==EX3 Section==

===BH3===

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

[[File:Nw3817_BH3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW3817_BH3_FREQ.LOG|NW3817_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0055 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW3817_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum of BH3===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163||93||A2''||yes||out-of-plane bend
|-
|1213||14||E'||very slight||bend
|-
|1213||14||E'||very slight||bend
|-
|2582||0||A1'||no||symmetric stretch
|-
|2715||126||E'||yes||asymmetric stretch
|-
|2715||126||E'||yes||asymmetric stretch
|}

[[File:nw3817_BH3_spectrum.PNG|500px]]

While there are six vibrational modes, only three peaks are seen on the spectrum. This is because there are E' vibrations that are of degenerate energy (thus the vibrations have the same frequency), meaning only one peak is seen at 1213(cm-1) and 2715(cm-1), when each peak corresponds to two vibrations. The vibration at 2582(cm-1) is a symmetric stretch with no overall change in dipole moment, thus the vibration is not IR active. The result is that there are only three peaks in the spectrum.

[[File:nw3817_BH3_MO.jpg]]

When comparing calculated MOs with their corresponding LCAOs, one can see that regions in the same phase fuse together and regions that are not in the same phase distort away from one another. There are clear similarities between the qualitative LCAOs and the corresponding real MOs, but the more complex the atomic orbital, the further the LCAO is from the real MO. For example, the boron 1s a1' is exactly as the LCAO predicts, but the anti bonding e' orbitals are distorted from the LCAO, with lobes of different phases distorting away from each other. This illustrates how qualitative MO theory is very useful for predicting the MOs of simple systems, and even in more complex systems can be used to sort out which atomic orbitals contribute to real MOs, but to get a truly accurate idea of real MOs in more complex systems than this (anti bonding orbitals especially), we must calculate them.

===NH3===
B3LYP/6-31G(d,p) level

[[File:nw3817_NH3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW_NH3_FREQ.LOG|NW_NH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.0136 -0.0021 0.0018 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

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

[[File:nw3817_NH3BH3_sym_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW_NH3BH3_SYM_OPT_FREQ.LOG|NW_NH3BH3_SYM_OPT_FREQ.LOG]]

<pre>
Low frequencies --- -0.0251 -0.0031 0.0007 17.1236 17.1259 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NH3BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Association Energy===
E(NH3)=-56.558 a.u.

E(BH3)=-26.615 a.u.

E(NH3BH3)=-83.225 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-0.052 a.u. = -136 kJ/mol

Ethane has a similar structure to NH3BH3, the same number of atoms, and is isoelectronic to it. The carbon-carbon single bond in ethane is about -377 kJ/mol<ref name=handbook />. This C-C bond is a strong bond and much deeper in energy than the N-B bond here. Another bond strength to compare is the o-o peroxide bond of strength -142 kJ/mol <ref name=wired />. The peroxide bond is a weak bond and the N-B bond is calculated to be even weaker than this, so the N-b dative bond is a weak bond.

===NI3===
B3LYP/6-31G(d,p)LANL2DZ level

frequency file: [[Media:NW_NI3_FREQ.LOG|NW_NI3_FREQ.LOG]]

[[File:nw3817_NI3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
</pre>

<pre>
Low frequencies --- -12.5522 -12.5460 -6.0047 -0.0040 0.0191 0.0664
Low frequencies --- 100.9969 100.9977 147.3377
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I distance: 2.184 Å

==Project Section: Metal Carbonyls==
===Predictions===
Given knowledge of metal-ligand back bonding from this year's Transition Metals and Organometallics lecture course, and given that these compounds are isoelectronic d6, back bonding should decrease as the metal center used goes from Ti to Fe across the period. The metal oxidation state increases (becomes more positive) from Ti2- to Fe2+ so the metal can less readily donate electrons into the C-O π* anti bonding orbital.

Since back bonding donates electrons into the C-O π* anti bonding orbital, increased back bonding decreases C-O bond strength, and thus C-O bond stretch frequency. C-O bond frequency should then increase with decreasing back bonding, therefore increasing across the period.

===[Cr(CO)6]===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Cr_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000110 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000336 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_CR_FREQ.LOG|NW_CR_FREQ.LOG]]

<pre>
Low frequencies --- -0.0008 0.0008 0.0009 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6547 66.6547
</pre>

<jmol><jmolApplet>
<title>[Cr(CO)6]</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===[Ti(CO)6]2-===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Ti_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000334 0.000450 YES
RMS Force 0.000121 0.000300 YES
Maximum Displacement 0.000726 0.001800 YES
RMS Displacement 0.000282 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_TI_FREQ.LOG|NW_TI_FREQ.LOG]]

<pre>
Low frequencies --- 0.0012 0.0015 0.0015 13.3364 13.3364 13.3364
Low frequencies --- 29.8194 29.8194 29.8194
</pre>

<jmol><jmolApplet>
<title>[Ti(CO)6]2-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_TI_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===[Fe(CO)6]2+===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Fe_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_FE_FREQ.LOG|NW_FE_FREQ.LOG]]

<pre>
Low frequencies --- -9.5131 -9.5131 -9.5131 0.0006 0.0010 0.0010
Low frequencies --- 82.3908 82.3908 82.3908
</pre>

<jmol><jmolApplet>
<title>[Fe(CO)6]2+</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Analysis===

{| class="wikitable"
|+ C-O Bond Lengths
|-
|Complex || C-O bond length (Å) || C-O asymmetric bond stretch frequency (cm-1) || C-O symmetric bond stretch frequency (cm-1)
|-
|Ti(CO)62-||1.183||1857||1992
|-
|V(CO)6-||1.166||1970||2097
|-
|Cr(CO)6||1.149||2086||2189
|-
|Mn(CO)6+||1.136||2199||2265
|-
|Fe(CO)62+||1.125||2297||2322
|}

The trend in C-O bond length largely goes as expected, decreasing from Ti to Fe as the metal center is more and more oxidised, and thus engages in less and less backbonding to the C-O π* anti bonding orbital. The result is that the C-O bond is less destabilised and thus shorter. Since bond stretch frequency is proportional with bond strength, the trend in asymmetric C-O bond stretch frequency is that it increases from Ti2- to Fe2+.

Inspecting the completely symmetric C-O bond stretch frequency, one can see that it as with the asymmetric stretch frequency, it increases across the period (increasing with C-O bond strength). These Frequencies cannot however be tested experimentally with IR as their being completely symmetrical means that they cause no change in dipole moment and are thus not IR active, and will not show up in an IR spectrum of the complex.

