View source for Yx6015IntroToMolecularModelling2

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

{| class="wikitable" border="1"
|-
! colspan="6" style="text-align: left;"|Information
|-
| colspan="3" align="center"|[[File:yx6015_nh3.png|200px]]
| colspan="3" align="center"|
  <jmol><jmolApplet>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>YX6015_NH3_OPTF_POP.LOG</uploadedFileContents>
  </jmolApplet></jmol>
|-
| colspan="6" style="text-align: center;"|NH<sub>3</sub> Ammonia
|-
| colspan="6" style="text-align: center;"|'''Calculation Details'''
|- 
| colspan="2" style="text-align: center;"|'''Method'''
| colspan="2" style="text-align: center;"|'''Basis Set'''
| colspan="2" style="text-align: center;"|'''Point Group'''
|- 
| colspan="2" style="text-align: center;"|RB3LYP
| colspan="2" style="text-align: center;"|6-31G(d,p)
| colspan="2" style="text-align: center;"|C<sub>3v</sub>
|-
| colspan="6" style="text-align: center;"|<b>Calculation Results</b>
|- 
| colspan="2" style="text-align: center;"|'''E(RB3LYP) /a.u.'''
| colspan="2" style="text-align: center;"|'''RMS Gradient /a.u.'''
| colspan="2" style="text-align: center;"|'''Dipole Moment /D'''
|-
| colspan="2" style="text-align: center;"|-56.55776873
| colspan="2" style="text-align: center;"|0.00000323
| colspan="2" style="text-align: center;"|1.8465
|-
| colspan="6" style="text-align: left;"|Click [[Media:YX6015_NH3_OPTF_POP.LOG| here]] for the log file.
|}
<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>

{| class="wikitable" border="1"
|-
!colspan="2" style="text-align: left;"|Vibration and Charge Window
|-
||[[File:Yx6015_nh3_vibrationwindow.PNG|230px]]
||[[File:yx6015_nh3_chargewindow.png|512px]]
|}

<ul>
<li> '''N-H Bond Length:''' 1.01792 Angstrom
<li> '''H-N-H Bond Angle:''' 105.741°
<li> '''Modes from the 3N-6 Rule:''' 6
<li> '''Degenerate Modes:''' 2, 3 and 5, 6
<li> '''Bending Vibration Modes:''' 1, 2 and 3
<li> '''Stretching Vibration Modes:''' 4, 5 and 6
<li> '''Highly Symmetric Mode:''' 4
<li> '''"Umbrella" Mode:''' 1
<li> '''Number of Experimental Spectrum Bands of Gaseous Ammonia:''' 4
</ul>

==N<sub>2</sub> and H<sub>2</sub> Molecule==
{| class="wikitable" border="1"
|-
! colspan="6" style="text-align: left;"|Information
! colspan="6" style="text-align: left;"|Information
|-
| colspan="3" align="center"|[[File:yx6015_n2.png|200px]] 
| colspan="3" align="center"|
  <jmol><jmolApplet>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>YX6015_N2_OPTF_POP.LOG</uploadedFileContents>
  </jmolApplet></jmol>
| colspan="3" align="center"|[[File:yx6015_h2.png|200px]]
| colspan="3" align="center"|
  <jmol><jmolApplet>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>YX6015_H2_OPTF_POP.LOG</uploadedFileContents>
  </jmolApplet></jmol>
|-
| colspan="6" style="text-align: center;"|N<sub>2</sub> Nitrogen
| colspan="6" style="text-align: center;"|H<sub>2</sub> Hydrogen
|-
| colspan="6" style="text-align: center;"|'''Calculation Details'''
|- 
| colspan="2" style="text-align: center;"|'''Method'''
| colspan="2" style="text-align: center;"|'''Basis Set'''
| colspan="2" style="text-align: center;"|'''Point Group'''
| colspan="2" style="text-align: center;"|'''Method'''
| colspan="2" style="text-align: center;"|'''Basis Set'''
| colspan="2" style="text-align: center;"|'''Point Group'''
|- 
| colspan="2" style="text-align: center;"|RB3LYP
| colspan="2" style="text-align: center;"|6-31G(d,p)
| colspan="2" style="text-align: center;"|D<sub>∞h</sub>
| colspan="2" style="text-align: center;"|RB3LYP
| colspan="2" style="text-align: center;"|6-31G(d,p)
| colspan="2" style="text-align: center;"|D<sub>∞h</sub>
|-
| colspan="6" style="text-align: center;"|<b>Calculation Results</b>
| colspan="6" style="text-align: center;"|<b>Calculation Results</b>
|- 
| colspan="2" style="text-align: center;"|'''E(RB3LYP) /a.u.'''
| colspan="2" style="text-align: center;"|'''RMS Gradient /a.u.'''
| colspan="2" style="text-align: center;"|'''Dipole Moment /D'''
| colspan="2" style="text-align: center;"|'''E(RB3LYP) /a.u.'''
| colspan="2" style="text-align: center;"|'''RMS Gradient /a.u.'''
| colspan="2" style="text-align: center;"|'''Dipole Moment /D'''
|-
| colspan="2" style="text-align: center;"|-109.52412868
| colspan="2" style="text-align: center;"|0.00000060
| colspan="2" style="text-align: center;"|0
| colspan="2" style="text-align: center;"|-1.17853936
| colspan="2" style="text-align: center;"|0.00000017
| colspan="2" style="text-align: center;"|0
|-
| colspan="6" style="text-align: left;"|Click [[Media:YX6015_N2_OPTF_POP.LOG| here]] for the log file.
| colspan="6" style="text-align: left;"|Click [[Media:YX6015_H2_OPTF_POP.LOG| here]] for the log file.

