Chapter 5. Quantum chemistry in Molecular Modeling


5.5 Energy calculations

Ab initio calculations give the absolute energy of the system of fixed nuclei and moving electrons. These are large numbers, for example for cyclohexane the HF energy with the 6-31G* basis set is -234.2080071 a.u., which is equal to 146967.86 kcal/mol.
Thus, the chemically significant energy quantities of a few kcal/mol are very much smaller than the computed quantity, and high accuracy is required.

The absolute energy is not a directly useful quantity. It can however be used to calculate the Heat of Formation with a reasonable accuracy. According to G1 and G2 theories [14, 15] the molecular structure and vibrational frequencies are first determined at the HF/6-31G* level.
The frequencies are used to calculate the zero-point energy. Then, the geometry is further optimized at the MP2 level. Subsequently, basis set effects and correlation energies are calculated at various levels of theory, to allow an extrapolation (using small empirical contributions !) to the limits of full CI and the Hartree-Fock limit, that is to the complete Schrödinger equation for the motionless molecule.
Finally, the zero-point vibrational energy is added. This procedure can account for heats of formation with an accuracy of < 2 kcal/mol, which rivals the quality of experimental data.

Other authors [16] calculate the heat of formation based on the 6-31G* calculation and bond increments, similar to the way MM2 deals with this.
This is a much less elaborate procedure than the G1 and G2 theories, but it is essentially empirical. The empirical corrections needed in G1 and G2 are of a very "mild" kind, they are not related to the structure of the species, but only depend on the number of electrons.

The isodesmic reaction approach allows a fairly accurate calculation of the heat of reactions, even at the HF level. Isodesmic reactions are defined as transformations in which the numbers of bonds of each formal type are conserved, and only the relationships among the bonds are altered [4, 6]. For example :

CH4 + CH3CH2OH   -->   CH3CH3 + CH3OH			(1)
CF4 + 3 CH4      -->   4 CH3F   		        (2)
Energy changes (kcal/mol) for these two reactions are :
		STO-3G	3-21G	6-31G*//STO-3G	experimental
deltaE (1)	 2.6	 4.8	   4.1		 5.0 (5.7)
deltaE (2)	53.5	62.4	  49.6		49.3 (52.8)
(The experimental numbers in parentheses are without correction for zero-point energy changes).

References:

[4] W.J. Hehre, L. Radom, P. von R. Schleyer and J.A. Pople
Ab initio molecular orbital theory, Wiley, 1986
[6] Spartan User's Guide, version 3.0,
Wavefunction, Inc., 1993.
[14] Pople, J.A.; Head-Gordon, M.; Fox, D.J.; Raghavachari, K.; Curtiss, L.A.,
J. Chem. Phys., 1989, 90, 5622 - 5629.
[15] Curtiss, L.A.; Raghavachari, K.; Trucks, G.W.; Pople, J.A.,
J. Chem. Phys., 1991, 94, 7221.


Next paragraph, 5.6 Quality of ab initio results
Previous paragraph 5.4 Limitations of the HF method; Electron correlation.
Chapter 5 MM Syllabus 1995 MODIFIED November 8, 1995
Fred Brouwer, Lab. of Organic Chemistry, University of Amsterdam.