Applications of Resolutions of the Coulomb Operator in Quantum Chemistry

Abstract

This dissertation shows that the Coulomb operator and the long-range Coulomb operators can be resolved as a sum of products of one-particle functions. These resolutions provide a potent new route to tackle quantum chemical problems. Replacing electron repulsion terms in Schrodinger equations by the truncated resolutions yields the reduced-rank Schrodinger equations (RRSE). RRSEs are simpler than the original equations but yield energies with chemical accuracy even for low-rank approximations. Resolutions of the Coulomb operator factorize Coulomb matrix elements to Cholesky-like sums of products of auxiliary integrals. This factorization is the key to the reduction of computational cost of quantum chemical methods.