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

ABSTRACT

This 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.

KEYWORDS:

• Electron correlation
• graphical unitary group approach
• multi-reference configuration interaction
• multi-reference second-order perturbation theory

Acknowledgments

This work is supported by the National Key R&D Program of China (grant No. 2017YFB0203404). The authors thank the financial support from the National Natural Science foundation of China (NSFC, grant No. 21673174, 21473134). This research is also supported by the Double First-class University Construction Project of Northwest University. Most importantly, the works in the present paper demonstrate the long-term effort of Zhenyi Wen and Yubin Wang on the Xi'an-CI package. In particular, Zhenyi Wen introduced the hole–particle symmetry in GUGA and Yubin Wang wrote down the unMRCISD and icMRCISD-WK programs. B. Suo, Y. Lei and H. Han would like to dedicate this paper to Zhenyi Wen on his 80th birthday and also to Yubin Wang for her 30 years’ cooperation with Wen.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

National Key R&D Program of China [grant number 2017YFB0203404]; National Natural Science Foundation of China [grant number 21473134], [grant number 21673174]; Double First-class University Construction Project of Northwest University.