Approximate Methods in Quantum Chemistry

Abstract

The goal of any semi-empirical or approximate method is the achievement of a compromise between ease and accuracy. In molecular quantum chemistry ease generally means speed of obtaining results. Any method to be of practical use must execute at least as rapidly as methods which are more accurate. As obvious as this would seem, many suggested methods suffer from exactly this disadvantage. The criterion of accuracy is somewhat more difficult to define. Accurate with respect to what? If an approximate method confines itself closely to an exact theory, then the results should reproduce those obtainable from a correct treatment of that theory. If a method introduces pure parameters, then, perhaps, it is best guided to this purpose also. But if a method introduces semi-empirical parameters chosen from experiment, there exists the tempting idea that the model might extend beyond the confinements of the theory and best be compared directly with experiment. As attractive as a direct relation to experiment is, the idea is easy to abuse and has often led to a different method for different observables. Nevertheless, it is difficult to deny the utility of the Pariser-Parr-Pople (1) pi election model, and especially some of its refinements (2), in organizing thought about π→π* spectra.