ChemWiki - User contributions [en]

Yh1817

2019-05-20T16:55:32Z

Yh1817: /* Introduction */

== Introduction ==

This page contains some general information on optimising BH3, NH3, NH3BH3, NI3 and two more complex cations. It lists the basis set, summary, item table and frequency data for each substance, and the data were obtained as proceeding through the optimisation steps. For the two cations, the descriptions are more theoretically based and the usefulness on LCAO approach in Inorganic Molecular Orbital Chemistry is strengthened.

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq(1/cm) Intensity IR active? Type stretch/bend modes symmetry
1 1164 92 yes bending out-of-plane A2
2 1214 14 slight bending in-plane E'
3 1214 14 slight bending in-plane E'
4 2580 0 no stretching symmetric A1
5 2713 126 yes stretching asymmetric E'
6 2713 126 yes stretching asymmetric E'
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

Figure 3.<ref name="Figure 3" />
<references>
<ref name="Figure 3">Hunt P. Lecture_4_Tut_MO_diagram_BH3. ''Inorganic Lecture Course''. London: Imperial College London; 2019.</ref>
</references>

----

==== Q1. Are there any significant differences between the real and LCAO MOs? ====

A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The atomic orbitals are 'mixed' in shape and characteristics of individual AO lobes and spheres disappear. The LCAO MOs are from simply combining atomic orbitals (AO lobes and spheres still identifiable) and the orbital sizes are varied based on extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====

A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. It is not accurate enough for more complex MOs or MOs of higher energy. To understand shapes (orbital overlap) and sizes of more complex MOs, calculations should be performed instead of simply drawing LCAOs.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Traditional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----

=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

{| class="wikitable" border="1"
|+ MO no.9
! real MO !! LCAO
|-
| [[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.15
! real MO !! LCAO
|-
| [[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.21(HOMO)
! real MO !! LCAO
|-
| [[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]] || [[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]
|}

It might be interesting looking at the structure of real MOs and spotting that the number of 'layers' of orbitals resembles that of the phases predicted by the LCAO MOs.

For example, the real MO no.9 ('''Figure 6''') has two 'layers' of orbital (one red layer and one green layer) while the phase of LCAO no.9 ('''Figure 7''') is 'split' into two portions (white and black). MO no.15 ('''Figure 9''') has three layers (red-green-red) while LCAO no.15 ('''Figure 10''') has three portions of phases (black-white-black). The same trend applies to MO no.21. In general, more 'switching' between phases, higher the energy of MO will be-this is nicely agreed with the above visualisation of MOs.

== End-piece ==

To conclude, this page summaries some software-generated (Gaussian & Gaussview) information and visualisation on simple molecules, and tries to apply the known information for problem solving, i.e. to calculate the dative bond energy of B-N. The mini project focuses on optimisation of the two cations provided and consideration regarding their charge distributions. The MOs of [N(CH3)4]+ are linked to corresponding LCAOs to get an idea on how well the LCAOs represent the real situation. In the future, more complex systems may be investigated based on similar approach, and therefore use information listed here as a reference of starting point.

Yh1817

2019-05-20T16:46:51Z

Yh1817: /* Part 1. Small Molecules */

== Introduction ==

This page contains some general information on optimising BH3, NH3, NH3BH3, NI3 and two more complex cations. It lists the basis set, summary, item table and frequency data for each substance, and the data were obtained as proceeding through the optimisation steps. For the two cations, the descriptions are more theoretical and the importance on Inorganic Molecular Orbital Chemistry is strengthened.

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq(1/cm) Intensity IR active? Type stretch/bend modes symmetry
1 1164 92 yes bending out-of-plane A2
2 1214 14 slight bending in-plane E'
3 1214 14 slight bending in-plane E'
4 2580 0 no stretching symmetric A1
5 2713 126 yes stretching asymmetric E'
6 2713 126 yes stretching asymmetric E'
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

Figure 3.<ref name="Figure 3" />
<references>
<ref name="Figure 3">Hunt P. Lecture_4_Tut_MO_diagram_BH3. ''Inorganic Lecture Course''. London: Imperial College London; 2019.</ref>
</references>

----

==== Q1. Are there any significant differences between the real and LCAO MOs? ====

A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The atomic orbitals are 'mixed' in shape and characteristics of individual AO lobes and spheres disappear. The LCAO MOs are from simply combining atomic orbitals (AO lobes and spheres still identifiable) and the orbital sizes are varied based on extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====

A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. It is not accurate enough for more complex MOs or MOs of higher energy. To understand shapes (orbital overlap) and sizes of more complex MOs, calculations should be performed instead of simply drawing LCAOs.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Traditional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----

=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

{| class="wikitable" border="1"
|+ MO no.9
! real MO !! LCAO
|-
| [[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.15
! real MO !! LCAO
|-
| [[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.21(HOMO)
! real MO !! LCAO
|-
| [[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]] || [[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]
|}

It might be interesting looking at the structure of real MOs and spotting that the number of 'layers' of orbitals resembles that of the phases predicted by the LCAO MOs.

