View source for Rep:Mod:01196499

== Introduction ==

The Wiki page for <i>Introduction to Molecular Modelling 2</i>. Submitted by Peter Gobbett

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

=== Calculation Data ===

{| class="wikitable" border="1"
|-
! colspan="3" style="text-align: left;"|Key Information
|-
| Common Name|| Ammonia
|-
| Molecular Formula|| NH<sub>3</sub>
|-
| Calculation Method|| RB3LYP
|-
| Basis Set|| 6-31G(D.P)
|-
| Final Energy (RB3LYP)|| -56.55776873 a.u.
|-
| RMS Gradient|| 0.00000485 a.u.
|-
| Point Group|| C<sub>3v</sub>
|-
| Optimised N-H Bond Distance|| 1.01798A
|-
| Optimised H-N-H Bond Angle|| 105.741<sup>o</sup>
|}

=== Item Table ===

<pre>

Item               Value     Threshold  Converged?
 Maximum Force            0.000004     0.000450     YES
 RMS     Force            0.000004     0.000300     YES
 Maximum Displacement     0.000072     0.001800     YES
 RMS     Displacement     0.000035     0.001200     YES

</pre>

=== Molecular Model ===

<jmol><jmolApplet>
  <title>NH3</title>
  <color>white</color>
  <size>500</size>
  <uploadedFileContents>PGOBBETT_NH3_OPT_1.LOG</uploadedFileContents>
  <script>frame 1.16</script>
</jmolApplet></jmol>

Click this [[Media:PGOBBETT_NH3_OPT_1.LOG | <u>link</u>]] for the full .log file

=== Frequency Analysis ===

[[File:PGOBBETT_NH3_VIBRATIONS.png|thumb|center|Gaussview vibration analysis window for an NH<sub>3</sub> molecule.]]

{| class="wikitable" border="1"
|-
! colspan="3" style="text-align: left;"|Frequency Analysis
|-
| No. of Modes (3N-6)|| 6
|-
| Degenerate Modes|| Modes 2&3, Modes 5&6
|-
| "Bending" vibration modes|| 1, 2, 3
|-
| "Bond Stretch" vibration modes|| 4, 5, 6
|-
| Mode of Highest Symmetry|| 4
|-
| "Umbrella" vibration mode|| 1
|-
| Bands in experimental spectrum|| 4 in therory (due to two degenerate pairs) but it is likely only modes 1 and 2&3 would be distinguishable above noise. 4 and 5&6 each have both high frequency and low intensity. 
|}

=== Charge Analysis ===



[[File:PGOBBETT_NH3_CHARGES.png|500px|thumb|center|Gaussview optimised NH<sub>3</sub> molecule showing charge distribution.]]


The above image shows the charge distribution in the optimised NH<sub>3</sub> molecule. The Nitrogen is negatively charged and each Hydrogen atom has a slight partial positive charge. This difference is reinforced by theory, with the concept of electronegativity.  Nitrogen is far more electronegative than Hydrogen, thus is better able to attract bonding electrons to itself. This accounts for the differences in charge. Thus, although the bonds are covalent, they have slight ionic character due to the difference in electronegativity. Thus they are polar bonds.

== H<sub>2</sub> Molecule == 

=== Calculation Data ===

{| class="wikitable" border="1"
|-
! colspan="3" style="text-align: left;"|Key Information
|-
| Common Name|| Hydrogen
|-
| Molecular Formula|| H<sub>2</sub>
|-
| Calculation Method|| RB3LYP
|-
| Basis Set|| 6-31G(D.P)
|-
| Final Energy (RB3LYP)|| -1.17853930 a.u.
|-
| RMS Gradient|| 0.00012170 a.u.
|-
| Point Group|| D<sub>∞h</sub>
|-
! colspan="3" style="text-align: left;"|Bond Length Analysis
|-
| Calculated Bond Length H-H|| 0.74309A
|-
| Literature Bond Length H-H<ref name="HH Bond Length" />|| 0.74A
|-
| Comment || The calculated bond length is equal to the literature reference, so the Gaussian model is highly accurate.
|}

