New schemes for internally contracted multi-reference configuration interaction.

In this work we present a new internally contracted multi-reference configuration interaction (MRCI) scheme by applying the graphical unitary group approach and the hole-particle symmetry. The latter allows a Distinct Row Table (DRT) to split into a number of sub-DRTs in the active space. In the new scheme a contraction is defined as a linear combination of arcs within a sub-DRT, and connected to the head and tail of the DRT through up-steps and down-steps to generate internally contracted configuration functions. The new scheme deals with the closed-shell (hole) orbitals and external orbitals in the same manner and thus greatly simplifies calculations of coupling coefficients and CI matrix elements. As a result, the number of internal orbitals is no longer a bottleneck of MRCI calculations. The validity and efficiency of the new ic-MRCI code are tested by comparing with the corresponding WK code of the MOLPRO package. The energies obtained from the two codes are essentially identical, and the computational efficiencies of the two codes have their own advantages.