2AlCl2Br --> Al2Cl4Br2

From the above calculation (Method: B3LYP/6-31G(d,p)LANL2DZ):

'''E(Al2Cl4Br2, Isomer 2)=''' -2352.41628799 a.u.

'''E(AlCl2Br) =''' -1176.19013679 a.u.

Association Energy = E(Al2Cl4Br2, Isomer 2) - 2E(AlCl2Br)

Dissociation Energy = - (Association Energy)

Dissociation Energy = 2E(AlCl2Br) - E(Al2Cl4Br2, Isomer 2) = 2(-1176.19013679) - (-2352.41628799) = 0.03601441 a. u.

'''Dissociation Energy in kJ/mol =''' 0.03601441 x 2625.5 = 95 kJ/mol (Round to whole no.)

The dissociation of the dimer into monomers is positive and endothermic as bonds are broken in the reaction. Bond breaking takes in energy.

'''Is the product more or less stable than the isolated monomers?'''

As Dissociation Energy = - (Association Energy), the association of the monomers into dimers is exothermic (association energy is negative) from the above calculation. This implies that the product (the Al2Cl4Br2 dimer) is more stable than the isolated monomers.

The AlCl2Br monomer is two electron short from a full octet. Hence, the Al centre is electron deficient. By forming dimer with lone pair electron donation from the bridging Cl, the electron deficiency at Al is relief with full octet fulfilled, making the system more stable overall.

== Reference ==

<ref name="energy">Atkins, P. W., and D. F. Shriver. Shriver and Atkins Inorganic Chemistry. Oxford University Press, 2006.</ref>

Rep:Mod:01181216201805

2018-05-16T13:20:57Z

Ccl216: /* Relative Energy of Isomer 1 and 2 */

= Inorganic Computational Lab =

== EX3 Section ==

=== BH3 ===

==== 1. B3LYP/3-21G Calculation Method====

''' Method and Basis Set:''' B3LYP/3-21G

[[File:Chinglam BH3table321.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM BH3OPT 321.LOG|CHINGLAM BH3OPT 321.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000174 0.000450 YES
RMS Force 0.000100 0.000300 YES
Maximum Displacement 0.000674 0.001800 YES
RMS Displacement 0.000397 0.001200 YES
</pre>

<jmol><jmolApplet>
<title> BH3(B3LYP/3-21G)</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM BH3OPT 321.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

==== 2. B3LYP/6-31G(d,p)Calculation Method ====

'''Method and Basis Set:''' B3LYP/6-31G(d,p)

[[File:Chinglam BH3table631.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM BH3OPT 631.LOG|CHINGLAM BH3OPT 631.LOG]]

'''Frequency analysis log file:''' [[Media:CHINGLAM BH3OPT 631 FREQ.LOG|CHINGLAM BH3OPT 631 FREQ.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000041 0.001800 YES
RMS Displacement 0.000027 0.001200 YES
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -4.8294 -1.2074 -0.0054 1.0243 9.1094 9.1890
Low frequencies --- 1162.9789 1213.1709 1213.1736
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> BH3(B3LYP/6-31G(d,p))</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM BH3OPT 631.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

====IR Vibrations====

{|border="1" cellpadding="1" cellspacing="0" align="center"
|+ IR Data of BH3
! Mode !! wavenumber (cm-1 !! Intensity (arbitrary units) !! symmetry !! IR active? !! type
|-
|1 || 1163 || 93 || A2 " ||yes ||out-of-plane bending
|-
|2 || 1213 || 14 ||E' ||very slight ||in-plane bending
|-
|3 || 1213 ||14 ||E' ||very slight ||in-plane bending
|-
|4 || 2582 ||0 ||A1' ||no ||symmetric stretch
|-
|5 || 2716 ||126 ||E' ||Yes ||asymmetric stretch
|-
|6 || 2716 ||126 ||E' ||Yes ||asymmetric stretch
|}

[[File:Chinglam BH3irspectrum.PNG|thumb|center|IR spectrum|800px]]

By the 3N-6 rule, there should be 6 different vibration modes. However, there is only three peaks found in the IR spectrum. Only one peak is observed for the in-plane bending vibration as mode 2 and 3 are degenerated in energy. The same applies to the asymmetric stretch modes (mode 5 and 6), which are also degenerated in energy. There is no change in the dipole moment of the molecule for mode 3 (the symmetrical stretching vibration) and hence it doesn't lead to infrared absorption.

==== MO of BH3 ====

[[File:ChingLam BH3MO 852.png|thumb|center|MO Diagram - LCAOs with the calculated MOs |600px]]

'''Are there any significant differences between the real and LCAO MOs? '''

The real (calculated) MOs are generally more diffused than the LCAO (linear combination of atomic orbitals) MOs, especially for the unoccupied orbitals high in energy (from MO 5 to MO 8 as labelled in the above diagram). Hence, the real MO can look quite different from the LCAO prediction (e.g. MO 6 - the H3 FO is much larger than the LCAO has predicted; MO 8 - the electron density is spread across the whole molecule, unlike the prediction)

'''What does this say about the accuracy and usefulness of qualitative MO theory?'''

