The direct CI method

Abstract

A thorough analysis of the direct CI method as applied to the case of a general set of reference configurations coupled to all single and double substitutions is presented. It is pointed out that there is no single strategy which proves optimal under all circumstances. A variety of procedures are therefore presented together with rules to enable the selection of the most favourable under a given circumstance. Much emphasis has been placed on organizing the calculations via a series of matrix multiplications, which enables a vector or array processing computer to be used to best effect. Some consideration is given to using an atomic integral (rather than molecular integral) driven scheme for some interactions, thus removing the necessity for a complete transformation of the molecular integrals to a molecular orbital basis, and the advantages and disadvantages of so doing are discussed. Improved procedures for carrying out both full and partial transformations of the molecular integrals are described. A number of test case calculations involving configuration lists of the order of 10⁴ to 10⁵ have been analysed in detail, to give a clear picture of the cost of the various interaction types which arise, and indicating that integrals carrying two external molecular orbital indices account for approximately 60 per cent of the cost in typical cases. Typically, a calculation involving 10⁵ configurations requires approximately two minutes of CRAY-1 computer time, allowing for ten iterations of the diagonalization procedure. The cost of the calculations are found, somewhat surprisingly, to be approximately linear in the dimension of the configuration space, indicating that calculations involving 10⁶ configurations are now quite feasible.