View source for Rep:Mod:MS8017

==NH<sub>3</sub> Molecule==
===NH<sub>3</sub> Molecule Calculation parameters===
Calculations for an ammonia molecule (NH3). Following parameters were used to carry out the optimisation
<ul>
<li><b>Calculation Method</b> = RB3LYP
<li><b>Calculation Type</b> = OPT+FREQ
<li><b>Basis Set</b> = 6-31G(d,p)
</ul>
GaussView .log files can be found [[Mod:MS8017#Optimisation, Log Files, Results|here]]

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

<ul>
<li><b>E(RB3LYP)</b> = -56.55776873 a.u.
<li><b>RMS Gradient Norm</b> = 0.00000485 a.u.
<li><b>Point Group</b> = C3<sub>V</sub>
</ul>
N-H bond length 1.01798 angstroms<br>
H-N-H bond angle 105.741 degrees<br>
The bond length and bond angles are close to experimental numbers. The differences are due to approximations in the calculation process<ref name="NH3 Bond" />

====NH<sub>3</sub> Jmol picture====

[[media:MS8017_NH3_OPTFRQ.LOG]]

<jmol><jmolApplet>
  <title>NH3 Molecule</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>MS8017_NH3_OPTFRQ.LOG</uploadedFileContents>
  <script>frame 1.16</script>
</jmolApplet></jmol>

====NH<sub>3</sub> Vibrations====
6 Vibrational modes were expected according to the 3n-6 rule (4 atoms).<br>
4 vibrational modes were found to be degenerate (2 bending modes and 2 stretching modes).<br>
Bending modes are numbere 1,2 and 3. Stretching modes are numbered 4,5 and 6.<br>
The modes with highest symmetries were 1 (bending) and 4 (stretching). Hydrogen atoms in these cases were performing the same motion relative to the nitrogen atom.<br>
The vibrational mode designated as 1 is the "umbrella" mode as it is mimicking the folding and unfolding of an umbrella.<br>
4 IR active vibrational modes are present, however only 2 are distinguishable in an experimental measurements. Modes 4,5 and 6 would be indistinguishable form noise

[[File:MS8017 NH3 VIB.PNG]]
[[File:MS8017_NH3_IR.PNG]]

====NH<sub>3</sub> Charge distribution====

Nitrogen is known to have higher electronegativity compared to hydrogen therefore we expect to see more electrons on the nitrogen atom. A negative number higher in magnitude is expected on the nitrogen atom compared to the hydrogen atoms.

[[File:MS8017 NH3 CHRG.PNG]]

===Haber-Bosch process===
[[File:MS8017_N2_MOL.PNG|right|thumb|Nitrogen molecule]]<br>
[[File:MS8017_H2_MOL.PNG|right|thumb|Hydrogen moleucle]]<br>
<ul>
<li>E(NH<sub>3</sub>)=-56.55776873 a.u.
<li>2*E(NH<sub>3</sub>)=-113.11553746 a.u.
<li>E(N<sub>2</sub>)=-109.52412868 a.u.
<li>E(H<sub>2</sub>)=-1.17853936 a.u.
<li>3*E(H<sub>2</sub>)=-3.53561808 a.u.
<li>ΔE=2*E(NH<sub>3</sub>)-[E(N<sub>2</sub>)+3*E(H<sub>2</sub>)]=-0.0557907 a.u. = -146.45 kJ.mol<sup>-1</sup>
</ul>
This reaction tells us that the ammonia gas is more stable as thermodynamically it is an exothermic reaction. This number is however different from measured values. This is due to it being a calculated value using approximations and not an empirically measured value.

