Assessment of various natural orbitals as the basis of large active space density matrix renormalization group calculations

TL;DR

This paper evaluates various natural orbitals as the basis for large active space DMRG calculations, demonstrating their impact on computational efficiency and proposing DMRG-CASCI as a cost-effective alternative to DMRG-CASSCF.

Contribution

It systematically assesses the effectiveness of different natural orbitals in DMRG calculations and introduces DMRG-CASCI with carefully chosen NOs as a less expensive alternative to standard methods.

Findings

Certain natural orbitals improve DMRG efficiency depending on system correlation characteristics.

DMRG-CASCI with selected NOs can outperform standard DMRG-CASSCF in cost and convergence.

Orbital ordering schemes influence the accuracy and efficiency of DMRG calculations.

Abstract

It is well-known that not only the orbital ordering but also the choice of the orbitals themselves as the basis may significantly influence the computational efficiency of density-matrix renormalization group (DMRG) calculations. In this study, for assessing the efficiency of using various natural orbitals (NOs) as the DMRG basis, we performed benchmark DMRG calculations with different bases, which included the NOs obtained by various traditional electron correlation methods, as well as NOs acquired from preliminary moderate DMRG calculations (e.g., preserved states less than 500). The tested systems included N$_2$, transition metal Cr$_2$ systems, as well as 1-D hydrogen polyradical chain systems under equilibrium and dissociation conditions and 2-D hydrogen aggregates. The results indicate that a good compromise between the requirement for low computational costs of acquiring NOs and the demand for high efficiency of NOs as the basis of DMRG calculations may be very dependent on the studied systems' diverse electron correlation characteristics and the size of the active space. It is also shown that a DMRG-complete active space configuration interaction (DMRG-CASCI) calculation in a basis of carefully chosen NOs can provide a less expensive alternative to the standard DMRG-CASSCF calculation and avoid the convergence difficulties of orbital optimization for large active spaces. The effect of different NO ordering schemes on DMRG-CASCI calculations is also discussed.