Introduction

Abstract

The quote above from Paul Adrian Maurice Dirac (1929) has been somewhat of an article of faith for modern quantum chemistry. Intensive efforts on the development of theory, algorithms, and techniques have made computational quantum chemistry a very successful representative of the “third way” in modern science—computer modeling has come into its own alongside experiment and theory. Fifty years ago this was a branch of science where predictions were at best qualitative, founded on rather approximate models. Many of these models were quite sophisticated, and much of the insight gained is still valid and valuable, but the developments in both methods and computer hardware up to the present have very much transformed this field. Today standard quantum chemical methods are capable of predicting results with chemical accuracy: reaction energies may be determined within a few kilojoules per mole, and spectral data within a few reciprocal centimeters. At least, this sort of reliability can be expected for “normal” areas of application. Dirac’s main contribution to science was a merging of the two great developments of 20th century physics—quantum mechanics and the (special) theory of relativity. Most of the successful development in quantum chemistry has been based on nonrelativistic quantum mechanics. This may be justified by considering that special relativity is needed primarily to describe objects moving at velocities approaching the speed of light, and that this is mostly not the case for chemical systems. After all, most chemical reactions and phenomena occur at energies below the relativistic domain. Or could relativistic effects nevertheless be important? Even without the recent advances in computational chemistry, it became clear fairly early that nonrelativistic theory was unable to explain certain trends in observed properties. A few examples will suffice to illustrate the anomalies. Experimental determination of the metal–carbon bond length in the group 12 dimethyl compounds showed an increase in bond length from Zn to Cd, but a decrease in bond length from Cd to Hg (Rao et al. 1960). The expected trend was an increase from Zn to Cd and again from Cd to Hg.