For example, the real MO no.9 ('''Figure 6''') has two 'layers' of orbital (one red layer and one green layer) while the phase of LCAO no.9 ('''Figure 7''') is 'split' into two portions (white and black). MO no.15 ('''Figure 9''') has three layers (red-green-red) while LCAO no.15 ('''Figure 10''') has three portions of phases (black-white-black). The same trend applies to MO no.21. In general, more 'switching' between phases, higher the energy of MO will be-this is nicely agreed with the above visualisation of MOs.

== End-piece ==

To conclude, this page summaries some software-generated (Gaussian & Gaussview) information and visualisation on simple molecules, and tries to apply the known information for problem solving, i.e. to calculate the dative bond energy of B-N. The mini project focuses on optimisation of the two cations provided and consideration regarding their charge distributions. The MOs of [N(CH3)4]+ are linked to corresponding LCAOs to get an idea on how well the LCAOs represent the real situation. In the future, more complex systems may be investigated based on similar approach, and therefore use information listed here as a reference of starting point.

Yh1817

2019-05-20T16:32:17Z

Yh1817: /* End-piece */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq(1/cm) Intensity IR active? Type stretch/bend modes symmetry
1 1164 92 yes bending out-of-plane A2
2 1214 14 slight bending in-plane E'
3 1214 14 slight bending in-plane E'
4 2580 0 no stretching symmetric A1
5 2713 126 yes stretching asymmetric E'
6 2713 126 yes stretching asymmetric E'
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

Figure 3.<ref name="Figure 3" />
<references>
<ref name="Figure 3">Hunt P. Lecture_4_Tut_MO_diagram_BH3. ''Inorganic Lecture Course''. London: Imperial College London; 2019.</ref>
</references>

----

==== Q1. Are there any significant differences between the real and LCAO MOs? ====

A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The atomic orbitals are 'mixed' in shape and characteristics of individual AO lobes and spheres disappear. The LCAO MOs are from simply combining atomic orbitals (AO lobes and spheres still identifiable) and the orbital sizes are varied based on extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====

A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. It is not accurate enough for more complex MOs or MOs of higher energy. To understand shapes (orbital overlap) and sizes of more complex MOs, calculations should be performed instead of simply drawing LCAOs.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Traditional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----

=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

{| class="wikitable" border="1"
|+ MO no.9
! real MO !! LCAO
|-
| [[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.15
! real MO !! LCAO
|-
| [[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.21(HOMO)
! real MO !! LCAO
|-
| [[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]] || [[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]
|}

It might be interesting looking at the structure of real MOs and spotting that the number of 'layers' of orbitals resembles that of the phases predicted by the LCAO MOs.

For example, the real MO no.9 ('''Figure 6''') has two 'layers' of orbital (one red layer and one green layer) while the phase of LCAO no.9 ('''Figure 7''') is 'split' into two portions (white and black). MO no.15 ('''Figure 9''') has three layers (red-green-red) while LCAO no.15 ('''Figure 10''') has three portions of phases (black-white-black). The same trend applies to MO no.21. In general, more 'switching' between phases, higher the energy of MO will be-this is nicely agreed with the above visualisation of MOs.

== End-piece ==

To conclude, this page summaries some software-generated (Gaussian & Gaussview) information and visualisation on simple molecules, and tries to apply the known information for problem solving, i.e. to calculate the dative bond energy of B-N. The mini project focuses on optimisation of the two cations provided and consideration regarding their charge distributions. The MOs of [N(CH3)4]+ are linked to corresponding LCAOs to get an idea on how well the LCAOs represent the real situation. In the future, more complex systems may be investigated based on similar approach, and therefore use information listed here as a reference of starting point.

Yh1817

2019-05-20T16:32:06Z

Yh1817: /* Three Valence MOs Chosen for [N(CH3)4]+ */

Yh1817

2019-05-20T16:31:28Z

Yh1817: /* Three Valence MOs Chosen for [N(CH3)4]+ */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq(1/cm) Intensity IR active? Type stretch/bend modes symmetry
1 1164 92 yes bending out-of-plane A2
2 1214 14 slight bending in-plane E'
3 1214 14 slight bending in-plane E'
4 2580 0 no stretching symmetric A1
5 2713 126 yes stretching asymmetric E'
6 2713 126 yes stretching asymmetric E'
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

Figure 3.<ref name="Figure 3" />
<references>
<ref name="Figure 3">Hunt P. Lecture_4_Tut_MO_diagram_BH3. ''Inorganic Lecture Course''. London: Imperial College London; 2019.</ref>
</references>

----

==== Q1. Are there any significant differences between the real and LCAO MOs? ====

A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The atomic orbitals are 'mixed' in shape and characteristics of individual AO lobes and spheres disappear. The LCAO MOs are from simply combining atomic orbitals (AO lobes and spheres still identifiable) and the orbital sizes are varied based on extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====

A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. It is not accurate enough for more complex MOs or MOs of higher energy. To understand shapes (orbital overlap) and sizes of more complex MOs, calculations should be performed instead of simply drawing LCAOs.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Traditional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----

=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

{| class="wikitable" border="1"
|+ MO no.9
! real MO !! LCAO
|-
| [[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.15
! real MO !! LCAO
|-
| [[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.21(HOMO)
! real MO !! LCAO
|-
| [[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]] || [[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]
|}

It might be interesting looking at the structure of real MOs and spotting that the number of 'layers' of orbitals resembles that of the phases predicted by the LCAO MOs.

