ChemWiki - User contributions [en]

Rep:Mod:Mywiki

2016-03-04T17:57:44Z

Mp3915:

==Ammonia==
Calculations were carried out using the programme "Gaussian".
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
 
===Item Table from 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>
It can be seen that all the items have converged. This shows that the optimisation of the molecule was successful.
===Bond angle and Bond Length===
The H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
View the log file here:
[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D∞H
|}
 
===Item Table from log file===
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
 
View the log file here:
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1. However, this does not show up in the infrared spectrum as N-N has no net dipole moment.
 
===Bond Length===
The bond length of Nitrogen is 1.10550 Angstrom.

 
== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D∞H
|}
 
===Item Table from log file===
<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> 

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol> 
View the log file here:
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment and therefore has zero intensity in the IR spectrum. 
===Bond Length===
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.
 
==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
The enthalpy of formation of ammonia is -45.73112 kJ mol-1- from this information, the formation of 2 moles of ammonia would be 91.46 kJ mol-1.[1] <ref name= "enthalpy"/> This is smaller than the Gaussian value of -146.5 kJ mol-1- this is due to the fact that the conditions used in Gaussian are different from actual experimental conditions.
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2).

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D∞H
|}
 
===Item Table from log file===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol> 
View the log file here:
[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207.
|}
 
===Mixing of Molecular orbitals:===
 
[[File:Chlorine_MO_diagram.png]] 
Figure 1 taken from http://web.utk.edu/~adcock00/g531ch17.pdf
 
As seen in the Molecular Orbital diagram, mixing occurs between bonding s and p σ orbitals when the two bonding orbitals are close in energy to each other. This is done to lower the energy of the lower energy sσ bonding orbital and to raise the energy of the higher energy pσ bonding orbital.[2] This is why one of the sigma bonding orbitals (formed from 3pz overlap along the internuclear axis) is higher in energy than the pi bonding orbitals (formed by 3px orbitals and 3py orbitals). Mixing allows greater orbital overlap and makes the formation of the molecule more exothermic.[2] <ref name ="molecularmixing"/>
==References==

<references>
<ref name="enthalpy">King, L. (1972). The enthalpies of ammonia ’ and formation, (January 1968), 675–683.
(King, 1972)</ref>
<ref name="molecularmixing">Inagaki, S., Fujimoto, H., & Fukui, K. (1976). Orbital mixing rule. Journal of the American Chemical Society, 98(14), 4054–4061. http://doi.org/10.1021/ja00430a006</ref>
</references>

Rep:Mod:Mywiki

2016-03-04T17:57:13Z

Mp3915:

==Ammonia==
Calculations were carried out using the programme "Gaussian".
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
 
===Item Table from 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>
It can be seen that all the items have converged. This shows that the optimisation of the molecule was successful.
===Bond angle and Bond Length===
The H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
View the log file here:
[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D∞H
|}
 
===Item Table from log file===
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
 
View the log file here:
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1. However, this does not show up in the infrared spectrum as N-N has no net dipole moment.
 
===Bond Length===
The bond length of Nitrogen is 1.10550 Angstrom.

 
== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D∞H
|}
 
===Item Table from log file===
<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> 

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol> 
View the log file here:
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment and therefore has zero intensity in the IR spectrum. 
===Bond Length===
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.
 
==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
The enthalpy of formation of ammonia is -45.73112 kJ mol-1- from this information, the formation of 2 moles of ammonia would be 91.46 kJ mol-1.[1] <ref name= "enthalpy"/> This is smaller than the Gaussian value of -146.5 kJ mol-1- this is due to the fact that the conditions used in Gaussian are different from actual experimental conditions.
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2).

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D∞H
|}
 
===Item Table from log file===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol> 
View the log file here:
[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207.
|}
 
===Mixing of Molecular orbitals:===
 
[[File:Chlorine_MO_diagram.png]] 
Figure 1 taken from http://web.utk.edu/~adcock00/g531ch17.pdf
 
As seen in the Molecular Orbital diagram, mixing occurs between bonding s and p σ orbitals when the two bonding orbitals are close in energy to each other. This is done to lower the energy of the lower energy sσ bonding orbital and to raise the energy of the higher energy pσ bonding orbital.[2] This is why one of the sigma bonding orbitals (formed from 3pz overlap along the internuclear axis) is higher in energy than the pi bonding orbitals (formed by 3px orbitals and 3py orbitals). Mixing allows greater orbital overlap and makes the formation of the molecule more exothermic.[2] <ref name ="molecularmixing"/>
==References==
<ref>
[1] </ref> 
<ref>
[2]

<references>
<ref name="enthalpy">King, L. (1972). The enthalpies of ammonia ’ and formation, (January 1968), 675–683.
(King, 1972)</ref>
<ref name="molecularmixing">Inagaki, S., Fujimoto, H., & Fukui, K. (1976). Orbital mixing rule. Journal of the American Chemical Society, 98(14), 4054–4061. http://doi.org/10.1021/ja00430a006</ref>
</references>

Rep:Mod:Mywiki

2016-03-04T17:56:08Z

Mp3915:

==Ammonia==
Calculations were carried out using the programme "Gaussian".
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
 
===Item Table from 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>
It can be seen that all the items have converged. This shows that the optimisation of the molecule was successful.
===Bond angle and Bond Length===
The H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
View the log file here:
[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D∞H
|}
 
===Item Table from log file===
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
 
View the log file here:
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1. However, this does not show up in the infrared spectrum as N-N has no net dipole moment.
 
===Bond Length===
The bond length of Nitrogen is 1.10550 Angstrom.

 
== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D∞H
|}
 
===Item Table from log file===
<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> 

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol> 
View the log file here:
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment and therefore has zero intensity in the IR spectrum. 
===Bond Length===
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.
 
==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
The enthalpy of formation of ammonia is -45.73112 kJ mol-1- from this information, the formation of 2 moles of ammonia would be 91.46 kJ mol-1.[1] <ref name= "1"/> This is smaller than the Gaussian value of -146.5 kJ mol-1- this is due to the fact that the conditions used in Gaussian are different from actual experimental conditions.
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2).

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D∞H
|}
 
===Item Table from log file===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol> 
View the log file here:
[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207.
|}
 
===Mixing of Molecular orbitals:===
 
[[File:Chlorine_MO_diagram.png]] 
Figure 1 taken from http://web.utk.edu/~adcock00/g531ch17.pdf
 
As seen in the Molecular Orbital diagram, mixing occurs between bonding s and p σ orbitals when the two bonding orbitals are close in energy to each other. This is done to lower the energy of the lower energy sσ bonding orbital and to raise the energy of the higher energy pσ bonding orbital.[2] This is why one of the sigma bonding orbitals (formed from 3pz overlap along the internuclear axis) is higher in energy than the pi bonding orbitals (formed by 3px orbitals and 3py orbitals). Mixing allows greater orbital overlap and makes the formation of the molecule more exothermic.[2] <ref name ="2"/>
==References==
<ref>
[1] </ref> 
<ref>
[2]

<references>
<ref name="1">King, L. (1972). The enthalpies of ammonia ’ and formation, (January 1968), 675–683.
(King, 1972)</ref>
<ref name="2">Inagaki, S., Fujimoto, H., & Fukui, K. (1976). Orbital mixing rule. Journal of the American Chemical Society, 98(14), 4054–4061. http://doi.org/10.1021/ja00430a006</ref>
</references>

Rep:Mod:Mywiki

2016-03-04T17:49:48Z

Mp3915:

==Ammonia==
Calculations were carried out using the programme "Gaussian".
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
 
===Item Table from 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>
It can be seen that all the items have converged. This shows that the optimisation of the molecule was successful.
===Bond angle and Bond Length===
The H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
View the log file here:
[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D∞H
|}
 
===Item Table from log file===
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
 
View the log file here:
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1. However, this does not show up in the infrared spectrum as N-N has no net dipole moment.
 
