Chapter 5. Quantum chemistry in Molecular Modeling


5.6 Quality of ab initio results

One of the most useful features of ab initio MO theory is that it allows the definition of "model chemistries". A theoretical model chemistry entails a method (e.g. Hartree-Fock or MP2 etc.) and a basis set.
The philosophy of a model chemistry is that it should be uniformly applicable and tested on as many systems as possible to learn about its performance. This turns out to be useful, because the reliability and accuracy of model chemistries can be systematically assessed in this way.

In the rest of this section we will focus on the performance of model chemistries that can be practically applied for organic molecules with present-day hardware and software, that is HF and MP2 methods with basis sets usually limited to the 6-31G(d) level. For more detailed comparisons see references 4, 6, 8 and 17.

Geometry

As far as equilibrium geometry is concerned, HF and MP2 ab initio models even with modest basis sets lead to excellent results. At present, HF/6-31G* or MP2/6-31G* are considered good and reliable methods for the determination of the geometries of organic molecules. In many cases the smaller basis sets 3-21G or even STO-3G can give useful results. The bond length calculated at the HF level is usually overestimated by ca. 0.01 - 0.02 Å as a result of the neglect of electron correlation. For examples see references 4, 6, 8 and 17.

For transition metal compounds and organometallics the results are less satisfactory. Because of the size of such systems, adequately large basis sets cannot be applied with the present generation of computers and programs. Moreover, electron correlation can be important. It is conceivable that a model chemistry based on Density Functional Theory will become available which covers this area of chemistry.

Vibrational frequencies

Due to the availability of analytic second derivatives of HF and MP2 wavefunctions, the calculation of vibrational frequencies and normal modes of organic molecules has become almost a routine matter [4, 6, 7]. It turns out that the results even with modest-basis HF models are quite good.
The frequencies are consistently overestimated, which is due to the neglect of correlation energy and of anharmonicity. Uniform scaling of the computed frequencies by a factor of 0.89 0.01 gives a good agreement for most cases. For MP2 the scaling factor should be closer to 1.0.
Of course, with dedicated empirical force fields a better fit of the spectra can be achieved, however at the expense of generality and of great effort.

Energies

The accurate computation of absolute or relative energies remains a major challenge. Even conformational energy differences and barriers are not reliably computed with HF or MP2 models using small basis sets (6-31G* or smaller).
Of course the demands on accuracy are very high in this case. On the other hand, a comparison between related systems (e.g. predicting a substituent effect) can often be made quite well.
Energies of reactions can be predicted relatively accurately, especially for isodesmic processes. When the number of formal bonds changes, electron correlation methods are essential. As mentioned in section 5.5, successful methods have been developed to estimate heats of formation on the basis of ab initio results.

Chemical reactions

The quality of the prediction of structures of transition states can hardly be verified by comparison with experiments, so the only way is to look at convergence of the computed values with increasing sophistication of the method employed.
Energies of transition states can be related to experimental activation energies.
In practice theoretical methods can at best to predict relative activation energies, in other words the selectivities of reactions. Often this is chemically more significant than the precise number : usually it doesn't really matter whether a product ratio is 50 : 1 or 100 : 1. To be able to predict whether products will be formed in a ratio of 3:1 or 1:3 one needs relative TS energies with an accuracy of roughly 1 to 2 kcal/mol, and this is feasible for some reactions, such as the Diels-Alder reaction [6].

References:

[4] W.J. Hehre, L. Radom, P. von R. Schleyer and J.A. Pople
Ab initio molecular orbital theory, Wiley, 1986
[5] Szabo and Ostlund
Modern Quantum Chemistry, McGraw-Hill, 1989.
[6] Spartan User's Guide, version 3.0,
Wavefunction, Inc., 1993.
[7] Foresman, J.B.; Frisch, A.
Exploring Chemistry with Electronic Structure Methods: A Guide to Using Gaussian, Gaussian Inc., 1993.
[8] D. Feller and E.R Davidson,
in Reviews in Computational Chemistry, K.B. Lipkowitz and D.B. Boyd, eds., VCH, 1990, pp. 1 - 43.
[17] Boyd, D.B.,
in Reviews in Computational Chemistry, K.B. Lipkowitz and D.B. Boyd, eds., VCH, Vol. 1, 1990, 321 - 354.


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Chapter 5 MM Syllabus 1995 MODIFIED November 8, 1995
Fred Brouwer, Lab. of Organic Chemistry, University of Amsterdam.