ChemWiki - User contributions [en]

Zl7710

2019-05-20T15:39:15Z

Zl6417: /* Results and Discussion */

==BH3==

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

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is a symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the non-bonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

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

'''NH3'''

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

'''NH3BH3'''

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
= ca. -135.4660 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol) or a B-H covalent bond (ca.345 kJ/mol) 3

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

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

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6, [Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

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

'''Cr(CO)6'''

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''[Mn(CO)6]+'''

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Predictions ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligands; The metal centres are of similar sizes but different oxidation states. Hence the bond lengths mainly depend on the degree of back-donation from the metal to the ligands.

A more electro-positive or positively-charged metal centre has stronger attractions to the d electrons and is less inclined to back-donate the e- density onto CO ligands. Hence the M-C bond will be longer and weaker compared to those with more back-donation. In addition, donation of d electrons onto π* of CO weakens and enlongates the C-O bond. Therefore,

• Electro-positivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

Assume the three metal centres are of the same size.

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond length: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron densities from the metal center and this phenomenon is called back-donation.
The three metals are similar except for the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C , which may be attributed to the fact that Cr has a larger radius than Mn2+ and that outweighs the effect of back-donation.

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations ====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally which gives the wavelength 2264 cm -1 with 0 intensity

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

3. https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf, (accessed May 19th 2019)

Zl7710

2019-05-20T15:38:01Z

Zl6417: /* Bond lengths */

==BH3==

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

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is a symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the non-bonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

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

'''NH3'''

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

'''NH3BH3'''

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
= ca. -135.4660 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol) or a B-H covalent bond (ca.345 kJ/mol) 3

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

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

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6, [Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

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

'''Cr(CO)6'''

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''[Mn(CO)6]+'''

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Predictions ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligands; The metal centres are of similar sizes but different oxidation states. Hence the bond lengths mainly depend on the degree of back-donation from the metal to the ligands.

A more electro-positive or positively-charged metal centre has stronger attractions to the d electrons and is less inclined to back-donate the e- density onto CO ligands. Hence the M-C bond will be longer and weaker compared to those with more back-donation. In addition, donation of d electrons onto π* of CO weakens and enlongates the C-O bond. Therefore,

• Electro-positivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

Assume the three metal centres are of the same size.

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond length: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron densities from the metal center and this phenomenon is called back-donation.
The three metals are similar except for the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C which may be attributed to the fact that Cr has a larger radius than Mn2+.

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations ====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally which gives the wavelength 2264 cm -1 with 0 intensity

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

3. https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf, (accessed May 19th 2019)

Zl7710

2019-05-20T15:36:26Z

Zl6417: /* Results and Discussion */

==BH3==

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

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is a symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the non-bonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

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

'''NH3'''

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

'''NH3BH3'''

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
= ca. -135.4660 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol) or a B-H covalent bond (ca.345 kJ/mol) 3

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

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

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6, [Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

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

'''Cr(CO)6'''

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''[Mn(CO)6]+'''

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Predictions ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligands; The metal centres are of similar sizes but different oxidation states. Hence the bond lengths mainly depend on the degree of back-donation from the metal to the ligands.

A more electro-positive or positively-charged metal centre has stronger attractions to the d electrons and is less inclined to back-donate the e- density onto CO ligands. Hence the M-C bond will be longer and weaker compared to those with more back-donation. In addition, donation of d electrons onto π* of CO weakens and enlongates the C-O bond. Therefore:

• Electro-positivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond length: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron densities from the metal center and this phenomenon is called back-donation.
The three metals are similar except for the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C which may be attributed to the fact that Cr has a larger radius than Mn2+.

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations ====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally which gives the wavelength 2264 cm -1 with 0 intensity

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

3. https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf, (accessed May 19th 2019)

Zl7710

2019-05-20T15:34:50Z

Zl6417: /* Results and Discussion */

==BH3==

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

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is a symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the non-bonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

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

'''NH3'''

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

'''NH3BH3'''

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
= ca. -135.4660 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol) or a B-H covalent bond (ca.345 kJ/mol) 3

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

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

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6, [Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

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

'''Cr(CO)6'''

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''[Mn(CO)6]+'''

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Predictions ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligands; The metal centres are of similar sizes but different oxidation states. Hence the bond lengths mainly depend on the degree of back-donation from the metal to the ligands.

