View source for Rep:Mod:ZY1416

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

{| class="wikitable"
|-
| Calculation Method || OPTF, RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| RMS Gradient || 0.00000485 <i>a.u.</i>
|-
| E(RB3LYP) || -56.55776873 <i>a.u.</i>
|-
| Point Group ||  C<sub>3V</sub>

|}

=== 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>
=== The molecule ===

<u>N-H bond distance</u> = 1.01798 Angstrom

<u>H-N-H bond angle</u> = 105.741 degrees
 <jmol><jmolApplet>
   <title>NH3 molecule</title>
   <color>black</color>
   <size>230</size>
   <script>frame 1.16</script>
   <uploadedFileContents>ZY1416_NH3_OPT.LOG</uploadedFileContents>
 </jmolApplet></jmol>

=== Analysis&Questions ===
[[File:ZY1416_Display_Vibrations.png|150px]|thumb]|right]]

Q:''how many modes do you expect from the 3N-6 rule?''

A: N=4 3*4-6=6 modes


Q:''which modes are degenerate (ie have the same energy)?''

A: modes #2 and #3 are degenerate(H-N-H scissoring) and modes #5 and #6 are degenerate(N-H asymmetric stretching).


Q:''which modes are "bending" vibrations and which are "bond stretch" vibrations?''

A: modes #1,#2 and #3 are bending vibrations and #4,#5,#6 are stretching vibrations.


Q:''which mode is highly symmetric?''

A: mode #4 the stretching N-H symmetric streching


Q:''one mode is known as the "umbrella" mode, which one is this?''

A: mode #1 N-H wagging


Q:''how many bands would you expect to see in an experimental spectrum of gaseous ammonia?''

A: 4 bands
=== Charge Analysis ===
[[File:ZY1416_Charge_Analysis.png|200px]|thumb|The charge distribution on NH3]]


The charge on the N- atom is -1.125 and the charge on the H- atoms is 0.375.

It is expected that the nitrogen atom has the negative charge and the hydrogen atoms have the positive charge because nitrogen is more electronegative than hydrogen.

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

{| class="wikitable"
|-
| Calculation Method || OPTF, RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| RMS Gradient || 0.00978744 <i>a.u.</i>
|-
| E(RB3LYP) || -109.52404119 <i>a.u.</i>
|-
| Point Group ||  D<sub>∞h</sub>

|}

=== Item Table ===
<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     0.000000     0.001200     YES
</pre>

=== Frequency ===
It is a homonuclear molecule with one single vibration at frequency 2457.33 cm<sup>-1</sup>. And this vibration is IR-inactive as there is no change in dipole moment.

[[File:ZY1416_Frequency_N2.png|200px]]

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

{| class="wikitable"
|-
| Calculation Method || OPTF, RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| RMS Gradient || 0.00005349 <i>a.u.</i>
|-
| E(RB3LYP) || -1.17853935 <i>a.u.</i>
|-
| Point Group ||  D<sub>∞h</sub>

|}

=== Item Table ===
<pre>
          Item               Value     Threshold  Converged?
  Maximum Force            0.000093     0.000450     YES
  RMS     Force            0.000093     0.000300     YES
  Maximum Displacement     0.000122     0.001800     YES
  RMS     Displacement     0.000172     0.001200     YES
</pre>

=== Frequency ===
It is a homonuclear molecule as well and it only has one vibration at frequency 4463.83 cm<sup>-1</sup>. And this vibration is IR-inactive as there is no change in dipole moment.

[[File:ZY1416_Frequency_H2.png|200px]]

== Haber-Bosch Reaction Energy Calculations ==
'''Calculated Result:'''

'''E(NH<sub>3</sub>)'''= -56.55776873 au and '''2*E(NH<sub>3</sub>)'''= <u>-113.11553746</u> au

'''E(N<sub>2</sub>)'''= <u>-109.52404119</u> au

'''E(H<sub>2</sub>)'''= -1.17853935 au and '''3*E(H<sub>2</sub>)'''= <u>-3.53561805</u> au

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

= -0.05587822 au 

= <u>-146.70826661</u> KJ/mol

(The ammonia product is thermodynamically more stable as the enthalpy change is negative.)

'''Investigation:'''

The calculated value for the standard enthalpy change of formation of ammonia is -73.354133305 KJ/mol but the experimental value is -45.8 KJ/mol<ref name="Haber" />. This difference can arise because of the different calculation method used. The value obtained from Gaussian View is just an approximation.

