Rep:Mod:CompChemEkart

Ammonia

Table 1: About ammonia optimization

Paramater	Data
Molecular formula	NH3
Calculation method	RB3LYP
Basis set	6-31G(d,p)
Final energy	-56.55776873 a.u.
RMS gradient	0.00000485 a.u.
Point group	C3v
N-H bond length	1.01798 Å
H-N-H bond angle	105.741°

Table 2: Optimization data - ammonia

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

Ammonia

The optimisation file is located here.

The template required to crop the image was acquired from Wikipedia.

File:Vibrations Ekart.png

Vibrations of ammonia

6 vibrational modes are to be expected from 3N-6 rule. There are two pairs of vibrational modes that are degenerate, namely 2 and 3, and 5 and 6. 1-3 are bending modes, while 4-6 are stretching modes. Vibrational mode number 4 is highly symmetric. Number 1 is also known as umbrella mode. In the spectrum there would probably be 4 bands, but the ones corresponding to bond stretches would be much less distinct.

Charge distribution is -1.125 for N atom and 0.375 for H atoms. Nitrogen is more electronegative than hydrogen, which means that such charges are to be expected.

Hydrogen

Table 3: About hydrogen optimization

Paramater	Data
Molecular formula	H2
Calculation method	RB3LYP
Basis set	6-31G(d,p)
Final energy	-1.15928020 a.u.
RMS gradient	0.09719500 a.u.
Point group	D∞h
H-H bond length	0.74279 Å

Hydrogen

Table 4: Optimization data - hydrogen

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

Nitrogen

Table 5: About nitrogen optimization

Paramater	Data
Molecular formula	N2
Calculation method	RB3LYP
Basis set	6-31G(d,p)
Final energy	-109.52412868 a.u.
RMS gradient	0.00000060 a.u.
Point group	D∞h
N-N bond length	1.10550 Å

Nitrogen

Table 6: Optimization data - nitrogen

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

Energetic balance of formation of ammonia

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=2*E(NH₃)-[E(N₂)+3*E(H₂)]=-0.05579070 a.u.

This means that the reaction enthalpy is ΔH=-146.48 kJ/mol. This is implying that ammonia gas is more stable than hydrogen and nitrogen gas on their own.

Water

Table 7: About water optimization

Paramater	Data
Molecular formula	H2O
Calculation method	RB3LYP
Basis set	6-31G(d,p)
Final energy	-76.41973740 a.u.
RMS gradient	0.00006276 a.u.
Point group	C2v
O-H bond length	0.96522 Å
H-O-H bond angle	103.745°

Water

Table 8: Optimization data - water

Item	Value	Threshold	Converged?
Maximum Force	0.000099	0.000450	YES
RMS Force	0.000081	0.000300	YES
Maximum Displacement	0.000114	0.001800	YES
RMS Displacement	0.000119	0.001200	YES

Table 9: Vibrations of water molecule

Reciprocal wavelength (cm-1)	Relative intensity
1665.00	70.3477
3801.05	1.6431
3914.23	20.2475

Relative charges on hydrogen atoms are 0.472, while on oxygen atom it is -0.944.

Molecular orbitals in water molecule

All the molecular orbitals are shown from the same perspective and at the same size. They are shown in increasing order of energy

Table 10: Molecular orbitals

Image	Name	Description
	1a1	Non-bonding orbital of oxygen made from its 1s orbital, extremely low in energy and fully occupied. This orbital virtually does not contribute to bonding.
	2a1	Bonding orbital made from 2s orbital of oxygen and bonding combination of 1s orbitals of hydrogens. It is still low in energy, but much less so than the previous one. It is fully occupied. It is very important for bonding of the molecule.
	1b2	Mixed orbital made from 2p orbitals of oxygen and antibonding combination of 1s orbitals of hydrogens. It is low in energy and fully occupied. It is important for the bonding of the molecule.
	3a1	Mixed orbital made from 2s and 2p orbitals of oxygen and bonding combination of 1s orbitals of hydrogens. It is close to HOMO in energy (but lower) and fully occupied. It is important for the bonding of the molecule.
	1b1	Non-bonding orbital of oxygen made from its 2p orbital. This orbital is HOMO and is fully occupied. It does not contribute to bonding much.
	4a1	Mixed orbital made as antibonding combination of 2s and 2p orbitals of oxygen and bonding combination of 1s orbitals of hydrogen. It is LUMO and is not occupied.
	2b2	Antibonding orbital made from 2p orbitals of oxygen and antibonding combination of 1s orbitals of hydrogen. It is just above LUMO in energy and is not occupied.
	3b2	This is the first molecular orbital not made from the aforementioned orbitals.

Hydrogen peroxyde

Table 11: About hydrogen peroxide optimization

Paramater	Data
Molecular formula	H2O2
Calculation method	RB3LYP
Basis set	6-31G(d,p)
Final energy	-151.54211147 a.u.
RMS gradient	0.00002366 a.u.
Point group	C2h
O-O bond length	1.46642 Å
O-H bond length	0.96948 Å
H-O-O bond angle	98.248°

Hydrogen peroxide

The data shown is close to the real data, but not quite alright, because the wrong structure has been achieved.

Table 12: Optimization data - hydrogen peroxide

Item	Value	Threshold	Converged?
Maximum Force	0.000045	0.000450	YES
RMS Force	0.000023	0.000300	YES
Maximum Displacement	0.000064	0.001800	YES
RMS Displacement	0.000041	0.001200	YES

Relative charges on hydrogen atoms are 0.483, while on oxygen atoms they are -0.483.