Algorithm for analytic nuclear energy gradients of state averaged DMRG-CASSCF theory with newly derived coupled-perturbed equations

Autor: Tsubasa Iino, Toru Shiozaki, Takeshi Yanai
Rok vydání: 2023
Předmět:
Zdroj: The Journal of Chemical Physics. 158:054107
ISSN: 1089-7690
0021-9606
DOI: 10.1063/5.0130636
Popis: We present an algorithm for evaluating analytic nuclear energy gradients of the state-averaged density matrix renormalization group complete-active-space self-consistent field (SA-DMRG-CASSCF) theory, based on newly derived coupled-perturbed (CP) DMRG-CASSCF equations. The Lagrangian for the conventional SA-CASSCF analytic gradient theory is extended to the SA-DMRG-CASSCF variant that can fully consider the whole set of constraints on the parameters of multi-root canonical matrix product states (MPSs) formed at all the DMRG block configurations. An efficient algorithm to solve the CP-DMRG-CASSCF equations for determining the multipliers was developed. The complexity of the resultant analytic gradient algorithm is overall the same as that of the unperturbed SA-DMRG-CASSCF algorithm. In addition, a reduced-scaling approach was developed to directly compute the SA reduced density matrices (SA-RDMs) and their perturbed ones without calculating separate state-specific RDMs. As part of our implementation scheme, we neglect the term associated with the constraint on the active-active (AA) orbital rotation in the Lagrangian. This rotation, usually realized by the orbital localization, regulates the noninvariance of the DMRG-CASSCF wavefunction to the AA rotation. Thus, errors from the true analytic gradients may be caused in this scheme. The proposed gradient algorithm was tested with the spin-adapted implementation by checking how accurately the computed analytic energy gradients reproduce the numerical gradients of SA-DMRG-CASSCF energies using a common number of renormalized basis. The illustrative applications show that the errors are sufficiently small when using a typical number of the renormalized basis, which is required to attain adequate accuracy in the DMRG's total energies.
Databáze: OpenAIRE
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