Development of Xi'an-CI package – applying the hole–particle symmetry in multi-reference electronic correlation calculations

Abstract

ABSTRACTThis mini-review introduces our works on the Xi'an-CI (configuration interaction) package using graphical unitary group approach (GUGA). Taking advantage of the hole-particle symmetry in GUGA, the Galfand states used to span the CI space are classified into CI subspaces according to the number of holes and particles, and the coupling coefficients used to calculate Hamiltonian matrix elements could be factorised into the segment factors in the hole, active and external spaces. An efficient multi-reference CI with single and double excitations (MRCISD) algorithm is thus developed that reduces the storage requirement and increases the number of correlated electrons significantly. The hole–particle symmetry also gives rise to a doubly contracted MRCISD approach. Moreover, the internally contracted Gelfand states are defined within the CI subspace arising from the hole–particle symmetry, which makes the implementation of internally contracted MRCISD in the framework of GUGA possible. In addition to MRCISD, the development of multi-reference second-order perturbation theory (MRPT2) also benefits from the hole–particle symmetry. A configuration-based MRPT2 algorithm is proposed and extended to the multi-state n-electron valence-state second-order perturbation theory.