Higher order singular value decomposition in quantum chemistry

Abstract

Higher order singular value decomposition is studied in the context of quantum chemistry, with particular focus on the decomposition of the 𝒯 ₂ amplitudes obtained from second order Møller Plesset perturbation (MP2) theory calculations. Our test calculations reveal that HOSVD transformed amplitudes yield considerably faster convergence in MP2 correlation energy, both in terms of amplitude and orbital truncation. Also, HOSVD orbitals display increased bonding/antibonding character compared to Hartree–Fock orbitals. In contrast to canonical MP2 theory, the leading amplitudes are those between corresponding occupied–virtual orbital pairs. The HOSVD orbitals are paired up automatically around the Fermi level in decreasing importance, so that the strongest occupied virtual–pair are the highest occupied molecular orbital and lowest unoccupied molecular orbital. We show that in the case of MP2 amplitudes, the HOSVD orbitals are equivalent to the unrelaxed MP2 natural orbitals. The least squares higher order orthogonal iteration algorithm yields only minor improvements over the sub-optimal truncated orbital space obtained from the HOSVD.

Keywords:

• higher order sigular value decomposition
• natural orbitals
• active spaces
• reduced rank separability

Acknowledgements

We thank J. Parkhill for invaluable discussions. This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the U.S. Department of Energy under Contract DEAC0376SF00098,and by a grant from the SciDac Program.