A more electro-positive or positively-charged metal centre has stronger attractions to the d electrons and is less inclined to back-donate the e- density onto CO ligands. Hence the M-C bond will be longer and weaker compared to those with more back-donation. In addition, donation of d electrons onto π* of CO weakens and enlongates the C-O bond. Therefore:

• Electro-positivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond length: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron densities from the metal center and this phenomenon is called back-donation.
The three metals are similar except for the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C which may

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations ====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally which gives the wavelength 2264 cm -1 with 0 intensity

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

3. https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf, (accessed May 19th 2019)

Zl7710

2019-05-20T15:33:21Z

Zl6417: /* Predictions */

==BH3==

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

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is a symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the non-bonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

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

'''NH3'''

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

'''NH3BH3'''

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
= ca. -135.4660 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol) or a B-H covalent bond (ca.345 kJ/mol) 3

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

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

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6, [Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

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

'''Cr(CO)6'''

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''[Mn(CO)6]+'''

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Predictions ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligands; The metal centres are of similar sizes but different oxidation states. Hence the bond lengths mainly depend on the degree of back-donation from the metal to the ligands.

A more electro-positive or positively-charged metal centre has stronger attractions to the d electrons and is less inclined to back-donate the e- density onto CO ligands. Hence the M-C bond will be longer and weaker compared to those with more back-donation. In addition, donation of d electrons onto π* of CO weakens and enlongates the C-O bond. Therefore:

• Electro-positivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond length: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron densities from the metal center and this phenomenon is called back-donation.
The three metals are similar except for the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations ====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally which gives the wavelength 2264 cm -1 with 0 intensity

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

3. https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf, (accessed May 19th 2019)

Zl7710

2019-05-20T15:26:29Z

Zl6417: /* Computation */

==BH3==

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

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is a symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the non-bonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

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

'''NH3'''

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

'''NH3BH3'''

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
= ca. -135.4660 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol) or a B-H covalent bond (ca.345 kJ/mol) 3

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

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

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6, [Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

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

'''Cr(CO)6'''

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

'''[Mn(CO)6]+'''

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

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

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Predictions ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron density from the metal center and this phenomenon is called back-donation.
The three metals are similar except the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations ====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally which gives the wavelength 2264 cm -1 with 0 intensity

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

3. https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf, (accessed May 19th 2019)

Zl7710

2019-05-20T15:25:49Z

Zl6417: /* Metal Carbonyls */

==BH3==

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

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is a symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the non-bonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

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

'''NH3'''

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

'''NH3BH3'''

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
= ca. -135.4660 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol) or a B-H covalent bond (ca.345 kJ/mol) 3

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

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

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6, [Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

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

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Predictions ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron density from the metal center and this phenomenon is called back-donation.
The three metals are similar except the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations ====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally which gives the wavelength 2264 cm -1 with 0 intensity

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

3. https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf, (accessed May 19th 2019)

Zl7710

2019-05-20T15:24:52Z

Zl6417: /* Association energies: Ammonia-Borane */

==BH3==

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

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is a symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the non-bonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

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

'''NH3'''

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

'''NH3BH3'''

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
= ca. -135.4660 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol) or a B-H covalent bond (ca.345 kJ/mol) 3

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

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

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

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

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Predictions ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron density from the metal center and this phenomenon is called back-donation.
The three metals are similar except the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations ====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally which gives the wavelength 2264 cm -1 with 0 intensity

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

3. https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf, (accessed May 19th 2019)

Zl7710

2019-05-20T15:17:58Z

Zl6417: /* Association energies: Ammonia-Borane */

==BH3==

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

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is a symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the non-bonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

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

'''NH3'''

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

'''NH3BH3'''

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
= ca. -135.4660 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol). 3

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

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

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

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

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Predictions ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron density from the metal center and this phenomenon is called back-donation.
The three metals are similar except the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations ====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally which gives the wavelength 2264 cm -1 with 0 intensity

