Multireference Correlation in Long Molecules with the Quadratic Scaling Density Matrix Renormalization Group

TL;DR

This paper introduces a quadratic-scaling local DMRG algorithm for accurately describing multireference correlations in large, long molecules, enabling precise energy calculations with reduced computational cost.

Contribution

The authors develop and implement a local ab initio DMRG method that scales quadratically with system size, without needing correlation domains, for large molecular systems.

Findings

Achieves exact correlation energies with microhartree precision

Successfully correlates up to 100 electrons in 100 orbitals

Demonstrates robustness and convergence in polyenes and hydrogen chains

Abstract

We have devised and implemented a local ab initio Density Matrix Renormalization Group (DMRG) algorithm to describe multireference nondynamic correlations in large systems. For long molecules that are extended in one of their spatial dimensions, this method allows us to obtain an exact characterisation of correlation, in the given basis, with a cost that scales only quadratically with the size of the system. The reduced scaling is achieved solely through integral screening and without the construction of correlation domains. We demonstrate the scaling, convergence, and robustness of the algorithm in polyenes and hydrogen chains. We converge to exact correlation energies (with 1-10 microhartree precision) in all cases and correlate up to 100 electrons in 100 active orbitals. We further use our algorithm to obtain exact energies for the metal-insulator transition in hydrogen chains and compare and contrast our results with those from conventional quantum chemical methods.