===Bond Length===
The bond length of Nitrogen is 1.10550 Angstrom.

 
== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D∞H
|}
 
===Item Table from log file===
<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> 

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol> 
View the log file here:
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment and therefore has zero intensity in the IR spectrum. 
===Bond Length===
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.
 
==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
The enthalpy of formation of ammonia is -45.73112 kJ mol-1- from this information, the formation of 2 moles of ammonia would be 91.46 kJ mol-1.[1] This is smaller than the Gaussian value of -146.5 kJ mol-1- this is due to the fact that the conditions used in Gaussian are different from actual experimental conditions.
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2).

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D∞H
|}
 
===Item Table from log file===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol> 
View the log file here:
[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207.
|}
 
===Mixing of Molecular orbitals:===
 
[[File:Chlorine_MO_diagram.png]] 
Figure 1 taken from http://web.utk.edu/~adcock00/g531ch17.pdf
 
As seen in the Molecular Orbital diagram, mixing occurs between bonding s and p σ orbitals when the two bonding orbitals are close in energy to each other. This is done to lower the energy of the lower energy sσ bonding orbital and to raise the energy of the higher energy pσ bonding orbital.[2] This is why one of the sigma bonding orbitals (formed from 3pz overlap along the internuclear axis) is higher in energy than the pi bonding orbitals (formed by 3px orbitals and 3py orbitals). Mixing allows greater orbital overlap and makes the formation of the molecule more exothermic.[2]
==References==
<ref>
[1] King, L. (1972). The enthalpies of ammonia ’ and formation, (January 1968), 675–683.
(King, 1972)</ref> 
<ref>
[2] Inagaki, S., Fujimoto, H., & Fukui, K. (1976). Orbital mixing rule. Journal of the American Chemical Society, 98(14), 4054–4061. http://doi.org/10.1021/ja00430a006
</ref>

Rep:Mod:Mywiki

2016-03-04T17:46:13Z

Mp3915:

==Ammonia==
Calculations were carried out using the programme "Gaussian".
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
 
===Item Table from 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>
It can be seen that all the items have converged. This shows that the optimisation of the molecule was successful.
===Bond angle and Bond Length===
The H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
View the log file here:
[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D∞H
|}
 
===Item Table from log file===
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
 
View the log file here:
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1. 
The Nitrogen molecule has no net dipole moment.
 
===Bond Length===
The bond length of Nitrogen is 1.10550 Angstrom.

 
== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D∞H
|}
 
===Item Table from log file===
<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> 

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol> 
View the log file here:
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment. 
===Bond Length===
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.
 
==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
The enthalpy of formation of ammonia is -45.73112 kJ mol-1- from this information, the formation of 2 moles of ammonia would be 91.46 kJ mol-1.[1] This is smaller than the Gaussian value of -146.5 kJ mol-1- this is due to the fact that the conditions used in Gaussian are different from actual experimental conditions.
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2).

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D∞H
|}
 
===Item Table from log file===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol> 
View the log file here:
[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207.
|}
 
===Mixing of Molecular orbitals:===
 
[[File:Chlorine_MO_diagram.png]] 
Figure 1 taken from http://web.utk.edu/~adcock00/g531ch17.pdf
 
As seen in the Molecular Orbital diagram, mixing occurs between bonding s and p σ orbitals when the two bonding orbitals are close in energy to each other. This is done to lower the energy of the lower energy sσ bonding orbital and to raise the energy of the higher energy pσ bonding orbital.[2] This is why one of the sigma bonding orbitals (formed from 3pz overlap along the internuclear axis) is higher in energy than the pi bonding orbitals (formed by 3px orbitals and 3py orbitals). Mixing allows greater orbital overlap and makes the formation of the molecule more exothermic.[2]
==References==
<ref>
[1] King, L. (1972). The enthalpies of ammonia ’ and formation, (January 1968), 675–683.
(King, 1972)</ref> 
<ref>
[2] Inagaki, S., Fujimoto, H., & Fukui, K. (1976). Orbital mixing rule. Journal of the American Chemical Society, 98(14), 4054–4061. http://doi.org/10.1021/ja00430a006
</ref>

Rep:Mod:Mywiki

2016-03-04T17:44:31Z

Mp3915:

==Ammonia==
Using the programme "Gaussian", calculations were carried out.
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
 
===Item Table from 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>
It can be seen that all the items have converged. This shows that the optimisation of the molecule was successful.
===Bond angle and Bond Length===
The H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
View the log file here:
[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D∞H
|}
 
===Item Table from log file===
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
 
View the log file here:
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1. 
The Nitrogen molecule has no net dipole moment.
 
===Bond Length===
The bond length of Nitrogen is 1.10550 Angstrom.

 
== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D∞H
|}
 
===Item Table from log file===
<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> 

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol> 
View the log file here:
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment. 
===Bond Length===
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.
 
==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
The enthalpy of formation of ammonia is -45.73112 kJ mol-1- from this information, the formation of 2 moles of ammonia would be 91.46 kJ mol-1.[1] This is smaller than the Gaussian value of -146.5 kJ mol-1- this is due to the fact that the conditions used in Gaussian are different from actual experimental conditions.
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2).

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D∞H
|}
 
===Item Table from log file===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol> 
View the log file here:
[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207.
|}
 
===Mixing of Molecular orbitals:===
 
[[File:Chlorine_MO_diagram.png]] 
Figure 1 taken from http://web.utk.edu/~adcock00/g531ch17.pdf
 
As seen in the Molecular Orbital diagram, mixing occurs between bonding s and p σ orbitals when the two bonding orbitals are close in energy to each other. This is done to lower the energy of the lower energy sσ bonding orbital and to raise the energy of the higher energy pσ bonding orbital.[2] This is why one of the sigma bonding orbitals (formed from 3pz overlap along the internuclear axis) is higher in energy than the pi bonding orbitals (formed by 3px orbitals and 3py orbitals). Mixing allows greater orbital overlap and makes the formation of the molecule more exothermic.[2]
==References==
<ref>
[1] King, L. (1972). The enthalpies of ammonia ’ and formation, (January 1968), 675–683.
(King, 1972)</ref> 
<ref>
[2] Inagaki, S., Fujimoto, H., & Fukui, K. (1976). Orbital mixing rule. Journal of the American Chemical Society, 98(14), 4054–4061. http://doi.org/10.1021/ja00430a006
</ref>

Rep:Mod:Mywiki

2016-03-04T17:37:48Z

Mp3915:

==Ammonia==
Using the programme "Gaussian", calculations were carried out.
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
 
===Item Table from 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>
It can be seen that all the items have converged. This shows that the optimisation of the molecule was successful.
===Bond angle and Bond Length===
The H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
View the log file here:
[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
 
===Item Table from log file===
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
 
View the log file here:
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1. 
The Nitrogen molecule has no net dipole moment.
 
===Bond Length===
The bond length of Nitrogen is 1.10550 Angstrom.

 
== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}
 
===Item Table from log file===
<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> 

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol> 
View the log file here:
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment. 
===Bond Length===
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.
 
