Rep:Mod:gaussian demo fdp
This wiki page has been prepared by Frederik Philippi to demonstrate demonstration ability. All calculations have been performed with the gaussian software package.[1]
Unless mentioned otherwise, Energies are given in Hartree and distances in Ångström.
Ammonia
The results obtained from the RB3LYP/6-31G(d,p) calculation on Ammonia are presented in this section.
Geometry
The N-H Bond distance was found to be 1.01798 Å. The H-N-H angle was found to be 105.74115°.
Atomic Charges
The following charges have been obtained with the Gaussian implementation of NBO 3.1:
NBO charge on Nitrogen: -1.125 NBO charge on Hydrogen: +0.375
This is in line with the expectation, as the nitrogen atom has a much higher electronegativity than hydrogen.[2] The charge also qualitatively mirrors the formal oxidation states of Nitrogen (-III) and Hydrogen (+I).
Frequency analysis
There are 3*N degrees of freedom in a three-dimensional environment, with N being the number of atoms. Of these degrees of freedom, three describe translations and three describe rotations of the entire molecule. Hence for NH3, there are 3*4-6=6 internal degrees of freedom which describe the vibrational modes. In the following, these modes will be discussed in order of increasing frequency.
The mode with the lowest frequency is the symmetric deformation/bending or 'umbrella' mode, which can be understood as causing the inversion and has A1 symmetry.
The two modes with harmonic frequencies of 1694 cm-1 (Note that gaussian provides wavenumbers rather than actual frequencies) are degenerate deformation modes of E symmetry.
The fourth mode is the symmetric stretching mode of A1 symmetry.
Finally, the last two modes are again degenerate modes of E symmetry, but for bond stretching rather than deformation.
As A1 and E transform like the cartesian axes under the symmetry operations of C3, all modes should be visible in an experimental IR, leading to four bands. However, two of them are of rather small intensity. The experimental spectrum will be further complicated as combinations are usually also observed.
Supporting Information
Output window of frequency calculation: ['Display Vibrations Window for NH3']
Logfile: [NH3 logfile]
Structure:
Ammoniak |
'Item' section of gaussian logfile:
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
Hydrogen
The results obtained from the RB3LYP/6-31G(d,p) calculation on Hydrogen are presented in this section.
A bond length of 0.74295 Å has been found.
Output window of frequency calculation: ['Display Vibrations Window for Hydrogen']
Logfile: [Hydrogen logfile]
'Item' section of gaussian logfile:
Item Value Threshold Converged? Maximum Force 0.000116 0.000450 YES RMS Force 0.000116 0.000300 YES Maximum Displacement 0.000140 0.001800 YES RMS Displacement 0.000215 0.001200 YES
Nitrogen
The results obtained from the RB3LYP/6-31G(d,p) calculation on Hydrogen are presented in this section.
The N-N bond length was found to be 1.10550, which is slightly shorter than obtained from the crystal structure of the compound cis-tetrakis(dimethylphenylphosphine)-bis(dinitrogen)-tungsten available from the Cambridge Structural Database under the deposition number [1137016].[3] The bond lengths reported in Dadkhah et al. are 1.11856 and 1.12644, respectively. The main reason for this cannot be identified because of the manifold contributions:
- The calculations were performed in vacuum in a universe containing only one Nitrogen molecule, in the absence of any external pertubations.
- The level of theory is relatively low and assumes the Born-Oppenheimer Approximations to be valid.
- Contributions by correlation, relativity, soc etc. are entirely neglected in the calculations
- The experimental bond lengths are influenced by packing effects and intermolecular interactions. This effect can be most intuitively understand just by inspecting the LUMO of Nitrogen, which is shown below.
For the Nitrogen molecule to be bonded to the Transition Metal centre, wave function overlap has to take place. Within the (frontier molecular) orbital approximation, this means that population is transferred from occupied d orbitals of the transition metal centre to unoccupied orbitals of the Nitrogen molecure and vice versa. Hence, the LUMO of Nitrogen shown above will be populated by d-π-interactions. As this is an antibonding MO, the bond order of Nitrogen will decrease. The same line of argument holds valid for the HOMO to HOMO-2 (Not shown here) of the Nitrogen molecule. These are the bonding π MOs of the Nitrogen molecule, which will be depopulated upon interaction with the transition metal centre, again decreasing the bond order and, by that, the bond length in the coordinating Nitrogen molecule.
Output window of frequency calculation: ['Display Vibrations Window for Nitrogen']
Note that the IR intensity of the one bond stretching mode in both N2 and H2 is zero. This fortunately is the case for all the homonuclear diatomic molecules (i.e. Oxygen and Nitrogen) in the air surrounding us, leaving only spurious gases like Methane or CO2 to contribute to the greenhouse effect.
Logfile:
[Nitrogen logfile]
'Item' section of gaussian logfile:
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
Haber Bosch
The summary of the Energies required to estimate the energetics of the Haber-Bosch process are presented below.
| Energy in a.u. | Energy in kJ/mol | |
|---|---|---|
| E(NH3) | -56.5577687299 | -148492.4 |
| 2*E(NH3) | -113.1155374598 | -296984.8 |
| E(N2) | -109.5241286760 | -287555.5 |
| E(H2) | -1.1785393398 | -3094.3 |
| 3*E(H2) | -3.5356180193 | -9282.8 |
| ΔE | -0.0557907645 | -146.5 |
As the reaction energy is negative, the reaction is predicted to be exothermic. Note that the above energies are internal electronic energies without zero point correction, entropic terms etc. Especially for small molecules in the gas phase, much more accurate energies can be obtained without much effort by switching to highly correlated calculations with large basis sets and including entropic terms in or beyond the RRHO approximation.
Little Molecules
For a number of very different calculations on little molecules as well as lots of colourful pictures please refer to this Report: [Physical Chemistry 08 Report]
Summary
all units given in a.u.
| System | Method | Basis set | internal Energy | RMS gradient | Point group |
|---|---|---|---|---|---|
| NH3 | RB3LYP | 6-31G(d,p) | -56.5577687299 | 4.854e-06 | C3v / 3m |
| H2 | RB3LYP | 6-31G(d,p) | -1.17853933975 | 6.678e-05 | D∞h |
| N2 | RB3LYP | 6-31G(d,p) | -109.524128676 | 4.984e-07 | D∞h |
References
- ↑ Gaussian 09, Revision C.01, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, T. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, and D. J. Fox, Gaussian, Inc., Wallingford CT, 2010.
- ↑ W. M. Haynes, D. R. Lide and T. J. Bruno, Eds., CRC Handbook of Chemistry and Physics, CRC Press, 95th edn., 2014.
- ↑ H.Dadkhah, J.R.Dilworth, K.Fairman, Chi Tat Kan, R.L.Richards, D.L.Hughes, Journal of the Chemical Society, Dalton Transactions, 1523, 1985.