View source for IMM2 Hans Chan 01196664

== Background ==
This investigation focuses on finding the optimised structure of molecules using quantum mechanical simulations. Optimisation was achieved by using the software [http://www.gaussian.com/ Gaussian]. In this workbook the results from optimisation of various molecules are reported.
The following are included for each molecule;
* Key information about the calculation,
* Results.
* Item Table,
* Rotatable 3D jmol file and image of the optimised structure,
* Link to the final file of the optimisation or frequency.

Non-interactive images of relevant molecules were generated using [http://gaussian.com/products/ Gaussview].

== Molecular Modelling==
=== Ammonia NH<sub>3</sub>===
<jmol><jmolApplet>
  <title>Ammonia </title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>HHC NH3 OPT POP.LOG</uploadedFileContents>
  <script>frame 16</script>
</jmolApplet></jmol>

==== <i>Optimisation</i> ====
The following settings were used for the optimisation of [[Media:HHC NH3 OPT POP.LOG| this molecule]](click link for the .log file);
{| class="wikitable"
!Calculation Type
!Calculation Method
!Basis Set
|-
|FREQ
|RB3LYP
|6-31G(d,p)
|}
The following results were generated;
{| class="wikitable"
!Final Energy
E(RB3LYP) /a.u.
!RMS
Gradient /a.u.
!Symmetry
|-
|<nowiki>-56.55776870</nowiki>
|0.00004995
|C<sub>3v</sub>
|}

The item table here shows that the structure has converged;<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000080     0.000450     YES
 RMS     Force            0.000053     0.000300     YES
 Maximum Displacement     0.000235     0.001800     YES
 RMS     Displacement     0.000117     0.001200     YES
</pre>

====<i>Geometry</i>====
[[File:NH3_Vib.png|300px|thumb|Figure 1: Vibrational modes of NH<sub>3</sub>.]][[File:NH3_Spectra.png|380px|thumb|right|Figure 2: IR Spectrum of NH<sub>3</sub>.]]
The molecule takes a trigonal pyramidal geometry. As the hydrogen atoms are in an identical chemical environment, they have identical bond angles and bond lengths. The bond angle and bond length are shown in the table below;
{| class="wikitable"
! colspan="2" |Geometry
|-
!N-H Length /Å
!H-N-H Angle /'''°'''
|-
|1.01808
|105.736
|}

====<i>Vibrational Modes</i>====
The vibrational modes of the molecule are shown in the table below;
{| class="wikitable"
! colspan="3" |Vibrational Modes
|-
|Mode
|Freq /Hz
|IR
|-
|1
|1090.18
|145.2524
|-
|2
|1694.09
|13.5417
|-
|3
|1694.09
|13.5417
|-
|4
|3460.20
|1.0662
|-
|5
|3588.67
|0.2753
|-
|6
|3588.67
|0.2753
|}
The above information was extracted from Gaussian's 'Vibrations' function (Figure 1).
# From the 3N-6 rule '''6 modes''' of vibration are expected in ammonia (N=4). This is consistent with what was calculated.
# Modes '''2 and 3''' (scissoring bends) and '''5 and 6''' (asymmetric stretches) are degenerate pairs as they have the same energy associated to them.
# Modes '''1 to 3''' corresponds to bends, and modes '''4 to 6''' corresponds to stretches.
# Mode '''4''' is highly symmetric.
# Mode '''1''' is a symmetric bend and is otherwise known as the 'umbrella' mode.
# In an experimental spectra of gaseous ammonia, '''4 bands''' should be expected. All the vibrational modes are associated with a change in dipole moment of the molecule , hence these oscillations are all IR active.<ref name="Atkins">P. Atkins and J. de Paula, ''Atkins' Physical Chemistry, Tenth Edition'', '''2014''', 416.</ref> However the degenerate pairs of vibrational modes correspond to the same frequency as given by <math>E=hf</math>, where <math>f</math> is the frequency and <math>h</math> is the Planck's constant.
Note that Gaussian predicts a spectra with apparently two bands instead of four (Figure 2). This is because modes 4 and 5-6 are significantly weaker in comparison with the other three modes. Close observation shows that Gaussian displays them as a very weak peak around 3500cm<sup>-1</sup>.