==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
The enthalpy of formation of ammonia is -45.73112 kJ mol-1- from this information, the formation of 2 moles of ammonia would be 91.46 kJ mol-1.[1] This is close to the value of -146.5kJ mol-1 that was calculated by the Gaussianview programme.
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}
 
===Item Table from log file===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol> 
View the log file here:
[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207.
|}
 
===Mixing of Molecular orbitals:===
 
[[File:Chlorine_MO_diagram.png]] 
Figure 1 taken from http://web.utk.edu/~adcock00/g531ch17.pdf
 
As seen in the Molecular Orbital diagram, mixing occurs between bonding s and p σ orbitals when the two bonding orbitals are close in energy to each other. This is done to lower the energy of the lower energy sσ bonding orbital and to raise the energy of the higher energy pσ bonding orbital.[2] This is why one of the sigma bonding orbitals (formed from 3pz overlap along the internuclear axis) is higher in energy than the pi bonding orbitals (formed by 3px orbitals and 3py orbitals). Mixing allows greater orbital overlap and makes the formation of the molecule more exothermic.[2]
==References==
<ref>
[1] King, L. (1972). The enthalpies of ammonia ’ and formation, (January 1968), 675–683.
(King, 1972)</ref> 
<ref>
[2] Inagaki, S., Fujimoto, H., & Fukui, K. (1976). Orbital mixing rule. Journal of the American Chemical Society, 98(14), 4054–4061. http://doi.org/10.1021/ja00430a006
</ref>

Rep:Mod:Mywiki

2016-03-04T17:35:40Z

Mp3915:

==Ammonia==
Using the programme "Gaussian", calculations were carried out.
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
 
===Item Table from 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>
It can be seen that all the items have converged. This shows that the optimisation of the molecule was successful.
===Bond angle and Bond Length===
The H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
View the log file here:
[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
 
===Item Table from log file===
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
 
View the log file here:
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1. 
The Nitrogen molecule has no net dipole moment.
 
===Bond Length===
The bond length of Nitrogen is 1.10550 Angstrom.

 
== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}
 
===Item Table from log file===
<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> 
===Bond Length===
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.
 
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol> 
View the log file here:
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
The enthalpy of formation of ammonia is -45.73112 kJ mol-1- from this information, the formation of 2 moles of ammonia would be 91.46 kJ mol-1.[1] This is close to the value of -146.5kJ mol-1 that was calculated by the Gaussianview programme.
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}
 
===Item Table from log file===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol> 
View the log file here:
[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207.
|}
 
===Mixing of Molecular orbitals:===
 
[[File:Chlorine_MO_diagram.png]] 
Figure 1 taken from http://web.utk.edu/~adcock00/g531ch17.pdf
 
As seen in the Molecular Orbital diagram, mixing occurs between bonding s and p σ orbitals when the two bonding orbitals are close in energy to each other. This is done to lower the energy of the lower energy sσ bonding orbital and to raise the energy of the higher energy pσ bonding orbital.[2] This is why one of the sigma bonding orbitals (formed from 3pz overlap along the internuclear axis) is higher in energy than the pi bonding orbitals (formed by 3px orbitals and 3py orbitals). Mixing allows greater orbital overlap and makes the formation of the molecule more exothermic.[2]
==References==
<ref>
[1] King, L. (1972). The enthalpies of ammonia ’ and formation, (January 1968), 675–683.
(King, 1972)</ref> 
<ref>
[2] Inagaki, S., Fujimoto, H., & Fukui, K. (1976). Orbital mixing rule. Journal of the American Chemical Society, 98(14), 4054–4061. http://doi.org/10.1021/ja00430a006
</ref>

Rep:Mod:Mywiki

2016-03-04T17:30:49Z

Mp3915:

==Ammonia==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
 
===Item Table from 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>
===Bond angle and Bond Length===
The H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
View the log file here:
[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
 
===Item Table from log file===
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
 
View the log file here:
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1. 
The Nitrogen molecule has no net dipole moment.
 
===Bond Length===
The bond length of Nitrogen is 1.10550 Angstrom.

 
== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}
 
===Item Table from log file===
<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> 
===Bond Length===
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.
 
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol> 
View the log file here:
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
The enthalpy of formation of ammonia is -45.73112 kJ mol-1- from this information, the formation of 2 moles of ammonia would be 91.46 kJ mol-1.[1] This is close to the value of -146.5kJ mol-1 that was calculated by the Gaussianview programme.
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}
 
===Item Table from log file===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol> 
View the log file here:
[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207.
|}
 
===Mixing of Molecular orbitals:===
 
[[File:Chlorine_MO_diagram.png]] 
Figure 1 taken from http://web.utk.edu/~adcock00/g531ch17.pdf
 
As seen in the Molecular Orbital diagram, mixing occurs between bonding s and p σ orbitals when the two bonding orbitals are close in energy to each other. This is done to lower the energy of the lower energy sσ bonding orbital and to raise the energy of the higher energy pσ bonding orbital.[2] This is why one of the sigma bonding orbitals (formed from 3pz overlap along the internuclear axis) is higher in energy than the pi bonding orbitals (formed by 3px orbitals and 3py orbitals). Mixing allows greater orbital overlap and makes the formation of the molecule more exothermic.[2]
==References==
<ref>
[1] King, L. (1972). The enthalpies of ammonia ’ and formation, (January 1968), 675–683.
(King, 1972)</ref> 
<ref>
[2] Inagaki, S., Fujimoto, H., & Fukui, K. (1976). Orbital mixing rule. Journal of the American Chemical Society, 98(14), 4054–4061. http://doi.org/10.1021/ja00430a006
</ref>

Rep:Mod:Mywiki

2016-03-04T17:26:43Z

Mp3915:

==Ammonia==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
 
===Item Table from 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>
===Bond angle and Bond Length===
The H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
 
===Item Table from log file===
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1. 
The Nitrogen molecule has no net dipole moment.
 
===Bond Length===
The bond length of Nitrogen is 1.10550 Angstrom.

 
== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}
 
===Item Table from log file===
<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> 
===Bond Length===
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.
 
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
The enthalpy of formation of ammonia is -45.73112 kJ mol-1- from this information, the formation of 2 moles of ammonia would be 91.46 kJ mol-1.[1] This is close to the value of -146.5kJ mol-1 that was calculated by the Gaussianview programme.
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}
 
===Item Table from log file===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207.
|}
 
===Mixing of Molecular orbitals:===
 
[[File:Chlorine_MO_diagram.png]] 
Figure 1 taken from http://web.utk.edu/~adcock00/g531ch17.pdf
 
As seen in the Molecular Orbital diagram, mixing occurs between bonding s and p σ orbitals when the two bonding orbitals are close in energy to each other. This is done to lower the energy of the lower energy sσ bonding orbital and to raise the energy of the higher energy pσ bonding orbital.[2] This is why one of the sigma bonding orbitals (formed from 3pz overlap along the internuclear axis) is higher in energy than the pi bonding orbitals (formed by 3px orbitals and 3py orbitals). Mixing allows greater orbital overlap and makes the formation of the molecule more exothermic.[2]
==References==
<ref>
[1] King, L. (1972). The enthalpies of ammonia ’ and formation, (January 1968), 675–683.
(King, 1972)</ref> 
<ref>
[2] Inagaki, S., Fujimoto, H., & Fukui, K. (1976). Orbital mixing rule. Journal of the American Chemical Society, 98(14), 4054–4061. http://doi.org/10.1021/ja00430a006
</ref>

Rep:Mod:Mywiki

2016-03-04T17:24:07Z

Mp3915:

==Ammonia==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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>
===Bond angle and Bond Length===
The H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1. 
The Nitrogen molecule has no net dipole moment.
 
===Bond Length===
The bond length of Nitrogen is 1.10550 Angstrom.

 
== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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> 
===Bond Length===
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.
 