===Calculated MOs of Cr(CO)6:===

===MO number 43: eg===
*Occupied MO

[[File:nw3817_Cr(CO)6_MO_43.jpg|400px]]

[[File:nw3817_Cr(CO)6_MO_43_LCAO_bonding.jpg]]

===MO number 47: t2g===
*Occupied MO

[[File:nw3817_Cr(CO)6_MO_47.jpg|400px]]

[[File:nw3817_Cr(CO)6_MO_47_LCAO_bonding.jpg]]

===MO number 56: t2g===
*Unoccupied MO

[[File:nw3817_Cr(CO)6_MO_56.jpg|400px]]
[[File:nw3817_Cr(CO)6_MO_56_LCAO_bonding.jpg]]

==References==
<references>
<ref name=handbook>CRC Handbook of Chemistry and Physics, 96th Edition.</ref>

<ref name=wired>http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html[Accessed 23 May 2019]</ref>
</references>

File:Nw3817 Cr(CO)6 MO 56 LCAO bonding.jpg

2019-05-24T16:13:00Z

Nw3817:

Nw3817

2019-05-24T16:12:33Z

Nw3817: /* MO number 43: eg */

==EX3 Section==

===BH3===

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

[[File:Nw3817_BH3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW3817_BH3_FREQ.LOG|NW3817_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0055 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW3817_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum of BH3===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163||93||A2''||yes||out-of-plane bend
|-
|1213||14||E'||very slight||bend
|-
|1213||14||E'||very slight||bend
|-
|2582||0||A1'||no||symmetric stretch
|-
|2715||126||E'||yes||asymmetric stretch
|-
|2715||126||E'||yes||asymmetric stretch
|}

[[File:nw3817_BH3_spectrum.PNG|500px]]

While there are six vibrational modes, only three peaks are seen on the spectrum. This is because there are E' vibrations that are of degenerate energy (thus the vibrations have the same frequency), meaning only one peak is seen at 1213(cm-1) and 2715(cm-1), when each peak corresponds to two vibrations. The vibration at 2582(cm-1) is a symmetric stretch with no overall change in dipole moment, thus the vibration is not IR active. The result is that there are only three peaks in the spectrum.

[[File:nw3817_BH3_MO.jpg]]

When comparing calculated MOs with their corresponding LCAOs, one can see that regions in the same phase fuse together and regions that are not in the same phase distort away from one another. There are clear similarities between the qualitative LCAOs and the corresponding real MOs, but the more complex the atomic orbital, the further the LCAO is from the real MO. For example, the boron 1s a1' is exactly as the LCAO predicts, but the anti bonding e' orbitals are distorted from the LCAO, with lobes of different phases distorting away from each other. This illustrates how qualitative MO theory is very useful for predicting the MOs of simple systems, and even in more complex systems can be used to sort out which atomic orbitals contribute to real MOs, but to get a truly accurate idea of real MOs in more complex systems than this (anti bonding orbitals especially), we must calculate them.

===NH3===
B3LYP/6-31G(d,p) level

[[File:nw3817_NH3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW_NH3_FREQ.LOG|NW_NH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.0136 -0.0021 0.0018 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

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

[[File:nw3817_NH3BH3_sym_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW_NH3BH3_SYM_OPT_FREQ.LOG|NW_NH3BH3_SYM_OPT_FREQ.LOG]]

<pre>
Low frequencies --- -0.0251 -0.0031 0.0007 17.1236 17.1259 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NH3BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Association Energy===
E(NH3)=-56.558 a.u.

E(BH3)=-26.615 a.u.

E(NH3BH3)=-83.225 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-0.052 a.u. = -136 kJ/mol

Ethane has a similar structure to NH3BH3, the same number of atoms, and is isoelectronic to it. The carbon-carbon single bond in ethane is about -377 kJ/mol<ref name=handbook />. This C-C bond is a strong bond and much deeper in energy than the N-B bond here. Another bond strength to compare is the o-o peroxide bond of strength -142 kJ/mol <ref name=wired />. The peroxide bond is a weak bond and the N-B bond is calculated to be even weaker than this, so the N-b dative bond is a weak bond.

===NI3===
B3LYP/6-31G(d,p)LANL2DZ level

frequency file: [[Media:NW_NI3_FREQ.LOG|NW_NI3_FREQ.LOG]]

[[File:nw3817_NI3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
</pre>

<pre>
Low frequencies --- -12.5522 -12.5460 -6.0047 -0.0040 0.0191 0.0664
Low frequencies --- 100.9969 100.9977 147.3377
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I distance: 2.184 Å

==Project Section: Metal Carbonyls==
===Predictions===
Given knowledge of metal-ligand back bonding from this year's Transition Metals and Organometallics lecture course, and given that these compounds are isoelectronic d6, back bonding should decrease as the metal center used goes from Ti to Fe across the period. The metal oxidation state increases (becomes more positive) from Ti2- to Fe2+ so the metal can less readily donate electrons into the C-O π* anti bonding orbital.

Since back bonding donates electrons into the C-O π* anti bonding orbital, increased back bonding decreases C-O bond strength, and thus C-O bond stretch frequency. C-O bond frequency should then increase with decreasing back bonding, therefore increasing across the period.

===[Cr(CO)6]===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Cr_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000110 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000336 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_CR_FREQ.LOG|NW_CR_FREQ.LOG]]

<pre>
Low frequencies --- -0.0008 0.0008 0.0009 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6547 66.6547
</pre>

<jmol><jmolApplet>
<title>[Cr(CO)6]</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===[Ti(CO)6]2-===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Ti_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000334 0.000450 YES
RMS Force 0.000121 0.000300 YES
Maximum Displacement 0.000726 0.001800 YES
RMS Displacement 0.000282 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_TI_FREQ.LOG|NW_TI_FREQ.LOG]]

<pre>
Low frequencies --- 0.0012 0.0015 0.0015 13.3364 13.3364 13.3364
Low frequencies --- 29.8194 29.8194 29.8194
</pre>

<jmol><jmolApplet>
<title>[Ti(CO)6]2-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_TI_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===[Fe(CO)6]2+===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Fe_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_FE_FREQ.LOG|NW_FE_FREQ.LOG]]

<pre>
Low frequencies --- -9.5131 -9.5131 -9.5131 0.0006 0.0010 0.0010
Low frequencies --- 82.3908 82.3908 82.3908
</pre>

<jmol><jmolApplet>
<title>[Fe(CO)6]2+</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Analysis===

{| class="wikitable"
|+ C-O Bond Lengths
|-
|Complex || C-O bond length (Å) || C-O asymmetric bond stretch frequency (cm-1) || C-O symmetric bond stretch frequency (cm-1)
|-
|Ti(CO)62-||1.183||1857||1992
|-
|V(CO)6-||1.166||1970||2097
|-
|Cr(CO)6||1.149||2086||2189
|-
|Mn(CO)6+||1.136||2199||2265
|-
|Fe(CO)62+||1.125||2297||2322
|}

The trend in C-O bond length largely goes as expected, decreasing from Ti to Fe as the metal center is more and more oxidised, and thus engages in less and less backbonding to the C-O π* anti bonding orbital. The result is that the C-O bond is less destabilised and thus shorter. Since bond stretch frequency is proportional with bond strength, the trend in asymmetric C-O bond stretch frequency is that it increases from Ti2- to Fe2+.

Inspecting the completely symmetric C-O bond stretch frequency, one can see that it as with the asymmetric stretch frequency, it increases across the period (increasing with C-O bond strength). These Frequencies cannot however be tested experimentally with IR as their being completely symmetrical means that they cause no change in dipole moment and are thus not IR active, and will not show up in an IR spectrum of the complex.