==Molecule of choice PH<sub>5</sub>==
<ul>
<li><b>Charge</b> = 0
<li><b>E(RB3LYP)</b> = -344.25491049 a.u.
<li><b>RMS Gradient Norm</b> = 0.00000471 a.u. 
<li><b>Dipole Moment</b> = 0.0000 Debye
<li><b>Point Group</b> = D3H
</ul>
GaussView .log file cna be found [[Mod:MS8017#Optimisation, Log Files, Results|here]]

<jmol><jmolApplet>
  <title>PH5 Molecule</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>MS8017_PH5_OPTFRQ.LOG</uploadedFileContents>
</jmolApplet></jmol>

====Charge Distribution on PH<sub>5</sub>====

[[File:MS8017_PH5_OPTFRQ.PNG]]<br>
The values obtained form GaussView (their signs) are same as expected. Hydrogen should have a negative charge as it is more electronegative in comparison to phosphorus. As observed there is a discrepancy between the charge on the axial hydrogen copared to equatoreal charge. This is due to Jahn Teller distortion <ref name="JahnTeller"/> and it can also be observed in bond lengths. H (axial) = 1.496Å and H (equatoreal) = 1.433Å
<ul>
<li> P = 0.412e
<li> H (axial) = -0.183
<li> H (equatoreal) = -0.015
</ul>

====Vibrations within PH<sub>5</sub>====

PH5 is not a linear molecule so we expect it to have 12 vibrational modes (3N-6).
[[File:MS8017_PH5_VIB.PNGthumb]]<br>
4 vibrations (No. 6,7,8 and 10) do not produce any peaks in the IR spectra as they have no change in the dipole moment. These vibrations are highly symmetrical.<br>
Multiple degenerate vibrational modes are present (No. 1 and 2, 4 and 5, 6 and 7, 11 and 12).
Only 4 peaks would be observed as multiple of these peaks are degenerate and some vibraitons are not IR active (No change in dipole)
[[File:MS8017_PH5_IR.PNG]]

====PH5 Molecular orbitals====

[[File:MS8017_PH5_HOMOLUMO.PNG]]<br>
Orbitals 1-5 are non bonding that are found in the "core" level of this molecule. The bonding/anti bonding orbitals for this molecule are found in the HOMO/LUMO region<br>
{|class="wikitable"
|-
!Molecular Orbital
!Description
|-
|[[File:ENERGY_MS8017_PH5_3S.PNG|600px]]
|Orbital formed by combining the 3s orbital of P and 1s orbital of H. Bonding orbital. Occupied.<br>
|-
|[[File:ENERGY_MS8017_PH5_HOMO.PNG|600px]]
|HOMO orbital of PH5. Formed by combining a 3dz2 (P) with a 1s of H. Bonding orbital. Occupied.
|-
|[[File:ENERGY_MS8017_PH5_LUMO.PNG|600px]]
|LUMO orbital of PH5. Contribution from 3d orbital of P and 1s orbital of H. Vacant. This orbital is a mixture of bonding and antibonding orbital.
|-
|[[File:ENERGY_MS8017_PH5_3SANTI.PNG|600px]]
|Antibonding 3s orbital. Antibonding orbital. Vacant.
|-
|[[File:ENERGY_MS8017_PH5_3PANTI.PNG|600px]]
|Antibonding orbital formed by combining 3p orbital of P with 1s orbital of H. Vacant<br>
|}