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
The enthalpy of formation of ammonia is -45.73112 kJ mol-1- from this information, the formation of 2 moles of ammonia would be 91.46 kJ mol-1.[1] This is close to the value of -146.5kJ mol-1 that was calculated by the Gaussianview programme.
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207.
|}
 
===Mixing of Molecular orbitals:===
 
[[File:Chlorine_MO_diagram.png]] 
Figure 1 taken from http://web.utk.edu/~adcock00/g531ch17.pdf
 
As seen in the Molecular Orbital diagram, mixing occurs between bonding s and p σ orbitals when the two bonding orbitals are close in energy to each other. This is done to lower the energy of the lower energy sσ bonding orbital and to raise the energy of the higher energy pσ bonding orbital.[2] This is why one of the sigma bonding orbitals (formed from 3pz overlap along the internuclear axis) is higher in energy than the pi bonding orbitals (formed by 3px orbitals and 3py orbitals). Mixing allows greater orbital overlap and makes the formation of the molecule more exothermic.[2]
==References==
<ref>
[1] King, L. (1972). The enthalpies of ammonia ’ and formation, (January 1968), 675–683.
(King, 1972)</ref> 
<ref>
[2] Inagaki, S., Fujimoto, H., & Fukui, K. (1976). Orbital mixing rule. Journal of the American Chemical Society, 98(14), 4054–4061. http://doi.org/10.1021/ja00430a006
</ref>

Rep:Mod:Mywiki

2016-03-04T17:18:31Z

Mp3915:

==Ammonia==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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> 

The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.
 
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
The enthalpy of formation of ammonia is -45.73112 kJ mol-1- from this information, the formation of 2 moles of ammonia would be 91.46 kJ mol-1.[1] This is close to the value of -146.5kJ mol-1 that was calculated by the Gaussianview programme.
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207.
|}
 
===Mixing of Molecular orbitals:===
 
[[File:Chlorine_MO_diagram.png]] 
Figure 1 taken from http://web.utk.edu/~adcock00/g531ch17.pdf
 
As seen in the Molecular Orbital diagram, mixing occurs between bonding s and p σ orbitals when the two bonding orbitals are close in energy to each other. This is done to lower the energy of the lower energy sσ bonding orbital and to raise the energy of the higher energy pσ bonding orbital.[2] This is why one of the sigma bonding orbitals (formed from 3pz overlap along the internuclear axis) is higher in energy than the pi bonding orbitals (formed by 3px orbitals and 3py orbitals). Mixing allows greater orbital overlap and makes the formation of the molecule more exothermic.[2]
==References==
<ref>
[1] King, L. (1972). The enthalpies of ammonia ’ and formation, (January 1968), 675–683.
(King, 1972)</ref> 
<ref>
[2] Inagaki, S., Fujimoto, H., & Fukui, K. (1976). Orbital mixing rule. Journal of the American Chemical Society, 98(14), 4054–4061. http://doi.org/10.1021/ja00430a006
</ref>

Rep:Mod:Mywiki

2016-03-04T17:18:03Z

Mp3915:

==Ammonia==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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> 

The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.
 
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
The enthalpy of formation of ammonia is -45.73112 kJ mol-1- from this information, the formation of 2 moles of ammonia would be 91.46 kJ mol-1.[1] This is close to the value of -146.5kJ mol-1 that was calculated by the Gaussianview programme.
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207.
|}
 
===Mixing of Molecular orbitals:===
 
[[File:Chlorine_MO_diagram.png]] 
Figure 1 taken from http://web.utk.edu/~adcock00/g531ch17.pdf
 
As seen in the Molecular Orbital diagram, mixing occurs between bonding s and p σ orbitals when the two bonding orbitals are close in energy to each other. This is done to lower the energy of the lower energy sσ bonding orbital and to raise the energy of the higher energy pσ bonding orbital.[2] This is why one of the sigma bonding orbitals (formed from 3pz overlap along the internuclear axis) is higher in energy than the pi bonding orbitals (formed by 3px orbitals and 3py orbitals). Mixing allows greater orbital overlap and makes the formation of the molecule more exothermic.[2]
==References==
<ref>
[1] King, L. (1972). The enthalpies of ammonia ’ and formation, (January 1968), 675–683.
(King, 1972)</ref> 
<ref>
[2] Inagaki, S., Fujimoto, H., & Fukui, K. (1976). Orbital mixing rule. Journal of the American Chemical Society, 98(14), 4054–4061. http://doi.org/10.1021/ja00430a006
</ref>

Rep:Mod:Mywiki

2016-03-04T17:17:07Z

Mp3915:

==Ammonia==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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> 

The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.
 
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
The enthalpy of formation of ammonia is -45.73112 kJ mol-1- from this information, the formation of 2 moles of ammonia would be 91.46 kJ mol-1.[1] This is close to the value of -146.5kJ mol-1 that was calculated by the Gaussianview programme.
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207.
|}
 
=== Mixing of Molecular orbitals: === 
[[File:Chlorine_MO_diagram.png]] 
Figure 1 taken from http://web.utk.edu/~adcock00/g531ch17.pdf
 
As seen in the Molecular Orbital diagram, mixing occurs between bonding s and p σ orbitals when the two bonding orbitals are close in energy to each other. This is done to lower the energy of the lower energy sσ bonding orbital and to raise the energy of the higher energy pσ bonding orbital.[2] This is why one of the sigma bonding orbitals (formed from 3pz overlap along the internuclear axis) is higher in energy than the pi bonding orbitals (formed by 3px orbitals and 3py orbitals). Mixing allows greater orbital overlap and makes the formation of the molecule more exothermic.[2]
==References==
<ref>
[1] King, L. (1972). The enthalpies of ammonia ’ and formation, (January 1968), 675–683.
(King, 1972)</ref> 
<ref>
[2] Inagaki, S., Fujimoto, H., & Fukui, K. (1976). Orbital mixing rule. Journal of the American Chemical Society, 98(14), 4054–4061. http://doi.org/10.1021/ja00430a006
</ref>

Rep:Mod:Mywiki

2016-03-04T17:16:37Z

Mp3915:

==Ammonia==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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> 

The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.
 
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
The enthalpy of formation of ammonia is -45.73112 kJ mol-1- from this information, the formation of 2 moles of ammonia would be 91.46 kJ mol-1.[1] This is close to the value of -146.5kJ mol-1 that was calculated by the Gaussianview programme.
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207.
|}
 
 Mixing of Molecular orbitals: 
[[File:Chlorine_MO_diagram.png]] 
Figure 1 taken from http://web.utk.edu/~adcock00/g531ch17.pdf
 
As seen in the Molecular Orbital diagram, mixing occurs between bonding s and p σ orbitals when the two bonding orbitals are close in energy to each other. This is done to lower the energy of the lower energy sσ bonding orbital and to raise the energy of the higher energy pσ bonding orbital.[2] This is why one of the sigma bonding orbitals (formed from 3pz overlap along the internuclear axis) is higher in energy than the pi bonding orbitals (formed by 3px orbitals and 3py orbitals). Mixing allows greater orbital overlap and makes the formation of the molecule more exothermic.[2]
==References==
<ref>
[1] King, L. (1972). The enthalpies of ammonia ’ and formation, (January 1968), 675–683.
(King, 1972)</ref> 
<ref>
[2] Inagaki, S., Fujimoto, H., & Fukui, K. (1976). Orbital mixing rule. Journal of the American Chemical Society, 98(14), 4054–4061. http://doi.org/10.1021/ja00430a006
</ref>

Rep:Mod:Mywiki

2016-03-04T17:15:41Z

Mp3915:

==Ammonia==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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> 

The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.
 