== SiH<sub>4</sub> ==
=== Summary ===

{| class="wikitable"
|-
| Calculation Method || OPTF, RB3LYP
|-
| Basis Set || 6-31G(d,p)
|-
| RMS Gradient || 0.00000002 <i>a.u.</i>
|-
| E(RB3LYP) || -291.88802760 <i>a.u.</i>
|-
| Point Group ||  T<sub>d</sub>
|-
| Si-H Bond Length || 1.48485 A
|-
| H-Si-H Bond Angle || 109.471 degrees (Tetrahedral)

|}

=== Item Table ===
<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     0.000000     0.001200     YES
</pre>

=== Information about the molecule ===
'''Charges''': The charge on the Si atom is +0.629 and the charge on the four identical H atoms is -0.157.

[[File:ZY1416_Charge_SiH4.png|150px]|thumb|The charge distribution of SiH4]]

'''Frequency''': There are 9 vibrational modes as expected from the 3N-6 rule where N=5 for the SiH4 molecule. The scissor symmetric and stretching symmetric vibrations have zero infrared intensity because they are IR-inactive.

{| class="wikitable" border="1"
|+ Frequency Analysis
! Frequency/cm<sup>-1</sup> !! Infrared Intensity!!Vibrational mode<ref name="Mode" />
|-
| 919.21 || 136.1485 || scissor asymmetric 
|-
| 919.21 || 136.1485 || scissor asymmetric 
|-
| 919.21 || 136.1485 || scissor asymmetric 
|-
| 978.78 || 0.0000 || H-Si-H scissor symmetric 
|-
| 978.78 || 0.0000 ||  H-Si-H scissor symmetric
|-
| 2244.40 || 0.0000 || H-Si stretching symmetric 
|-
| 2254.90 || 143.3961 || H–Si stretching asymmetric 
|-
| 2254.90 || 143.3961 || H–Si stretching asymmetric
|-
| 2254.90 || 143.3961 || H–Si stretching asymmetric
|}

=== MO Analysis ===
These three filled MOs are degenerate i.e. they have the same energy -3.64 au. They are formed from the antibonding overlap between 2p orbitals.

[[File:ZY1416_MO_5.png|150px]]
[[File:ZY1416_MO_4.PNG|150px]]
[[File:ZY1416_MO_3.PNG|150px]]

This is the HOMO(-0.35 au). It is formed from the bonding overlap between H 1s and Si 3p orbitals and the molecular orbital is 1t<sub>2</sub>. The energy gets much higher compared to the energy of MOs formed by core AOs.

[[File:ZY1416_MO_9.png|150px]]

This is the LUMO(0.05 au). It is formed from the antibonding overlap between H 1s and Si 3p orbitals and the molecular orbital is 2t<sub>2</sub>*.

[[File:ZY1416_MO_10.PNG|150px]]

=== Calculation ===
Formation of SiH4: Si(s) + 2 H2(g) ---> SiH4(g)

'''E(H<sub>2</sub>)'''= -1.17853935 au '''2*E(H<sub>2</sub>)'''= -2.35707870 au

'''E(Si-H)'''= -291.88802760 au 

'''ΔE=E(SiH<sub>4</sub>)-[2*E(H<sub>2</sub>)]'''= -289.5309489 au = -760163.5642431 KJ/mol

The experimental standard enthalpy change of formation of SiH<sub>4</sub> is +34.31 KJ/mol<ref name="Silane" />
The calculated value is obtained from the formation of solid state SiH<sub>4</sub> while the gaseous SiH4 is formed when determining the value of the standard enthalpy of formation. The differnce is because the sublimation of SiH<sub>4</sub> is a very endothermic process.

== Reference==
<references>
<ref name="Haber">Zumdahl, Steven S. (2009). Chemical Principles 6th Ed. Houghton Mifflin Company. p. A22. ISBN 0-618-94690-X.</ref>
<ref name="Mode">Cardona M 1983 ''Phys. Status Solidi b'' '''118''' 463</ref>
<ref name="Silane">Chase, M.W., Jr., NIST-JANAF Themochemical Tables, Fourth Edition, J. Phys. Chem. Ref. Data, Monograph 9, 1998, 1-1951.</ref>

</references>