====<i>Charges</i>====
[[File:NH3_Q.png|800px|thumb|right|Figure 3: Charges on NH<sub>3</sub>.]]
The relative charge distributions on the atoms as calculated by Gaussain are shown below;
{| class="wikitable"
! colspan="2" |Relative Charge
|-
!N
!H
|-
|<nowiki>-1.125</nowiki>
|0.375
|}
The charges on the atoms computed by Gaussian are as expected; Due to the relative electronegativity of nitrogen in comparison with hydrogen (nitrogen 3.04 and hydrogen 2.20 on the Pauling Scale),<ref name="electronegativity">J.E. Huheey, E.A. Keiter, and R.L. Keiter, ''Inorganic Chemistry : Principles of Structure and Reactivity, 4th edition'', HarperCollins,'''1993'''.</ref> the assigned relative charge on nitrogen is negative (Figure 3). The sum of the charges on all atoms give zero, which is consistent physically as the molecule has no overall charge.

=== Hydrogen H<sub>2</sub> ===
<jmol><jmolApplet>
  <title>Hydrogen </title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>HHC H2 OPT POP.LOG</uploadedFileContents>
  <script>frame 12</script>
</jmolApplet></jmol>

====<i>Optimisation</i>====
The following settings were used for the optimisation of [[Media: HHC H2 OPT POP.LOG|this molecule]](click link for the .log file);
{| class="wikitable"
!Calculation Type
!Calculation Method
!Basis Set
|-
|FREQ
|RB3LYP
|6-31G(d,p)
|}
The following results were generated;
{| class="wikitable"
!Final Energy
E(RB3LYP) /a.u.
!RMS
Gradient /a.u.
!Symmetry
|-
|<nowiki>-1.17853936</nowiki>
|0.00000017
|D<sub>∞h<sub>
|}
The item table here shows that the structure has converged; <pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000450     YES
 RMS     Force            0.000000     0.000300     YES
 Maximum Displacement     0.000000     0.001800     YES
 RMS     Displacement     0.000001     0.001200     YES
</pre>

====<i>Geometry</i>====
The molecule is linear. The bond angle and bond length are shown in the table below;
{| class="wikitable"
! colspan="2" |Geometry
|-
!H-H Length /Å
!H-H Angle /'''°'''
|-
|0.60000
|180
|}
 
====<i>Vibrational Modes</i>====
The vibrational mode of the molecule is shown below;
{| class="wikitable"
! colspan="3" |Vibrational Modes
|-
|Mode
|Freq /Hz
|IR
|-
|1
|4465.58
|0.0000
|}
As it is a diatomic molecule the only vibrational mode is a stretch. No overall change in dipole moment renders the molecule IR inactive, as predicted by Gaussian.

=== Nitrogen N<sub>2</sub>===
<jmol><jmolApplet>
  <title>Nitrogen </title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>HHC N2 OPT POP.LOG</uploadedFileContents>
  <script>frame 26</script>
</jmolApplet></jmol>

====<i>Optimisation</i>====
The following settings were used for the optimisation of [[Media: HHC N2 OPT POP.LOG|this molecule]](click link for the .log file);
{| class="wikitable"
!Calculation Type
!Calculation Method
!Basis Set
|-
|FREQ
|RB3LYP
|6-31G(d,p)
|}
The following results were generated;
{| class="wikitable"
!Final Energy
E(RB3LYP) /a.u.
!RMS
Gradient /a.u.
!Symmetry
|-
|<nowiki>-109.52412868</nowiki>
|0.00000079
|D<sub>∞h<sub>
|}
The item table here shows that the structure has converged; <pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000001     0.000450     YES
 RMS     Force            0.000001     0.000300     YES
 Maximum Displacement     0.000000     0.001800     YES
 RMS     Displacement     0.000001     0.001200     YES
</pre>