===Calculated MOs of Cr(CO)6:===

===MO number 43: eg===
*Occupied MO

[[File:nw3817_Cr(CO)6_MO_43.jpg|400px]]

[[File:nw3817_Cr(CO)6_MO_43_LCAO_bonding.jpg]]

===MO number 47: t2g===
*Occupied MO

[[File:nw3817_Cr(CO)6_MO_47.jpg|400px]]

[[File:nw3817_Cr(CO)6_MO_47_LCAO_bonding.jpg]]

===MO number 56: t2g===
*Unoccupied MO

[[File:nw3817_Cr(CO)6_MO_56.jpg|500px]]

==References==
<references>
<ref name=handbook>CRC Handbook of Chemistry and Physics, 96th Edition.</ref>

<ref name=wired>http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html[Accessed 23 May 2019]</ref>
</references>

Nw3817

2019-05-24T16:12:24Z

Nw3817: /* MO number 47: t2g */

==EX3 Section==

===BH3===

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

[[File:Nw3817_BH3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW3817_BH3_FREQ.LOG|NW3817_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0055 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW3817_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum of BH3===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163||93||A2''||yes||out-of-plane bend
|-
|1213||14||E'||very slight||bend
|-
|1213||14||E'||very slight||bend
|-
|2582||0||A1'||no||symmetric stretch
|-
|2715||126||E'||yes||asymmetric stretch
|-
|2715||126||E'||yes||asymmetric stretch
|}

[[File:nw3817_BH3_spectrum.PNG|500px]]

While there are six vibrational modes, only three peaks are seen on the spectrum. This is because there are E' vibrations that are of degenerate energy (thus the vibrations have the same frequency), meaning only one peak is seen at 1213(cm-1) and 2715(cm-1), when each peak corresponds to two vibrations. The vibration at 2582(cm-1) is a symmetric stretch with no overall change in dipole moment, thus the vibration is not IR active. The result is that there are only three peaks in the spectrum.

[[File:nw3817_BH3_MO.jpg]]

When comparing calculated MOs with their corresponding LCAOs, one can see that regions in the same phase fuse together and regions that are not in the same phase distort away from one another. There are clear similarities between the qualitative LCAOs and the corresponding real MOs, but the more complex the atomic orbital, the further the LCAO is from the real MO. For example, the boron 1s a1' is exactly as the LCAO predicts, but the anti bonding e' orbitals are distorted from the LCAO, with lobes of different phases distorting away from each other. This illustrates how qualitative MO theory is very useful for predicting the MOs of simple systems, and even in more complex systems can be used to sort out which atomic orbitals contribute to real MOs, but to get a truly accurate idea of real MOs in more complex systems than this (anti bonding orbitals especially), we must calculate them.

===NH3===
B3LYP/6-31G(d,p) level

[[File:nw3817_NH3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW_NH3_FREQ.LOG|NW_NH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.0136 -0.0021 0.0018 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

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

[[File:nw3817_NH3BH3_sym_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW_NH3BH3_SYM_OPT_FREQ.LOG|NW_NH3BH3_SYM_OPT_FREQ.LOG]]

<pre>
Low frequencies --- -0.0251 -0.0031 0.0007 17.1236 17.1259 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NH3BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Association Energy===
E(NH3)=-56.558 a.u.

E(BH3)=-26.615 a.u.

E(NH3BH3)=-83.225 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-0.052 a.u. = -136 kJ/mol

Ethane has a similar structure to NH3BH3, the same number of atoms, and is isoelectronic to it. The carbon-carbon single bond in ethane is about -377 kJ/mol<ref name=handbook />. This C-C bond is a strong bond and much deeper in energy than the N-B bond here. Another bond strength to compare is the o-o peroxide bond of strength -142 kJ/mol <ref name=wired />. The peroxide bond is a weak bond and the N-B bond is calculated to be even weaker than this, so the N-b dative bond is a weak bond.

===NI3===
B3LYP/6-31G(d,p)LANL2DZ level

frequency file: [[Media:NW_NI3_FREQ.LOG|NW_NI3_FREQ.LOG]]

[[File:nw3817_NI3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
</pre>

<pre>
Low frequencies --- -12.5522 -12.5460 -6.0047 -0.0040 0.0191 0.0664
Low frequencies --- 100.9969 100.9977 147.3377
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I distance: 2.184 Å

==Project Section: Metal Carbonyls==
===Predictions===
Given knowledge of metal-ligand back bonding from this year's Transition Metals and Organometallics lecture course, and given that these compounds are isoelectronic d6, back bonding should decrease as the metal center used goes from Ti to Fe across the period. The metal oxidation state increases (becomes more positive) from Ti2- to Fe2+ so the metal can less readily donate electrons into the C-O π* anti bonding orbital.

Since back bonding donates electrons into the C-O π* anti bonding orbital, increased back bonding decreases C-O bond strength, and thus C-O bond stretch frequency. C-O bond frequency should then increase with decreasing back bonding, therefore increasing across the period.

===[Cr(CO)6]===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Cr_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000110 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000336 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_CR_FREQ.LOG|NW_CR_FREQ.LOG]]

<pre>
Low frequencies --- -0.0008 0.0008 0.0009 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6547 66.6547
</pre>

<jmol><jmolApplet>
<title>[Cr(CO)6]</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===[Ti(CO)6]2-===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Ti_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000334 0.000450 YES
RMS Force 0.000121 0.000300 YES
Maximum Displacement 0.000726 0.001800 YES
RMS Displacement 0.000282 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_TI_FREQ.LOG|NW_TI_FREQ.LOG]]

<pre>
Low frequencies --- 0.0012 0.0015 0.0015 13.3364 13.3364 13.3364
Low frequencies --- 29.8194 29.8194 29.8194
</pre>

<jmol><jmolApplet>
<title>[Ti(CO)6]2-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_TI_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===[Fe(CO)6]2+===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Fe_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_FE_FREQ.LOG|NW_FE_FREQ.LOG]]

<pre>
Low frequencies --- -9.5131 -9.5131 -9.5131 0.0006 0.0010 0.0010
Low frequencies --- 82.3908 82.3908 82.3908
</pre>

<jmol><jmolApplet>
<title>[Fe(CO)6]2+</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Analysis===

{| class="wikitable"
|+ C-O Bond Lengths
|-
|Complex || C-O bond length (Å) || C-O asymmetric bond stretch frequency (cm-1) || C-O symmetric bond stretch frequency (cm-1)
|-
|Ti(CO)62-||1.183||1857||1992
|-
|V(CO)6-||1.166||1970||2097
|-
|Cr(CO)6||1.149||2086||2189
|-
|Mn(CO)6+||1.136||2199||2265
|-
|Fe(CO)62+||1.125||2297||2322
|}

The trend in C-O bond length largely goes as expected, decreasing from Ti to Fe as the metal center is more and more oxidised, and thus engages in less and less backbonding to the C-O π* anti bonding orbital. The result is that the C-O bond is less destabilised and thus shorter. Since bond stretch frequency is proportional with bond strength, the trend in asymmetric C-O bond stretch frequency is that it increases from Ti2- to Fe2+.

Inspecting the completely symmetric C-O bond stretch frequency, one can see that it as with the asymmetric stretch frequency, it increases across the period (increasing with C-O bond strength). These Frequencies cannot however be tested experimentally with IR as their being completely symmetrical means that they cause no change in dipole moment and are thus not IR active, and will not show up in an IR spectrum of the complex.