For example, the real MO no.9 ('''Figure 6''') has two 'layers' of orbital (one red layer and one green layer) while the phase of LCAO no.9 ('''Figure 7''') is 'split' into two portions (white and black). MO no.15 ('''Figure 9''') has three layers (red-green-red) while LCAO no.15 ('''Figure 10''') has three portions of phases (black-white-black). The same trend applies to MO no.21. In general, more 'switching' between phases, higher the energy of MO will be-this is nicely agreed with the above visualisation of MOs.

----
== End-piece ==

To conclude, this page summaries some software-generated (Gaussian & Gaussview) information and visualisation on simple molecules, and tries to apply the known information for problem solving, i.e. to calculate the dative bond energy of B-N. The mini project focuses on optimisation of the two cations provided and consideration regarding their charge distributions. The MOs of [N(CH3)4]+ are linked to corresponding LCAOs to get an idea on how well the LCAOs represent the real situation. In the future, more complex systems may be investigated based on similar approach, and therefore use information listed here as a reference of starting point.

Yh1817

2019-05-20T16:06:05Z

Yh1817: /* Three Valence MOs Chosen for [N(CH3)4]+ */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq(1/cm) Intensity IR active? Type stretch/bend modes symmetry
1 1164 92 yes bending out-of-plane A2
2 1214 14 slight bending in-plane E'
3 1214 14 slight bending in-plane E'
4 2580 0 no stretching symmetric A1
5 2713 126 yes stretching asymmetric E'
6 2713 126 yes stretching asymmetric E'
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

Figure 3.<ref name="Figure 3" />
<references>
<ref name="Figure 3">Hunt P. Lecture_4_Tut_MO_diagram_BH3. ''Inorganic Lecture Course''. London: Imperial College London; 2019.</ref>
</references>

----

==== Q1. Are there any significant differences between the real and LCAO MOs? ====

A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The atomic orbitals are 'mixed' in shape and characteristics of individual AO lobes and spheres disappear. The LCAO MOs are from simply combining atomic orbitals (AO lobes and spheres still identifiable) and the orbital sizes are varied based on extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====

A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. It is not accurate enough for more complex MOs or MOs of higher energy. To understand shapes (orbital overlap) and sizes of more complex MOs, calculations should be performed instead of simply drawing LCAOs.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Traditional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----

=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

{| class="wikitable" border="1"
|+ MO no.9
! real MO !! LCAO
|-
| [[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.15
! real MO !! LCAO
|-
| [[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.21(HOMO)
! real MO !! LCAO
|-
| [[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]] || [[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]
|}

It might be interesting looking at the structure of real MOs and spoting that the number of 'layers' of orbitals resemble that of the phases predicted by the LCAO MOs. For example, the real MO no.9 ('''Figure 6''') has two 'layers' of orbital (one red layer and one green layer) while the phase of LCAO no.9 ('''Figure 7''') is 'split' into two portions (white and black). MO no.15 ('''Figure 9''') has three layers

Yh1817

2019-05-20T15:19:47Z

Yh1817: /* Q2. What does this say about the accuracy and usefulness of qualitative MO theory? */

Yh1817

2019-05-20T14:56:40Z

Yh1817: /* Q2. What does this say about the accuracy and usefulness of qualitative MO theory? */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq(1/cm) Intensity IR active? Type stretch/bend modes symmetry
1 1164 92 yes bending out-of-plane A2
2 1214 14 slight bending in-plane E'
3 1214 14 slight bending in-plane E'
4 2580 0 no stretching symmetric A1
5 2713 126 yes stretching asymmetric E'
6 2713 126 yes stretching asymmetric E'
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

Figure 3.<ref name="Figure 3" />
<references>
<ref name="Figure 3">Hunt P. Lecture_4_Tut_MO_diagram_BH3. ''Inorganic Lecture Course''. London: Imperial College London; 2019.</ref>
</references>

----

==== Q1. Are there any significant differences between the real and LCAO MOs? ====

A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The atomic orbitals are 'mixed' in shape and characteristics of individual AO lobes and spheres disappear. The LCAO MOs are from simply combining atomic orbitals (AO lobes and spheres still identifiable) and the orbital sizes are varied based on extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====

A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Traditional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----

