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NH3 molecule

  • N-H Bond distance:1.01798 Angstrom
  • H-N-H Bond angle: 105.7412 Degree
  • Calculation method: RB3LYP
  • Basis set: 6-31G(d,p)
  • Final energy E(RB3LYP): -56.55776873 a.u.
  • RMS gradient: 0.00000485 a.u.
  • Dipole moment: 1.8466 Debye
  • Point group of your molecule: 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

Rotatable 3d images of optimized NH3

Link

File:ANGUS PHUNT NH3 OPTF POP.LOG

Vibrational analysis of NH3

Vibrational anlysis of an optimised NH3 molecule.

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

6 modes

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

Vibrational modes 2 and 3, 5 and 6 are degenerate as their stretching frequencies are the same.

(3)Which modes are "bending" vibrations and which are "bond stretch" vibrations?

Bending: Vibrational modes 1,2,3

Stretching: Vibrational modes 4,5,6

(4)Which mode is highly symmetric?

Vibrational mode 4

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

Vibrational mode 1

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

2 bands are expected to see in the experimental spectrum of NH3. Although there are 6 vibrational frequency calculated according to GaussView,vibrational modes 2 and 3, 5 and 6 are degenerate. So 4 bands should be observed. However, vibrational modes 4,5 and 6 are of very low intensity comparing to the peak intensity according to the table. They can not be observed.

Charges on NH3

  • Charge on nitrogen: -1.125 a.u.
  • Charge on each hydrogen: 0.375 a.u.

The electronegativities of N and H are 3.04 and 2.1 respectively. As nitrogen atom is more electronegative than hydrogen atom, nitrogen atom tends to attract electrons to itself in a covalent bond. Therefore, negative charge is expected on nitrogen atom and positive charge is expected on the three hydrogen atoms.

H2 molecule

  • H-H Bond distance:0.74279 Angstrom
  • Calculation method: RB3LYP
  • Basis set: 6-31G(d,p)
  • Final energy E(RB3LYP): -1.17853936 a.u.
  • RMS gradient: 0.00000017 a.u.
  • Point group of your molecule: 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     0.000001     0.001200     YES

Rotatable 3d images of optimized H2

Link

File:ANGUS PHUNT H2 OPTF POP.LOG

Vibrational analysis of H2

Vibrational analysis of an optimized H2 molecule.









N2 molecule

  • N-N Bond distance:1.110550 Angstrom
  • Calculation method: RB3LYP
  • Basis set: 6-31G(d,p)
  • Final energy E(RB3LYP): - 109.52412868 a.u.
  • RMS gradient: 0.00000060 a.u.
  • Point group of your molecule: D*H
 
 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

Rotatable 3d images of optimized N2

Link

File:ANGUS PHUNT N2 OPTF POP.LOG

Vibrational analysis of N2

Vibrational analysis of an optimized N2 molecule.










Literature values of vibrational frequency of N2

  • There is a difference between the value obtained in Gaussview and the literature value. The frequency obtained in Gaussview is at 0 Kelvin but not for the literature values. The lower the temperature is, the lower the stretching frequency is.
  • Value obtained using GaussView: 2457 cm-1
  • Literature value: 2863 cm-1[1]
  1. ↑ Barnes, A. Journal of Molecular Structure 1980, 60, 343–346.

Haber-Bosch process analysis

  • E(NH3)= -56.557769 a.u.
  • 2*E(NH3)= -113.115538 a.u.
  • E(N2)= -109.524129 a.u.
  • E(H2)= -1.178539 a.u.
  • 3*E(H2)= -3.535618 a.u.
  • ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -146.48 kJ/mol
  • As ΔE is negative(exothermic), which means that the ammonia product is in lower energy than the gaseous reactants. Therefore, the ammonia product is more stable.