|}
<pre>
 N2      Item               Value     Threshold  Converged?     H2	Item               Value     Threshold  Converged?
 Maximum Force            0.000001     0.000450     YES 	Maximum Force            0.000000     0.000450     YES
 RMS     Force            0.000001     0.000300     YES		RMS     Force            0.000000     0.000300     YES
 Maximum Displacement     0.000000     0.001800     YES		Maximum Displacement     0.000000     0.001800     YES
 RMS     Displacement     0.000000     0.001200     YES		RMS     Displacement     0.000001     0.001200     YES
</pre>

==Reactivity==
We can determine the energy for the reaction of N2 + 3H2 -> 2NH3.
<ul>
<li>E(NH3)= -56.55776873 a.u.</li>
<li>2*E(NH3)= -113.11553746 a.u.</li> 
<li>E(N2)= -109.52412868 a.u.</li>
<li>E(H2)= -1.17853936 a.u.</li>
<li>3*E(H2)= -3.53561808 a.u.</li>
<li>ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.05579070 a.u.= -146.47 kJ/mol</li>
</ul>

The products are more stable. The energy change is very different from experimental enthalpy change (ΔH = −92.4 kJ mol<sup>−1</sup>). This shows the inadequacy of using simple DFT methods to calculate thermodynamic data.

==CH<sub>4</sub>Molecule==
{| class="wikitable" border="1"
|-
! colspan="6" style="text-align: left;"|Information
|-
| colspan="3" align="center"|[[File:yx6015_ch4.png|256px]]
| colspan="3" align="center"|
  <jmol><jmolApplet>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>YX6015_CH4_OPTF_POP.LOG</uploadedFileContents>
  </jmolApplet></jmol>
|-
| colspan="6" style="text-align: center;"|CH<sub>4</sub> Methane
|-
| colspan="6" style="text-align: center;"|'''Calculation Details'''
|- 
| colspan="2" style="text-align: center;"|'''Method'''
| colspan="2" style="text-align: center;"|'''Basis Set'''
| colspan="2" style="text-align: center;"|'''Point Group'''
|- 
| colspan="2" style="text-align: center;"|RB3LYP
| colspan="2" style="text-align: center;"|6-31G(d,p)
| colspan="2" style="text-align: center;"|T<sub>d</sub>
|-
| colspan="6" style="text-align: center;"|<b>Calculation Results</b>
|- 
| colspan="2" style="text-align: center;"|'''E(RB3LYP) /a.u.'''
| colspan="2" style="text-align: center;"|'''RMS Gradient /a.u.'''
| colspan="2" style="text-align: center;"|'''Dipole Moment /D'''
|-
| colspan="2" style="text-align: center;"|-40.52401404
| colspan="2" style="text-align: center;"|0.00003263
| colspan="2" style="text-align: center;"|0
|-
| colspan="6" style="text-align: left;"|Click [[Media:YX6015_CH4_OPTF_POP.LOG| here]] for the log file.
|}