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
The enthalpy of formation of ammonia is -45.73112 kJ mol-1- from this information, the formation of 2 moles of ammonia would be 91.46 kJ mol-1.[1] This is close to the value of -146.5kJ mol-1 that was calculated by the Gaussianview programme.
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207.
|}
 
Mixing of Molecular orbitals: 
[[File:Chlorine_MO_diagram.png]] 
Figure 1 taken from http://web.utk.edu/~adcock00/g531ch17.pdf
 
As seen in the Molecular Orbital diagram, mixing occurs between bonding s and p σ orbitals when the two bonding orbitals are close in energy to each other. This is done to lower the energy of the lower energy sσ bonding orbital and to raise the energy of the higher energy pσ bonding orbital.[2] This is why one of the sigma bonding orbitals (formed from 3pz overlap along the internuclear axis) is higher in energy than the pi bonding orbitals (formed by 3px orbitals and 3py orbitals). Mixing allows greater orbital overlap and makes the formation of the molecule more exothermic.[2]
==References==
<ref>
[1] King, L. (1972). The enthalpies of ammonia ’ and formation, (January 1968), 675–683.
(King, 1972)</ref> 
<ref>
[2] Inagaki, S., Fujimoto, H., & Fukui, K. (1976). Orbital mixing rule. Journal of the American Chemical Society, 98(14), 4054–4061. http://doi.org/10.1021/ja00430a006
</ref>

Rep:Mod:Mywiki

2016-03-04T17:14:40Z

Mp3915:

==Ammonia==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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> 

The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.
 
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
The enthalpy of formation of ammonia is -45.73112 kJ mol-1- from this information, the formation of 2 moles of ammonia would be 91.46 kJ mol-1.[1] This is close to the value of -146.5kJ mol-1 that was calculated by the Gaussianview programme.
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207.
|}
 
Mixing of Molecular orbitals: 
[[File:Chlorine_MO_diagram.png]] 
Figure 1 taken from http://web.utk.edu/~adcock00/g531ch17.pdf
 
As seen in the Molecular Orbital diagram, mixing occurs between bonding s and p σ orbitals when the two bonding orbitals are close in energy to each other. This is done to lower the energy of the lower energy sσ bonding orbital and to raise the energy of the higher energy pσ bonding orbital.[2] This is why one of the sigma bonding orbitals (formed from 3pz overlap along the internuclear axis) is higher in energy than the pi bonding orbitals (formed by 3px orbitals and 3py orbitals). Mixing allows greater orbital overlap and makes the formation of the molecule more exothermic.[2]
==References==
<ref>
[1] King, L. (1972). The enthalpies of ammonia ’ and formation, (January 1968), 675–683.
(King, 1972)
[2] Inagaki, S., Fujimoto, H., & Fukui, K. (1976). Orbital mixing rule. Journal of the American Chemical Society, 98(14), 4054–4061. http://doi.org/10.1021/ja00430a006
</ref>

Rep:Mod:Mywiki

2016-03-04T17:01:38Z

Mp3915:

==Ammonia==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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> 

The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.
 
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
The enthalpy of formation of ammonia is -45.73112 kJ mol-1- from this information, the formation of 2 moles of ammonia would be 91.46 kJ mol-1.[1] This is close to the value of -146.5kJ mol-1 that was calculated by the Gaussianview programme.
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207.
|}
 
Mixing of Molecular orbitals: 
[[File:Chlorine_MO_diagram.png]] 
Figure 1 taken from http://web.utk.edu/~adcock00/g531ch17.pdf
 
As seen in the Molecular Orbital diagram, mixing occurs between bonding sigma orbitals when two or more bonding sigma orbitals are close in energy to each other. This is done to lower the energy of the lower energy sigma bonding orbital and to raise the energy of the higher energy sigma bonding orbital. This is why one of the sigma bonding orbitals (formed from 3pz overlap along the internuclear axis) is higher in energy than the pi bonding orbitals (formed by 3px and 3py)
==References==
<ref>
[1] King, L. (1972). The enthalpies of ammonia ’ and formation, (January 1968), 675–683.
(King, 1972)
</ref>

Rep:Mod:Mywiki

2016-03-04T16:51:00Z

Mp3915:

==Ammonia==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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> 

The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.
 
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
The enthalpy of formation of ammonia is -45.73112 kJ mol-1- from this information, the formation of 2 moles of ammonia would be 91.46 kJ mol-1.[1] This is close to the value of -146.5kJ mol-1 that was calculated by the Gaussianview programme.
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207.
|}
 
Mixing of Molecular orbitals: 
[[File:Chlorine_MO_diagram.png]] 
Figure 1 taken from http://web.utk.edu/~adcock00/g531ch17.pdf
 
==References==
<ref>
[1] King, L. (1972). The enthalpies of ammonia ’ and formation, (January 1968), 675–683.
(King, 1972)
</ref>

Rep:Mod:Mywiki

2016-03-04T16:50:18Z

Mp3915:

==Ammonia==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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> 

The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.
 
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
The enthalpy of formation of ammonia is -45.73112 kJ mol-1- from this information, the formation of 2 moles of ammonia would be 91.46 kJ mol-1.[1] This is close to the value of -146.5kJ mol-1 that was calculated by the Gaussianview programme.
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207.
|}
Mixing of Molecular orbitals:
[[File:Chlorine_MO_diagram.png]]
Figure 1 taken from http://web.utk.edu/~adcock00/g531ch17.pdf
 
==References==
<ref>
[1] King, L. (1972). The enthalpies of ammonia ’ and formation, (January 1968), 675–683.
(King, 1972)
</ref>

Rep:Mod:Mywiki

2016-03-04T16:49:23Z

Mp3915:

==Ammonia==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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> 

The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.
 
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
The enthalpy of formation of ammonia is -45.73112 kJ mol-1- from this information, the formation of 2 moles of ammonia would be 91.46 kJ mol-1.[1] This is close to the value of -146.5kJ mol-1 that was calculated by the Gaussianview programme.
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207.
|}
Mixing of Molecular orbitals:
[[File:Chlorine_MO_diagram.png]]

 
==References==
<ref>
[1] King, L. (1972). The enthalpies of ammonia ’ and formation, (January 1968), 675–683.
(King, 1972)
</ref>

File:Chlorine MO diagram.png

2016-03-04T16:46:58Z

Mp3915:

Rep:Mod:Mywiki

2016-03-04T16:40:31Z

Mp3915:

==Ammonia==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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> 

The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.
 
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
The enthalpy of formation of ammonia is -45.73112 kJ mol-1- from this information, the formation of 2 moles of ammonia would be 91.46 kJ mol-1.[1] This is close to the value of -146.5kJ mol-1 that was calculated by the Gaussianview programme.
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}
==References==
<ref>
[1] King, L. (1972). The enthalpies of ammonia ’ and formation, (January 1968), 675–683.
(King, 1972)
</ref>

Rep:Mod:Mywiki

2016-03-04T16:13:49Z

Mp3915:

==Ammonia==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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> 

The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.
 