=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

{| class="wikitable" border="1"
|+ MO no.9
! real MO !! LCAO
|-
| [[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.15
! real MO !! LCAO
|-
| [[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.21(HOMO)
! real MO !! LCAO
|-
| [[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]] || [[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]
|}

Yh1817

2019-05-20T14:55:53Z

Yh1817: /* Q1. Are there any significant differences between the real and LCAO MOs? */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq(1/cm) Intensity IR active? Type stretch/bend modes symmetry
1 1164 92 yes bending out-of-plane A2
2 1214 14 slight bending in-plane E'
3 1214 14 slight bending in-plane E'
4 2580 0 no stretching symmetric A1
5 2713 126 yes stretching asymmetric E'
6 2713 126 yes stretching asymmetric E'
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

Figure 3.<ref name="Figure 3" />
<references>
<ref name="Figure 3">Hunt P. Lecture_4_Tut_MO_diagram_BH3. ''Inorganic Lecture Course''. London: Imperial College London; 2019.</ref>
</references>

----

==== Q1. Are there any significant differences between the real and LCAO MOs? ====

A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The atomic orbitals are 'mixed' in shape and characteristics of individual AO lobes and spheres disappear. The LCAO MOs are from simply combining atomic orbitals (AO lobes and spheres still identifiable) and the orbital sizes are varied based on extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Traditional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----

=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

{| class="wikitable" border="1"
|+ MO no.9
! real MO !! LCAO
|-
| [[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.15
! real MO !! LCAO
|-
| [[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.21(HOMO)
! real MO !! LCAO
|-
| [[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]] || [[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]
|}

Yh1817

2019-05-20T14:37:53Z

Yh1817: /* BH3 (better basis set) */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq(1/cm) Intensity IR active? Type stretch/bend modes symmetry
1 1164 92 yes bending out-of-plane A2
2 1214 14 slight bending in-plane E'
3 1214 14 slight bending in-plane E'
4 2580 0 no stretching symmetric A1
5 2713 126 yes stretching asymmetric E'
6 2713 126 yes stretching asymmetric E'
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

Figure 3.<ref name="Figure 3" />
<references>
<ref name="Figure 3">Hunt P. Lecture_4_Tut_MO_diagram_BH3. ''Inorganic Lecture Course''. London: Imperial College London; 2019.</ref>
</references>

----

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Traditional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----

=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

{| class="wikitable" border="1"
|+ MO no.9
! real MO !! LCAO
|-
| [[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.15
! real MO !! LCAO
|-
| [[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.21(HOMO)
! real MO !! LCAO
|-
| [[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]] || [[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]
|}

Yh1817

2019-05-20T14:33:54Z

Yh1817: /* BH3 (better basis set) */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes symmetry
1 1164 92 yes bending out-of-plane A2
2 1214 14 yes bending in-plane E'
3 1214 14 yes bending in-plane E'
4 2580 0 no stretching symmetric A1
5 2713 126 yes stretching asymmetric E'
6 2713 126 yes stretching asymmetric E'
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

Figure 3.<ref name="Figure 3" />
<references>
<ref name="Figure 3">Hunt P. Lecture_4_Tut_MO_diagram_BH3. ''Inorganic Lecture Course''. London: Imperial College London; 2019.</ref>
</references>

----

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Traditional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----

=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

{| class="wikitable" border="1"
|+ MO no.9
! real MO !! LCAO
|-
| [[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.15
! real MO !! LCAO
|-
| [[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.21(HOMO)
! real MO !! LCAO
|-
| [[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]] || [[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]
|}

Yh1817

2019-05-20T14:33:19Z

Yh1817: /* BH3 (better basis set) */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes symmetry
1 1164 92 yes bending out-of-plane A2
2 1214 14 yes bending in-plane E'
3 1214 14 yes bending in-plane E'
4 2580 0 no stretching symmetric A1
5 2713 126 yes stretching asymmetric E'
6 2713 126 yes stretching asymmetric E'
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

Figure 3.<ref name="Figure 3" />
<references>
<ref name="Figure 3">Hunt P. Lecture_4_Tut_MO_diagram_BH3. ''Inorganic Lecture Course''. London: Imperial College London; 2019.</ref>
</references>

----

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Traditional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----

=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

{| class="wikitable" border="1"
|+ MO no.9
! real MO !! LCAO
|-
| [[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.15
! real MO !! LCAO
|-
| [[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.21(HOMO)
! real MO !! LCAO
|-
| [[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]] || [[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]
|}

Yh1817

2019-05-17T19:30:01Z

Yh1817: /* Molecular Orbital Diagram of BH3 */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

Figure 3.<ref name="Figure 3" />
<references>
<ref name="Figure 3">Hunt P. Lecture_4_Tut_MO_diagram_BH3. ''Inorganic Lecture Course''. London: Imperial College London; 2019.</ref>
</references>

----

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Traditional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----

