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

Abstract

It is well-known that not only the orbital ordering but also the choice of the orbitals itself 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 N2, transition metal Cr2 systems, as well as 1D hydrogen polyradical chain systems under equilibrium and dissociation conditions and 2D 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-complete active space self-consistent field (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.

Second-Order Self-Consistent-Field Density-Matrix Renormalization Group

“…This ansatz was first exploited for DMRG-SCF in the [augmented Hessian (AH)] Newton-Raphson-like (NR) implementation by Ghosh and co-workers 26 and Wouters et al 36,37 . Its implementation was also described by Ma and Ma 38 who, in addition, presented a pilot DMRG-SCF implementation of the Werner-Meyer (WM) MCSCF algorithm 39 . Their common basis is the construction of operators which are obtained from taking the first and second derivatives of the energy with respect to the variational parameters.…”

Investigation of metal–insulator-like transition through theab initiodensity matrix renormalization group approach

“…Finally, we will investigate the effect of the orbital basis on the DMRG results. Although, several DMRG works can be found in literature where various orbital basis were employed to study quantum chemical systems [11][12][13][14][15][16][17][18][19][20][21] , no rigorous analysis in terms of resulting entanglement patterns have been carried out, yet. As we will show, the use of different basis as well as the starting Hartree-Fock configuration can have a huge impact on the effectiveness of the method.…”

Density-matrix renormalization group algorithm with multi-level active space

“…When using canonical-type orbitals, one reasonable choice is to use the bonding/anti-bonding ordering, which has been recommended by many groups. 22,25,69 However, in most cases, it is not straightforward and it is also extremely time-consuming to pick up the desired bonding/anti-bonding ordering manually, and as such, there are some other suggested automatic strategies, such as reverse Cuthill-McKee algorithm, 22,24,116 genetic algorithm, 32 Minimum Bandwidth by Perimeter Search, 71 and algorithms from graph theory. 63,87 Since the ML-DMRG strategy changes the orbital ordering when partitioning orbital spaces, it is of great importance to also investigate the ML-type orbital ordering effect on DMRG calculations.…”

“…It is well-known that the orbital ordering would significantly affect the DMRG performances, and there were many informative suggestions 22,[24][25][26]34,35,46,56,57,63,69 on how to construct an optimal orbital ordering before implementing the computationally expensive DMRG calculations. When using canonical-type orbitals, one reasonable choice is to use the bonding/anti-bonding ordering, which has been recommended by many groups.…”

“…44,45 Alternatively, one could also carefully choose various molecular orbitals from other lowlevel electron-correlation calculations as DMRG basis. 55,69,76 An important feature of DMRG is that it allows to capture all types of electron correlation effects (dynamical and nondynamical) in a given active space in a consistent way. In many cases, choosing a fixed number M of preserved states in DMRG-based calculations is feasible but not economic.…”