==Optimisation, Log Files, Results==
====NH<sub>3</sub>====
<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
 Predicted change in Energy=-5.986279D-10
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.018          -DE/DX =    0.0                 !
 ! R2    R(1,3)                  1.018          -DE/DX =    0.0                 !
 ! R3    R(1,4)                  1.018          -DE/DX =    0.0                 !
 ! A1    A(2,1,3)              105.7412         -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              105.7412         -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              105.7412         -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)           -111.8571         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
nh3 optimisation
File Name = MS8017_NH3_OPTFRQ
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -56.55776873 a.u.
RMS Gradient Norm = 0.00000485 a.u.
Imaginary Freq = 0
Dipole Moment = 1.8466 Debye
Point Group = C3V
</pre>
[[media:MS8017_NH3_OPTFRQ.LOG]]
====N<sub>2</sub> Optimization====
<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     0.000000     0.001200     YES
 Predicted change in Energy=-3.401057D-13
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.1055         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
N2 optimization
File Name = MS8017_N2_OPTFRQ
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -109.52412868 a.u.
RMS Gradient Norm = 0.00000060 a.u.
Imaginary Freq = 0
Dipole Moment = 0.0000 Debye
Point Group = D*H
</pre>
[[media:MS8017_N2_OPTFRQ.LOG]]
====H<sub>2</sub> Optimization====
<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
 Predicted change in Energy=-1.164080D-13
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  0.7428         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
H2 optimisation
File Name = MS8017_H2_OPTFRQ
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -1.17853936 a.u.
RMS Gradient Norm = 0.00000017 a.u.
Imaginary Freq = 0
Dipole Moment = 0.0000 Debye
Point Group = D*H
</pre>
[[media:MS8017_H2_OPTFRQ.LOG]]
====PH<sub>5</sub> Optimisation====
<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000009     0.000450     YES
 RMS     Force            0.000004     0.000300     YES
 Maximum Displacement     0.000055     0.001800     YES
 RMS     Displacement     0.000022     0.001200     YES
 Predicted change in Energy=-1.032823D-09
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.4332         -DE/DX =    0.0                 !
 ! R2    R(1,3)                  1.4869         -DE/DX =    0.0                 !
 ! R3    R(1,4)                  1.4869         -DE/DX =    0.0                 !
 ! R4    R(1,5)                  1.4332         -DE/DX =    0.0                 !
 ! R5    R(1,6)                  1.4332         -DE/DX =    0.0                 !
 ! A1    A(2,1,3)               90.0            -DE/DX =    0.0                 !
 ! A2    A(2,1,4)               90.0            -DE/DX =    0.0                 !
 ! A3    A(2,1,5)              120.0            -DE/DX =    0.0                 !
 ! A4    A(2,1,6)              120.0            -DE/DX =    0.0                 !
 ! A5    A(3,1,5)               90.0            -DE/DX =    0.0                 !
 ! A6    A(3,1,6)               90.0            -DE/DX =    0.0                 !
 ! A7    A(4,1,5)               90.0            -DE/DX =    0.0                 !
 ! A8    A(4,1,6)               90.0            -DE/DX =    0.0                 !
 ! A9    A(5,1,6)              120.0            -DE/DX =    0.0                 !
 ! A10   L(3,1,4,2,-1)         180.0            -DE/DX =    0.0                 !
 ! A11   L(3,1,4,2,-2)         180.0            -DE/DX =    0.0                 !
 ! D1    D(2,1,5,3)             90.0            -DE/DX =    0.0                 !
 ! D2    D(2,1,6,3)            -90.0            -DE/DX =    0.0                 !
 ! D3    D(2,1,5,4)            -90.0            -DE/DX =    0.0                 !
 ! D4    D(2,1,6,4)             90.0            -DE/DX =    0.0                 !
 ! D5    D(2,1,6,5)            180.0            -DE/DX =    0.0                 !
 ! D6    D(3,1,6,5)            -90.0            -DE/DX =    0.0                 !
 ! D7    D(4,1,6,5)             90.0            -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad
</pre>
<pre>
PH5 optimisation
File Name = MS8017_PH5_OPTFRQ
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -344.25491049 a.u.
RMS Gradient Norm = 0.00000471 a.u.
Imaginary Freq = 
Dipole Moment = 0.0000 Debye
Point Group = D3H
</pre>
[[media:MS8017_PH5_OPTFRQ.LOG]]
==References==
<references>
<ref name="JahnTeller">Jahn, H.A., Teller, E. (1937). "Stability of polyatomic molecules in degenerate electronic states - I—Orbital degeneracy". ''Proc. R. Soc. A. '' 161 (A905): 220–235. [http://rspa.royalsocietypublishing.org/content/161/905/220/ DOI: 10.1098/rspa.1937.0142]</ref>

<ref name="NH3 Bond">NIST Computational Chemistry Comparison and Benchmark Database ,
NIST Standard Reference Database Number 101, 
Release 18, October 2016, Editor: Russell D. Johnson III ,
https://cccbdb.nist.gov/exp2x.asp?casno=7664417</ref>
</refrences>