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

3. https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf, (accessed May 19th 2019)

Zl7710

2019-05-20T15:08:27Z

Zl6417: /* Molecular Orbitals of BH3 */

==BH3==

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

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is a symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the non-bonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

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

'''NH3'''

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

'''NH3BH3'''

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol). 3

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

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

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

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

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Predictions ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron density from the metal center and this phenomenon is called back-donation.
The three metals are similar except the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations ====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally which gives the wavelength 2264 cm -1 with 0 intensity

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

3. https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf, (accessed May 19th 2019)

Zl7710

2019-05-20T15:08:07Z

Zl6417: /* Molecular Orbitals of BH3 */

==BH3==

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

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is a symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the non-bonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

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

'''NH3'''

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

'''NH3BH3'''

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol). 3

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

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

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

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

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Predictions ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron density from the metal center and this phenomenon is called back-donation.
The three metals are similar except the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations ====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally which gives the wavelength 2264 cm -1 with 0 intensity

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

3. https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf, (accessed May 19th 2019)

Zl7710

2019-05-20T15:07:32Z

Zl6417: /* Molecular Orbitals of BH3 */

==BH3==

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

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is a symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

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

'''NH3'''

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

'''NH3BH3'''

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol). 3

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

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

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

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

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Predictions ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron density from the metal center and this phenomenon is called back-donation.
The three metals are similar except the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations ====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally which gives the wavelength 2264 cm -1 with 0 intensity

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

3. https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf, (accessed May 19th 2019)

Zl7710

2019-05-20T15:04:59Z

Zl6417: /* References */

==BH3==

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

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is a symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

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

'''NH3'''

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

'''NH3BH3'''

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol). 3

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

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

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

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

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Predictions ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron density from the metal center and this phenomenon is called back-donation.
The three metals are similar except the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations ====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally which gives the wavelength 2264 cm -1 with 0 intensity

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

3. https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf, (accessed May 19th 2019)

Zl7710

2019-05-20T15:04:14Z

Zl6417: /* Vibrational spectrum of BH3 */

==BH3==

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

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is a symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

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

'''NH3'''

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

'''NH3BH3'''

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol). 3

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

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

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

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

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Predictions ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron density from the metal center and this phenomenon is called back-donation.
The three metals are similar except the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations ====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally which gives the wavelength 2264 cm -1 with 0 intensity

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

Zl7710

2019-05-20T15:03:16Z

Zl6417: /* Metal Carbonyls */

==BH3==

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

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

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

'''NH3'''

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

'''NH3BH3'''

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol). 3

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

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

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

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

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Predictions ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron density from the metal center and this phenomenon is called back-donation.
The three metals are similar except the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations ====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally which gives the wavelength 2264 cm -1 with 0 intensity

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

Zl7710

2019-05-20T15:02:31Z

Zl6417: /* NI3 Using a mixture of basis-sets and psuedo-potentials */

==BH3==

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

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

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

'''NH3'''

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

'''NH3BH3'''

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol). 3

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

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

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Predictions ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron density from the metal center and this phenomenon is called back-donation.
The three metals are similar except the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations ====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally which gives the wavelength 2264 cm -1 with 0 intensity

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

Zl7710

2019-05-20T15:01:51Z

Zl6417: /* Association energies: Ammonia-Borane */

==BH3==

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

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

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

'''NH3'''

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

'''NH3BH3'''

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol). 3

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Predictions ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron density from the metal center and this phenomenon is called back-donation.
The three metals are similar except the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations ====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally which gives the wavelength 2264 cm -1 with 0 intensity

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

Zl7710

2019-05-20T15:00:58Z

Zl6417: /* Association energies: Ammonia-Borane */

==BH3==

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

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

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

'''NH3'''

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

'''NH3BH3'''

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Predictions ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron density from the metal center and this phenomenon is called back-donation.
The three metals are similar except the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations ====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally which gives the wavelength 2264 cm -1 with 0 intensity

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

Zl7710

2019-05-20T15:00:28Z

Zl6417: /* Association energies: Ammonia-Borane */

==BH3==

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

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

B3LYP/6-31G(d,p)

