Externally-Contracted Multireference Configuration Interaction Method Using a DMRG Reference Wave Function

Abstract

The recent development of the density matrix renormalization group (DMRG) method in multireference quantum chemistry makes it practical to evaluate static correlation in a large active space, while dynamic correlation provides a critical correction to the DMRG reference for strong-correlated systems and is usually obtained using multireference perturbation (MRPT) or configuration interaction (MRCI) methods with internal contraction (ic) approximation. These methods can use an active space scalable to relatively larger size references than has previously been possible. However, they are still hardly applicable to systems with an active space larger than 30 orbitals and/or a large basis set because of high computation and storage costs of high-order reduced density matrices (RDMs) and the crucial dependence of the MRCI Hamiltonian dimension on the number of virtual orbitals. In this work, we propose a new effective implementation of DMRG-MRCI, in which we use reconstructed CASCI-type configurations from DMRG wave function via the entropy-driving genetic algorithm (EDGA) [ Luo et al. J. Chem. Theory Comput. 2017 , 13 , 4699 - 4710 . ] and integrate it with MRCI by an external contraction (ec) scheme. This bypasses the bottleneck of computing high-order RDMs in traditional DMRG dynamic correlation methods with ic approximation, and the number of MRCI configurations is not dependent on the number of virtual orbitals. Therefore, the DMRG-ec-MRCI method is promising for dealing with a larger active space than 30 orbitals and large basis sets. We demonstrate the capability of our DMRG-ec-MRCI method in several benchmark applications, including the evaluation of the potential energy curve of Cr, single-triplet gaps of higher n-acene molecules, and the energy of the Eu-BTBP(NO) complex.

Multi-reference Epstein–Nesbet perturbation theory with density matrix renormalization group reference wavefunction

“…[61] Two different schemes for efficiently sampling the most important configurations are recently proposed, Monte Carlo based samplingreconstructed CAS (SR-CAS) algorithm by Boguslawski et al [62] and the EDGA proposed by some of us [63]. Our recent work [30] illustrated that it is possible to use a limited number (e.g. thousands, or tens of thousands) of most important configurations that obtained by EDGA to achieve a wave function completeness of 0.99 for large active spaces.…”

“…[4] However, electron correlation in realistic chemical systems is far more complicated than a restricted active space calculation can handle, and dynamic correlation outside the active space needs to be considered in order to get quantitative results. Over the last few years, a number of methods have been proposed to achieve this goal, including arXiv:1909.11954v1 [cond-mat.str-el] 26 Sep 2019 DMRG-canonical transformation (CT) [22], DMRG-complete active space secondorder perturbation theory (CASPT2) [23,24], DMRG-N -electron valence perturbation theory (NEVPT2) [25,26,27], DMRG-multi-reference configuration interaction (MRCI) [28,29,30], and DMRG-tailored coupled cluster (TCC) [31,32], matrix product state perturbation theory (MPSPT) [33,34]. Because of the too huge number of the reference configurations within a very large active space in DMRG calculation, usually internally contraction (ic) [35,36] or external contraction (ec) [37] approximations and/or a truncation for reference configurations have to be adopted in these post-DMRG dynamic correlation calculations.…”

“…chromium dimer (Cr 2 ) with an active space of (12e, 42o), oligocenes with active spaces up to (38e, 38o) and Eu-BTBP(NO 3 ) 3 complex with an active space of (38e, 36o). [30] However, for the purpose of dealing with even larger active spaces, the development of economic treatments for dynamic electron correlations on top of DMRG calculations is still highly necessary.…”

Portably parallel construction of a configuration‐interaction wave function from a matrix–product state using the Charm++ framework

“…A quantitative MR result can be expected if all the essential configurations were obtained in the reference wave function. [36,48,49] New hybrid approaches, such as the external-contracted MRCI (ec-MRCI) [48] and the Epstein-Nesbet perturbation theory (ENPT), [50] have been successively developed to combine the advantages of the DMRG approach in the acquisition of static correlations with those of the selected CI approach in the MR correlations. Unlike the conventional approaches that are fully or partially based on the reduceddensity matrices of AS, [51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68] these approaches convert the wave function, from its MPS to its CI forms (MPS-to-CI), via the procedures that were reported by Moritz et al, [69] Boguslawski et al, [70] and one of the authors of this paper.…”

“…[71] As pointed out by Boguslawski et al, [70] the sampled CI wave function could be employed for the following purposes: (a) to deeply understand the quality of the converged DMRG result, as the electronic energy is not sufficient as a sole criterion, to assess the obtained accuracy [69,72,73] ; (b) to compare the different DMRG calculations since the proposed CI decomposition can be obtained for any converged DMRG calculation, [70] (c) to optimize the DMRG convergence, employing the CI decomposition, to study the purpose and time the various electronic configurations were picked up (e.g., the CI-DEAS utility, which was reported by Stein and Reiher, [74] can be employed to accelerate the DMRG convergence), and (d) to sample important determinants which may then be used as input to a MRCI procedure. [36,[48][49][50]68,75] However, the improvement of the computational efficiency of these procedures is highly desirable, as a superlarge Hilbert space is generally employed in the samplings.…”