Configuration Interaction Description of Electron Correlation

Abstract

The fundamental goal of quantum ehemistry is the development of a qualitatively eorreet set of eoneepts for deseribing the ehemieal and physieal properties of molecules. When this goal is aehieved, a well-trained ehemist should be able to correlate and predict the behavior of most ehemieal systems without extensive ea1culation. In order to achieve this goal it is neeessary to obtain high-aeeuraey wave funetions for a few typieal ehemieal systems. Further it is neeessary to understand these wave fune-tions on two levels. First one must understand what types of terms and efIeets must be ineluded in the mathematieal deseription of the wave funetion. This level of understanding has probably now been attained as aresult of twenty years of large-seale ealculations. On the second levelone must understand the relationship between the physieal and ehemieal properties of the constituent parts of the system and the physi-eal and ehemieal properties exhibited by the system itself. This level of understanding has proven frustratingly diffieuIt to achieve by the direet ab-initio approaeh. A seeondary goal of quantum ehemistry, which has recently beeome possible, is the routine tabulation of physieal properties of ehemieal systems from the results of high-aeeuraey ealculations. Such tabulations, whether obtained from experiment or theory, are of value only if the properties tabulated are useful in furthering our understanding of nature. Tabulation of a few potential surfaees for ehemieal reaetions, for example, is of value beeause such surfaees are needed in the development of better theories of ehemieal reaetions. During the 50 years that quantum ehemistry has existed there have been many methods proposed for eomputing wave funetions. Sinee the advent of high-speed eomputers there has been an emphasis on developing a feasible, high-aeeuraey proee-dure for polyatomic molecules. Most of the major obstac1es to this development have been overcome in the last 20 years so that today modest accuraey for small polyatomic systems is possible. Sinee manyaspeets of the present method are fairly new, further teehnologieal refinements ean be expeeted to Iower the computing eost eonsiderably. Expansion of the wave funetion as a linear eombination of configurations seems inevitable beeause of the elose eonneetion of linear veetor spaees with the basie postulates of quantum meehanics (Dirac, 1958). Calculation of the wave function then involves evaluation of matrix elements of the hamiltonian between eonfigurations and the calculation of the expansion eoeffieients. The expansion eoeffieients ean be found by perturbation theory provided the eonfigurations are all approximately eigenfune-tions of the hamiltonian. Otherwise the eoeffieients must be found by the linear variation method from a seeular equation for a truneated, diserete set of eonfigurations.