'''NH3'''

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

'''NH3BH3'''

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Predictions ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron density from the metal center and this phenomenon is called back-donation.
The three metals are similar except the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations ====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally which gives the wavelength 2264 cm -1 with 0 intensity

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

Zl7710

2019-05-20T14:59:09Z

Zl6417: /* BH3 */

==BH3==

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

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Predictions ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron density from the metal center and this phenomenon is called back-donation.
The three metals are similar except the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations ====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally which gives the wavelength 2264 cm -1 with 0 intensity

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

Zl7710

2019-05-19T18:12:51Z

Zl6417: /* Results and Discussion */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Predictions ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron density from the metal center and this phenomenon is called back-donation.
The three metals are similar except the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations ====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally which gives the wavelength 2264 cm -1 with 0 intensity

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

Zl7710

2019-05-19T18:12:09Z

Zl6417: /* Results and Discussion */

Zl7710

2019-05-19T18:11:41Z

Zl6417: /* Prediction */

Zl7710

2019-05-19T18:10:33Z

Zl6417: /* Analysis of C-O vibrations */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron density from the metal center and this phenomenon is called back-donation.
The three metals are similar except the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations ====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally which gives the wavelength 2264 cm -1 with 0 intensity

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

Zl7710

2019-05-19T18:09:15Z

Zl6417: /* Analysis of C-O vibrations = */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron density from the metal center and this phenomenon is called back-donation.
The three metals are similar except the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations ====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally with no intensity calculated.

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

Zl7710

2019-05-19T18:08:57Z

Zl6417: /* Vibrational frequencies */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron density from the metal center and this phenomenon is called back-donation.
The three metals are similar except the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

====Analysis of C-O vibrations =====

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally with no intensity calculated.

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

Zl7710

2019-05-19T18:07:41Z

Zl6417: /* Metal Carbonyls */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron density from the metal center and this phenomenon is called back-donation.
The three metals are similar except the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

Overall charges on the CO ligands:

[Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

The sum of the absolute value of metal charge and oxidation state:

[Fe(CO)6]2+ (3.504) > [Mn(CO)6]+ (3.048) > Cr(CO)6 (2.450)

Besides the overall charge on the CO ligands:

[Fe(CO)6]2+ (0.408) < [Mn(CO)6]+ (0.508) < Cr(CO)6 (0.584)

These results are in consistent with the predictions.

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally with no intensity calculated.

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

Zl7710

2019-05-19T18:03:01Z

Zl6417: /* Atomic charges */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron density from the metal center and this phenomenon is called back-donation.
The three metals are similar except the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the sum of the absolute value of atomic charge and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally with no intensity calculated.

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

Zl7710

2019-05-19T18:02:04Z

Zl6417: /* Metal Carbonyls */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Atomic charges ====

CO ligand is both a σ-donor and π-donor which donates electron density to the metal center; Besides, it is also a π-acceptor which can accept electron density from the metal center and this phenomenon is called back-donation.
The three metals are similar except the oxidation states which determine the degree of back-donation.

The higher the oxidation state of the metal is, the more donation of electron density from ligands (consider electrostatic forces) and less back-donation from the metal are.

Hence the a sum of the |atomic charge| and oxidation state:

[Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally with no intensity calculated.

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

Zl7710

2019-05-19T17:49:24Z

Zl6417: /* Molecular orbitals of Cr(CO)6 */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally with no intensity calculated.

==== Selected Valence Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

Zl7710

2019-05-19T17:42:44Z

Zl6417: /* Molecular orbitals of Cr(CO)6 */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally with no intensity calculated.

==== Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|'''t2g''' || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|'''eg''' || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

Zl7710

2019-05-19T17:41:48Z

Zl6417: /* Molecular orbitals of Cr(CO)6 */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally with no intensity calculated.

==== Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u. Overall bonding.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u. Overall bonding.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u. Overall bonding.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

Zl7710

2019-05-19T17:39:44Z

Zl6417: /* References */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally with no intensity calculated.

==== Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)

2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

Zl7710

2019-05-19T17:39:27Z

Zl6417: /* References */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally with no intensity calculated.

==== Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==
<pre>
1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)
2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)
</pre>

Zl7710

2019-05-19T17:38:58Z

Zl6417: /* References */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally with no intensity calculated.

==== Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019);
2. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

Zl7710

2019-05-19T17:38:45Z

Zl6417: /* Molecular orbitals of Cr(CO)6 */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally with no intensity calculated.

==== Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

==References==

1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf, (accessed May 19th 2019)
1. Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/teaching_MOs_year2/L7_Notes_web_printing.pdf, (accessed May 19th 2019)

Zl7710

2019-05-19T17:35:00Z

Zl6417: /* NI3 Using a mixture of basis-sets and psuedo-potentials */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally with no intensity calculated.

==== Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

Zl7710

2019-05-19T17:34:30Z

Zl6417: /* Metal Carbonyls */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally with no intensity calculated.

==== Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

Zl7710

2019-05-19T17:33:10Z

Zl6417:

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

'''MO. Figure 1 BH3.''' '''1'''

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Metal Carbonyls ==

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally with no intensity calculated.

==== Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

Zl7710

2019-05-19T17:30:31Z

Zl6417: /* Molecular Orbitals of BH3 */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px||left|thumb| '''MO. Figure 1[1] BH3''']]

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Metal Carbonyls ==

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally with no intensity calculated.

==== Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

Zl7710

2019-05-19T17:27:50Z

Zl6417: /* Molecular orbitals of Cr(CO)6 */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

Figure. MO orbitals of BH3 calculated by Gaussview [1]

(Orbital Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf)

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Metal Carbonyls ==

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally with no intensity calculated.

==== Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions between metal and ligands. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO. (Shown in MO.Figure 2 above)

This is relatively deeper in energy but higher than the eg orbital shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO. (Shown in MO.Figure 2 above)

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is deep energy due to strong σ-σ interactions and relative low energy of 5σ orbitals.

Zl7710

2019-05-19T17:24:27Z

Zl6417: /* Molecular orbitals of Cr(CO)6 */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

Figure. MO orbitals of BH3 calculated by Gaussview [1]

(Orbital Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf)

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Metal Carbonyls ==

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally with no intensity calculated.

==== Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands. (Shown in MO.Figure 2 above)

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO.

This is relatively deeper in energy but higher than the eg shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO.

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is relatively deep energy due to strong σ-σ interactions.

Zl7710

2019-05-19T17:22:26Z

Zl6417: /* Molecular orbitals */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

Figure. MO orbitals of BH3 calculated by Gaussview [1]

(Orbital Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf)

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Metal Carbonyls ==

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally with no intensity calculated.

==== Molecular orbitals of Cr(CO)6====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands.

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO.

This is relatively deeper in energy but higher than the eg shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO.

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is relatively deep energy due to strong σ-σ interactions.

Zl7710

2019-05-19T17:21:59Z

Zl6417: /* Molecular orbitals */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

Figure. MO orbitals of BH3 calculated by Gaussview [1]

(Orbital Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf)

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Metal Carbonyls ==

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally with no intensity calculated.

==== Molecular orbitals ====

<pre>
Take the MOs of Cr(CO)6 as an example.
</pre>

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands.

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO.

This is relatively deeper in energy but higher than the eg shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO.

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is relatively deep energy due to strong σ-σ interactions.

Zl7710

2019-05-19T17:21:24Z

Zl6417: /* Molecular orbitals */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

Figure. MO orbitals of BH3 calculated by Gaussview [1]

(Orbital Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf)

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Metal Carbonyls ==

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally with no intensity calculated.

==== Molecular orbitals ====

'''Take the MOs of Cr(CO)6 as an example.
'''

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

'''Note:'''
<pre>
• 1π is the π-donor MO;
• 5σ is the σ-donor FO and HOMO of CO;
• 2π* is the π-acceptor FO and LUMO of CO.
</pre>

'''Define the axis as:''' [[File:zl6417_axis.png]]

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands.

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO.

This is relatively deeper in energy but higher than the eg shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO.

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is relatively deep energy due to strong σ-σ interactions.