====<i>Geometry</i>====
The molecule is linear. The bond angle and bond length are shown in the table below;
{| class="wikitable"
! colspan="2" |Geometry
|-
!N-N Length /Å
!N-N Angle /'''°'''
|-
|1.10550
|180
|}

====<i>Vibrational Modes</i>====
The vibrational mode of the molecule is shown below;
{| class="wikitable"
! colspan="3" |Vibrational Modes
|-
|Mode
|Freq /Hz
|IR
|-
|1
|2457.33
|0.0000
|}
As it is a diatomic molecule the only vibrational mode is a stretch. No overall change in dipole moment renders the molecule IR inactive, as predicted by Gaussian. Note that the vibration frequency of the nitrogen molecule is lower. The vibrational angular frequency is given by <math>\omega =\sqrt{k/\mu}</math>, where <math>k</math> is the bond spring constant and <math>\mu</math> is the system's reduced mass. Although nitrogen has a stronger bond (a larger <math>k</math>), the much lighter hydrogen molecule give an appreciably smaller reduced mass, resulting in a higher vibrational frequency.

===Reaction Energy Consideration - Bosch-Haber Process===
The Bosch-Haber Process converts nitrogen and hydrogen gas into ammonia;

N<sub>2</sub> + 3 H<sub>2</sub> → 2 NH<sub>3</sub> 

The energy change of the reaction can be predicted using the energies of the molecules as calculated by Gaussian. The following table summarises the energies of the molecules computed above.
{| class="wikitable"
! colspan="3" |Energy /a.u.
|-
|E(NH<sub>3</sub>)
|E(N<sub>2</sub>)
|E(H<sub>2</sub>)
|-
|<nowiki>-56.55776870</nowiki>
|<nowiki>-109.52412868</nowiki>
|<nowiki>-1.17853936</nowiki>
|}
The total energy change of the process is thus;

ΔE = 2 × E(NH<sub>3</sub>) - [ E(N<sub>2</sub>) + 3 × E(H<sub>2</sub>) ]

= 2 × -56.55776870 - [ -109.52412868 + 3 × -1.17853936 ]

= -113.1155374 - [ -109.52412868 + -3.53561808 ]

= -0.05579064 a.u. = -146.478 kJ·mol<sup>−1</sup>.

A negative solution shows that the reaction is exothermic, and the sum of energies of the product is lower than the sum of energies of the reactants. This products are hence more stable than the reactants.
The solution is by no means accurate compared to an empirical value of −91.88kJ·mol<sup>-1</sup> under standard conditions. <ref name="Haber-Bosch">K. T. Klemola, ''Chem. Eng. Ed.'', 48 (2), '''2014''', 115–120.</ref> This can be attributed to the fact that computational calculations do not take reaction conditions into account.

===Silanone H<sub>2</sub>SiO===
<jmol><jmolApplet>
  <title>Silanone</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents> HHC H2SIO OPT POP.LOG </uploadedFileContents>
  <script>frame 14</script>
</jmolApplet></jmol>
Note that silanone is also the general name assigned to the silicon analogues of ketones. Here the silicon equivalent of formaldehyde is concerned.

====<i>Optimisation</i>====
The following settings were used for the optimisation of [[Media: HHC H2SIO OPT POP.LOG|this molecule]](click link for the .log file);
{| class="wikitable"
!Calculation Type
!Calculation Method
!Basis Set
|-
|FREQ
|RB3LYP
|6-31G(d,p)
|}
The following results were generated;
{| class="wikitable"
!Final Energy
E(RB3LYP) /a.u.
!RMS
Gradient /a.u.
!Symmetry
|-
|<nowiki>-365.90001403</nowiki>
|0.00000941
|C<sub>2v</sub>
|}
The item table here shows that the structure has converged; <pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000023     0.000450     YES
 RMS     Force            0.000009     0.000300     YES
 Maximum Displacement     0.000023     0.001800     YES
 RMS     Displacement     0.000017     0.001200     YES
</pre>

