Universal basis sets and Cholesky decomposition of the two-electron integral matrix

Abstract

It is shown that, for a one-centre universal even-tempered basis set containing N functions, only N of the N( N + 1)/2 eigenvalues of the two-electron integral matrix are larger than some small δ as N becomes large and thus only N of the rows or columns of the matrix are linearly independent in this limit. It is demonstrated that the same degree of linear dependence exists in the case of a many-centre universal basis set. This approximate numerical linear dependence can be effectively exploited in atomic and molecular electronic structure calculations using universal systematic sequences of even-tempered basis sets by means of a Cholesky decomposition of the two-electron integral matrix. This opens up the possibility of using large, flexible basis sets in high precision calculations on small molecules, in studies of extended molecular systems, and in relativistic electronic structure calculations.