The qualitative MO theory are more accurate and useful for occupied MOs with low energy. Above the HOMO (highest occupied molecular orbital), the prediction are less accurate.

=== NH3 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)

[[File:ChingLam NH3 sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM NH3 6313.LOG|CHINGLAM NH3 6313.LOG]]

'''Frequency analysis log file:''' [[Media:CHINGLAM NH3 6313 FREQ.LOG|CHINGLAM NH3 6313 FREQ.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000017 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000028 0.001200 YES
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -0.2239 -0.0404 -0.0040 7.1998 7.2613 27.9769
Low frequencies --- 1089.9671 1694.2126 1694.2129
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> NH3 (B3LYP/6-31G(d,p))</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM NH3 6313.LOG</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== NH3-BH3 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)

[[File:ChingLam NH3BH3 sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:CHINGLAM NH3BH3 OPT3.LOG|CHINGLAM NH3BH3 OPT3.LOG]]

'''Frequency analysis log file:''' [[Media:CHINGLAM NH3BH3 OPT3 FREQ2.LOG|CHINGLAM NH3BH3 OPT3 FREQ2.LOG]]

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000052 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000423 0.001800 YES
RMS Displacement 0.000145 0.001200 YES
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -0.1703 -0.0781 -0.0066 12.6039 12.6146 12.8091
Low frequencies --- 263.1708 632.8934 638.8999
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> NH3-BH3 (B3LYP/6-31G(d,p))</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>CHINGLAM NH3BH3 OPT3 FREQ2.mol</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== Association energies: Ammonia-Borane ===

From the above calculation (Method: B3LYP/6-31G(d,p)) :

'''E(NH3)=''' -56.55776862 a.u.

'''E(BH3)= ''' -26.61532363 a.u.

''' E(NH3-BH3)=''' -83.22469020 a.u.

ΔE=E(NH3-BH3)-[E(NH3)+E(BH3)]

'''ΔE=''' (-83.22469020)- [(-56.55776862)+ (-26.61532363)] = -0.05159795 a.u. ≈ -0.05160 a.u. (5 d.p.)

'''ΔE=''' 2625.5 x -0.05159795 ≈ ''' -135 kJ / mol '''

ΔE is negative, implying that the reaction is overall exothermic - the bond forming process is energy releasing. The association energy of the adduct is 135 kJ/mol. The means that the B-N dative bond is quite week relative to the stronger covalent bonds (For reference, some mean bond enthalpies data <ref name="energy" /> are listed as following: C-H 420 kJ/mol, C-C 350 kJ/mol, O-H 463 kJ/mol). However, the enthalpy of B-N dative bond is quite similar to some of the weak covalent bond (O-O 146 kJ/mol, I-I 151 kJ/mol) and much higher than the enthalpy of hydrogen bonding (HO-H -- OH 2 22 kJ/mol).

Overall, B-N dative bond is consider to be weak comparing to covalent bonds, but it is much stronger than H-bonding and van der Waals interactions.

=== BBr3 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam BBr3 sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:Log 10047290 Ching BBr3.log|Log 10047290 Ching BBr3.log]]

'''Frequency analysis log file:''' [[Media:Log 10047294 Ching BBr3 freq.log|Log 10047294 Ching BBr3 freq.log]]

'''DSpace link:''' {{DOI|10042/202401}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES
Predicted change in Energy=-4.027119D-10
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -0.0137 -0.0064 -0.0046 2.4315 2.4315 4.8421
Low frequencies --- 155.9631 155.9651 267.7052
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Log 10047290 Ching BBr3.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

== Project Section -- Lewis Acids and Bases - Main Group Halide==

The Isomers of AlBr2Cl4:

[[File:ChingLamisomers Al2Br2Cl4.jpg|thumb|center|The Isomers of AlBr2Cl4|400px]]

=== AlBr2Cl4 (2 Bridging Br Ions) - Isomer 1 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam Al2Br2Cl4bridge sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:ChingLam Al2Br2Cl4 Brbridge.log|ChingLam Al2Br2Cl4 Brbridge.log]]

'''Frequency analysis log file:''' [[Media:ChingLam Al2Br2Cl4 Brbridge freq.log|ChingLam Al2Br2Cl4 Brbridge freq.log]]