====<i>Geometry</i>====
[[File:H2SiO_Vib.png|250px|thumb|Figure 4: Vibrational modes of H<sub>2</sub>SiO.]][[File:H2SiO_Spectra.png|380px|thumb|right|Figure 5: IR Spectrum of H<sub>2</sub>SiO.]]
The molecule is roughly trigonal planar around the central silicon. The bond angles and bond lengths are shown in the table below;
{| class="wikitable"
! colspan="4" |Geometry
|-
!Si=O Length /Å
!Si-H Length /Å
!H-Si=O Angles /'''°'''
!H-Si-H Angle /'''°'''
|-
|1.53172
|1.48652
|124.156
|111.686
|}
It can be seen that the H-Si=O angle and the H-Si-H angle are not exactly 120°, which would be the case if the molecule was indeed trigonal planar. This is a result of the higher electron density in the Si=O double bond repelling the Si-H single bonds.

====<i>Vibrational Modes</i>====
The vibrational modes of the molecule is shown below;
{| class="wikitable"
! colspan="4" |Vibrational Modes
|-
|Mode
|Freq /Hz
|IR
|Type
|-
|1
|698.63
|58.6111
|Bending (Wagging)
|-
|2
|712.10
|61.2043
|Bending (Rocking)
|-
|3
|1037.98
|55.3456
|Bending (Scissoring)
|-
|4
|1219.23
|64.9588
|Scissoring Bend and Stretch
|-
|5
|2230.72
|49.9752
|Symmetric Stretch
|-
|6
|2247.73
|185.7008
|Asymmetric Stretch
|}
All of the above are associated with a change in dipole moment in silanone and are therefore IR active. None of the modes are degenerate so six distinct vibrational frequencies are expected (Figure 5). The wide peaks at both ends of the spectrum are two unresolved peaks - the low frequency 'doublet' corresponds to Modes 1 and 2 and the peak at around 2200cm<sup>-1</sup> are Modes 5 and 6.

====<i>Charges</i>====
[[File:H2SiO_Q.png|200px|thumb|right|Figure 6: Charges on H<sub>2</sub>SiO.]]
The relative charge distributions on the atoms as calculated by Gaussain are shown below;
{| class="wikitable"
! colspan="3" |Relative Charge
|-
!Si
!H
!O
|-
|1.472
|<nowiki>-1.001</nowiki>
|<nowiki>-0.236</nowiki>
|}
The sum of the charges is again zero, which is consistent theoretically as the molecule has no overall charge (Figure 6). Oxygen is, relative to the other atoms, the most electronegative (3.44 on the Pauling Scale) and is thus assigned the most negative charge value. Silicon has the lowest electronegativity (1.9 on the Pauling Scale)<ref name="electronegativity">J.E. Huheey, E.A. Keiter, and R.L. Keiter, ''Inorganic Chemistry : Principles of Structure and Reactivity, 4th edition'', HarperCollins,'''1993'''.</ref> and has a positive charge distribution. The hydrogen atoms have an electronegativity between the two, accounting for the charge distribution.