===Calculated MOs of Cr(CO)6:===

===MO number 43: eg===
*Occupied MO

[[File:nw3817_Cr(CO)6_MO_43.jpg|400px]]

[[File:nw3817_Cr(CO)6_MO_43_LCAO_bonding.jpg|500px]]

===MO number 47: t2g===
*Occupied MO

[[File:nw3817_Cr(CO)6_MO_47.jpg|400px]]

[[File:nw3817_Cr(CO)6_MO_47_LCAO_bonding.jpg]]

===MO number 56: t2g===
*Unoccupied MO

[[File:nw3817_Cr(CO)6_MO_56.jpg|500px]]

==References==
<references>
<ref name=handbook>CRC Handbook of Chemistry and Physics, 96th Edition.</ref>

<ref name=wired>http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html[Accessed 23 May 2019]</ref>
</references>

File:Nw3817 Cr(CO)6 MO 47 LCAO bonding.jpg

2019-05-24T16:12:02Z

Nw3817:

Nw3817

2019-05-24T16:11:34Z

2019-05-24T15:47:57Z

Nw3817: /* MO number 43: eg */

==EX3 Section==

===BH3===

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

[[File:Nw3817_BH3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW3817_BH3_FREQ.LOG|NW3817_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0055 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW3817_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum of BH3===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163||93||A2''||yes||out-of-plane bend
|-
|1213||14||E'||very slight||bend
|-
|1213||14||E'||very slight||bend
|-
|2582||0||A1'||no||symmetric stretch
|-
|2715||126||E'||yes||asymmetric stretch
|-
|2715||126||E'||yes||asymmetric stretch
|}

[[File:nw3817_BH3_spectrum.PNG|500px]]

While there are six vibrational modes, only three peaks are seen on the spectrum. This is because there are E' vibrations that are of degenerate energy (thus the vibrations have the same frequency), meaning only one peak is seen at 1213(cm-1) and 2715(cm-1), when each peak corresponds to two vibrations. The vibration at 2582(cm-1) is a symmetric stretch with no overall change in dipole moment, thus the vibration is not IR active. The result is that there are only three peaks in the spectrum.

[[File:nw3817_BH3_MO.jpg]]

When comparing calculated MOs with their corresponding LCAOs, one can see that regions in the same phase fuse together and regions that are not in the same phase distort away from one another. There are clear similarities between the qualitative LCAOs and the corresponding real MOs, but the more complex the atomic orbital, the further the LCAO is from the real MO. For example, the boron 1s a1' is exactly as the LCAO predicts, but the anti bonding e' orbitals are distorted from the LCAO, with lobes of different phases distorting away from each other. This illustrates how qualitative MO theory is very useful for predicting the MOs of simple systems, and even in more complex systems can be used to sort out which atomic orbitals contribute to real MOs, but to get a truly accurate idea of real MOs in more complex systems than this (anti bonding orbitals especially), we must calculate them.

===NH3===
B3LYP/6-31G(d,p) level

[[File:nw3817_NH3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW_NH3_FREQ.LOG|NW_NH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.0136 -0.0021 0.0018 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

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

[[File:nw3817_NH3BH3_sym_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW_NH3BH3_SYM_OPT_FREQ.LOG|NW_NH3BH3_SYM_OPT_FREQ.LOG]]

<pre>
Low frequencies --- -0.0251 -0.0031 0.0007 17.1236 17.1259 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NH3BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Association Energy===
E(NH3)=-56.558 a.u.

E(BH3)=-26.615 a.u.

E(NH3BH3)=-83.225 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-0.052 a.u. = -136 kJ/mol

Ethane has a similar structure to NH3BH3, the same number of atoms, and is isoelectronic to it. The carbon-carbon single bond in ethane is about -377 kJ/mol<ref name=handbook />. This C-C bond is a strong bond and much deeper in energy than the N-B bond here. Another bond strength to compare is the o-o peroxide bond of strength -142 kJ/mol <ref name=wired />. The peroxide bond is a weak bond and the N-B bond is calculated to be even weaker than this, so the N-b dative bond is a weak bond.

===NI3===
B3LYP/6-31G(d,p)LANL2DZ level

frequency file: [[Media:NW_NI3_FREQ.LOG|NW_NI3_FREQ.LOG]]

[[File:nw3817_NI3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
</pre>

<pre>
Low frequencies --- -12.5522 -12.5460 -6.0047 -0.0040 0.0191 0.0664
Low frequencies --- 100.9969 100.9977 147.3377
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I distance: 2.184 Å

==Project Section: Metal Carbonyls==
===Predictions===
Given knowledge of metal-ligand back bonding from this year's Transition Metals and Organometallics lecture course, and given that these compounds are isoelectronic d6, back bonding should decrease as the metal center used goes from Ti to Fe across the period. The metal oxidation state increases (becomes more positive) from Ti2- to Fe2+ so the metal can less readily donate electrons into the C-O π* anti bonding orbital.

Since back bonding donates electrons into the C-O π* anti bonding orbital, increased back bonding decreases C-O bond strength, and thus C-O bond stretch frequency. C-O bond frequency should then increase with decreasing back bonding, therefore increasing across the period.

===[Cr(CO)6]===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Cr_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000110 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000336 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_CR_FREQ.LOG|NW_CR_FREQ.LOG]]

<pre>
Low frequencies --- -0.0008 0.0008 0.0009 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6547 66.6547
</pre>

<jmol><jmolApplet>
<title>[Cr(CO)6]</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===[Ti(CO)6]2-===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Ti_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000334 0.000450 YES
RMS Force 0.000121 0.000300 YES
Maximum Displacement 0.000726 0.001800 YES
RMS Displacement 0.000282 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_TI_FREQ.LOG|NW_TI_FREQ.LOG]]

<pre>
Low frequencies --- 0.0012 0.0015 0.0015 13.3364 13.3364 13.3364
Low frequencies --- 29.8194 29.8194 29.8194
</pre>

<jmol><jmolApplet>
<title>[Ti(CO)6]2-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_TI_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===[Fe(CO)6]2+===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Fe_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_FE_FREQ.LOG|NW_FE_FREQ.LOG]]

<pre>
Low frequencies --- -9.5131 -9.5131 -9.5131 0.0006 0.0010 0.0010
Low frequencies --- 82.3908 82.3908 82.3908
</pre>

<jmol><jmolApplet>
<title>[Fe(CO)6]2+</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Analysis===

{| class="wikitable"
|+ C-O Bond Lengths
|-
|Complex || C-O bond length (Å) || C-O asymmetric bond stretch frequency (cm-1) || C-O symmetric bond stretch frequency (cm-1)
|-
|Ti(CO)62-||1.183||1857||1992
|-
|V(CO)6-||1.166||1970||2097
|-
|Cr(CO)6||1.149||2086||2189
|-
|Mn(CO)6+||1.136||2199||2265
|-
|Fe(CO)62+||1.125||2297||2322
|}

The trend in C-O bond length largely goes as expected, decreasing from Ti to Fe as the metal center is more and more oxidised, and thus engages in less and less backbonding to the C-O π* anti bonding orbital. The result is that the C-O bond is less destabilised and thus shorter. Since bond stretch frequency is proportional with bond strength, the trend in asymmetric C-O bond stretch frequency is that it increases from Ti2- to Fe2+.

Inspecting the completely symmetric C-O bond stretch frequency, one can see that it as with the asymmetric stretch frequency, it increases across the period (increasing with C-O bond strength). These Frequencies cannot however be tested experimentally with IR as their being completely symmetrical means that they cause no change in dipole moment and are thus not IR active, and will not show up in an IR spectrum of the complex.