File:Zl6417 axis.png

2019-05-19T17:20:41Z

Zl6417: Zl6417 uploaded a new version of File:Zl6417 axis.png

Zl7710

2019-05-19T17:14:56Z

Zl6417: /* Molecular orbitals */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

Figure. MO orbitals of BH3 calculated by Gaussview [1]

(Orbital Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf)

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Metal Carbonyls ==

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally with no intensity calculated.

==== Molecular orbitals ====

'''Take the MOs of Cr(CO)6 as an example.
'''

MO diagram of the ligand CO '''2'''

{| class="wikitable"
|+
|-
|[[File:zl6417_co.png|500px|thumb|'''MO.Figure 2.'''|left]]
|}

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands.

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO.

This is relatively deeper in energy but higher than the eg shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO.

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is relatively deep energy due to strong σ-σ interactions.

File:Zl6417 co.png

2019-05-19T17:07:08Z

Zl6417:

File:Zl6417 axis.png

2019-05-19T17:06:51Z

Zl6417:

Zl7710

2019-05-19T16:58:44Z

Zl6417: /* Molecular orbitals */

==BH3==

B3LYP/6-31G(d,p)

[[File:Zl5417_bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000064 0.001800 YES
RMS Displacement 0.000039 0.001200 YES

</pre>

Frequency file: [[Media:ZL6417_BH3_FREQ.LOG| ZL6417_BH3_FREQ.log]]

<pre>
Low frequencies --- -7.5936 -1.5614 -0.0055 0.6514 6.9319 7.1055
Low frequencies --- 1162.9677 1213.1634 1213.1661

</pre>

<jmol><jmolApplet>
<title>Optimised BH3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL6417_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
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|-
|2716
|126
|E'
|yes
|asymmetric stretch
|}

[[File:Zl6417_bh3_spectrum.PNG]]

Although there are six vibrations shown in the table above, in the spectrum there are only three peaks, which can be explained by two reasons:

1. There are two doubly degenerate sets of vibrations being 1213 and 2716 cm-1 respectively

2. The vibration at 2581 cm-1 is symmetric stretch which involves no dipole change. Hence this vibration is not IR active and doesn't appear in the spectrum.

Hence there are only three peaks in the spectrum being 1163, 1213 and 2716 cm-1.

== Molecular Orbitals of BH3 ==

[[File:zl6417_mo_bh3.png|1000px]]

Figure. MO orbitals of BH3 calculated by Gaussview [1]

(Orbital Taken from http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year2a/Tut_MO_diagram_BH3.pdf)

Comparing the real MOs with the LCAOs, they have similar shapes but there are some differences.

1. For the occupied orbitals 2a1' and 1e', the real orbitals are perfectly predicted by the MO theory, but the real orbitals are more delocalized than the LCAO ones.

2. For the unoccupied orbitals, the nonbonding orbital 1a2" is perfectly predicted. Whereas 3a1' has an 'odd' p-like orbital on the centre boron atom, and the lobes of 2e' are more distorted or delocalised.

To sum up, qualitative MO theory can better predict the bonding or non-bonding orbitals with a good accuracy, and it is useful for qualitative analysis of frontier orbitals (HOMO and LUMO). On the other hand, it is less accurate or useful for predictions of antibonding orbitals

== Association energies: Ammonia-Borane ==

NH3

[[File:Zl6417_nh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000013 0.001800 YES
RMS Displacement 0.000007 0.001200 YES
</pre>

Low frequencies --- -0.0138 -0.0032 -0.0015 7.0783 8.0932 8.0937
Low frequencies --- 1089.3840 1693.9368 1693.9368

Frequency file: [[Media:zl64171_NH3_FREQ.LOG| zl6417_NH3_FREQ.LOG.log]]

NH3BH3

[[File:Zl6417_nh3bh3_opt.PNG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000114 0.000300 YES
Maximum Displacement 0.000849 0.001800 YES
RMS Displacement 0.000493 0.001200 YES
</pre>

Low frequencies --- -0.0139 -0.0049 -0.0030 20.4189 20.4428 48.1383
Low frequencies --- 267.4176 632.7852 640.1442

Frequency file: [[Media:zl6417_NH3BH3_FREQ.LOG| zl6417_NH3BH3_FREQ.LOG]]

