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NH3 molecule

General Information

calculation method: RB3LYP

basis set: 6-31G(d.p)

final energy E(RB3LYP) in atomic units (au): -56.55776873

RMS gradient: 0.00000485

point group of your molecule: C3V

N-H bond distance=1.01798

N-H-N bond angle= 109.471


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


Jmol 3D Model

test molecule


The optimisation file is liked to here


Display Vibrations

Questions about Display Vibrations

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

which modes are degenerate (ie have the same energy)? 5 6

which modes are "bending" vibrations and which are "bond stretch" vibrations? 1 2 3, 4 5 6

which mode is highly symmetric? 4

one mode is known as the "umbrella" mode, which one is this? 1

how many bands would you expect to see in an experimental spectrum of gaseous ammonia? 4


charge

charge on the N-atom: -1.125 charge on the H-atoms: 0.375 Since N atom is more electronegative than H atom, the charge on N atom is negative while that on H is positive.


H2 molecule

General Information

H-H bond distance = 0.74309

H-H bond angle = 180°

Calculation Method: RB3LYP

Basis Set: 6-31G(d,p)

final energy E(RB3LYP) in atomic units (au): -1.17853930

RMS gradient: 0.00012170

Point Group: D*H


Item Table


         Item               Value     Threshold  Converged?
 Maximum Force            0.000211     0.000450     YES
 RMS     Force            0.000211     0.000300     YES
 Maximum Displacement     0.000278     0.001800     YES
 RMS     Displacement     0.000393     0.001200     YES


Jmol 3D Model

test molecule

The optimisation file is liked to here


Display Vibrations

N2 molecule

General Information

H-H bond distance = 1.10550

H-H bond angle = 180°

Calculation Method: RB3LYP

Basis Set: 6-31G(d,p)

final energy E(RB3LYP) in atomic units (au): -109.52412868

RMS gradient: 0.00000365

Point Group: D*H


Item Table


         Item               Value     Threshold  Converged?
 Maximum Force            0.000006     0.000450     YES
 RMS     Force            0.000006     0.000300     YES
 Maximum Displacement     0.000002     0.001800     YES
 RMS     Displacement     0.000003     0.001200     YES


Jmol 3D Model

test molecule

The optimisation file is liked to here


Display Vibrations

Reaction Energies

E(NH3)= -56.55776873 a.u

2*E(NH3)= -113.11553746 a.u

E(N2)= -109.52412298 a.u

E(H2)= -1.17853930 a.u

3*E(H2)= -3.5356179 a.u

ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -113.11553746-(-109.52412298-3.5356179)=-0.05579658 a.u= -146.50 kJ/mol

Since the energy difference is negative, the ammonia product is more stable.


F2 molecule

General Information

F-F bond distance = 1.16000 Å

F-F bond angle = 180°

Calculation Method: RB3LYP

Basis Set: 6-31G(d,p)

Total Energy: -199.42620785 a.u.

RMS Gradient Norm: 0.23253407 a.u.

Point Group: D*H


Item Table


         Item               Value     Threshold  Converged?
 Maximum Force            0.000128     0.000450     YES 
 RMS     Force            0.000128     0.000300     YES 
 Maximum Displacement     0.000156     0.001800     YES
 RMS     Displacement     0.000221     0.001200     YES 


Jmol 3D Model

test molecule

The optimisation file is liked to here


Display Vibrations

charge

There is the same charge on 2 F atoms and F2 molecule does not carry on a overall charge.


Molecular Orbital

MO1

MO2

MO3

MO4

MO5

Summary

MO1 and MO2 are bonding and anti-bonding orbitals respectively formed by 2s AOs of each F atom. Both of them are sigma bonds.

2p AOs of F atom contribute to the formation of MO3, MO4 and MO5. MO3 and MO4 are occupied and bonding while MO5 is anti-bonding orbital. MO3 and MO5 are sigma MOs formed by 2 pz AOs and, MO4 is pi MOs which is formed by 2 Px AOs.

MO3 and MO4 are bonding orbitals, they have relatively lower energy in HOMO region, at -0.58753 a.u. and -0.52332 a.u.

Also, MO5 is the LUMO with energy (-0.12679 a.u.)