Rep:Mod:ZY3915

NH3 molecule

N-H bond distance: B=1.01798

H-N-H bond angle: A=105.741

Molecule name	Ammonia
Calculation method	B3LYP
Basis set	6-31G(d,p)
Final energy E(RB3LYP)	-56.55776873au
Point group	C₃V

 
         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

test molecule

The optimisation file is linked to here

Vibrations

How many modes do you expect from the 3N-6 rule?

 3*4-6=6; so,6 modes

Which modes are degenerate (ie have the same energy)?

 mode2 and mode3(both have frequency of 1693.95); mode5 and mode6(frequency of 3589.82)

Which modes are "bending" vibrations and which are "bond stretch" vibrations?

 mode1 2 3 are "bending"; mode4 5 6 are "bond stretch"

Which mode is highly symmetric?

 mode1 and mode4

One mode is known as the "umbrella" mode, which one is this?

 mode1

How many bands would you expect to see in an experimental spectrum of gaseous ammonia?

 2, because mode1 2 and 3 have strong infrared signals while signals of the rest are negligible so those(mode4 5 and 6)will not be there in the experimental spectrum.
However the total number of bands will be 2, as mode2 and mode3 are identical in frequency.

Charges

Charge distribution
1(N)	2(H)	3(H)	4(H)
-1.125	0.375	0.375	0.375

The Haber-Bosch process

H2

Molecule name           Hydrogen
Calculation Method	RB3LYP
Basis Set	        6-31G(d,p)
Charge	                0
Spin	                Singlet
E(RB3LYP)	       -1.17853936	 a.u.
RMS Gradient Norm	0.00000222	 a.u.
Imaginary Freq	        0
Dipole Moment	        0.0000	         Debye
Point Group	        D∞H

         Item               Value     Threshold  Converged?
 Maximum Force            0.000004     0.000450     YES
 RMS     Force            0.000004     0.000300     YES
 Maximum Displacement     0.000005     0.001800     YES
 RMS     Displacement     0.000007     0.001200     YES

N2

Molecule name           Nitrogen
Calculation Method	RB3LYP
Basis Set	        6-31G(d,p)
Charge	                0
Spin	                Singlet
E(RB3LYP)	       -109.52412868	 a.u.
RMS Gradient Norm	0.00000001	 a.u.
Imaginary Freq	        0
Dipole Moment	        0.0000	         Debye
Point Group	        D∞H

         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

E(NH3)=-56.5577687au

2*E(NH3)=-113.1155375au

E(N2)=-109.5241287au

E(H2)=-1.1785394au

3*E(H2)=-3.5356181au

ΔE=2*E(NH3)-[E(N2)+3*E(H2)]=-0.0557907au=-146.47849401kJ/mol

so the energy for converting hydrogen and nitrogen gas into ammonia gas is -146.47849401kJ/mol, which means the ammonia product is more stable than the gaseous reactants

CO molecule

test molecule

The optimisation file is linked to here

Molecule name           Carbon monoxide
Calculation Method	RB3LYP
Basis Set	        6-31G(d,p)
Charge	                0
Spin	                Singlet
E(RB3LYP)	       -113.30945314	 a.u.
RMS Gradient Norm	0.00000002	 a.u.
Imaginary Freq	        0
Dipole Moment	        0.0599	         Debye
Point Group	        C∞V

         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

Vibrations

There is only one mode of vibration (bond stretch) for this molecule as the only band in the experimental spectrum and this mode is highly symmetric.

Charges

Charge distribution
1(C)	2(O)
0.506	-0.506

Moleuclar Orbitals

HOMO-6:1σ bonding orbital(contributed by 1s orbital of carbon and 1s orbital of oxygen)
This orbital is occupied by two electrons,and is very deep in energy (-19.25805) that AOs do not have much overlap.

HOMO-2:1π bonding orbital(contributed by 2p orbital of carbon and 2p orbital of oxygen)
The energy of this orbital is deep in energy (-0.46743) but very close to that of HOMO and the orbital is occupied by two electrons.

HOMO-1:2π bonding orbital(contributed by 2p orbital of carbon and 2p orbital of oxygen)
This orbital is occupied by two electrons and it has the same energy as HOMO-2(-0.46743).

HOMO:3σ bonding orbital(contributed by 2p orbital of carbon and 2p orbital of oxygen)
This orbital is the HOMO that contribute the most to the C-O bond and it has two electrons in it.

LUMO+2:3σ* antibonding orbital(contributed by 2p orbital of carbon and 2p orbital of oxygen)
This orbital has no electron in it and the calculated shape is not consistent with the prediction on text books due to optimisation focusing on orbitals with electrons in it.