<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T16:08:42Z

Mp3915:

==Ammonia==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

== Hydrogen ==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Chlorine==
===Summary of Results===

{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T16:07:31Z

Mp3915:

==Ammonia==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

== Hydrogen ==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Chlorine==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

===Molecular Orbitals in Chlorine===

{| class="wikitable" border="1"
|+ M.O.s in Chlorine
! Orbital !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T16:06:10Z

Mp3915:

==Ammonia==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Nitrogen ==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

== Hydrogen ==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Chlorine==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! M.O. !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T16:03:57Z

Mp3915:

==Molecule name: Ammonia==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Molecule name: Nitrogen ==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

== Molecule name: Hydrogen ==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Molecule name: Chlorine==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! M.O. !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T16:03:31Z

Mp3915:

==Molecule name: Ammonia==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Molecule name: Nitrogen ==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

== Molecule name: Hydrogen ==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

==Haber-Bosch Reaction Energy==
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Molecule name: Chlorine==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! M.O. !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T16:02:21Z

Mp3915:

==Molecule name: Ammonia==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]] 
===Vibrations of NH3 molecule in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Molecule name: Nitrogen ==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]] 
===Vibrations of N2 in IR spectrum===
[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

== Molecule name: Hydrogen ==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]] 
===Vibrations of H2 in IR spectrum===
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia Haber-Bosch Reaction Energy N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Molecule name: Chlorine==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
===Vibrations of Cl2 in IR spectrum===
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! M.O. !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T15:59:46Z

Mp3915: /* Summary of Results */

==Molecule name: Ammonia==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]]
===Vibrations in IR spectrum===
[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Molecule name: Nitrogen ==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]]

[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

== Molecule name: Hydrogen ==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]]
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia Haber-Bosch Reaction Energy N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Molecule name: Chlorine==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! M.O. !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T15:57:32Z

Mp3915:

==Molecule name: Ammonia==
===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]]

[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Molecule name: Nitrogen ==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]]

[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

== Molecule name: Hydrogen ==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]]
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia Haber-Bosch Reaction Energy N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Molecule name: Chlorine==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! M.O. !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T15:57:19Z

Mp3915: /* Molecule name: Ammonia */

==Molecule name: Ammonia==
+ ===Summary of Results===
{| class="wikitable" border="1"
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]]

[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Molecule name: Nitrogen ==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]]

[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

== Molecule name: Hydrogen ==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]]
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia Haber-Bosch Reaction Energy N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Molecule name: Chlorine==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! M.O. !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T15:56:02Z

Mp3915:

==Molecule name: Ammonia==
{| class="wikitable" border="1"
|+ ===Summary of Results===
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]]

[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

== Molecule name: Nitrogen ==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]]

[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

== Molecule name: Hydrogen ==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]]
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia Haber-Bosch Reaction Energy N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

==Molecule name: Chlorine==

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! M.O. !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T15:49:34Z

Mp3915:

Molecule name: Ammonia
{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]]

[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

 Molecule name: Nitrogen 

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]]

[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

 Molecule name: Hydrogen 

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]]
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.
Haber-Bosch Reaction Energy
{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

Molecule name: Chlorine

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! M.O. !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T15:45:08Z

Mp3915:

Molecule name: Ammonia
{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]]

[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

 Molecule name: Nitrogen 

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]]

[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

 Molecule name: Hydrogen 

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]]
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}
Since the reaction is exothermic, it can be seen that the formation of ammonia is favoured, over the formation of its gaseous reactants (N2 and H2)

Molecule name: Chlorine

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! M.O. !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T15:41:49Z

Mp3915:

Molecule name: Ammonia
{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]]

[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

 Molecule name: Nitrogen 

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]]

[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

 Molecule name: Hydrogen 

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]]
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3) || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}

Molecule name: Chlorine

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! M.O. !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T15:40:48Z

Mp3915:

Molecule name: Ammonia
{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]]

[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

 Molecule name: Nitrogen 

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]]

[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

 Molecule name: Hydrogen 

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]]
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3)= || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}

Molecule name: Chlorine

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! M.O. !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T15:40:09Z

Mp3915:

Molecule name: Ammonia
{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]]

[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

 Molecule name: Nitrogen 

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]]

[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

 Molecule name: Hydrogen 

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]]
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

{| class="wikitable" border="1"
|+ Reaction Energy for formation of Ammonia N2 + 3H2 -> 2NH3
| E(NH3)= || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}

Molecule name: Chlorine

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! M.O. !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T15:38:09Z

Mp3915:

Molecule name: Ammonia
{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]]

[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

 Molecule name: Nitrogen 

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]]

[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

 Molecule name: Hydrogen 

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]]
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

{| class="wikitable" border="1"
|+ Reaction Energy
| E(NH3)= || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}

Molecule name: Chlorine

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! M.O. !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T15:35:58Z

Mp3915:

Molecule name: Ammonia
{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]]

[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

 Molecule name: Nitrogen 

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]]

[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

 Molecule name: Hydrogen 

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]]
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

{| class="wikitable" border="1"
|Reaction Energy
! heading !! heading
|-
| E(NH3)= || -56.55776873 a.u.
|-
| 2*E(NH3) || -113.1155375 a.u.
|-
| E(N2) || -109.52412868 a.u.
|-
| E(H2) || -1.17853936 a.u.
|-
| 3*E(H2) || -3.53561808 a.u.
|-
| ΔE=2*E(NH3)-[E(N2)+3*E(H2)] || -0.0557907 a.u. 
= -146.5 kJ mol-1
|}

Molecule name: Chlorine

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! M.O. !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T15:32:04Z

Mp3915:

Molecule name: Ammonia
{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]]

[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

 Molecule name: Nitrogen 

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]]

[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

 Molecule name: Hydrogen 

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]]
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

E(NH3)= -56.55776873 a.u.
2*E(NH3)= -113.1155375 a.u.
E(N2)=-109.52412868 a.u.
E(H2)= -1.17853936 a.u.
3*E(H2)= -3.53561808 a.u.
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907 a.u. = -146.48 kJ mol-1

Molecule name: Chlorine

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! M.O. !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T15:27:14Z

Mp3915:

Molecule name: Ammonia
{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]]

[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95 cm-1), and 5 and 6 (3589.82 cm-1) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

 Molecule name: Nitrogen 

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]]

[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31 cm-1.

The Nitrogen molecule has no net dipole moment.

 Molecule name: Hydrogen 

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]]
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68 cm-1. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

E(NH3)= -56.55776873 a.u.
2*E(NH3)= -113.1155375 a.u.
E(N2)=-109.52412868 a.u.
E(H2)= -1.17853936 a.u.
3*E(H2)= -3.53561808 a.u.
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907 a.u.

Molecule name: Chlorine

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30 cm-1. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! M.O. !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T15:22:54Z

Mp3915:

Molecule name: Ammonia
{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]]

[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95), and 5 and 6 (3589.82) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

 Molecule name: Nitrogen 

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]]

[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31.

The Nitrogen molecule has no net dipole moment.

 Molecule name: Hydrogen 

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]]
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

E(NH3)= -56.55776873 a.u.
2*E(NH3)= -113.1155375 a.u.
E(N2)=-109.52412868 a.u.
E(H2)= -1.17853936 a.u.
3*E(H2)= -3.53561808 a.u.
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907 a.u.

Molecule name: Chlorine

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -920.34987886 a.u.
|-
| RMS Gradient Norm: || 0.00002948 a.u.
|-
| Point Group: || D*H
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! M.O. !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T15:19:49Z

Mp3915:

Molecule name: Ammonia
{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]]

[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95), and 5 and 6 (3589.82) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

 Molecule name: Nitrogen 

{| class="wikitable" border="1"
|+ Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -109.52412868 a.u.
|-
| RMS Gradient Norm: || 0.00000365 a.u.
|-
| Point Group: || D*H
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]]

[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31.

The Nitrogen molecule has no net dipole moment.