<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000063     0.000450     YES
 RMS     Force            0.000034     0.000300     YES
 Maximum Displacement     0.000179     0.001800     YES
 RMS     Displacement     0.000095     0.001200     YES
</pre>
{| class="wikitable" border="1"
|-
!colspan="9" style="text-align: left;"|Vibration properties
|-
|style="text-align: center;"|'''Mode'''
|style="text-align: center;"|'''Frequency /cm<sup>-1</sup>'''
|style="text-align: center;"|'''Intensity
|style="text-align: center;"|'''Mode'''
|style="text-align: center;"|'''Frequency /cm<sup>-1</sup>'''
|style="text-align: center;"|'''Intensity
|style="text-align: center;"|'''Mode'''
|style="text-align: center;"|'''Frequency /cm<sup>-1</sup>'''
|style="text-align: center;"|'''Intensity
|-
|style="text-align: center;"|1
|style="text-align: center;"|1356.20
|style="text-align: center;"|14.1008
|style="text-align: center;"|4
|style="text-align: center;"|1578.58
|style="text-align: center;"|0
|style="text-align: center;"|7
|style="text-align: center;"|3162.33
|style="text-align: center;"|25.3343
|-
|style="text-align: center;"|2
|style="text-align: center;"|1356.20
|style="text-align: center;"|14.1008
|style="text-align: center;"|5
|style="text-align: center;"|1578.58
|style="text-align: center;"|0
|style="text-align: center;"|8
|style="text-align: center;"|3162.33
|style="text-align: center;"|25.3343
|-
|style="text-align: center;"|3
|style="text-align: center;"|1356.20
|style="text-align: center;"|14.1008
|style="text-align: center;"|6
|style="text-align: center;"|3046.46
|style="text-align: center;"|0
|style="text-align: center;"|9
|style="text-align: center;"|3162.33
|style="text-align: center;"|25.3343
|-
|colspan="3" style="text-align: left;"|This is a bending motion of the entire molecule, with medium intensity. 3 degenerate modes due to 3 different orientation of bending.
|colspan="3" style="text-align: left;"|These are 2 degenerate symmetric bends and 1 symmetric stretching. There is no change in dipole moment thus resulting in it having 0 intensity and not absorbing any infrared radiation.
|colspan="3" style="text-align: left;"|These are due to 3 different stretching of the molecule with degenerate energy levels. As stretching is more energetic than bending, it occurs at higher energy level with higher intensity.
|}

{| class="wikitable" border="1"
|-
!colspan="5" style="text-align: left;"|Charge Distribution
|-
|colspan="2" style="text-align: left;"|Unsurprisingly, as the center carbon atom is more electronegative than the hydrogen atom, more electron is distributed around the center carbon.
|colspan="3" align="center"|[[File:yx6015_ch4_chargewindow.tif|512px]]
|}

{| class="wikitable" border="1"
|-
!colspan="5" style="text-align: left;"|Molecular Orbitals
|-
|colspan="2" style="text-align: left;"| MO10(E=+0.52915) This is a high energy unoccupied anti-bonding MO, and is similar to MO11 and MO12, with different spatial orientation.
|colspan="3" align="center"|[[File:yx6015_ch4_mo10.tif|256px]]
|-
|colspan="2" style="text-align: left;"| MO9 (E=+0.17677) This is a high energy unoccupied anti-bonding MO, and is similar to MO8 and MO7, with different spatial orientation. Notably, this shows less nodal region as compared to MO10, possibly resulting in its lowering in energy.
|colspan="3" align="center"|[[File:yx6015_ch4_mo987.tif|256px]]
|-
|colspan="2" style="text-align: left;"| MO6 (E=+0.11824) This is a anti-bonding LUMO. This is visually similar to MO2, with the main difference being the size of the orbital (i.e. MO2 is smaller). While no nodal region is shown, the large size of the orbital contributed to its high energy.
|colspan="3" align="center"|[[File:yx6015_ch4_mo6.tif|256px]]
|-
|colspan="2" style="text-align: left;"| MO5 (E=-0.38831) This is a bonding HOMO, and is similar to MO4 and MO3, with different spatial orientation. The nodal region is noticeably smaller, resulting in its low energy.
|colspan="3" align="center"|[[File:yx6015_ch4_mo543.tif|256px]]
|-
|colspan="2" style="text-align: left;"| MO1 (E=-10.16707) This is a very low energy occupied bonding MO and is entirely around the center carbon atom. This is possibly entirely due to the 1s orbital of the carbon atom.
|colspan="3" align="center"|[[File:yx6015_ch4_mo1.tif|256px]]
|}

