Application of Cholesky-Like Matrix Decomposition Methods to the Evaluation of Atomic Orbital Integrals and Integral Derivatives

摘要

When viewed as a square two-indexed matrix, the array of atomic orbital based, two-electron integrals (ij/kl) is a positive semidefinite array. Beebe and Linderberg showed, in 1977, that actual or near linear dependencies often exist within the types of atomic orbital basis sets employed in conventional quantum chemical calculations. In fact, large (i.e., higher quality) bases were shown to be substantially more redundant than smaller or more spatially separated bases. In situations where these exists significant basis near redundancy, the rank (r) of the ij/kl) = V sub I, J matrix of integrals will be significantly smaller than the matrix dimension M. (kr)