=== Item Table ===

<pre>

Item               Value     Threshold  Converged?
 Maximum Force            0.000211     0.000450     YES
 RMS     Force            0.000211     0.000300     YES
 Maximum Displacement     0.000278     0.001800     YES
 RMS     Displacement     0.000393     0.001200     YES

</pre>

=== Molecular Model ===

<jmol><jmolApplet>
  <title>H2</title>
  <color>white</color>
  <size>500</size>
  <uploadedFileContents>PGOBBETT_H2_OPT_1.LOG</uploadedFileContents>
  <script>frame 1.14</script>
</jmolApplet></jmol>

Click this [[Media:PGOBBETT_H2_OPT_1.LOG | <u>link</u>]] for the full .log file

=== Frequency Analysis ===


{| class="wikitable" border="1"
|-
! colspan="3" style="text-align: left;"|Gaussview Analysis
|-
| colspan="3" align="center"|[[File:PGOBBETT_H2_VIBRATIONS.png|500px|thumb|center|Gaussview vibration analysis window for an H<sub>2</sub> molecule.]]
|-
! colspan="3" style="text-align: left;"|Frequency Analysis
|-
| No. of Modes (3N-5)|| 1
|-
| Comment|| Shows a symmetrical stretch. Intensity is zero as molecule is symmetrical, so no dipole moment is created. 
|}

=== Charge Analysis ===



[[File:PGOBBETT_H2_CHARGES.png|500px|thumb|center|Gaussview optimised H<sub>2</sub> molecule showing charge distribution.]]


The above image shows the charge distribution in the optimised H<sub>2</sub> molecule. The molecule is diatomic and of the same element, thus there is no charge difference and the bond is fully covalent.

== N<sub>2</sub> Molecule ==

=== Calculation Data ===

{| class="wikitable" border="1"
|-
! colspan="3" style="text-align: left;"|Key Information
|-
| Common Name|| Nitrogen
|-
| Molecular Formula|| N<sub>2</sub>
|-
| Calculation Method|| RB3LYP
|-
| Basis Set|| 6-31G(D.P)
|-
| Final Energy (RB3LYP)|| -109.52412868 a.u.
|-
| RMS Gradient|| 0.00000365 a.u.
|-
| Point Group|| D<sub>∞h</sub>
|-
! colspan="3" style="text-align: left;"|Bond Length Analysis
|-
| Calculated Bond Length N-N|| 1.10550A
|-
| Literature Bond Length N-N<ref name="NN Bond Length" />|| 1.0976A
|-
| Comment || The calculated bond length is very close to the literature reference, so the Gaussian model is highly accurate.
|}

=== Item Table ===

<pre>

Item               Value     Threshold  Converged?
 Maximum Force            0.000006     0.000450     YES
 RMS     Force            0.000006     0.000300     YES
 Maximum Displacement     0.000002     0.001800     YES
 RMS     Displacement     0.000003     0.001200     YES

</pre>

=== Molecular Model ===

<jmol><jmolApplet>
  <title>N2</title>
  <color>white</color>
  <size>500</size>
  <uploadedFileContents>PGOBBETT_N2_OPT_1.LOG</uploadedFileContents>
  <script>frame 1.12</script>
</jmolApplet></jmol>

Click this [[Media:PGOBBETT_N2_OPT_1.LOG | <u>link</u>]] for the full .log file

=== Frequency Analysis ===

{| class="wikitable" border="1"
|-
! colspan="3" style="text-align: left;"|Gaussview Analysis
|-
| colspan="3" align="center"|[[File:PGOBBETT_N2_VIBRATIONS.png|500px|thumb|center|Gaussview vibration analysis window for an N<sub>2</sub> molecule.]]
|-
! colspan="3" style="text-align: left;"|Frequency Analysis
|-
| No. of Modes (3N-5)|| 1
|-
| Comment|| Shows a symmetrical stretch. Intensity is zero as molecule is symmetrical, so no dipole moment is created. 
|}

=== Charge Analysis ===



[[File:PGOBBETT_N2_CHARGES.png|500px|thumb|center|Gaussview optimised N<sub>2</sub> molecule showing charge distribution.]]