==CH<sub>3</sub><sup>+</sup> and CH<sub>3</sub><sup>-</sup> Molecules==
{| class="wikitable" border="1"
|-
! colspan="6" style="text-align: left;"|Information
! colspan="6" style="text-align: left;"|Information
|-
| colspan="3" align="center"|[[File:yx6015_ch3+.png|200px]] 
| colspan="3" align="center"|
  <jmol><jmolApplet>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>YX6015_CH3+_OPTF_POP.LOG</uploadedFileContents>
  </jmolApplet></jmol>
| colspan="3" align="center"|[[File:yx6015_ch3-.png|200px]]
| colspan="3" align="center"|
  <jmol><jmolApplet>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>YX6015_CH3-_OPTF_POP.LOG</uploadedFileContents>
  </jmolApplet></jmol>
|-
| colspan="6" style="text-align: center;"|CH<sub>3</sub><sup>+</sup> Carbocation
| colspan="6" style="text-align: center;"|CH<sub>3</sub><sup>-</sup> Carbanion
|-
| colspan="6" style="text-align: center;"|'''Calculation Details'''
|- 
| colspan="2" style="text-align: center;"|'''Method'''
| colspan="2" style="text-align: center;"|'''Basis Set'''
| colspan="2" style="text-align: center;"|'''Point Group'''
| colspan="2" style="text-align: center;"|'''Method'''
| colspan="2" style="text-align: center;"|'''Basis Set'''
| colspan="2" style="text-align: center;"|'''Point Group'''
|- 
| colspan="2" style="text-align: center;"|RB3LYP
| colspan="2" style="text-align: center;"|6-31G(d,p)
| colspan="2" style="text-align: center;"|D<sub>3h</sub>
| colspan="2" style="text-align: center;"|RB3LYP
| colspan="2" style="text-align: center;"|6-31G(d,p)
| colspan="2" style="text-align: center;"|C<sub>3v</sub>
|-
| colspan="6" style="text-align: center;"|<b>Calculation Results</b>
| colspan="6" style="text-align: center;"|<b>Calculation Results</b>
|- 
| colspan="2" style="text-align: center;"|'''E(RB3LYP) /a.u.'''
| colspan="2" style="text-align: center;"|'''RMS Gradient /a.u.'''
| colspan="2" style="text-align: center;"|'''Dipole Moment /D'''
| colspan="2" style="text-align: center;"|'''E(RB3LYP) /a.u.'''
| colspan="2" style="text-align: center;"|'''RMS Gradient /a.u.'''
| colspan="2" style="text-align: center;"|'''Dipole Moment /D'''
|-
| colspan="2" style="text-align: center;"|-39.48468012
| colspan="2" style="text-align: center;"|0.00010036
| colspan="2" style="text-align: center;"|0
| colspan="2" style="text-align: center;"|-39.79602794
| colspan="2" style="text-align: center;"|0.00010504
| colspan="2" style="text-align: center;"|1.7169
|-
| colspan="6" style="text-align: left;"|Click [[Media:YX6015_CH3+_OPTF_POP.LOG| here]] for the log file.
| colspan="6" style="text-align: left;"|Click [[Media:YX6015_CH3-_OPTF_POP.LOG| here]] for the log file.
|}
<pre>
CH3+    Item               Value     Threshold  Converged?     CH3-    Item               Value     Threshold  Converged?
Maximum Force            0.000201     0.000450     YES 	       Maximum Force            0.000173     0.000450     YES
RMS     Force            0.000131     0.000300     YES         RMS     Force            0.000114     0.000300     YES
Maximum Displacement     0.000569     0.001800     YES         Maximum Displacement     0.000510     0.001800     YES
RMS     Displacement     0.000373     0.001200     YES         RMS     Displacement     0.000372     0.001200     YES
</pre>


{| class="wikitable" border="1"
|-
! colspan="6" style="text-align: left;"|Electron Density Comparison
|-
|colspan="2" style="text-align: center;"|CH<sub>3</sub><sup>+</sup>
|colspan="2" style="text-align: center;"|Description
|colspan="2" style="text-align: center;"|CH<sub>3</sub><sup>-</sup>
|-
|colspan="2"|[[File:Yx6015 ch3+ electrondensity.png|400px]] 
|colspan="2" style="text-align: left;"|The images are produced as electrostatic potential mapped onto a surface of electron density on the same scale, with blue being electron deficient and red being electron rich. Carbocation is one of the most important intermediate in organic chemistry and reacts as a electrophile. This can be clearly seen by the electron distribution. On the other hand, carbanion has a electron - rich lone pair, and it is the lone pair that provides its nucleophilicity and reactivity.
|colspan="2"|[[File:Yx6015 ch3- electrondensity.png|400px]]
|}