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NH₃ Analysis

NH₃ Summary

NH₃ Summary

Calculation Method	Basis Set	Final Energy	RMS Gradient	Point Group
RB3LYP	6-31G(d,p)	-56.55776873 au	0.00000485	C3v

Optimised bond length= 1.01798

Bond angle= 105.7

Item table

           Item               Value     Threshold  Converged?
 Maximum Force            0.000004     0.000450     YES
 RMS     Force            0.000004     0.000300     YES
 Maximum Displacement     0.000072     0.001800     YES
 RMS     Displacement     0.000035     0.001200     YES
 Predicted change in Energy=-5.986279D-10
 Optimization completed.
    -- Stationary point found.

File:NH3 OPTIMISATION pop.LOG

Jmol NH₃

test molecule

This Molecule is the most stable for ammonia

NH₃ Vibrations

NH₃ Vibrations

Number of modes	Degenerate modes	Modes that bend	Modes that stretch	Which is symmetric
6	5 and 6, 2 and 3	1,2 and 3	4,5 and 6	1 and 4

Umbrella mode= 1

expected bands in an experimental spectrum of gaseous ammonia?= 2

Vibrational analysis of NH₃

NH₃ Charge Distribution

Nitrogen (red)= -1.25 Hydrogen (green)= 0.375

N₂

Summary

N₂ Summary

Calculation Method	Basis Set	Final Energy	RMS Gradient	Point Group
RB3LYP	6-31G(d,p)	-109.52412868 au	0.00000060	D*H

Optmised bond length= 1.1055 A

Bond angle= 180

Frequency= 2457.33, IR= 0

Item table

 Item               Value     Threshold  Converged?
 Maximum Force            0.000001     0.000450     YES
 RMS     Force            0.000001     0.000300     YES
 Maximum Displacement     0.000000     0.001800     YES
 RMS     Displacement     0.000000     0.001200     YES
 Predicted change in Energy=-3.401116D-13
 Optimization completed.
    -- Stationary point found.

File:N2 OPTIMISATION.LOG

test molecule

N₂ Vibrations

N₂ Charge Distribution

Diatomic with same atoms of equal negativity, hence no charges

H₂

H₂ Summary

H₂ Summary

Calculation Method	Basis Set	Final Energy	RMS Gradient	Point Group
RB3LYP	6-31G(d,p)	-1.17853936 au	0.00000017	D*H

Optimised bond length 0.74279 A

Bond angle=180

Item table

         Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000450     YES
 RMS     Force            0.000000     0.000300     YES
 Maximum Displacement     0.000000     0.001800     YES
 RMS     Displacement     0.000001     0.001200     YES
 Predicted change in Energy=-1.164080D-13
 Optimization completed.
    -- Stationary point found.

File:H2 OPTIMISATION.LOG

Jmol H₂

test molecule

Vibrations H₂

Frequency= 4464.68 , IR=0

H₂ Charge Distribution

Charge Distribution of H₂

Diatomic with same atoms of equal negativity, hence no charges

Haber-Bosch reaction

N2 + 3H2 -> 2NH3

NH₃ Energies of species

E(NH3)	2*E(NH3)	E(N2)	E(H2)	3*E(H2)
-56.55776873 au	-113.115537 au	-109.52412868 au	-1.17853936 au	-3.53561808 au

Change in energy= 2*E(NH3)-[E(N2)+3*E(H2)]=- 0.005579024 au = -146.47727512 KJ/mol

reactants are less stable

CH4

Summary

N₂ Summary

Calculation Method	Basis Set	Final Energy	RMS Gradient	Point Group
RB3LYP	6-31G(d,p)	-40.52401404 au	0.00003263	TD

Optimised bond length= 1.09197 A Bond angle= 109.47

Item table

       Item               Value     Threshold  Converged?
 Maximum Force            0.000063     0.000450     YES
 RMS     Force            0.000034     0.000300     YES
 Maximum Displacement     0.000179     0.001800     YES
 RMS     Displacement     0.000095     0.001200     YES
 Predicted change in Energy=-2.256043D-08
 Optimization completed.
    -- Stationary point found.

File:CH4 OPTIMISATION.LOG

Jmol CH₄

test molecule

This is the most stable form of methane

Vibrations

CH₄ Vibrations

Number of modes	Degenerate modes	Modes that bend	Modes that stretch	Which is symmetric
0	1,2 and 3;4 and 5; 7,8 and 9)	1,2,3 and 4	5,6,7,8 and 9	6,5 and 4

expected bands in an experimental spectrum?= 2

Charge Distribution

CH₄ Bending

CH₄ MO's

MO 1

This occupied orbital is very deep in energy with -10.17 au. This 1s from the carbon, which does not contribute towards bonding, makes up the MO. Its small size and stability is due to its proximity to the carbon nucleus and large attractive forces. Very little overlap is seen with the Hydrogens.

MO 2

The contribution from each AO is from each atom, to form the MO. Contribution of 2s from Carbon and 1s from each hydrogen atom. There is a large degree of mixing. Quite deep in energy and more than MO 3, however, there is also contribution from the 2p Carbon orbitals. This is a bonding orbital. Its energy is found as -0.69041 au.

MO 3- sp₃

This is the bonding HOMO, given that MO 3,4 and 5 are all degenerate. Three AO P orbitals of Carbon; px, py, pz hybridise with its 2s to bond to to each 1s Hydrogen orbital.Its energy is found to be -0.38831 auand is higher than MO 2 due to the energy of the orbitals involved- being further away from the nucleus.

MO 4-LUMO

This orbital is unoccupied and the lowest-unoccupied molecular orbital- it is anti-bonding 1s orbital from Carbon. Its energy is positive as 0.11824 au, and is lower in energy than the anti-bonding hybridised MO.

MO 5

This anti-bonding orbital related to the anti bonding of the hybridised Carbon sp₃ and the 1s on each Hydrogen. Higher in energy than the LUMO. Its energy is 0.17677 au and has of course, 2 other MO's that are degenerate to it- MO 8 and 9.

Water

Summary

H₂O Summary

Calculation Method	Basis Set	Final Energy	RMS Gradient	Point Group
RB3LYP	6-31G(d,p)	-76.41973740 au	0.00006276	C2V

Optimised bond length= 0.96522

Bond angle= 103.7

Item Table

Item Value Threshold Converged?

Maximum Force            0.000099     0.000450     YES
RMS     Force            0.000081     0.000300     YES
Maximum Displacement     0.000115     0.001800     YES
RMS     Displacement     0.000120     0.001200     YES
Predicted change in Energy=-1.939669D-08
Optimization completed.
   -- Stationary point found.

File:H2O OPTIMISATION.LOG

Jmol H₂O

test molecule

This Jmol shows the most stable form of the molecule

H₂O Vibrations

CH₄ Vibrations

Number of modes	Degenerate modes	Modes that bend	Modes that stretch	Which is symmetric
3	0	0	3	1 and 2