The above image shows the charge distribution in the optimised N<sub>2</sub> molecule. The molecule is diatomic and of the same element, thus there is no charge difference and the bond is fully covalent.

== Reaction Energies ==

<b>Haber–Bosch process</b> :  3H<sub>2</sub> + N<sub>2</sub> → 2NH<sub>3</sub>

{| class="wikitable" border="1"
|-
! colspan="3" style="text-align: left;"|Energy Data
|-
| E (NH<sub>3</sub>) || -56.55776873 a.u.
|-
| 2x E (NH<sub>3</sub>) || -113.1155375 a.u.
|-
| E (N<sub>2</sub>) || -109.52412868 a.u.
|-
| E (H<sub>2</sub>)|| -1.17853930 a.u.
|-
| 3x E (H<sub>2</sub>)|| -3.5356179 a.u.
|-
| ΔE|| -0.05579092 a.u.
|-
| ΔE|| -146.479071618 kJmol<sup>-1</sup>
|-
| Comments|| The reaction is <i>exothermic</i>. Thus, the product (NH<sub>3</sub>) must be thermodynamically more stable than the reactants (H<sub>2</sub> and N<sub>2</sub>).
|}

== F<sub>2</sub> Molecule == 

=== Calculation Data ===

{| class="wikitable" border="1"
|-
! colspan="3" style="text-align: left;"|Key Information
|-
| Common Name|| Fluorine
|-
| Molecular Formula|| F<sub>2</sub>
|-
| Calculation Method|| RB3LYP
|-
| Basis Set|| 6-31G(D.P)
|-
| Final Energy (RB3LYP)|| -199.49825218 a.u.
|-
| RMS Gradient|| 0.00007365 a.u.
|-
| Point Group|| D<sub>∞h</sub>
|-
! colspan="3" style="text-align: left;"|Bond Length Analysis
|-
| Calculated Bond Length F-F|| 1.40281A
|-
| Literature Bond Length F-F<ref name="FF Bond Length" />|| 1.45A
|-
| Comment || The calculated bond length is very close to the literature reference, so the Gaussian model is highly accurate.
|}

=== Item Table ===

<pre>

Item               Value     Threshold  Converged?
 Maximum Force            0.000128     0.000450     YES
 RMS     Force            0.000128     0.000300     YES
 Maximum Displacement     0.000156     0.001800     YES
 RMS     Displacement     0.000221     0.001200     YES

</pre>

=== Molecular Model ===

<jmol><jmolApplet>
  <title>F2</title>
  <color>white</color>
  <size>500</size>
  <uploadedFileContents>PGOBBETT_F2_OPT_1.LOG</uploadedFileContents>
  <script>frame 1.12</script>
</jmolApplet></jmol>

Click this [[Media:PGOBBETT_F2_OPT_1.LOG | <u>link</u>]] for the full .log file

=== Frequency Analysis ===


{| class="wikitable" border="1"
|-
! colspan="3" style="text-align: left;"|Gaussview Analysis
|-
| colspan="3" align="center"|[[File:PGOBBETT_F2_VIBRATIONS.png|500px|thumb|center|Gaussview vibration analysis window for an F<sub>2</sub> molecule.]]
|-
! colspan="3" style="text-align: left;"|Frequency Analysis
|-
| No. of Modes (3N-5)|| 1
|-
| Comment|| Shows a symmetrical stretch. Intensity is zero as molecule is symmetrical, so no dipole moment is created. 
|}

=== Charge Analysis ===



[[File:PGOBBETT_F2_CHARGES.png|500px|thumb|center|Gaussview optimised H<sub>2</sub> molecule showing charge distribution.]]


The above image shows the charge distribution in the optimised F<sub>2</sub> molecule. The molecule is diatomic and of the same element, thus there is no charge difference and the bond is fully covalent.

