Efficient and scalable wave function compression using corner hierarchical matrices

Kenneth O Berard; Hongji Gao; Alexander Teplukhin; Xiangmin Jiao; Benjamin G Levine

doi:10.1063/5.0231409

Efficient and scalable wave function compression using corner hierarchical matrices

J Chem Phys. 2024 Nov 28;161(20):204106. doi: 10.1063/5.0231409.

Authors

Kenneth O Berard^{1

2}, Hongji Gao^{1

3}, Alexander Teplukhin^{1

2}, Xiangmin Jiao^{1

3}, Benjamin G Levine^{1

2}

Affiliations

¹ Institute for Advanced Computational Science, Stony Brook University, Stony Brook, New York 11794, USA.
² Department of Chemistry, Stony Brook University, Stony Brook, New York 11794, USA.
³ Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York 11794, USA.

PMID: 39584551
DOI: 10.1063/5.0231409

Abstract

The exponential scaling of complete active space and full configuration interaction (CI) calculations limits the ability of quantum chemists to simulate the electronic structures of strongly correlated systems. Herein, we present corner hierarchically approximated CI (CHACI), an approach to wave function compression based on corner hierarchical matrices (CH-matrices)-a new variant of hierarchical matrices based on block-wise low-rank decomposition. By application to dodecacene, a strongly correlated molecule, we demonstrate that CH matrix compression provides superior compression compared to truncated global singular value decomposition. The compression ratio is shown to improve with increasing active space size. By comparison of several alternative schemes, we demonstrate that superior compression is achieved by (a) using a blocking approach that emphasizes the upper-left corner of the CI vector, (b) sorting the CI vector prior to compression, and (c) optimizing the rank of each block to maximize information density.