=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

{| class="wikitable" border="1"
|+ MO no.9
! real MO !! LCAO
|-
| [[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.15
! real MO !! LCAO
|-
| [[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.21(HOMO)
! real MO !! LCAO
|-
| [[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]] || [[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]
|}

Yh1817

2019-05-17T19:29:39Z

Yh1817: /* Molecular Orbital Diagram of BH3 */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

Figure 3.<ref name="Figure 3" />
<references>
<ref name="Figure 3">Hunt P. Lecture_4_Tut_MO_diagram_BH3. ''Inorganic Lecture Course''. London: Imperial College London; 2019.</ref>
</references>

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Traditional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----

=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

{| class="wikitable" border="1"
|+ MO no.9
! real MO !! LCAO
|-
| [[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.15
! real MO !! LCAO
|-
| [[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.21(HOMO)
! real MO !! LCAO
|-
| [[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]] || [[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]
|}

Yh1817

2019-05-17T19:29:31Z

Yh1817: /* Molecular Orbital Diagram of BH3 */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

Figure 3.<ref name="Figure 3" />
<references>
<ref name="Figure 3">Hunt P. Lecture_4_Tut_MO_diagram_BH3. ''Inorganic Lecture Course''. London: Imperial College London; 2019.</ref>
</references>

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Traditional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----

=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

{| class="wikitable" border="1"
|+ MO no.9
! real MO !! LCAO
|-
| [[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.15
! real MO !! LCAO
|-
| [[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.21(HOMO)
! real MO !! LCAO
|-
| [[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]] || [[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]
|}

Yh1817

2019-05-17T19:29:24Z

Yh1817: /* Molecular Orbital Diagram of BH3 */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

Figure 3.<ref name="Figure 3" />
<references>
<ref name="Figure 3">Hunt P. Lecture_4_Tut_MO_diagram_BH3. ''Inorganic Lecture Course''. London: Imperial College London; 2019.</ref>
</references>

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Traditional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----

=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

{| class="wikitable" border="1"
|+ MO no.9
! real MO !! LCAO
|-
| [[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.15
! real MO !! LCAO
|-
| [[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.21(HOMO)
! real MO !! LCAO
|-
| [[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]] || [[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]
|}

Yh1817

2019-05-17T19:29:15Z

Yh1817: /* Molecular Orbital Diagram of BH3 */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

Figure 3.<ref name="Figure 3" />
<references>
<ref name="Figure 3">Hunt P. Lecture_4_Tut_MO_diagram_BH3. ''Inorganic Lecture Course''. London: Imperial College London; 2019.</ref>
</references>

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Traditional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----

=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

{| class="wikitable" border="1"
|+ MO no.9
! real MO !! LCAO
|-
| [[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.15
! real MO !! LCAO
|-
| [[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.21(HOMO)
! real MO !! LCAO
|-
| [[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]] || [[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]
|}

Yh1817

2019-05-17T19:28:56Z

Yh1817: /* Molecular Orbital Diagram of BH3 */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

Figure 3.<ref name="Figure 3" />
<references>
<ref name="Figure 3">Hunt P. Lecture_4_Tut_MO_diagram_BH3. ''Inorganic Lecture Course''. London: Imperial College London; 2019.</ref>
</references>

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Traditional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----

=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

{| class="wikitable" border="1"
|+ MO no.9
! real MO !! LCAO
|-
| [[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.15
! real MO !! LCAO
|-
| [[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.21(HOMO)
! real MO !! LCAO
|-
| [[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]] || [[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]
|}

Yh1817

2019-05-17T19:28:42Z

Yh1817: /* Molecular Orbital Diagram of BH3 */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

Figure 3.<ref name="Figure 3" />
<references>
<ref name="Figure 3">Hunt P. Lecture_4_Tut_MO_diagram_BH3. ''Inorganic Lecture Course''. London: Imperial College London; 2019.</ref>
</references>

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Traditional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----

=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

{| class="wikitable" border="1"
|+ MO no.9
! real MO !! LCAO
|-
| [[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.15
! real MO !! LCAO
|-
| [[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.21(HOMO)
! real MO !! LCAO
|-
| [[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]] || [[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]
|}

Yh1817

2019-05-17T19:28:21Z

Yh1817: /* Molecular Orbital Diagram of BH3 */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]
Figure 3.<ref name="Figure 3" />
<references>
<ref name="Figure 3">Hunt P. Lecture_4_Tut_MO_diagram_BH3. ''Inorganic Lecture Course''. London: Imperial College London; 2019.</ref>
</references>

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Traditional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----

=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

{| class="wikitable" border="1"
|+ MO no.9
! real MO !! LCAO
|-
| [[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.15
! real MO !! LCAO
|-
| [[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.21(HOMO)
! real MO !! LCAO
|-
| [[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]] || [[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]
|}

Yh1817

2019-05-17T16:11:30Z

Yh1817: /* [N(CH3)4]+: Transitional Presentation */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Traditional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----