 Molecule name: Hydrogen 

{| class="wikitable" border="1"
|Summary of Results
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -1.17853936 a.u.
|-
| RMS Gradient Norm: || 0.00000017 a.u.
|-
| Point Group: || D*H
|}

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]]
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

E(NH3)= -56.55776873 a.u.
2*E(NH3)= -113.1155375 a.u.
E(N2)=-109.52412868 a.u.
E(H2)= -1.17853936 a.u.
3*E(H2)= -3.53561808 a.u.
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907 a.u.

Molecule name: Chlorine
Calculation Method: RB3LYP
Basis Set: 6-31G(d,p)
Final Energy E(RB3LYP): -920.34987886 a.u.
RMS Gradient Norm: 0.00002948 a.u.
Point Group: D*H

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! M.O. !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T15:16:14Z

Mp3915:

Molecule name: Ammonia 
 
Basis Set: 
Final Energy E(RB3LYP): -56.55776873 a.u. 
RMS Gradient Norm: 0.00000485 a.u. 
Point Group: C3V 
{| class="wikitable" border="1"
|+ Results Summary
|-
| Calculation method: || RB3LYP
|-
| Basis Set: || 6-31G(d,p)
|-
| Final Energy E(RB3LYP): || -56.55776873 a.u.
|-
| RMS Gradient Norm: || 0.00000485 a.u.
|-
| Point Group: || C3V
|}
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]]

[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95), and 5 and 6 (3589.82) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

 Molecule name: Nitrogen 
Calculation Method: RB3LYP 
Basis Set: 6-31G(d,p) 
Final Energy E(RB3LYP) -109.52412868 a.u. 
RMS Gradient Norm: 0.00000365 a.u. 
Point Group: D*H 
{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| Calculation method: || cell
|-
| Basis Set: || cell
|-
| Final Energy E(RB3LYP): || cell
|-
| RMS Gradient Norm: || cell
|-
| Point Group: || cell
|}
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]]

[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31.

The Nitrogen molecule has no net dipole moment.

 Molecule name: Hydrogen 
Calculation Method: RB3LYP 
Basis Set: 6-31G(d,p) 
Final energy E(RB3LYP): -1.17853936 a.u. 
RMS Gradient Norm: 0.00000017 a.u. 
Point Group: D*H 
{| class="wikitable" border="1"
|+ caption
! heading !! heading
|-
| Calculation method: || cell
|-
| Basis Set: || cell
|-
| Final Energy E(RB3LYP): || cell
|-
| RMS Gradient Norm: || cell
|-
| Point Group: || cell
|}

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]]
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

E(NH3)= -56.55776873 a.u.
2*E(NH3)= -113.1155375 a.u.
E(N2)=-109.52412868 a.u.
E(H2)= -1.17853936 a.u.
3*E(H2)= -3.53561808 a.u.
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907 a.u.

Molecule name: Chlorine
Calculation Method: RB3LYP
Basis Set: 6-31G(d,p)
Final Energy E(RB3LYP): -920.34987886 a.u.
RMS Gradient Norm: 0.00002948 a.u.
Point Group: D*H

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! M.O. !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T15:10:34Z

Mp3915:

Molecule name: Ammonia 
Calculation method: RB3LYP 
Basis Set:6-31G(d,p) 
Final Energy E(RB3LYP): -56.55776873 a.u. 
RMS Gradient Norm: 0.00000485 a.u. 
Point Group: C3V 
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]]

[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95), and 5 and 6 (3589.82) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

 Molecule name: Nitrogen 
Calculation Method: RB3LYP 
Basis Set: 6-31G(d,p) 
Final Energy E(RB3LYP) -109.52412868 a.u. 
RMS Gradient Norm: 0.00000365 a.u. 
Point Group: D*H 
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]]

[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31.

The Nitrogen molecule has no net dipole moment.

 Molecule name: Hydrogen 
Calculation Method: RB3LYP 
Basis Set: 6-31G(d,p) 
Final energy E(RB3LYP): -1.17853936 a.u. 
RMS Gradient Norm: 0.00000017 a.u. 
Point Group: D*H 

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]]
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

E(NH3)= -56.55776873 a.u.
2*E(NH3)= -113.1155375 a.u.
E(N2)=-109.52412868 a.u.
E(H2)= -1.17853936 a.u.
3*E(H2)= -3.53561808 a.u.
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907 a.u.

Molecule name: Chlorine
Calculation Method: RB3LYP
Basis Set: 6-31G(d,p)
Final Energy E(RB3LYP): -920.34987886 a.u.
RMS Gradient Norm: 0.00002948 a.u.
Point Group: D*H

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! M.O. !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is a sigma bonding orbital.
- This is formed by the overlap of the 3s orbitals of each chlorine atom. 
- The A.O.s overlap in phase. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - This M.O. is a pi bonding orbital.
- The two 3p orbitals overlap in phase. 
- The p orbitals overlap "sideways".
- The electrons are held above and below the plane of the bond, but not on the internuclear axis.
- There is a nodal plane at the internuclear axis for all pi orbitals.
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - This M.O. is a pi antibonding orbital.
- The two 3p orbitals overlap out of phase. 
- "Sideways" overlap of p orbitals, nodal plane at internuclear axis.
- This molecular orbital is the HOMO in molecular chlorine. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "end to end" overlap of the two 3pz orbitals, i.e., along the internuclear axis, with the lobes pointing towards each other. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis ("end to end" overlap of the two 3pz orbitals with the lobes pointing towards each other) 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T14:58:08Z

Mp3915:

Molecule name: Ammonia 
Calculation method: RB3LYP 
Basis Set:6-31G(d,p) 
Final Energy E(RB3LYP): -56.55776873 a.u. 
RMS Gradient Norm: 0.00000485 a.u. 
Point Group: C3V 
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]]

[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95), and 5 and 6 (3589.82) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

 Molecule name: Nitrogen 
Calculation Method: RB3LYP 
Basis Set: 6-31G(d,p) 
Final Energy E(RB3LYP) -109.52412868 a.u. 
RMS Gradient Norm: 0.00000365 a.u. 
Point Group: D*H 
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]]

[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31.

The Nitrogen molecule has no net dipole moment.

 Molecule name: Hydrogen 
Calculation Method: RB3LYP 
Basis Set: 6-31G(d,p) 
Final energy E(RB3LYP): -1.17853936 a.u. 
RMS Gradient Norm: 0.00000017 a.u. 
Point Group: D*H 

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]]
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

E(NH3)= -56.55776873 a.u.
2*E(NH3)= -113.1155375 a.u.
E(N2)=-109.52412868 a.u.
E(H2)= -1.17853936 a.u.
3*E(H2)= -3.53561808 a.u.
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907 a.u.

Molecule name: Chlorine
Calculation Method: RB3LYP
Basis Set: 6-31G(d,p)
Final Energy E(RB3LYP): -920.34987886 a.u.
RMS Gradient Norm: 0.00002948 a.u.
Point Group: D*H

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 
 Molecular orbitals in chlorine: 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! M.O. !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is formed by the overlap of the 3s orbitals of each chlorine atom. 
- This is a bonding sigma orbital. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - pi bonding orbital: The two 3p orbitals overlap in phase. 
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - The two 3p orbitals overlap out of phase. 
- This molecular orbital is the HOMO. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "side-on" overlap of the two 3pz orbitals. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis "Sideways". 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T14:57:00Z

Mp3915:

Molecule name: Ammonia 
Calculation method: RB3LYP 
Basis Set:6-31G(d,p) 
Final Energy E(RB3LYP): -56.55776873 a.u. 
RMS Gradient Norm: 0.00000485 a.u. 
Point Group: C3V 
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]]

[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95), and 5 and 6 (3589.82) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

 Molecule name: Nitrogen 
Calculation Method: RB3LYP 
Basis Set: 6-31G(d,p) 
Final Energy E(RB3LYP) -109.52412868 a.u. 
RMS Gradient Norm: 0.00000365 a.u. 
Point Group: D*H 
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]]

[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31.

