Rep:Mod:sf3014
NH3 Molecule
NH molecule |
Calculations Information
Calculation Type = FREQ Calculation Method = RB3LYP Basis Set = 6-31G(d,p) Charge = 0 Spin = Singlet E(RB3LYP) = -56.44397188 a.u. RMS Gradient Norm = 0.05399560 a.u. Imaginary Freq = Dipole Moment = 1.5008 Debye Point Group = C3V
Optimisation Output
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
Predicted change in Energy=-5.986273D-10
Optimized N-H bond length = 1.018 Å
Vibrational Modes
| Modes | Frequency (cm-1) | Intensity (au) |
|---|---|---|
| 1 | 1090 | 145 |
| 2 | 1694 | 14 |
| 3 | 1694 | 14 |
| 4 | 3461 | 1 |
| 5 | 3590 | 0 |
| 6 | 3590 | 0 |
The expected number of vibrational modes = 3N-6, where N is the number of atoms. Therefore, there are 6 vibrational modes but modes 2 and 3, and 5 and 6 are degenerate. The stretching modes are 4, 5 and 6, and the bending modes are 2 and 3. Mode 4, is a sysmetric stretch vibrational mode. The mode 1, is known as an umbrella mode. The number of bands expected to see in an experimental spectrum of gaseous NH3 is 4.
Charge Analysis
| Atom | Charge Density |
|---|---|
| N | -1.125 |
| H | 0.375 |
The charge density of N and H atoms in the NH3 molecule has been reported by Hunt et. al. [1] as -1.5053 and +0.351, respectively. These values were based on neutral bond orbital (NBO) analysis. The charge density of N in the NH3 molecule is negative due to the contribution of the lone pair of electrons.
N2 Molecule
N molecule |
Calculations Information
Calculation Type = FREQ Calculation Method = RB3LYP Basis Set = 6-31G(d,p) Charge = 0 Spin = Singlet E(RB3LYP) = -109.52412417 a.u. RMS Gradient Norm = 0.00219852 a.u. Imaginary Freq = Dipole Moment = Debye Point Group = D*H
Optimisation Output
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 Predicted change in Energy=-3.400975D-13
File:SF3014 N2 OPTIMISATION.LOG
Vibrational Modes
One vibrational mode with frequency of 2457 cm-1.
N2 Bond Length
The N-N bond length in the Chloro-nitrogen-2-phenylethenyl-bis(tri-isopropylphosphine)-ruthenium(ii) ([| ATALEM]) complex is 1.088 Å [2], where the optimized parameters from the B3LYP calculations gave an N-N bond length of 1.1055 Å. The N-N bond length was stated by Weber et. al. [3] as 1.09 Å. The difference in N-N bond length (± 0.01 Å) between the calculated and experimental values, for both free and coordinated N2 molecules, are too small to be significant.
H2 Molecule
N molecule |
Calculations Information
Calculation Type = FREQ Calculation Method = RB3LYP Basis Set = 6-31G(d,p) Charge = 0 Spin = Singlet E(RB3LYP) = -1.15928020 a.u. RMS Gradient Norm = 0.09719500 a.u. Imaginary Freq = Dipole Moment = 0.0000 Debye Point Group = D*H
Optimisation Output
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 Predicted change in Energy=-1.164080D-13
Optimized H-H bond length = 0.7428 Å
File:SF3014 H2 OPTIMISATION.LOG
Vibrational Modes
One vibrational mode with frequency of 4466 cm-1.
Determining the Energy of NH3 Formation
| NH3 | N2 | H2 |
|---|---|---|
| -56.5577687299 | -109.52412417 | -1.17853935735 |
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]=
ΔE=2*(-56.5577687299)-[E(-109.52412417)+3*E(-1.17853935735)]= -0.055795218 a.u.
ΔE=-146.5 Kj/mol
The energy of NH3 formation is exothermic, so the direction of the reaction favours the NH3 gas.