<pre>
E(NH3)= -56.55776873 a.u.
E(BH3)=-26.61532360 a.u.
E(NH3BH3)= -83.22468864 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
=-0.05159631 a.u.
=-135.4660523 kJ/mol
</pre>

Based on the calculated bond energy, this dative bond (ca. 135 kJ/mol) between BH3 and NH3 is relatively weak compared to a covalent bond between B and N (ca. 378 kJ/mol).
(Value taken from https://notendur.hi.is/agust/rannsoknir/papers/2010-91-CRC-BDEs-Tables.pdf)

== NI3 Using a mixture of basis-sets and psuedo-potentials ==

Frequency file: [[Media:ZL_NI3_FREQ_3.LOG| ZL_NI3_FREQ_3.LOG]]

[[File:zl6417_Ni3_opt.GIF]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000064 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.000488 0.001800 YES
RMS Displacement 0.000278 0.001200 YES

</pre>

<jmol><jmolApplet>
<title>Optimised NI3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZL_NI3_FREQ_3.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Low frequencies --- -12.7380 -12.7319 -6.2907 -0.0040 0.0188 0.0633
Low frequencies --- 101.0326 101.0333 147.4124
</pre>

'''Optimised N-I distance: 2.184 Å'''

== Metal Carbonyls ==

In this mini investigation project, the three metal carbonyl compounds were computated and analysed: Cr(CO)6,[Mn(CO)6]+ and [Fe(CO)6]2+. These are all isostructural and isoelectronic d6 with low spin due the strong field ligand CO.

=== Computation ===

Cr(CO)6

[[File:zl6417_Cr.png]]

Frequency file: [[Media:zl6417_CR_FREQ.LOG| zl6417_CR_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000155 0.000450 YES
RMS Force 0.000063 0.000300 YES
Maximum Displacement 0.000705 0.001800 YES
RMS Displacement 0.000378 0.001200 YES
</pre>

Low frequencies --- 0.0016 0.0017 0.0017 11.7424 11.7424 11.7424
Low frequencies --- 66.6546 66.6546 66.6546

<jmol><jmolApplet>
<title>Optimised Cr(CO)6 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_CR_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Mn(CO)6]+

[[File:zl6417_Mn.png]]

Frequency file: [[Media:zl6417_MN_FREQ.LOG| zl6417_MN_FREQ.LOG]]
<pre>
Item Value Threshold Converged?
Maximum Force 0.000070 0.000450 YES
RMS Force 0.000029 0.000300 YES
Maximum Displacement 0.000345 0.001800 YES
RMS Displacement 0.000185 0.001200 YES
</pre>

Low frequencies --- -0.0009 -0.0007 0.0006 6.1493 6.1493 6.1493
Low frequencies --- 76.3727 76.3727 76.3727

<jmol><jmolApplet>
<title>Optimised [Mn(CO)6]+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_MN_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

[Fe(CO)6]2+

[[File:zl6417_Fe.png]]

Frequency file: [[Media:zl6417_FE_FREQ.LOG| zl6417_FE_FREQ.LOG]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000377 0.000450 YES
RMS Force 0.000193 0.000300 YES
Maximum Displacement 0.000880 0.001800 YES
RMS Displacement 0.000420 0.001200 YES
</pre>

Low frequencies --- -12.1458 -12.1458 -12.1458 -0.0009 -0.0006 0.0003
Low frequencies --- 81.4550 81.4550 81.4550

<jmol><jmolApplet>
<title>Optimised [Fe(CO)6]2+ molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>zl6417_FE_FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

== Metal Carbonyls ==

=== Prediction ===

==== Bond lengths ====

The complexes are all d6 low spin octahedral with 6 CO ligand; The metal centres are of similar size but different oxidation state. Hence the bond lengths mainly depends on the degree of back-donation from the metal to the ligand.

More electropositive or postively-charge metal centre is less inclined to back-donate the e- density onto CO ligand. Hence the M-C bond will be longer and weaker compared to those with larger back-donation. In addition, donating of d electrons onto π* of C≡O weakens the triple bond and enlongate the C≡O bond. Therefore:

• Electropositivity of the metal centre: Fe2+ > Mn+ > Cr

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• M-C bond length: Fe-C > Mn-C > Cr-C

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

==== Vibrational frequencies ====

The more the back-donation from the metal center to the π* is, the weaker the C≡O bond is. Hence back-donation decreases the vibrational frequency of C≡O bond.

