Multireference perturbation theory for large restricted and selected active space reference wave functions

A multireference second-order perturbation theory (MRPT2) has been developed which allows the use of reference wave functions with large active spaces and arbitrary configuration selection. Internally contracted configurations are used as a basis for all configuration subspaces of the first-order wave function for which the overlap matrix depends only on the second-order density matrix of the reference function. Some other subspaces which would require the third- or fourth-order density matrices are left uncontracted. This removes bottlenecks of the complete active space second order pertubation theory (CASPT2) caused by the need to construct and diagonalize large overlap matrices. Preliminary applications of the new method for 1,2-dihydronaphthalene (DHN) and free base porphin are presented in which the effect of applying occupancy restrictions in the reference wave function (restricted active space second-order perturbation theory, RASPT2) and reference configuration selection (general MRPT2) on electronic excitation energies is tested. In the case of the S-0-S-1 transition of DHN rapid convergence of the RASPT2 and MRPT2 excitation energies towards the CASPT2 value with increasing number of reference configurations is observed. In the calculations for the lowest five states of porphin all 24 valence pi-orbitals were included in the active space of restricted active space self-consistent field (MCSCF) and MRPT2 calculations. From the RASSCF wave functions different subsets of reference configurations were selected on the basis of their coefficients. In this case convergence of the excitation energies with decreasing selection threshold is found to be rather slow, indicating the need for more elaborate selection schemes. The computed excitation energies are in good agreement with previous CASPT2 results obtained with much smaller active spaces. (C) 2000 American Institute of Physics. [S0021-9606(00)30613-4].