A systematic CI procedure with modified virtual orbitals

Abstract

The use of modified virtual orbitals is studied in a systematic conventional CI procedure which offers considerable potential in regard to convergence and extension to larger systems. The method is applied to the HCN molecule by using 37 basis functions, and analysis of energy expectation values, together with the one-electron density, yields some insight into the physical content of CI wavefunctions. IN T R 0 DUCT I 0 NIn a recent article1 we introduced a simple scheme for the construction of a set of modified virtual orbitals (MVOs) with convergence properties superior to those of the familiar canonical virtual orbital set. The MVO set is constructed so that the virtual orbitals are drawn toward the nuclear centers, and can interact more strongly with the nuclei. This is achieved by solving a modified SCF eigenvalue problem, solely in the SCF virtual orbital subspace, in the presence of the extra potential term $, ,. The operator V,, represents the attractive potential between a single electron and all the nuclei, z is the sum of nuclear charges, and X is a parameter. For reasons of brevity details of the method and relevant references can be found in ref. 1.The traditional CI method has been described as the worst way of constructing correlated wavefunctions, except for any other known method.2 The underlying reason is that CI methods are plagued by slow convergence and involve lengthy transformations, diagonalizations, and configuration selection procedures. A comprehensive and thorough review of the CI procedure can be found elsewhere."The problem of scale is a formidable one in the traditional CI method which involves spin-adapted configuration functions (CFS). The number of possible double-excitation CFs that can be generated by promotion from the parent SCF-CF alone is of the order 1/2(nmc)2(nviA)2. Hence, if an increase in basis set size is contemplated, the number of such CFs increases as (nvirJ2, whereas extension to larger systems means an increase in candidate CFS of at least an order (nm,)2; in general, nvirt will also increase. This is one reason why CI is generally restricted to a range of relatively small molecules with "good" basis sets, for the performance of molecular CI calculations with "relatively poor" basis sets has produced results "worse" than that of the SCF itself.4As an alternative we can try to reduce the number of contributing orbitals by constraining some to be doubly occupied (frozen-core approxi m a t i~n ) .~!~ This, however, has led to deficiencies in certain expectation values7 and to a total lack of correlation between the motions of unlike spin electrons in the high-density regions around the heavy-atom centers.8A reduction in the number of virtual orbitals can, of course, be achieved by truncating the CI at an arbitrary but convenient point.g Both this and the frozen-core approximation, however, can ignore certain single and direct double promotions that have proved to be important in obtaining reliable expectation values.1° All these methods attempt to reduce the scale o...