Rep:Mod:04050310

NH3 Molecule

Optimisation

NH₃ Optimisation

Calculation type	Result
File Name	ANMOL_PHUNT_NH3_OPTF_POP
File Type	.log
Calculation Type	OPT FREQ
Basis Set	6-31G(d,p)
Charge	0
Spin	Singlet
E(RB3LYP)	-56.55776873
RMS Gradient Norm	0.00000485
Imaginary Freq	0
Dipole Moment	1.8466
Point Group	C3V
Job cpu time:	0 days 0 hours 0 minutes 9.0 seconds
N-H bond distance:	1.01798
H-N-H bond angle:	105.741

"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=-5.986276D-10

Optimisation link

NH3 molecule

The optimisation file is linked here

Vibration Modes

No negative frequencies shows that the energy of the molecule is at its local minimum. The absence of a net dipole moment results in no IR active vibrational modes.

Atomic Charge

Atom	Charge
Hydrogen	+0.375
Nitrogen	-1.125

The above image shows that nitrogen is more electronegative than hydrogen causing it to have a negative charge and the hydrogens to have a positive charge.

Number of Modes (based on 3N-6 rule)	6
Degenerate Modes	2 and 3, 5 and 6
"Bending" Vibrations	1089.54 Hz (1), 1693.95 Hz (2 and 3)
"Bond Stretch" Vibrations	3461.29 Hz (4), 3589.82 Hz (5 and 6)
Highly Symmetric Mode	4
"Umbrella" Mode	1
Bands Expected in an Experimental Spectrum	4

N2 Molecule

Optimisation

N₂ Optimisation

Calculation type	Result
Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
Point Group	D∞h
Final Energy E(RB3LYP)/a.u.	-109.52412868
RMS Gradient/a.u.	0.00000060
Spin	Singlet
Bond Length/Å	1.10550

"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     0.000000     0.001200     YES
 Predicted change in Energy=-1.076088D-15

Optimisation link

N2 molecule

The optimisation file is linked here

Vibration Modes

No negative frequencies shows that the energy of the molecule is at its local minimum. The absence of a net dipole moment results in no IR active vibrational modes.

Atomic Charge

Atom	Charge
Nitrogen	0.000

The above image shows that the charge is equally shared between the atoms as there is no electronegativity difference between two identical N atoms.

H2 Molecule

Optimisation

H₂ Optimisation

Calculation type	Result
Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
Point Group	D∞h
Final Energy E(RB3LYP)/a.u.	-1.17853936
RMS Gradient/a.u.	0.00000222
Spin	Singlet
Bond Length/Å	0.74280

"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

Optimisation link

H2 molecule

The optimisation file is linked here

Vibration Modes

No negative frequencies shows that the energy of the molecule is at its local minimum. The absence of a net dipole moment results in no IR active vibrational modes.

Atomic Charge

Atom	Charge
Hydrogen	0.000

The above image shows that the charge is equally shared between the atoms as there is no electronegativity difference between two identical H atoms.

Energetics of Haber-Bosch process

N₂ + 3H₂ → 2NH₃

Energy	Value in a.u.
E(NH3)	-56.55776873
2*E(NH3)	-113.11553746
E(N2)	-109.52412868
E(H2)	-1.17853936
3*E(H2)	-3.53561808
ΔE=2*E(NH3) - [E(N2) + 3*E(H2)]	-0.05579070

The energy change is ΔE= -0.05579070×2625.5= -146.48 kJmol^-1. Since the enthalpy change is negative, the reaction is exothermic. Since the energy decreases, it can be confirmed that ammonia is more stable than nitrogen and hydrogen.

Cl2 Molecule

Cl₂ Optimisation

Calculation type	Result
Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
Point Group	D∞h
Final Energy E(RB3LYP)/a.u.	-920.34987886
RMS Gradient/a.u.	0.00002510
Spin	Singlet
Bond Length/Å	2.04174

"Item" Table

  Item               Value     Threshold  Converged?
 Maximum Force            0.000043     0.000450     YES
 RMS     Force            0.000043     0.000300     YES
 Maximum Displacement     0.000121     0.001800     YES
 RMS     Displacement     0.000172     0.001200     YES
 Predicted change in Energy=-5.277246D-09

Optimisation link

Cl2 molecule

The optimisation file is linked here

Vibration Modes

No negative frequencies shows that the energy of the molecule is at its local minimum. The absence of a net dipole moment results in no IR active vibrational modes.

This is an IR spectrum of chlorine.

Atomic Charge

Atom	Charge
Chlorine	0.000

The above image shows that the charge is equally shared between the atoms as there is no electronegativity difference between two identical Cl atoms.

Molecular Orbitals

In GaussView, a degeneracy threshold of 0.001 was used to create an MO diagram of degeneracy.

Table of some occupied MOs.

MO	Image	Energy/a.u.	Energy	Orbitals
2		-101.60298	Very deep in energy due to high nucleus penetration	Fully occupied non-bonding 1s orbital
3		-9.51828	Much less deep in energy than 1s, although still considerable penetration towards the nucleus	Occupied non-bonding 2s orbital
7		-7.27045	Similar in energy as the 2s	Occupied non bonding 2p orbital
13		-0.47392	Much less deep in energy than 2p	Occupied σ bonding 3px-3px head-on overlap of chlorine orbitals.
17		-0.31361	Similar in energy to σ bonding 3px-3px. The reason for this is due mixing (hybridisation) that causes inversion of the σ and π molecular orbital energies. This means that the destabilised 3p σ bond gets closer in energy to the 3p π* bond.	Occupied 3p π* anti-bonding orbital