=== Molecular Orbitals ===

{| class="wikitable" border="1"
|-
! colspan="3" style="text-align: left;"|Molecular Orbital Energies
|-
| colspan="3" align="center"|[[File:PGOBBETT_F2_MO_energies.png|500px|thumb|center|Respective energies of the molecular orbitals in a molecule of F<sub>2</sub>. The MOs formed from the 1s orbitals (1&2) are significantly deeper in energy than the higher order MOs. This is why they are rarely considered to have any effect on the bonding of fluorine. MO 10 is the LUMO as it is the lowest energy orbital that is not occupied. Similarly, MOs 8&9 are the HOMO, as the highest energy occupied orbitals (they are degenerate to one another).]]
|}

{| class="wikitable" border="1"
|-
! colspan="3" style="text-align: left;"| 1σ<sub>g</sub> / 1σ<sub>u</sub>*
|-
| colspan="3" align="center"|[[File:PGOBBETT_F2_MO_1ss.png|500px|thumb|center|1σ bonding MO made up of the 1s AOs. This MO is very deep in energy, so there is effectively no overlap hence this MO contributes little to the bonding in F<sub>2</sub>. The corresponding antibonding orbital is shown below.]]
|-
| colspan="3" align="center"|[[File:PGOBBETT_F2_MO_1sA.png|500px|center|]]
|}

{| class="wikitable" border="1"
|-
! colspan="3" style="text-align: left;"| 2σ<sub>g</sub> /2σ<sub>u</sub>*
|-
| colspan="3" align="center"|[[File:PGOBBETT_F2_MO_2s.png|500px|thumb|center|2σ bonding MO made up of the 2s AOs. The electrons in the MO are valence electrons, hence there is good overlap between the AOs. As F is too electronegative for mixing, the bonding orbital is cancelled out by the antibonding orbital also formed by the 2s electrons (below). As the antibonding orbital is filled, the bonding effect of the bonding orbital is not notable.]]
|-
| colspan="3" align="center"|[[File:PGOBBETT_F2_MO_2sA.png|500px|center|]]
|}

{| class="wikitable" border="1"
|-
! colspan="3" style="text-align: left;"| 3σ<sub>g</sub> / 3σ<sub>u</sub>*
|-
| colspan="3" align="center"|[[File:PGOBBETT_F2_MO_2p.png|500px|thumb|center|3σ bonding MO made up of the 2p AOs that are orientated along the line of the bond. The electrons in the MO are valence electrons, hence there is good overlap between the AOs. As the antibonding orbital (below) is not filled, the bonding effect of this MO is significant. The antibonding MO is the LUMO of the F<sub>2</sub> molecule.]]
|-
| colspan="3" align="center"|[[File:PGOBBETT_F2_MO_2pA.png|500px|center|]]
|}

{| class="wikitable" border="1"
|-
! colspan="3" style="text-align: left;"| 1π<sub>u</sub> / 1π<sub>g</sub>*
|-
| colspan="3" align="center"|[[File:PGOBBETT_F2_MO_2p_pi.png|500px|center|]]
|-
| colspan="3" align="center"|[[File:PGOBBETT_F2_MO_2p_pi_2.png|500px|thumb|center|Both orientations of the  pi MOs. Made up of the 2p AOs that are not orientated along the line of the bond, the electrons in the MO are valence electrons, hence there is good overlap between the AOs. As the antibonding orbital (below) is only partially filled, the bonding effect of this MO is significant. The antibonding MO is also the HOMO]]
|-
| colspan="3" align="center"|[[File:PGOBBETT_F2_MO_2p_piA.png|500px|center|]]
|}

== ClF<sub>3</sub> Molecule ==

=== Calculation Data ===

{| class="wikitable" border="1"
|-
! colspan="3" style="text-align: left;"|Key Information
|-
| Common Name|| Sarin
|-
| Molecular Formula|| ClF<sub>3</sub>
|-
| Calculation Method|| RB3LYP
|-
| Basis Set|| 6-31G(D.P)
|-
| Final Energy (RB3LYP)|| -759.46531688 a.u.
|-
| RMS Gradient|| 0.00002465 a.u.
|-
| Point Group|| C<sub>2v</sub>
|-
! colspan="3" style="text-align: left;"|Bond Length Analysis
|-
| Calculated Bond Length Cl-F|| 1.72863A and 1.65143A
|-
| Literature Bond Length Cl-F<ref name="ClF Bond Length" />|| 1.698A and 1.598A
|-
| Comment || The calculated bond length is fairly close to the literature reference, so the Gaussian model is accurate.
|}