===Calculated MOs of Cr(CO)6:===

===MO number 43: eg===
*Occupied MO

[[File:nw3817_Cr(CO)6_MO_43.jpg|200px]]

===MO number 47: t2g===
*Occupied MO

===MO number 56: t2g===
*Unoccupied MO

==References==
<references>
<ref name=handbook>CRC Handbook of Chemistry and Physics, 96th Edition.</ref>

<ref name=wired>http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html[Accessed 23 May 2019]</ref>
</references>

Nw3817

2019-05-24T15:47:42Z

Nw3817: /* MO number 43: eg */

==EX3 Section==

===BH3===

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

[[File:Nw3817_BH3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW3817_BH3_FREQ.LOG|NW3817_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0055 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW3817_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum of BH3===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163||93||A2''||yes||out-of-plane bend
|-
|1213||14||E'||very slight||bend
|-
|1213||14||E'||very slight||bend
|-
|2582||0||A1'||no||symmetric stretch
|-
|2715||126||E'||yes||asymmetric stretch
|-
|2715||126||E'||yes||asymmetric stretch
|}

[[File:nw3817_BH3_spectrum.PNG|500px]]

While there are six vibrational modes, only three peaks are seen on the spectrum. This is because there are E' vibrations that are of degenerate energy (thus the vibrations have the same frequency), meaning only one peak is seen at 1213(cm-1) and 2715(cm-1), when each peak corresponds to two vibrations. The vibration at 2582(cm-1) is a symmetric stretch with no overall change in dipole moment, thus the vibration is not IR active. The result is that there are only three peaks in the spectrum.

[[File:nw3817_BH3_MO.jpg]]

When comparing calculated MOs with their corresponding LCAOs, one can see that regions in the same phase fuse together and regions that are not in the same phase distort away from one another. There are clear similarities between the qualitative LCAOs and the corresponding real MOs, but the more complex the atomic orbital, the further the LCAO is from the real MO. For example, the boron 1s a1' is exactly as the LCAO predicts, but the anti bonding e' orbitals are distorted from the LCAO, with lobes of different phases distorting away from each other. This illustrates how qualitative MO theory is very useful for predicting the MOs of simple systems, and even in more complex systems can be used to sort out which atomic orbitals contribute to real MOs, but to get a truly accurate idea of real MOs in more complex systems than this (anti bonding orbitals especially), we must calculate them.

===NH3===
B3LYP/6-31G(d,p) level

[[File:nw3817_NH3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW_NH3_FREQ.LOG|NW_NH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.0136 -0.0021 0.0018 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

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

[[File:nw3817_NH3BH3_sym_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW_NH3BH3_SYM_OPT_FREQ.LOG|NW_NH3BH3_SYM_OPT_FREQ.LOG]]

<pre>
Low frequencies --- -0.0251 -0.0031 0.0007 17.1236 17.1259 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NH3BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Association Energy===
E(NH3)=-56.558 a.u.

E(BH3)=-26.615 a.u.

E(NH3BH3)=-83.225 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-0.052 a.u. = -136 kJ/mol

Ethane has a similar structure to NH3BH3, the same number of atoms, and is isoelectronic to it. The carbon-carbon single bond in ethane is about -377 kJ/mol<ref name=handbook />. This C-C bond is a strong bond and much deeper in energy than the N-B bond here. Another bond strength to compare is the o-o peroxide bond of strength -142 kJ/mol <ref name=wired />. The peroxide bond is a weak bond and the N-B bond is calculated to be even weaker than this, so the N-b dative bond is a weak bond.

===NI3===
B3LYP/6-31G(d,p)LANL2DZ level

frequency file: [[Media:NW_NI3_FREQ.LOG|NW_NI3_FREQ.LOG]]

[[File:nw3817_NI3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
</pre>

<pre>
Low frequencies --- -12.5522 -12.5460 -6.0047 -0.0040 0.0191 0.0664
Low frequencies --- 100.9969 100.9977 147.3377
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I distance: 2.184 Å

==Project Section: Metal Carbonyls==
===Predictions===
Given knowledge of metal-ligand back bonding from this year's Transition Metals and Organometallics lecture course, and given that these compounds are isoelectronic d6, back bonding should decrease as the metal center used goes from Ti to Fe across the period. The metal oxidation state increases (becomes more positive) from Ti2- to Fe2+ so the metal can less readily donate electrons into the C-O π* anti bonding orbital.

Since back bonding donates electrons into the C-O π* anti bonding orbital, increased back bonding decreases C-O bond strength, and thus C-O bond stretch frequency. C-O bond frequency should then increase with decreasing back bonding, therefore increasing across the period.

===[Cr(CO)6]===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Cr_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000110 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000336 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_CR_FREQ.LOG|NW_CR_FREQ.LOG]]

<pre>
Low frequencies --- -0.0008 0.0008 0.0009 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6547 66.6547
</pre>

<jmol><jmolApplet>
<title>[Cr(CO)6]</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===[Ti(CO)6]2-===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Ti_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000334 0.000450 YES
RMS Force 0.000121 0.000300 YES
Maximum Displacement 0.000726 0.001800 YES
RMS Displacement 0.000282 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_TI_FREQ.LOG|NW_TI_FREQ.LOG]]

<pre>
Low frequencies --- 0.0012 0.0015 0.0015 13.3364 13.3364 13.3364
Low frequencies --- 29.8194 29.8194 29.8194
</pre>

<jmol><jmolApplet>
<title>[Ti(CO)6]2-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_TI_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===[Fe(CO)6]2+===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Fe_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_FE_FREQ.LOG|NW_FE_FREQ.LOG]]

<pre>
Low frequencies --- -9.5131 -9.5131 -9.5131 0.0006 0.0010 0.0010
Low frequencies --- 82.3908 82.3908 82.3908
</pre>

<jmol><jmolApplet>
<title>[Fe(CO)6]2+</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Analysis===

{| class="wikitable"
|+ C-O Bond Lengths
|-
|Complex || C-O bond length (Å) || C-O asymmetric bond stretch frequency (cm-1) || C-O symmetric bond stretch frequency (cm-1)
|-
|Ti(CO)62-||1.183||1857||1992
|-
|V(CO)6-||1.166||1970||2097
|-
|Cr(CO)6||1.149||2086||2189
|-
|Mn(CO)6+||1.136||2199||2265
|-
|Fe(CO)62+||1.125||2297||2322
|}

The trend in C-O bond length largely goes as expected, decreasing from Ti to Fe as the metal center is more and more oxidised, and thus engages in less and less backbonding to the C-O π* anti bonding orbital. The result is that the C-O bond is less destabilised and thus shorter. Since bond stretch frequency is proportional with bond strength, the trend in asymmetric C-O bond stretch frequency is that it increases from Ti2- to Fe2+.

Inspecting the completely symmetric C-O bond stretch frequency, one can see that it as with the asymmetric stretch frequency, it increases across the period (increasing with C-O bond strength). These Frequencies cannot however be tested experimentally with IR as their being completely symmetrical means that they cause no change in dipole moment and are thus not IR active, and will not show up in an IR spectrum of the complex.

