Efficient methods for configuration interaction calculations

Abstract

Advanced techniques are developed to provide efficient economic treatment of the large scale eigenvalue problem posed when configuration interaction is carried out on SCF basis sets of moderate size. When the characteristic properties of the hamiltonian matrix are examined in light of the type of solution required, partitioning of the configuration space is shown to result in an expansion of the problem about a limited core of states, where the small but cumulative interactions of vast regions of the remaining space are reduced to the form of an effective potential. With proper selection of the core, the evaluation of this potential can be readily and accurately truncated to a level involving minimum expenditure in time and effort. In particular only diagonal elements and a strip of the full CI matrix are required to achieve an accuracy of 1 – 5 kcal/mole with complete treatment for configuration spaces of order tens of thousands. In addition, a close look at current theory on the generation of matrix elements between spin symmetry adapted configurations leads to simplified expressions where the matrix elements are derived in the form of a weighted sum of molecular integrals in which the weighting coefficients represent the integrated value of the wavefunctions over spin coordinates. For typical cases of low multiplicity and limited numbers of open shells the list of unique parameters needed to generate all weights are shown to be readily stored as a program library. Actual times for matrix element generation are believed to be an order of magnitude faster than current techniques. Practical demonstration of the accuracy and efficiency of the method is provided by calculations on formaldehyde, water, and ethylene.