HCl molecule

  • H-Cl Bond distance:1.28599 Angstrom
  • Calculation method: RB3LYP
  • Basis set: 6-31G(d,p)
  • Final energy E(RB3LYP): -460.80077875 a.u.
  • RMS gradient: 0.00005211 a.u.
  • Dipole moment:1.4334 Debye
  • Point group of your molecule: C*V
 Item                      Value      Threshold  Converged?
 Maximum Force            0.000090     0.000450     YES
 RMS     Force            0.000090     0.000300     YES
 Maximum Displacement     0.000139     0.001800     YES
 RMS     Displacement     0.000197     0.001200     YES

Rotatable 3d images of optimized HCl

Link

File:ANGUS PHUNT HCL OPTF POP.LOG

Vibrational analysis of HCl

Vibrational analysis of an optimized HCl molecule.










Literature values of vibrational frequency of HCl

  • There is a difference between the value obtained in Gaussview and the literature value. The frequency obtained in Gaussview is at 0 Kelvin but not for the literature values. The lower the temperature is, the lower the stretching frequency is.
  • Value obtained using GaussView: 2957 cm-1
  • Literature value: 2818 cm-1[1]
  1. ↑ Barnes, A. Journal of Molecular Structure 1980, 60, 343–346.

Charges on HCl

  • Charge on chlorine: -0.284 a.u.
  • Charge on hydrogen: 0.284 a.u.

The electronegativities of Cl and H are 3.16 and 2.1 respectively. As chlorine atom is more electronegative than hydrogen atom, chlorine atom tends to attract electrons to itself in a covalent bond. Therefore, negative charge is expected to be on the chlorine atom and positive charge is expected on the hydrogen atom. As HCl is a diatomic molecule, the two charges are equal but opposite.

Moleuclar Orbital Analysis of HCl

MOs analysis of HCl molecule
MO diagrams Description
First MO of the HCl molecule.
  • 1s AO of chlorine atom contributes to this MO
  • This MO is non-bonding
  • This MO is occupied
  • This MO is very deep in energy of -101.56 a.u.
  • This is a σ MO
Second MO of the HCl molecule.
  • 2s AO of chlorine atom contributes to this MO
  • This MO is non-bonding
  • This MO is occupied
  • This MO is deep in energy of -9.47 a.u.
  • This is a σ MO
Thrid MO of the HCl molecule.
  • 2pz AO of chlorine atom contributes to this MO
  • This MO is non-bonding
  • This MO is occupied
  • This MO is deep in energy of -7.24 a.u.
  • This is a σ MO
Forth MO of the HCl molecule.
Fifth MO of the HCl molecule.
  • 2px and 2pyAOs of chlorine atom contribute to these two degenerate MOs
  • These MOs are non-bonding
  • These MOs are occupied
  • These MOs have energies of -7.23 a.u.
  • These are π MOs
Sixth MO of the HCl molecule.
  • 3s AO of chlorine atom contributes to this MO
  • This MO is non-bonding
  • This MO is occupied
  • This MO has an energy of -0.85 a.u.
  • This is a σ MO
Seventh MO of the HCl molecule.
  • 1s AO of hydrogen atom and 3pz AO of chlorine atom contributes to this MO
  • This MO is bonding
  • This MO is occupied
  • This MO has an energy of -0.47 a.u., which is high enough to interact with 1s AO of hydrogen atom
  • This is a σ MO
Eighth MO of the HCl molecule.
HOMO(Ninth MO) MO of the HCl molecule.
  • 3px and 3pyAOs of chlorine atom contribute to these two degenerate MOs
  • These MOs are non-bonding
  • These MOs are occupied
  • These MOs have energies of -0.33 a.u.
  • The ninth MO is the HOMO of HCl molecule
  • These are π MOs
LUMO(Tenth MO) of the HCl molecule.
  • Interaction between 1s AO of hydrogen atom and 3pz AO of chlorine atom contributes to this MO
  • The two AOs are out of phase
  • This MO is anti-bonding
  • This MO is unoccupied
  • This MO is high in energy of 0.014 a.u.
  • This is a σ* MO
  • It is the LUMO of HCl molecule


First ten MO energies of the HCl molecule.
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