===Calculated MOs of Cr(CO)6:===

===MO number 43: eg===
*Occupied MO

[[File:nw3817_Cr(CO)6_MO_43.jpg]]

===MO number 47: t2g===
*Occupied MO

===MO number 56: t2g===
*Unoccupied MO

==References==
<references>
<ref name=handbook>CRC Handbook of Chemistry and Physics, 96th Edition.</ref>

<ref name=wired>http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html[Accessed 23 May 2019]</ref>
</references>

File:Nw3817 Cr(CO)6 MO 43.jpg

2019-05-24T15:47:21Z

Nw3817:

Nw3817

2019-05-24T15:46:48Z

Nw3817: /* Analysis */

==EX3 Section==

===BH3===

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

[[File:Nw3817_BH3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW3817_BH3_FREQ.LOG|NW3817_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0055 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW3817_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum of BH3===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163||93||A2''||yes||out-of-plane bend
|-
|1213||14||E'||very slight||bend
|-
|1213||14||E'||very slight||bend
|-
|2582||0||A1'||no||symmetric stretch
|-
|2715||126||E'||yes||asymmetric stretch
|-
|2715||126||E'||yes||asymmetric stretch
|}

[[File:nw3817_BH3_spectrum.PNG|500px]]

While there are six vibrational modes, only three peaks are seen on the spectrum. This is because there are E' vibrations that are of degenerate energy (thus the vibrations have the same frequency), meaning only one peak is seen at 1213(cm-1) and 2715(cm-1), when each peak corresponds to two vibrations. The vibration at 2582(cm-1) is a symmetric stretch with no overall change in dipole moment, thus the vibration is not IR active. The result is that there are only three peaks in the spectrum.

[[File:nw3817_BH3_MO.jpg]]

When comparing calculated MOs with their corresponding LCAOs, one can see that regions in the same phase fuse together and regions that are not in the same phase distort away from one another. There are clear similarities between the qualitative LCAOs and the corresponding real MOs, but the more complex the atomic orbital, the further the LCAO is from the real MO. For example, the boron 1s a1' is exactly as the LCAO predicts, but the anti bonding e' orbitals are distorted from the LCAO, with lobes of different phases distorting away from each other. This illustrates how qualitative MO theory is very useful for predicting the MOs of simple systems, and even in more complex systems can be used to sort out which atomic orbitals contribute to real MOs, but to get a truly accurate idea of real MOs in more complex systems than this (anti bonding orbitals especially), we must calculate them.

===NH3===
B3LYP/6-31G(d,p) level

[[File:nw3817_NH3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW_NH3_FREQ.LOG|NW_NH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.0136 -0.0021 0.0018 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

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

[[File:nw3817_NH3BH3_sym_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW_NH3BH3_SYM_OPT_FREQ.LOG|NW_NH3BH3_SYM_OPT_FREQ.LOG]]

<pre>
Low frequencies --- -0.0251 -0.0031 0.0007 17.1236 17.1259 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NH3BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Association Energy===
E(NH3)=-56.558 a.u.

E(BH3)=-26.615 a.u.

E(NH3BH3)=-83.225 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-0.052 a.u. = -136 kJ/mol

Ethane has a similar structure to NH3BH3, the same number of atoms, and is isoelectronic to it. The carbon-carbon single bond in ethane is about -377 kJ/mol<ref name=handbook />. This C-C bond is a strong bond and much deeper in energy than the N-B bond here. Another bond strength to compare is the o-o peroxide bond of strength -142 kJ/mol <ref name=wired />. The peroxide bond is a weak bond and the N-B bond is calculated to be even weaker than this, so the N-b dative bond is a weak bond.

===NI3===
B3LYP/6-31G(d,p)LANL2DZ level

frequency file: [[Media:NW_NI3_FREQ.LOG|NW_NI3_FREQ.LOG]]

[[File:nw3817_NI3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
</pre>

<pre>
Low frequencies --- -12.5522 -12.5460 -6.0047 -0.0040 0.0191 0.0664
Low frequencies --- 100.9969 100.9977 147.3377
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I distance: 2.184 Å

==Project Section: Metal Carbonyls==
===Predictions===
Given knowledge of metal-ligand back bonding from this year's Transition Metals and Organometallics lecture course, and given that these compounds are isoelectronic d6, back bonding should decrease as the metal center used goes from Ti to Fe across the period. The metal oxidation state increases (becomes more positive) from Ti2- to Fe2+ so the metal can less readily donate electrons into the C-O π* anti bonding orbital.

Since back bonding donates electrons into the C-O π* anti bonding orbital, increased back bonding decreases C-O bond strength, and thus C-O bond stretch frequency. C-O bond frequency should then increase with decreasing back bonding, therefore increasing across the period.

===[Cr(CO)6]===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Cr_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000110 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000336 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_CR_FREQ.LOG|NW_CR_FREQ.LOG]]

<pre>
Low frequencies --- -0.0008 0.0008 0.0009 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6547 66.6547
</pre>

<jmol><jmolApplet>
<title>[Cr(CO)6]</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===[Ti(CO)6]2-===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Ti_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000334 0.000450 YES
RMS Force 0.000121 0.000300 YES
Maximum Displacement 0.000726 0.001800 YES
RMS Displacement 0.000282 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_TI_FREQ.LOG|NW_TI_FREQ.LOG]]

<pre>
Low frequencies --- 0.0012 0.0015 0.0015 13.3364 13.3364 13.3364
Low frequencies --- 29.8194 29.8194 29.8194
</pre>

<jmol><jmolApplet>
<title>[Ti(CO)6]2-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_TI_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===[Fe(CO)6]2+===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Fe_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_FE_FREQ.LOG|NW_FE_FREQ.LOG]]

<pre>
Low frequencies --- -9.5131 -9.5131 -9.5131 0.0006 0.0010 0.0010
Low frequencies --- 82.3908 82.3908 82.3908
</pre>

<jmol><jmolApplet>
<title>[Fe(CO)6]2+</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Analysis===

{| class="wikitable"
|+ C-O Bond Lengths
|-
|Complex || C-O bond length (Å) || C-O asymmetric bond stretch frequency (cm-1) || C-O symmetric bond stretch frequency (cm-1)
|-
|Ti(CO)62-||1.183||1857||1992
|-
|V(CO)6-||1.166||1970||2097
|-
|Cr(CO)6||1.149||2086||2189
|-
|Mn(CO)6+||1.136||2199||2265
|-
|Fe(CO)62+||1.125||2297||2322
|}

The trend in C-O bond length largely goes as expected, decreasing from Ti to Fe as the metal center is more and more oxidised, and thus engages in less and less backbonding to the C-O π* anti bonding orbital. The result is that the C-O bond is less destabilised and thus shorter. Since bond stretch frequency is proportional with bond strength, the trend in asymmetric C-O bond stretch frequency is that it increases from Ti2- to Fe2+.

Inspecting the completely symmetric C-O bond stretch frequency, one can see that it as with the asymmetric stretch frequency, it increases across the period (increasing with C-O bond strength). These Frequencies cannot however be tested experimentally with IR as their being completely symmetrical means that they cause no change in dipole moment and are thus not IR active, and will not show up in an IR spectrum of the complex.