=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

{| class="wikitable" border="1"
|+ MO no.9
! real MO !! LCAO
|-
| [[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.15
! real MO !! LCAO
|-
| [[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.21(HOMO)
! real MO !! LCAO
|-
| [[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]] || [[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]
|}

Yh1817

2019-05-17T16:09:36Z

Yh1817: /* Three Valence MOs Chosen for [N(CH3)4]+ */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Transitional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----
=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

{| class="wikitable" border="1"
|+ MO no.9
! real MO !! LCAO
|-
| [[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.15
! real MO !! LCAO
|-
| [[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.21(HOMO)
! real MO !! LCAO
|-
| [[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]] || [[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]
|}

Yh1817

2019-05-17T16:06:05Z

Yh1817: /* Three Valence MOs Chosen for [N(CH3)4]+ */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Transitional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----
=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

{| class="wikitable" border="1"
|+ MO no.9
! real MO !! LCAO
|-
| [[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.15
! real MO !! LCAO
|-
| [[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.21(HOMO)
! real MO !! LCAO
|-
| [[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]] || [[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]
|}

Yh1817

2019-05-17T16:05:45Z

Yh1817: /* Three Valence MOs Chosen for [N(CH3)4]+ */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Transitional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----
=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

{| class="wikitable" border="1"
|+ MO no.9
! real MO !! LCAO
|-
| [[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.15
! real MO !! LCAO
|-
| [[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.21(HOMO)
! real MO !! LCAO
|-
| [[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]] || [[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]
|}

Yh1817

2019-05-17T16:05:23Z

Yh1817: /* Three Valence MOs Chosen for [N(CH3)4]+ */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Transitional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----
=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

{| class="wikitable" border="1"
|+ MO no.9
! real MO !! LCAO
|-
| [[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.15
! real MO !! LCAO
|-
| [[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]] || [[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]
|}

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

{| class="wikitable" border="1"
|+ MO no.21(HOMO)
! real MO !! LCAO
|-
| [[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]] || [[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]
|}

Yh1817

2019-05-17T15:59:57Z

Yh1817: /* Three Valence MOs Chosen for [N(CH3)4]+ */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Transitional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----
=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

[[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]][[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

[[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]][[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

[[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]][[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]

Yh1817

2019-05-17T15:59:25Z

Yh1817: /* Three Valence MOs Chosen for [N(CH3)4]+ */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Transitional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----
=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

[[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]][[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

[[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]][[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

[[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]][[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]

Yh1817

2019-05-17T15:59:09Z

Yh1817: /* Three Valence MOs Chosen for [N(CH3)4]+ */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Transitional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----
=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams: MO number 9, 15 and 21. All these MOs shows bonding character.

[[File:Yh17 mo 09.PNG|thumb|left|'''Figure 6.'''MO no.9 of [N(CH3)4]+.]][[File:Yh17 LCAO 09.PNG|thumb|center|'''Figure 7.'''LCAO to MO no.9 of [N(CH3)4]+.]]

[[File:Yh17 methylnote1.PNG|thumb|left|'''Figure 8.'''Detailed notation of the above LCAO on methyl goups.]]

[[File:Yh17 mo 15.PNG|thumb|left|'''Figure 9.'''MO no.15 of [N(CH3)4]+.]][[File:Yh17 LCAO 15.PNG|thumb|center|'''Figure 10.'''LCAO to MO no.15 of [N(CH3)4]+.]]

[[File:Yh17 methylnote2.PNG|thumb|left|'''Figure 11.'''Detailed notation of the above and below LCAOs on methyl goups.]]

[[File:Yh17 mo homo.PNG|thumb|left|'''Figure 12.'''MO no.21(HOMO) of [N(CH3)4]+.]][[File:Yh17 LCAO 21.PNG|thumb|center|'''Figure 13.'''LCAO to MO no.21 of [N(CH3)4]+.]]

File:Yh17 LCAO 21.PNG

2019-05-17T15:58:01Z

Yh1817:

File:Yh17 mo homo.PNG

2019-05-17T15:57:10Z

Yh1817:

File:Yh17 methylnote2.PNG

2019-05-17T15:56:10Z

Yh1817:

File:Yh17 LCAO 15.PNG

2019-05-17T15:54:56Z

Yh1817:

File:Yh17 mo 15.PNG

2019-05-17T15:54:33Z

Yh1817:

File:Yh17 methylnote1.PNG

2019-05-17T15:53:23Z

Yh1817:

File:Yh17 LCAO 09.PNG

2019-05-17T15:50:54Z

Yh1817:

File:Yh17 mo 09.PNG

2019-05-17T15:23:12Z

Yh1817:

Yh1817

2019-05-17T15:19:47Z

Yh1817: /* BH3 */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Transitional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----
=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams.

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 6.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 7.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

Yh1817

2019-05-17T15:19:29Z

Yh1817: /* BH3 */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Transitional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----
=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams.