=== Item Table ===

<pre>

 Item               Value     Threshold  Converged?
 Maximum Force            0.000050     0.000450     YES
 RMS     Force            0.000028     0.000300     YES
 Maximum Displacement     0.000204     0.001800     YES
 RMS     Displacement     0.000134     0.001200     YES

</pre>

=== Molecular Model ===

<jmol><jmolApplet>
  <title>Sarin</title>
  <color>white</color>
  <size>500</size>
  <uploadedFileContents>PGOBBETT_CLF3_OPT_1.LOG</uploadedFileContents>
  <script>frame 1.16</script>
</jmolApplet></jmol>

Click this [[Media:PGOBBETT_CLF3_OPT_1.LOG | <u>link</u>]] for the full .log file

=== Frequency Analysis ===

{| class="wikitable" border="1"
|-
! colspan="3" style="text-align: left;"|Gaussview Analysis
|-
| colspan="3" align="center"|[[File:PGOBBETT_CLF3_VIBRATIONS.png|500px|thumb|center|Gaussview vibration analysis window for a  molecule of ClF<sub>3</sub>.]]
|-
! colspan="3" style="text-align: left;"|Frequency Analysis
|-
| No. of Modes (3N-6)|| 6
|-
| Degenerate Modes|| None
|-
| "Bending" vibration modes|| 1-3
|-
| "Bond Stretch" vibration modes|| 4-6
|-
| Comment|| Due to the bent T-shaped nature of the molecule, none of the stretches are degenerate. number 6 would have the strongest intensity in an experimental spectrum, while 3&4 may not show due to their poor intensity. 
|}

=== Charge Analysis ===



[[File:PGOBBETT_CLF3_CHARGES.png|500px|thumb|center|Gaussview optimised ClF<sub>3</sub> molecule showing charge distribution.]]

Clearly, the more electronegative fluorine molecules are more negatively charged than the central chlorine atom (comparatively, the more electropostive atom). The model also shows that there is a disparity between the charges of the axial fluorine atoms and the equatorial fluorine. I would hypothesize that this is due to the differing bond lengths, with the axial fluorines being further away from the electropostive chlorine. However, the method of charge analysis Gaussian uses is not based on electronegativity values, so no quantitative analysis can be made.

== Sarin Molecule ==

=== Calculation Data ===

{| class="wikitable" border="1"
|-
! colspan="3" style="text-align: left;"|Key Information
|-
| Common Name|| Sarin
|-
| Molecular Formula|| (CH<sub>3</sub>)<sub>2</sub>CHOP(O)(CH<sub>3</sub>)F
|-
| Calculation Method|| RB3LYP
|-
| Basis Set|| 6-31G(D.P)
|-
| Final Energy (RB3LYP)|| -750.20043140 a.u.
|-
| RMS Gradient|| 0.00000766 a.u.
|-
| Point Group|| None
|}

=== Item Table ===

<pre>

 Item               Value     Threshold  Converged?
 Maximum Force            0.000026     0.000450     YES
 RMS     Force            0.000004     0.000300     YES
 Maximum Displacement     0.001100     0.001800     YES
 RMS     Displacement     0.000250     0.001200     YES

</pre>

=== Molecular Model ===

<jmol><jmolApplet>
  <title>Sarin</title>
  <color>white</color>
  <size>500</size>
  <uploadedFileContents>PGOBBETT_SARIN_OPT_1.LOG</uploadedFileContents>
  <script>frame 1.44</script>
</jmolApplet></jmol>

Click this [[Media:PGOBBETT_SARIN_OPT_1.LOG | <u>link</u>]] for the full .log file

=== Frequency Analysis ===

[[File:PGOBBETT_Sarin_VIBRATIONS.png|thumb|center|Gaussview vibration analysis window for a Sarin molecule.]]