===Calculated MOs of Cr(CO)6:===

===MO number 43: eg===
*Occupied MO

===MO number 47: t2g===
*Occupied MO

===MO number 56: t2g===
*Unoccupied MO

==References==
<references>
<ref name=handbook>CRC Handbook of Chemistry and Physics, 96th Edition.</ref>

<ref name=wired>http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html[Accessed 23 May 2019]</ref>
</references>

Nw3817

2019-05-24T15:37:48Z

Nw3817: /* Analysis */

==EX3 Section==

===BH3===

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

[[File:Nw3817_BH3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW3817_BH3_FREQ.LOG|NW3817_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0055 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW3817_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum of BH3===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163||93||A2''||yes||out-of-plane bend
|-
|1213||14||E'||very slight||bend
|-
|1213||14||E'||very slight||bend
|-
|2582||0||A1'||no||symmetric stretch
|-
|2715||126||E'||yes||asymmetric stretch
|-
|2715||126||E'||yes||asymmetric stretch
|}

[[File:nw3817_BH3_spectrum.PNG|500px]]

While there are six vibrational modes, only three peaks are seen on the spectrum. This is because there are E' vibrations that are of degenerate energy (thus the vibrations have the same frequency), meaning only one peak is seen at 1213(cm-1) and 2715(cm-1), when each peak corresponds to two vibrations. The vibration at 2582(cm-1) is a symmetric stretch with no overall change in dipole moment, thus the vibration is not IR active. The result is that there are only three peaks in the spectrum.

[[File:nw3817_BH3_MO.jpg]]

When comparing calculated MOs with their corresponding LCAOs, one can see that regions in the same phase fuse together and regions that are not in the same phase distort away from one another. There are clear similarities between the qualitative LCAOs and the corresponding real MOs, but the more complex the atomic orbital, the further the LCAO is from the real MO. For example, the boron 1s a1' is exactly as the LCAO predicts, but the anti bonding e' orbitals are distorted from the LCAO, with lobes of different phases distorting away from each other. This illustrates how qualitative MO theory is very useful for predicting the MOs of simple systems, and even in more complex systems can be used to sort out which atomic orbitals contribute to real MOs, but to get a truly accurate idea of real MOs in more complex systems than this (anti bonding orbitals especially), we must calculate them.

===NH3===
B3LYP/6-31G(d,p) level

[[File:nw3817_NH3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW_NH3_FREQ.LOG|NW_NH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.0136 -0.0021 0.0018 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

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

[[File:nw3817_NH3BH3_sym_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW_NH3BH3_SYM_OPT_FREQ.LOG|NW_NH3BH3_SYM_OPT_FREQ.LOG]]

<pre>
Low frequencies --- -0.0251 -0.0031 0.0007 17.1236 17.1259 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NH3BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Association Energy===
E(NH3)=-56.558 a.u.

E(BH3)=-26.615 a.u.

E(NH3BH3)=-83.225 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-0.052 a.u. = -136 kJ/mol

Ethane has a similar structure to NH3BH3, the same number of atoms, and is isoelectronic to it. The carbon-carbon single bond in ethane is about -377 kJ/mol<ref name=handbook />. This C-C bond is a strong bond and much deeper in energy than the N-B bond here. Another bond strength to compare is the o-o peroxide bond of strength -142 kJ/mol <ref name=wired />. The peroxide bond is a weak bond and the N-B bond is calculated to be even weaker than this, so the N-b dative bond is a weak bond.

===NI3===
B3LYP/6-31G(d,p)LANL2DZ level

frequency file: [[Media:NW_NI3_FREQ.LOG|NW_NI3_FREQ.LOG]]

[[File:nw3817_NI3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
</pre>

<pre>
Low frequencies --- -12.5522 -12.5460 -6.0047 -0.0040 0.0191 0.0664
Low frequencies --- 100.9969 100.9977 147.3377
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I distance: 2.184 Å

==Project Section: Metal Carbonyls==
===Predictions===
Given knowledge of metal-ligand back bonding from this year's Transition Metals and Organometallics lecture course, and given that these compounds are isoelectronic d6, back bonding should decrease as the metal center used goes from Ti to Fe across the period. The metal oxidation state increases (becomes more positive) from Ti2- to Fe2+ so the metal can less readily donate electrons into the C-O π* anti bonding orbital.

Since back bonding donates electrons into the C-O π* anti bonding orbital, increased back bonding decreases C-O bond strength, and thus C-O bond stretch frequency. C-O bond frequency should then increase with decreasing back bonding, therefore increasing across the period.

===[Cr(CO)6]===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Cr_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000110 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000336 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_CR_FREQ.LOG|NW_CR_FREQ.LOG]]

<pre>
Low frequencies --- -0.0008 0.0008 0.0009 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6547 66.6547
</pre>

<jmol><jmolApplet>
<title>[Cr(CO)6]</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===[Ti(CO)6]2-===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Ti_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000334 0.000450 YES
RMS Force 0.000121 0.000300 YES
Maximum Displacement 0.000726 0.001800 YES
RMS Displacement 0.000282 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_TI_FREQ.LOG|NW_TI_FREQ.LOG]]

<pre>
Low frequencies --- 0.0012 0.0015 0.0015 13.3364 13.3364 13.3364
Low frequencies --- 29.8194 29.8194 29.8194
</pre>

<jmol><jmolApplet>
<title>[Ti(CO)6]2-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_TI_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===[Fe(CO)6]2+===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Fe_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_FE_FREQ.LOG|NW_FE_FREQ.LOG]]

<pre>
Low frequencies --- -9.5131 -9.5131 -9.5131 0.0006 0.0010 0.0010
Low frequencies --- 82.3908 82.3908 82.3908
</pre>

<jmol><jmolApplet>
<title>[Fe(CO)6]2+</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Analysis===

{| class="wikitable"
|+ C-O Bond Lengths
|-
|Complex || C-O bond length (Å) || C-O asymmetric bond stretch frequency (cm-1) || C-O symmetric bond stretch frequency (cm-1)
|-
|Ti(CO)62-||1.183||1857||1992
|-
|V(CO)6-||1.166||1970||2097
|-
|Cr(CO)6||1.149||2086||2189
|-
|Mn(CO)6+||1.136||2199||2265
|-
|Fe(CO)62+||1.125||2297||2322
|}

The trend in C-O bond length largely goes as expected, decreasing from Ti to Fe as the metal center is more and more oxidised, and thus engages in less and less backbonding to the C-O π* anti bonding orbital. The result is that the C-O bond is less destabilised and thus shorter. Since bond stretch frequency is proportional with bond strength, the trend in asymmetric C-O bond stretch frequency is that it increases from Ti2- to Fe2+.

Inspecting the completely symmetric C-O bond stretch frequency, one can see that it as with the asymmetric stretch frequency, it increases across the period (increasing with C-O bond strength). These Frequencies cannot however be tested experimentally with IR as their being completely symmetrical means that they cause no change in dipole moment and are thus not IR active, and will not show up in an IR spectrum of the complex.