• Degree of back-donation: [Fe(CO)6]2+ < [Mn(CO)6]+ < Cr(CO)6

• Vibrational frequency of Carbonyl: [Fe(CO)6]2+ > [Mn(CO)6]+ > Cr(CO)6

=== Results and Discussion ===

==== Bond lengths ====

{| class="wikitable"
|+
|-
|Complex || M-C / Å || C≡O / Å
|-
|Cr(CO)6
|1.915
|1.149
|-
|[Mn(CO)6]+
|1.908
|1.136
|-
|[Fe(CO)6]2+
|1.942
|1.125
|}

• M-C bond length: Fe-C > Cr-C > Mn-C 

• C≡O bond lengthe: Fe-C < Mn-C < Cr-C

According to the results, the C≡O bond lengths are consistent with theoretical predictions.

However, there is a discrepancy for the M-C bond lengths: Cr-C > Mn-C 

==== Atomic Charges ====

{| class="wikitable"
|+
|-
| Metal Complexes || Metal || Carbon || Oxygen || CO
|-
|Cr(CO)6
|( -2.450 )
|( 0.827 )
|(-0.419 )
|( 0.408 )
|-
|[Mn(CO)6]+
|( -2.048 )
|( 0.834 )
|( -0.326 )
|( 0.508 )
|-
|[Fe(CO)6]2+
|( -1.504 )
|( 0.815 )
|(-0.231 )
|( 0.584 )
|}

==== Vibrational frequencies ====

CO frequency:

{| class="wikitable"
|+
|-
|Complex || v(CO)/ cm-1
|-
|Cr(CO)6
|2086
|-
|[Mn(CO)6]+
|2198
|-
|[Fe(CO)6]2+
|2298
|}

Based on the data, Fe(CO)62+ has the largest v(CO) value while Cr(CO)6 has the lowest frequency. Hence the results are consistent with the predictions.

Take Cr(CO)6 as an example to analyse the '''C-O vibrations''' of metal complexes of Oh point group.

{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity (arbitrary units) || symmetry || IR active? || type
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2199
|879
|T1u
|yes
|assymetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2212
|0
|Eg
|no
|symmetric stretch
|-
|2264
|0
|A1
|no
|symmetric stretch
|}

Based on '''Group Theory''', the irreducible representation of Cr(CO)6 is '''A1+Eg+T1u'''. A1 and Eg induce no change in dipole moment therefore not IR active. T1u is anti-symmetric stretch of the apical carbonyl ligands so IR active. Hence there is only one CO peak visible on the IR spectrum

And although the totally symmetric CO vibration A1 cannot be analysed by IR, it can be analysed computationally with no intensity calculated.

==== Molecular orbitals ====

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_a_cal.png]]
|[[File:zl6417_t2g_a.png]]
|}

'''MO Energy''': -0.25746 a.u.

This is the HOMO '''t2g''' and can be drawn as a LCAO of metal '''dxy''' and '''2π*''' of ligands.

It is the highest-energy valence orbital due to anti-bonding characters within the CO ligands, and relatively weak π interactions. It is also one of the triply-degenerate '''t2g''' orbitals for Oh complexes in crystal field theory.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_t2g_b_cal.png]]
|[[File:zl6417_t2g_b.png]]
|}

'''MO Energy''': -0. 48463 a.u.

This '''t2g''' orbital can be explained as a LCAO of '''dxy''' and '''1π''' orbitals on CO.

This is relatively deeper in energy but higher than the eg shown below due to weaker side-side π interactions compared to head-head σ interactions.

{| class="wikitable"
|+
|-
|Calculation || LCAO
|-
|[[File:zl6417_eg_cal.png]]
|[[File:zl6417_eg.png]]
|}

'''MO Energy''': -0.57300 a.u.

This '''eg''' orbital can be drawn as a LCAO of '''dz2''' orbital of metal and six '''5σ''' of CO.

This interaction is bonding because there is constructive overlap and no node between the metal centre and ligands. This orbital is relatively deep energy due to strong σ-σ interactions.