Journal
JOURNAL OF CHEMICAL THEORY AND COMPUTATION
Volume 14, Issue 8, Pages 4063-4071Publisher
AMER CHEMICAL SOC
DOI: 10.1021/acs.jctc.8b00273
Keywords
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Funding
- U.S. National Science Foundation [CHE 1665333]
- OAC [1657286]
- Simons Collaboration on the Many-Electron Problem
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We describe a low cost alternative to the standard variational DMRG (density matrix renormalization group) algorithm that is analogous to the combination of the selected configuration interaction plus perturbation theory (SCI+PT). We denote the resulting method p-DMRG (perturbative DMRG) to distinguish it from the standard variational DMRG. p-DMRG is expected to be useful for systems with very large active spaces, for which variational DMRG becomes too expensive. Similar to SCI+PT, in p-DMRG, a zeroth-order wave function is first obtained by a standard DMRG calculation but with a small bond dimension. Then, the residual correlation is recovered by a second-order perturbative treatment. We discuss the choice of partitioning for perturbation theory, which is crucial for its accuracy and robustness. To circumvent the problem of a large bond dimension in the first-order wave function, we use a Article sum of matrix product states to expand the first-order wave function, yielding substantial savings in computational cost and memory. We also propose extrapolation schemes to reduce the errors in the zeroth- and first-order wave functions. Numerical results for Cr-2 with a (28e, 76o) active space and 1,3-butadiene with an (22e, 82o) active space reveal that p-DMRG provides ground state energies of a similar quality to variational DMRG with very large bond dimensions but at a significantly lower computational cost. This suggests that p-DMRG will be an efficient tool for benchmark studies in the future.
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