==References==
<references>
<ref name=handbook>CRC Handbook of Chemistry and Physics, 96th Edition.</ref>

<ref name=wired>http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html[Accessed 23 May 2019]</ref>
</references>

Nw3817

2019-05-24T15:34:33Z

Nw3817: /* Predictions */

==EX3 Section==

===BH3===

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

[[File:Nw3817_BH3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW3817_BH3_FREQ.LOG|NW3817_BH3_FREQ.LOG]]

<pre>
Low frequencies --- -2.2126 -1.0751 -0.0055 2.2359 10.2633 10.3194
Low frequencies --- 1162.9860 1213.1757 1213.1784
</pre>

<jmol><jmolApplet>
<title>BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW3817_BH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Vibrational spectrum of BH3===

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|1163||93||A2''||yes||out-of-plane bend
|-
|1213||14||E'||very slight||bend
|-
|1213||14||E'||very slight||bend
|-
|2582||0||A1'||no||symmetric stretch
|-
|2715||126||E'||yes||asymmetric stretch
|-
|2715||126||E'||yes||asymmetric stretch
|}

[[File:nw3817_BH3_spectrum.PNG|500px]]

While there are six vibrational modes, only three peaks are seen on the spectrum. This is because there are E' vibrations that are of degenerate energy (thus the vibrations have the same frequency), meaning only one peak is seen at 1213(cm-1) and 2715(cm-1), when each peak corresponds to two vibrations. The vibration at 2582(cm-1) is a symmetric stretch with no overall change in dipole moment, thus the vibration is not IR active. The result is that there are only three peaks in the spectrum.

[[File:nw3817_BH3_MO.jpg]]

When comparing calculated MOs with their corresponding LCAOs, one can see that regions in the same phase fuse together and regions that are not in the same phase distort away from one another. There are clear similarities between the qualitative LCAOs and the corresponding real MOs, but the more complex the atomic orbital, the further the LCAO is from the real MO. For example, the boron 1s a1' is exactly as the LCAO predicts, but the anti bonding e' orbitals are distorted from the LCAO, with lobes of different phases distorting away from each other. This illustrates how qualitative MO theory is very useful for predicting the MOs of simple systems, and even in more complex systems can be used to sort out which atomic orbitals contribute to real MOs, but to get a truly accurate idea of real MOs in more complex systems than this (anti bonding orbitals especially), we must calculate them.

===NH3===
B3LYP/6-31G(d,p) level

[[File:nw3817_NH3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW_NH3_FREQ.LOG|NW_NH3_FREQ.LOG]]

<pre>
Low frequencies --- -0.0136 -0.0021 0.0018 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NH3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===NH3BH3===

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

[[File:nw3817_NH3BH3_sym_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file: [[Media:NW_NH3BH3_SYM_OPT_FREQ.LOG|NW_NH3BH3_SYM_OPT_FREQ.LOG]]

<pre>
Low frequencies --- -0.0251 -0.0031 0.0007 17.1236 17.1259 37.1326
Low frequencies --- 265.7816 632.2034 639.3483
</pre>

<jmol><jmolApplet>
<title>NH3BH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NH3BH3_SYM_OPT_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Association Energy===
E(NH3)=-56.558 a.u.

E(BH3)=-26.615 a.u.

E(NH3BH3)=-83.225 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-0.052 a.u. = -136 kJ/mol

Ethane has a similar structure to NH3BH3, the same number of atoms, and is isoelectronic to it. The carbon-carbon single bond in ethane is about -377 kJ/mol<ref name=handbook />. This C-C bond is a strong bond and much deeper in energy than the N-B bond here. Another bond strength to compare is the o-o peroxide bond of strength -142 kJ/mol <ref name=wired />. The peroxide bond is a weak bond and the N-B bond is calculated to be even weaker than this, so the N-b dative bond is a weak bond.

===NI3===
B3LYP/6-31G(d,p)LANL2DZ level

frequency file: [[Media:NW_NI3_FREQ.LOG|NW_NI3_FREQ.LOG]]

[[File:nw3817_NI3_summary_table.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
</pre>

<pre>
Low frequencies --- -12.5522 -12.5460 -6.0047 -0.0040 0.0191 0.0664
Low frequencies --- 100.9969 100.9977 147.3377
</pre>

<jmol><jmolApplet>
<title>NI3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_NI3_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimised N-I distance: 2.184 Å

==Project Section: Metal Carbonyls==
===Predictions===
Given knowledge of metal-ligand back bonding from this year's Transition Metals and Organometallics lecture course, and given that these compounds are isoelectronic d6, back bonding should decrease as the metal center used goes from Ti to Fe across the period. The metal oxidation state increases (becomes more positive) from Ti2- to Fe2+ so the metal can less readily donate electrons into the C-O π* anti bonding orbital.

Since back bonding donates electrons into the C-O π* anti bonding orbital, increased back bonding decreases C-O bond strength, and thus C-O bond stretch frequency. C-O bond frequency should then increase with decreasing back bonding, therefore increasing across the period.

===[Cr(CO)6]===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Cr_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000110 0.000450 YES
RMS Force 0.000041 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000336 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_CR_FREQ.LOG|NW_CR_FREQ.LOG]]

<pre>
Low frequencies --- -0.0008 0.0008 0.0009 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6547 66.6547
</pre>

<jmol><jmolApplet>
<title>[Cr(CO)6]</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===[Ti(CO)6]2-===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Ti_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000334 0.000450 YES
RMS Force 0.000121 0.000300 YES
Maximum Displacement 0.000726 0.001800 YES
RMS Displacement 0.000282 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_TI_FREQ.LOG|NW_TI_FREQ.LOG]]

<pre>
Low frequencies --- 0.0012 0.0015 0.0015 13.3364 13.3364 13.3364
Low frequencies --- 29.8194 29.8194 29.8194
</pre>

<jmol><jmolApplet>
<title>[Ti(CO)6]2-</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_TI_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===[Fe(CO)6]2+===

B3LYP/6-31G(d,p)LANL2DZ level

[[File:nw3817_Fe_summary.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000222 0.000450 YES
RMS Force 0.000077 0.000300 YES
Maximum Displacement 0.000254 0.001800 YES
RMS Displacement 0.000094 0.001200 YES
</pre>

Frequency analysed log file: [[Media:NW_FE_FREQ.LOG|NW_FE_FREQ.LOG]]

<pre>
Low frequencies --- -9.5131 -9.5131 -9.5131 0.0006 0.0010 0.0010
Low frequencies --- 82.3908 82.3908 82.3908
</pre>

<jmol><jmolApplet>
<title>[Fe(CO)6]2+</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>NW_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

===Analysis===

{| class="wikitable"
|+ C-O Bond Lengths
|-
|Complex || C-O bond length (Å) || C-O asymmetric bond stretch frequency (cm-1) || C-O symmetric bond stretch frequency (cm-1)
|-
|Ti(CO)62-||1.183||1857||1992
|-
|V(CO)6-||1.166||1970||2097
|-
|Cr(CO)6||1.149||2086||2189
|-
|Mn(CO)6+||1.136||2199||2265
|-
|Fe(CO)62+||1.125||2297||2322
|}

The trend in C-O bond length largely goes as expected, decreasing from Ti to Fe as the metal center is more and more oxidised, and thus engages in less and less backbonding to the C-O π* anti bonding orbital. The result is that the C-O bond is less destabilised and thus shorter. Since bond stretch frequency is proportional with bond strength, the trend in asymmetric C-O bond stretch frequency is that it increases from Ti2- to Fe2+.

==References==
<references>
<ref name=handbook>CRC Handbook of Chemistry and Physics, 96th Edition.</ref>

<ref name=wired>http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html[Accessed 23 May 2019]</ref>
</references>

Nw3817