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 6.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 7.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

Yh1817

2019-05-17T15:19:12Z

Yh1817: /* BH3 */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|frame|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----

=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Transitional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----
=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams.

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 6.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 7.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

Yh1817

2019-05-17T15:13:38Z

Yh1817: /* Charge Distribution */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|thumb|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----
=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

----
=== [N(CH3)4]+: Transitional Presentation ===

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

----
=== Three Valence MOs Chosen for [N(CH3)4]+ ===

Three occupied MOs are chosen to draw their LCAO MO diagrams.

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 6.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 7.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

Yh1817

2019-05-16T19:38:54Z

Yh1817: /* Charge Distribution */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|thumb|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----
=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''

A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''

A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

Yh1817

2019-05-16T19:38:27Z

Yh1817: /* Charge Distribution */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|thumb|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----
=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

'''Q3. What does the "formal" positive charge on the N represent in the traditional picture?'''
A3. It should be representing the overall charge of the cation, since the charges on all H atoms add up to +3.228 and the charges on C and N atoms add up to -2.227, so the overall charge is +1. The charge is written on N might due to the fact that this is convenient (only need one notation rather than 12 notations on all the H!) and N is donating its lone pair to one C to form a dative bond, making it more electron deficient.

'''Q4. On what atoms is the positive charge actually located for this cation?'''
A4. Only hydrogen atoms are bearing the positive charge in [N(CH3)4]+.

Yh1817

2019-05-16T19:18:48Z

Yh1817: /* Charge Distribution */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|thumb|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----
=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

Yh1817

2019-05-16T19:18:35Z

Yh1817: /* Charge Distribution */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|thumb|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----
=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 4.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 5.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

Yh1817

2019-05-16T19:17:48Z

Yh1817: /* Charge Disytibution */

== Part 1. Small Molecules ==

=== BH3 ===

'''B3LYP/3-21G level'''

[[File:Yh bh3 opt summarysnip321.PNG|thumb|left|'''Table 1.'''The summary table for BH3 using B3LYP/3-21G.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000919 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>

[[File:Bh3 opt energyandgradient321.PNG|thumb|left|'''Figure 1.'''The energy and energy gradient for BH3 using B3LYP/3-21G.]]

----
=== BH3 (better basis set) ===

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

[[File:Yh bh3 opt d3hsummary.PNG|thumb|left|'''Table 2.'''The summary table for BH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 BH3 FREQ.LOG| YH17 BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.2260 -0.1035 -0.0054 48.0278 49.0875 49.0880
Low frequencies --- 1163.7224 1213.6715 1213.6741
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 BH3 FREQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

<pre>
Mode Freq Intensity IR active? Type stretch/bend modes
1 1164 92 yes bending out-of-plane
2 1214 14 yes bending in-plane
3 1214 14 yes bending in-plane
4 2580 0 no stretching symmetric
5 2713 126 yes stretching asymmetric
6 2713 126 yes stretching asymmetric
</pre>

[[File:Yh17 IR spec.PNG|frame|left|'''Figure 2.'''The IR spectrum for BH3 using B3LYP/6-21G(d,p).]]

There are only three peaks in the IR spectrum rather than six. This is because modes 2,3 are degenerate and modes 5,6 are degenerate, so only two peaks are shown for these four modes. Mode 1 is also IR active due to change in dipole moment so it shows up as a peak. The remaining mode 4 is not IR active as the symmetric stretch makes no overall change in dipole moment of the molecule, so it is not seen in the spectrum.

==== Molecular Orbital Diagram of BH3 ====

[[File:Yh17 finalmo fromref.PNG|frame|left|'''Figure 3.'''The MO diagram for BH3. The 'real' orbitals are placed next to their corresponding linear combination of atomic orbitals (LCAO).]]

==== Q1. Are there any significant differences between the real and LCAO MOs? ====
A1. The real MOs are obtained from calculation and hence more accurate in terms of relative sizes of orbitals and shapes etc. The LCAO MOs are from simply combining atomic orbitals and the orbital sizes are varied based on qualitative analysis of bonding/antibonding interactions and extent of energy match, and are therefore less accurate. However, LCAO MOs resemble well with the approximate shape and phase of real MOs, which indicates that LCAO MOs are adequate for qualitative analysis of orbital interaction.

==== Q2. What does this say about the accuracy and usefulness of qualitative MO theory? ====
A2. Qualitative MO theory is generally useful in predicting the forms and phases (hence the relative energies) and works well for simple MOs. To get a more accurate result for more complex MOs or MOs of higher energy, calculations should be performed to understand better on shapes (orbital overlap) and sizes of orbitals.