'''DSpace link:''' {{DOI|10042/202404}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000029 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000664 0.001800 YES
RMS Displacement 0.000278 0.001200 YES
Predicted change in Energy=-1.390401D-08
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>
Low frequencies --- -5.1253 -5.0805 -3.1847 -0.0051 -0.0047 -0.0045
Low frequencies --- 14.8608 63.2610 86.0512
</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ChingLam Al2Br2Cl4 Brbridge.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== AlBr2Cl4 (The Isomer with Trans Terminal Br and Bridging Cl Ions) - Isomer 2 ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam Al2Br2Cl4trans sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:ChingLam Al2Br2Cl4 Transopt.log|ChingLam Al2Br2Cl4 Transopt.log]]

'''Frequency analysis log file:''' [[Media:ChingLam Al2Br2Cl4 Transopt freq.log|ChingLam Al2Br2Cl4 Transopt freq.log]]

'''DSpace link:''' {{DOI|10042/202406}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000084 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.001800 0.001800 YES
RMS Displacement 0.000622 0.001200 YES
Predicted change in Energy=-1.168706D-07
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>

Low frequencies --- -3.5004 -2.4150 0.0007 0.0025 0.0027 0.7437
Low frequencies --- 17.7463 49.0305 72.9456

</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ChingLam Al2Br2Cl4 Transopt.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== Relative Energy of Isomer 1 and 2 ===

'''E(Isomer 1)=''' -2352.40630796 a.u.

'''E(Isomer 2)=''' -2352.41628799 a.u.

Relative Energy = E(Isomer 1)- E(Isomer 2) = (-2352.40630796) - (-2352.41628799) = 0.00998002999 a.u.

'''Relative Energy in kJ/mol =''' 0.00998002999 x 2625.5 = 26 kJ/mol (Round to whole no.)

'''Discuss the relative stability of these conformers with respect to the bridging ions.'''

The above calculations demonstrate that isomer 2 is lower in energy comparing to isomer 1 by 26 kJ/mol. This implies that isomer 2 is more stable than isomer 1. The difference in the stability is due to the difference bridging ions of the conformer. Isomer 2 has two Cl ions as the bridging atoms, while isomer 1 has two bridging Br ions. Cl is in row 3 of the periodic table and Br is in row 4. As Cl and Al are in the same row in the periodic table, their valence orbitals would be similar in size and energy comparing to Br. In the case for isomer 2 in the bridging region of the molecule, there would be better overlaps between the fragment orbitals (FOs) and greater stabilization from smaller FOs energy difference comparing to isomer 1. Apart from the electronic perspectives, Cl ions are smaller than Br ions, which makes the Cl bridging more sterically favorable and contributes to the higher stability.

=== AlCl2Br (Monomer) ===

'''Method and Basis Set:''' B3LYP/6-31G(d,p)LANL2DZ

[[File:ChingLam Almonomer sumtable.PNG|thumb|center|Image of the Summary Table Produced by Gaussview|400px]]

'''Optimization log file:''' [[Media:ChingLam AlBrCl2optu.log|ChingLam AlBrCl2optu.log]]

'''Frequency analysis log file:''' [[Media:ChingLam AlBrCl2optu freq.log|ChingLam AlBrCl2optu freq.log]]

'''DSpace link:''' {{DOI|10042/202409}}

''' Item Table '''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000681 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984435D-08
Optimization completed.
</pre>

'''Low Frequencies Lines from the Frequency Analysis Log File '''

<pre>

Low frequencies --- 0.0010 0.0029 0.0037 1.3569 3.6367 4.2604
Low frequencies --- 120.5042 133.9178 185.8950

</pre>

'''Jmol Image'''
<jmol><jmolApplet>
<title> B3LYP/6-31G(d,p)LANL2DZ </title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ChingLam AlBrCl2optu.log</uploadedFileContents>
<script>frame 1.16</script>
</jmolApplet></jmol>

=== Dissociation energy of Isomer 2 into 2AlCl2Br ===

2AlCl2Br --> Al2Cl4Br2

From the above calculation (Method: B3LYP/6-31G(d,p)LANL2DZ):

E(Al2Cl4Br2, Isomer 2)= -2352.41628799 a.u.

E(AlCl2Br) = -1176.19013679 a.u.

Association Energy = E(Al2Cl4Br2, Isomer 2) - 2E(AlCl2Br)

Dissociation Energy = - (Association Energy)

Dissociation Energy = 2E(AlCl2Br) - E(Al2Cl4Br2, Isomer 2) = 2(-1176.19013679) - (-2352.41628799) = 0.03601441 a. u.

Dissociation Energy = 0.03601441 x 2625.5 = 95 kJ/mol (Round to whole no.)

The dissociation of the dimer into monomers is positive and endothermic as bonds are broken in the reaction.

'''Is the product more or less stable than the isolated monomers?'''

== Reference ==

<ref name="energy">Atkins, P. W., and D. F. Shriver. Shriver and Atkins Inorganic Chemistry. Oxford University Press, 2006.</ref>