Multi-reference Møller–Plesset theory: computational strategies for large molecules

Abstract

We propose computational strategies and algorithms to perform multi-reference Møller–Plesset (MR-MP2) calculations efficiently for large molecules. As zeroth-order reference we employ restricted configuration interaction wave functions expressed in terms of an active space of Hartree–Fock one-particle functions (RAS-CI). To accelerate the convergence of the perturbation expansion and to keep the zeroth-order spaces as small as possible (i.e. Dim<1000) we use improved (average) virtual orbitals. The length of the first-order space (single and double excitations with respect to all reference configurations) is reduced by selecting the most important configurations from the full space based on the magnitude of their H0 diagonal matrix element. The two-electron integrals in the MO basis are calculated semi-directly with the resolution of the identity (RI) method which avoids computationally demanding 4-index transformations. The errors introduced by the approximations can systematically be reduced and are found to be insignificant in applications to chemical problems. As examples we present MR-MP2 results for excitation and reaction energies of molecules for which single-reference perturbation theory is not adequate. With our approach, investigation of systems as large as porphin or C60 are possible on low-cost personal computers.