{| class="wikitable" border="1"
|-
! colspan="3" style="text-align: left;"|Frequency Analysis
|-
| No. of Modes (3N-6)|| 48
|-
| Degenerate Modes|| None
|-
| "Bending" vibration modes|| 1-38
|-
| "Bond Stretch" vibration modes|| 39-48
|-
! colspan="3" style="text-align: left;"|Gaussview IR Spectrum
|-
| colspan="3" align="center"|[[File:PGOBBETT_Sarin_IR.png|500px|thumb|center|Gaussview predicted IR spectrum for a Sarin molecule.]]
|}

=== Charge Analysis ===



[[File:PGOBBETT_Sarin_CHARGES.png|500px|thumb|center|Gaussview optimised NH<sub>3</sub> molecule showing charge distribution.]]


The charge distribution for Sarin is very interesting. 

All three CH<sub>3</sub> group carbons have a slight negative charge, on account of each being bonded to three more electropositive hydrogen atoms. The CH<sub>3</sub> carbon bonded to the central phosphorus atom is especially negative, on account of the significant (relative) electropositivity of the phosphorus atom.

The carbon of the CH group is slightly positively charged, on account of being bonded to three more electronegative atoms. The main contributor is likely the oxygen atom; oxygen is significantly more electronegative than carbon.

Both oxygen atoms are negatively charged. The fluorine atom is also negatively charged. This makes sense, as oxygen and fluorine are the two most electronegative elements known. The numerical disparity shown in the image is likely due to the functions Gaussian is using, as it does not account for electronegativity. Hence, no quantitative analysis is possible.

=== Molecular Orbitals ===

{| class="wikitable" border="1"
|-
! colspan="3" style="text-align: left;"| Bonding
|-
| colspan="3" align="center"|[[File:PGOBBETT_Sarin_MO_13.png|500px|thumb|center|The 13th MO is the first bonding orbital: all below are too deep in energy]]
|}

{| class="wikitable" border="1"
|-
! colspan="3" style="text-align: left;"| Complexity increases
|-
| colspan="3" align="center"|[[File:PGOBBETT_Sarin_MO_16.png|500px|center]]
|-
| colspan="3" align="center"|[[File:PGOBBETT_Sarin_MO_19.png|500px|center]]
|-
| colspan="3" align="center"|[[File:PGOBBETT_Sarin_MO_22.png|500px|thumb|center|The complexity of the MOs rapidly increases for such a large molecule, with both bonding and antibonding characteristics. Pictured are MOs 16, 17 and 22.]]
|}

{| class="wikitable" border="1"
|-
! colspan="3" style="text-align: left;"| HOMO
|-
| colspan="3" align="center"|[[File:PGOBBETT_Sarin_MO_37_HOMO.png|500px|thumb|center|Showing the HOMO of Sarin: MO number 38.]]
|}

{| class="wikitable" border="1"
|-
! colspan="3" style="text-align: left;"| LUMO
|-
| colspan="3" align="center"|[[File:PGOBBETT_Sarin_MO_38_LUMO.png|500px|thumb|center|Showing the LUMO of Sarin: MO number 39.]]
|}

{| class="wikitable" border="1"
|-
! colspan="3" style="text-align: left;"| Number 42
|-
| colspan="3" align="center"|[[File:PGOBBETT_Sarin_MO_42.png|500px|thumb|center|Included just for the sheer aesthetic value.]]
|}

== References ==
<references>

<ref name="HH Bond Length">Chung Chieh (2006). "Bond Lengths and Energies" http://www.science.uwaterloo.ca/~cchieh/cact/c120/bondel.html (Accessed at 12:03 on 10/03/2017</ref>

<ref name="NN Bond Length">Greenwood and Earnshaw (1984). "Chemistry of the Elements, pp. 412–6."</ref>

<ref name="ClF Bond Length">Smith, D. F. (1953). "The Microwave Spectrum and Structure of Chlorine Trifluoride". The Journal of Chemical Physics. 21 (4): 609–614. http://aip.scitation.org/doi/10.1063/1.1698976 (Accessed at 11:44 on 10/03/2017)</ref>

<ref name="FF Bond Length">Brockway, L. O. (1938). "The Internuclear Distance in the Fluorine Molecule". Journal of the American Chemical Society. 60 (6): 1348–1349. http://pubs.acs.org/doi/abs/10.1021/ja01273a021 (Accessed at 11:53 on 10/03/2017)</ref>

</references>