The Nitrogen molecule has no net dipole moment.

 Molecule name: Hydrogen 
Calculation Method: RB3LYP 
Basis Set: 6-31G(d,p) 
Final energy E(RB3LYP): -1.17853936 a.u. 
RMS Gradient Norm: 0.00000017 a.u. 
Point Group: D*H 

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]]
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

E(NH3)= -56.55776873 a.u.
2*E(NH3)= -113.1155375 a.u.
E(N2)=-109.52412868 a.u.
E(H2)= -1.17853936 a.u.
3*E(H2)= -3.53561808 a.u.
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907 a.u.

Molecule name: Chlorine
Calculation Method: RB3LYP
Basis Set: 6-31G(d,p)
Final Energy E(RB3LYP): -920.34987886 a.u.
RMS Gradient Norm: 0.00002948 a.u.
Point Group: D*H

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 
Molecular orbitals in chlorine: 
The two 3px orbitals of each chlorine overlap "head on" two molecular orbitals- a pi bonding orbital and a pi antibonding orbital. Both these orbitals are fully occupied. 

 

 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! M.O. !! Description
|-
| [[File:3s_bonding.png]] || - This M.O. is formed by the overlap of the 3s orbitals of each chlorine atom. 
- This is a bonding sigma orbital. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - pi bonding orbital: The two 3p orbitals overlap in phase. 
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - The two 3p orbitals overlap out of phase. 
- This molecular orbital is the HOMO. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "side-on" overlap of the two 3pz orbitals. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis "Sideways". 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}

Rep:Mod:Mywiki

2016-03-04T14:56:12Z

Mp3915:

Molecule name: Ammonia 
Calculation method: RB3LYP 
Basis Set:6-31G(d,p) 
Final Energy E(RB3LYP): -56.55776873 a.u. 
RMS Gradient Norm: 0.00000485 a.u. 
Point Group: C3V 
<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 H-N-H bond angle is 105.74115 degrees.
The N-H bond length is 1.01798 Angstrom.
<jmol><jmolApplet>
<title>Ammonia molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA NH3 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MALA NH3 OPTF POP.LOG]]

[[File:display_ammonia.png]]

From the 3N-6 rule, 3 vibrational modes are expected. Modes 2 and 3 (1693.95), and 5 and 6 (3589.82) are degenerate.
Modes 1 and 2(or 3) are bending vibrations, while Modes 4 and 5 (or 6) are stretching vibrations.
Mode 4 is highly symmetric (as the dipole doesn't change)
Mode 1 is the "umbrella" mode.
3 bands would be expected to show up in an experimental spectrum of gaseous ammonia.

Since Nitrogen is more electronegative than Hydrogen, you'd expect N to have a negative charge, and H to have a positive charge. This is confirmed by the calculations which give N having a charge of -1.125 and H 0.375.

 Molecule name: Nitrogen 
Calculation Method: RB3LYP 
Basis Set: 6-31G(d,p) 
Final Energy E(RB3LYP) -109.52412868 a.u. 
RMS Gradient Norm: 0.00000365 a.u. 
Point Group: D*H 
<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>

<jmol><jmolApplet>
<title>Nitrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MALA N2 OPTF POP.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:MALA N2 OPTF POP.LOG]]

[[File:display_n2_vibrations.png]]

For linear molecules, the 3N-5 rule is followed. This predicts the number of vibrational modes in nitrogen to be 1- which is in agreement with our calculation.
There is one stretching vibration at 2457.31.

The Nitrogen molecule has no net dipole moment.

 Molecule name: Hydrogen 
Calculation Method: RB3LYP 
Basis Set: 6-31G(d,p) 
Final energy E(RB3LYP): -1.17853936 a.u. 
RMS Gradient Norm: 0.00000017 a.u. 
Point Group: D*H 

<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>
The H-H bond length is 0.74279 Angstrom. It is a linear molecule, and like nitrogen, has no net dipole since it is symmetric.

<jmol><jmolApplet>
<title>Hydrogen molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>H2_mp.LOG</uploadedFileContents>
</jmolApplet></jmol>
[[FILE:H2_mp.LOG]]
[[File:H2_mp_vibrations.png]]

Since Hydrogen is linear, the 3N-5 rule is followed and 1 vibrational mode is predicted. This is the stretching frequency at 4465.68. This is a very high frequency since hydrogen atoms and small and thus the hydrogen bond is strong.
Like nitrogen, hydrogen has no net dipole moment.

E(NH3)= -56.55776873 a.u.
2*E(NH3)= -113.1155375 a.u.
E(N2)=-109.52412868 a.u.
E(H2)= -1.17853936 a.u.
3*E(H2)= -3.53561808 a.u.
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907 a.u.

Molecule name: Chlorine
Calculation Method: RB3LYP
Basis Set: 6-31G(d,p)
Final Energy E(RB3LYP): -920.34987886 a.u.
RMS Gradient Norm: 0.00002948 a.u.
Point Group: D*H

<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000143 0.001800 YES
RMS Displacement 0.000202 0.001200 YES
</pre>

The Cl-Cl bond length is 2.04176 Angstrom, and the molecule is linear.

<jmol><jmolApplet>
<title>Chlorine molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>MP_CL2_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>

[[FILE:MP_CL2_OPTF_POP.LOG]] 
[[File:chlorine_vibrations_mp.png]] 
Chlorine follows the 3N-5 rule and 1 vibrational mode is predicted. This is the stretching vibration at 520.30. This frequency is small since Chlorine atoms are big and the bond length is large.
Like the other diatomic gases, chlorine has no net dipole moment. 
Molecular orbitals in chlorine: 
The two 3px orbitals of each chlorine overlap "head on" two molecular orbitals- a pi bonding orbital and a pi antibonding orbital. Both these orbitals are fully occupied. 

 

 

{| class="wikitable" border="1"
|+ Molecular Orbitals in Chlorine
! heading !! heading
|-
| [[File:3s_bonding.png]] || - This M.O. is formed by the overlap of the 3s orbitals of each chlorine atom. 
- This is a bonding sigma orbital. 
- The M.O. is lower in energy than the M.O.s formed by the overlap of 3p orbitals (all the M.O.s above) 
- It has an energy of -0.93312. 
|-
| [[File:3px_bonding.png]] || - pi bonding orbital: The two 3p orbitals overlap in phase. 
- This has an energy of -0.40694 
|-
| [[File:3px_antibonding.png]] || - The two 3p orbitals overlap out of phase. 
- This molecular orbital is the HOMO. 
- This is higher in energy than the bonding orbital and has an energy of -0.31361.
|-
| [[File:3pz_antibonding.png]]|| - This M.O. is a bonding sigma orbital. 
- It is formed as a result of "side-on" overlap of the two 3pz orbitals. 
- The atomic orbitals overlap in phase. 
- The orbital is higher in energy than the bonding pi M.O.s formed by the 3px and 3py orbitals. 
- This is due to 'mixing' of the sigma bonding orbitals. 
- Thus the energy of this molecular orbital is -0.47392 
- This M.O. is fully occupied, and is the second HOMO after the pi antibonding orbitals (2pi*) 
|-
| [[File:3pz_antibonding_actual.png]] || - This M.O. is the antibonding sigma orbital. 
- The 3pz orbitals overlap along the internuclear axis "Sideways". 
- The atomic orbitals overlap out of phase. 
- This orbital is unoccupied, and is the LUMO. 
- It has an energy of -0.14207. 
|}