====<i>Molecular Orbitals</i>====
[[File:H2SiO_EE.png|200px|thumb|right|Figure 7: Molecular orbital energy levels of H<sub>2</sub>SiO.]]
The electronic energy levels of the molecule is shown in Figure 7. The following are some of the molecular orbitals of silanone;
{| class="wikitable"
!Energy Level
!Surface
!Description
|-
|1-3
|[[File:MO 1-3.png|200px]]
|These are the core s-electrons from the silicon and oxygen atom. E(1) cannot be seen on Gaussview because it is hidden within the atom. These electrons do not contribute too much to the overall MO. The oribtals shown on the left are the 2s electrons from both atoms.
|-
|4-6
|[[File:MO 4-6.png|200px]]
|These are the 2p orbitals from the silicon core. These do not contribute a lot to the MO either.
|-
|7
|[[File:Hhc MO 7.png|200px]]
|Orbital 7 contribute to some form of σ-bond between silicon and oxygen. The absence of a different phase on the smaller node is of interest; the silicon is expected to be sp<sup>2</sup> hybridised, which should generate a smaller green node on the opposite side of the silicon atom. This could be a result of further integration of AO's between the hydrogen atoms and silicon.
|-
|8,10
|[[File:Hhc MO 8-10.png|200px]]
|E(8) seems to be the σ-bonds joining the hydrogen atoms to the silicon. E(10) is possibly the corresponding σ* orbital. When joined together however they do not completely cancel as expected in an occupied bond-antibond MO pair; the node on the Si-H σ-bonds remain. It is possible that these two combine to give the σ-bonds between silicon and hydrogen.
|-
|9,12
|[[File:Hhc MO 9-12.png|200px]]
|E(9) is some form of extended π-bond in the whole molecule. It is in the plane of the trigonal molecule, as opposed to being vertical in a conventional π-bond. E(12), the HOMO, appears to be the complimentary π-antibond. As both orbitals are occupied, it might be in agreement with the fact that this bond is not predicted in Valence Bond theory.
|-
|11,13
|[[File:Hhc MO 11-13.png|200px]]
|E(11) is a π-bond between the silicon and the oxygen. The unoccupied E(13) is the complimentary π*-antibond, and also the LUMO.
|}

Detailed knowledge of fragment point groups should allow better analysis.

===Reaction Energy Consideration - Silanone Synthesis===
The following process converts ethylene oxide and silylene into silanone and ethene in SF<sub>6</sub> bath gas;<ref name="Silanone">R. Becerra, J. P. Cannady, O. Goulder, R. Walsh, ''J. Phys. Chem. A'', 114 (2), '''2010''', 784–793.</ref>

H<sub>4</sub>C<sub>2</sub>O + H<sub>2</sub>Si → H<sub>2</sub>SiO + H<sub>4</sub>C<sub>2</sub>

The energy change of the reaction can be predicted using the energies of the molecules as calculated by Gaussian. The following table summarises the energies of the molecules computed in Gaussian.

{| class="wikitable"
! colspan="4" |Energy /a.u.
|-
|E(H<sub>4</sub>C<sub>2</sub>O)
|E(H<sub>2</sub>Si)
|E(H<sub>2</sub>SiO)
|E(H<sub>4</sub>C<sub>2</sub>)
|-
|<nowiki>-153.79194941</nowiki>
|<nowiki>-290.61526271</nowiki>
|<nowiki>-365.90001403</nowiki>
|<nowiki>-78.59380796</nowiki>
|}

Relevant .log files:
*[[Media: HHC H2SI OPT POP GIF.LOG|H<sub>2</sub>Si]]
*[[Media: HHC H4C2O OPT POP.LOG|H<sub>4</sub>C<sub>2</sub>O]]
*[[Media: HHC H4C2 OPT POP.LOG|H<sub>4</sub>C<sub>2</sub>]] 

The total energy change of the process is thus;

ΔE = [ E(H<sub>4</sub>C<sub>2</sub>) + E(H<sub>2</sub>SiO) ] - [ E(H<sub>2</sub>Si) + E(H<sub>4</sub>C<sub>2</sub>O) ]

= ( -78.59380796 - 365.90001403 ) - ( -290.61526271 - 153.79194941 )

= -0.08660987 a.u. = -227.394 kJ·mol<sup>−1</sup>

The first calculations used to predict this reaction, executed at the MP2 and QCISD levels of theory using 6-31G basis, gave a value of -61.8kcal·mol<sup>−1</sup>, or -258.57kJ·mol<sup>−1</sup>.<ref name="Silanone2000">Y. Apeloig, S. Sklenak, ''Can. J. Chem.'', (78), '''2000''', 1496–1510.</ref> Both suggest a highly exothermic reaction, however without an experimental value for comparison no conclusions can be drawn.

==References==
<references>
</references>