Summary of Nh3, H2 and N2 molecules

Gaussian summaries
Molecule	NH3	H2	N2	H2S	BH3
Calculation Method	RB3LYP	RB3LYP	RB3LYP	RB3LYP	RB3LYP
Basis Set	6-31G(d,p)	6-31G(d,p)	6-31G(d,p)	6-31G(d,p)	6-31G(d,p)
E(RB3LYP) (a.u.)	-56.55776873	-1.17853936	-109.52412868	-399.39162414	-26.61532364
RMS Gradient (a.u.)	0.00000485	0.00000017	0.00000060	0.00012068	0.00000211
Point Group	C3V	D*H	D*H	C2V	D3H
Bond lenght (pm)	101.798	74.279	110.550	134.737	119.232
Bond angle (°)	105.741	180	180	92.681	120

NH3

Media:KKasuk_nh3_optf_pop.LOG

NH3 Vibrations
Mode	Frequency	Infrared
Bend 1	1089.54	145.3814
Bend 2	1693.95	13.5545
Bend 3	1693.95	13.5545
Stretch 1	3461.29	1.0608
Stretch 2	3589.82	0.2711
Stretch 3	3589.82	0.2711

•Expected nodes in NH3 molecule from 3N-6 rule is 6.

•Stretch 2&3 and Bend 2&3 are degenerate.

•Bend 1 is called the "umbrella" mode and Stretch 1 is highly symmetric.

•In the experimental spectrum of NH3(g) only 2 bands are seen: 1) "Umbrella" Bend; 2) degenerate Bend 2&3. Stretches give too low peaks to be recognised from the noise.

NH3 Charges

It is expected that H in ammonia have a positive and N has a negative charge because N atom has a much larger electronegativity.

NH3 Charges
Molecule	NH3	Electronegativity
H Charge	0.375	2.1
N Charge	-1.125	3.0
Overall Charge	0

H2

H2 dipole moment is zero and because its vibrational mode doesn't induce a dipole, it's not seen on IR spectra.

H2 Vibrations
Mode	Frequency	Infrared
Stretch 1	4465.68	0.0000

N2

N2 dipole moment is zero and because its vibrational mode doesn't induce a dipole, it's not seen on IR spectra.

N2 Vibrations
Mode	Frequency	Infrared
Stretch 1	2457.33	0.0000

H2S

Media:KKASUK_H2S_OPTF_POP.LOG

H2S Vibrations
Mode	Frequency	Infrared
Bend 1	1223.61	4.9220
Stretch 1	2691.87	6.7347
Stretch 2	2711.64	8.6219

•Expected nodes in H2S molecule from 3N-6 rule is 3.

•No modes are degenerate.

•Stretch 1 is highly symmetric.

H2S Charges

It is expected that Hydrogen atoms in Hydrogen Sulfide have a positive and Sulphur has a negative charge because S atom has a larger electronegativity than H atoms. Charge on S atom in H2S is smaller however compared to N in NH3 because of the difference in electronegativities (S=2.5 ;N=3) and number of H atoms.

H2S Charges
Molecule	H2S	Electronegativity
H Charge	0.156	2.1
S Charge	-0.312	2.5
Overall Charge	0

H2S Molecular Orbitals

H2S Molecular Orbitals
Orbital	Constituent Orbitals	Character	Energy
11	3s (S), 3pz (S) & σ* (H2)	Anti-Bonding	0.057804
10 (LUMO)	3py (S) & σ* (H2)	Anti-Bonding	0.021261
9 (HOMO)	3px (S)	Non-Bonding	-0.26181
8	3pz (S) & σ (H2)	Bonding	-0.36725
7	3py (S) & σ* (H2)	Bonding	-0.44963
6	3s (S) & σ (H2)	Bonding	-0.74654
5	2p (S)	Non-Bonding	-5.9055
4	2p (S)	Non-Bonding	-5.9127
3	2p (S)	Non-Bonding	-5.9159
2	2s (S)	Non-Bonding	-7.9512
1	1s (S)	Non-Bonding	-88.8874

The first 5 orbitals on S are too small and low in energy to interact with 1s orbitals on Hydrogen atoms. Bonding orbitals are 6-8 which bond with either H2 bonding (σ) or antibonding (σ*) molecular orbital. The highest occupied molecular orbital (HOMO) is 9th MO which is also non-bonding due to no orbital overlap between Sulphur's AO and H2 MO. The lowest unoccupied molecular orbital (LUMO) is 10th MO, which is also the first antibonding MO. Due to fully occupied bonding MOs and not occupied antibonding MOs, H2S is energetically very stable.

BH3

BH3 Vibrations
Mode	Frequency	Infrared
Bend 1	1162.97	92.5682
Bend 2	1213.14	14.0550
Bend 3	1213.14	14.0544
Stretch 1	2582.58	0.0000
Stretch 2	2715.72	126.3320
Stretch 3	2715.72	126.3260

•Expected nodes in BH3 molecule from 3N-6 rule is 6.

•Stretch 2&3 and Bend 2&3 are degenerate.

•Bend 1 is called the "umbrella" mode.

•Stretch 1 is symmetric, therefore induces no dipole and is not seen on IR spectrum.

•In the experimental spectrum of NH3(g) only 3 bands are seen: 1) "Umbrella" Bend; 2) degenerate Bend 2&3; 3) degenerate Stretch 2&3. Degenerate modes both give one peak and Stretch 1 induces no dipole.

BH3 Charges

It is expected that B atom in BH3 has a positive and H atoms have a negative charge.

BH3 Charges
Molecule	BH3	Electronegativity
H Charge	-0.099	2.1
B Charge	0.297	2.0
Overall Charge	0

Haber-Bosch Reaction energy

Calculating the energy difference between the reactants and product of Haber-Bosch reaction
Energy	Value
E(NH3)	-56.55776873 a.u.
2*E(NH3)	-113.11553746 a.u.
E(N2)	-109.52412868 a.u.
E(H2)	-1.17853936 a.u.
3*E(H2)	-3.53561808 a.u.
ΔE=2E(NH3)-[E(N2)+3E(H2)]	-0.0557907 a.u. = -146.48 kJ/mol

Reaction between H2 and N2 is exothermic, 146.48 kJ/mol of energy is released in the making of NH3.

Item tables

 NH3
         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

 H2
         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

 N2
         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

 H2S
         Item               Value     Threshold  Converged?
 Maximum Force            0.000175     0.000450     YES
 RMS     Force            0.000145     0.000300     YES
 Maximum Displacement     0.000472     0.001800     YES
 RMS     Displacement     0.000386     0.001200     YES

 BH3
         Item               Value     Threshold  Converged?
 Maximum Force            0.000004     0.000450     YES
 RMS     Force            0.000003     0.000300     YES
 Maximum Displacement     0.000017     0.001800     YES
 RMS     Displacement     0.000011     0.001200     YES