Molecular Orbital Calculations and
- - 1970 - -
KENNETH B. WIBERG
O. Sinanoglu and K.B. Wiberg,
Sigma Molecular Orbital Theory,
Yale University Press, 1970.
Organic chemists usually are interested in three quantities by which molecules, transient species, and activated complexes may be described:
- a) the heat of formatiön (or heat of atomization);
- b) the geometry, and
- c) the charge distribution.
If these three quantities could be calculated, chemical transformation could be discussed in detail and the necessity for a variety of "effects" would in many cases be eliminated. The organic chemist then asks: What is the possibility of calculating these quantities with a precision which would be useful in discussing chemical transformations?
This would require a precision of ± 1 kcal/mole (±0.04 eV or ±0.0015 au.!) in the heat of formation, ±0.02 A in bond lengths, ±1 to 20 in bond anges, and ±0.05 in electron density.
If one were asked to calculate the quantities with this precision by a present-day ab initio method, the proposition would clearly be absurd. The ab initio calculations are simply not that good, and as long as the Hartree-Fock approach is used, they cannot be that good for the correlation energy, and correlation effects on the wave functions are not included. As discussed in Chapter III, the correlation energy is an appreciable part (~20 per cent) of the heat of atomization.
In addition to being incapable of realizing chemically useful precision, the ab initio methods also suffer from complexity in calculation and high cost in computer time. Neither is desirable for calculations which are to be carried out frequently.
It then appears that the semiempirical methods provide the best possibiity for obtaining chemically useful results. This was early seen with the Hückel pi-MO calculations which use as primitive a semiempirical method as can be imagined. Yet, the method when properly calibrated could give "resonance energies" for condensed aromatic systems to ±1 kcal/mole and could give the positions of the first and second pi-->pi* transitions with good accuracy. However, it must be noted that good results with spectra are obtained only if the calculated and observed transition energies are plotted against each other. The resultant plot has a nonzero intercept corresponding to a finite transition energy tor a zero calculated energy. Abnormal intercepts should be expected in these treatments because part of the error in the treatment (i.e., terms which were neglected) may be absorbed in the intercept.
The pi-MO methods are not particularly useful in studying organic chemical phenomena
because they include only a small and special part of the molecule. The more recent semiempirical sigma-MO methods have provided the possibility of examining all types of chemical transformations and potentially provide a tool which cannot be neglected by the organic chemist.
I believe that cooperation between physical and organic (inorganic) chemists is needed to make real progress in the use of sigma-MO methods. On the part of the physical chemists, there is a need for an increased willingness to solve the problems of how to properly calculate repulsion integrals and still maintain rotational invariance (1), of how to include correlation effects in the semiempirical framework, and of whether or not various degrees of neglect of differential overlap may be maintained. In addition, when the methods are tested against experimental data, it seems only reasonable that both data sets be on the same basis and correspond to minimum-energy geometries (2).
The organic chemist should take the responsibility of thoroughly testing new methods as they become available, to learn enough about the methods to be able to use them intelligently, and to be willing to think in terms of molecular orbitals rather than localized bonds when considering carbonium ions and other delocalized species. The often-strange discussions of hyperconjugation result from an attempt to stretch valance-bond language too far. The charge alternation in carbonium ions certainly requires an MO description and the same is true of spin densities in free radicals.
If the organic chemist is not willing to do the above, he stands a good chance of being bypassed in the future interesting developments in the field. Further, the organic chemist has a wealth of knowledge concerning the transformations of organic compounds, and this can provide many useful tests of the theoretical methods. Finally, it in unlikely that any group other than the organic chemists will have the motivation to make many varied tests of the theories.
References and Notes
(1) Pople et al.,
[J. Chem. Phys. 43, S129 (1965) (reprinted as Chapter VI-5)]
maintain rotational invariance using only one averaged repulsion integral between
a pair of atoms and ignoring the distinction among s, psigma and
Klopman [J. Am. Chem. Soc. 86, 4550 (1964)] uses a different,
but still essentially artificial method for handling the problem.
It is probable that part of the difficulty in obtaining good
agreement between calculated and observed bond lengths for the series single,
double, and triple bonds [see Wiberg, J. Am. Chem. Soc. 90, 59 (1968)]
results from the use of inappropriate repulsion integrals.
(2) For example,
Baird ard Dewar [J. Am. Chem. Soc. 89, 3966 (1967)] carried
out sigma-MO calculations of the energies of a number of molecules using observed
geometries as inputs. However, the parameters used would not give the observed
geometries if the energies were minimized with respects to geometry. Further,
they compared the calculated energies with the observed energies without
correcting the latter for zeropoint energies or for the change in energy on going
from 25°C to 0°K.
Last updated : August 10, 2002 - 7:30 CET