----

=== NH3 ===

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

[[File:Yh nh3summary.PNG|thumb|left|'''Table 3.'''The summary table for NH3 using B3LYP/6-21G(d,p).]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000016 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3 FREQ.LOG| YH17 NH3 FREQ.LOG]]

<pre>
Low frequencies --- -8.5646 -8.5588 -0.0044 0.0454 0.1784 26.4183
Low frequencies --- 1089.7603 1694.1865 1694.1865
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NEWNH3OP.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== NH3BH3 ===

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

[[File:Yh17 nh3bh3summary.PNG|thumb|left|'''Table 4.'''The summary table of NH3BH3 using B3LYP/6-31G(d,p) level.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000123 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000535 0.001800 YES
RMS Displacement 0.000296 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 NH3BH3 FREQ.LOG| YH17 NH3BH3 FREQ.LOG]]

<pre>
Low frequencies --- -0.0013 -0.0010 -0.0006 14.9014 21.5976 37.1828
Low frequencies --- 265.7882 632.1719 639.5776
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 NH3BH3 OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Association Energies: Ammonia-Borane ===

E(NH3) = -26.6153 a.u.

E(BH3) = -56.5577 a.u.

E(NH3BH3) = -83.2246 a.u.

ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.0516 a.u. = -135 kJ/mol

From the calculation it can be seen that B-N dative bond is relatively weak compared to B-N covalent bond (389 kJ/mol), which is nearly three times strength of the dative bond with the same species.

----

=== NI3 ===

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

Frequency analysis log file:
[[Media:Yh17 NI3 FREQ NEW C3V.LOG| Yh17 NI3 FREQ NEW C3V.LOG]]

[[File:Yh17 ni3summary c3v.PNG|thumb|left|'''Table 5.'''The summary table of NI3 using B3LYP/6-31G(d,p) level LANL2DZ.]]

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

<pre>
Low frequencies --- -22.5765 -22.5730 -19.6620 0.0038 0.0043 0.0250
Low frequencies --- 101.5687 101.5689 153.1297
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Yh17 NI3 OPT NEW C3V.LOG</uploadedFileContents>
</jmolApplet></jmol>

Optimized N-I distance: 2.185 Å

== Part 2. Mini Project ==

=== [N(CH3)4]+ ===

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

[[File:Yh17 N opt summary.PNG|thumb|left|'''Table 6.'''The summary table of [N(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 n optTdsummary.PNG|thumb|center|'''Table 7.'''The summary table of [N(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001657 0.001800 YES
RMS Displacement 0.000429 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 N FREQ.LOG| YH17 N FREQ.LOG]]

<pre>
Low frequencies --- 0.0007 0.0007 0.0008 35.6280 35.6280 35.6280
Low frequencies --- 217.6926 316.6598 316.6598
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 N OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----

=== [P(CH3)4]+ ===

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

[[File:Yh17 P optsummary.PNG|thumb|left|'''Table 8.'''The summary table of [P(CH3)4]+ using B3LYP/6-31G(d,p).]][[File:Yh17 P freqsummary.PNG|thumb|center|'''Table 9.'''The summary table of [P(CH3)4]+ for frequency calculation, point group Td.]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000135 0.000450 YES
RMS Force 0.000032 0.000300 YES
Maximum Displacement 0.000862 0.001800 YES
RMS Displacement 0.000343 0.001200 YES
</pre>

Frequency analysis log file:
[[Media:YH17 P FREQ.LOG| YH17 P FREQ.LOG]]

<pre>
Low frequencies --- -0.0037 -0.0034 -0.0014 51.3389 51.3389 51.3389
Low frequencies --- 186.8906 211.6326 211.6326
</pre>

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>YH17 P OPT.LOG</uploadedFileContents>
</jmolApplet></jmol>

----
=== Charge Distribution ===

[[File:Yh17 charge N.PNG|thumb|left|'''Figure 3.'''The charge distribution of [N(CH3)4]+. Colour range -0.450 to +0.450.]][[File:Yh17 charge P.PNG|thumb|center|'''Figure 4.'''The charge distribution of [P(CH3)4]+. Colour range -0.450 to +0.450.]]

{| class="wikitable" border="1"
|+ Compare [N(CH3)4]+ and [P(CH3)4]+
! [N(CH3)4]+ !! [P(CH3)4]+
|-
| charge on N: -0.295 || charge on P: +1.666
|-
| charge on C: -0.483 || charge on C: -1.060
|-
| charge on H: +0.269 || charge on H: +0.298
|-
| N is quite electronegative hence it bears high electron density. The carbon atoms also bear negative charges while the H atoms are positive. || P is more electropositive than both N and C since it is much larger (so nucleus more shielded). It bears positive charge while all the negative charges are on the carbon atoms.
|}

Yh1817

2019-05-16T19:16:39Z

Yh1817: /* [P(CH3)4]+ */

File:Yh17 charge P.PNG

2019-05-16T18:19:02Z

Yh1817:

File:Yh17 charge N.PNG

2019-05-16T18:15:17Z

Yh1817:

Yh1817

2019-05-16T18:09:23Z

Yh1817: /* [N(CH3)4]+ */

Yh1817

2019-05-16T16:25:56Z

Yh1817: /* [N(CH3)4]+ */