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arXiv:1610.08394 · Chemical Physics Letters

A general second order complete active space self-consistent-field solver for large-scale systems

Qiming Sun, Jun Yang, Garnet Kin‐Lic Chan

Published Mar 5, 2017• 131 citations
arXivHTMLPDF
DOI
10.1016/j.cplett.2017.03.004

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Abstract An algorithm that accelerates the convergence of the iterative optimization of the complete active space self‐consistent field (CASSCF) wavefunction so as to find a optimum solution in fewer macroiterations is described. The algorithm is oriented to large‐scale CASSCF problems that are to be solved with a combination of density matrix renormalization group (DMRG) method for the configuration interaction (CI) process. The algorithm is based on the alternating (or two‐step) CASSCF optimization in which the CI and molecular orbital (MO) parameters are optimized separately. Convergence ratio is improved by finding further optimized MOs from a linear extrapolation of the MO sets of the iteration history. The acceleration results in fewer diagonalizations in a total CASSCF calculation to save a considerable computational cost. The convergence performance is examined in a couple of realistic applications on SiC 3 and poly(phenyl)carbenes. For poly(phenyl)carbenes, the large‐size CASSCF calculations with CAS(30e,30o) that entails full π valence space as well as sp 2 orbital space of carbenes are performed by using the practical implementation of DMRG‐CASSCF in conjunction with the acceleration technique. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

International Journal of Quantum Chemistry•Jan 1, 2009•106 citations
We present a second-order perturbation theory based on a density matrix renormalization group self-consistent field (DMRG-SCF) reference function. The method reproduces the solution of the complete active space with second-order perturbation theory (CASPT2) when the DMRG reference function is represented by a sufficiently large number of renormalized many-body basis, thereby being named DMRG-CASPT2 method. The DMRG-SCF is able to describe non-dynamical correlation with large active space that is insurmountable to the conventional CASSCF method, while the second-order perturbation theory provides an efficient description of dynamical correlation effects. The capability of our implementation is demonstrated for an application to the potential energy curve of the chromium dimer, which is one of the most demanding multireference systems that require best electronic structure treatment for non-dynamical and dynamical correlation as well as large basis sets. The DMRG-CASPT2/cc-pwCV5Z calculations were performed with a large (3d double-shell) active space consisting of 28 orbitals. Our approach using large-size DMRG reference addressed the problems of why the dissociation energy is largely overestimated by CASPT2 with the small active space consisting of 12 orbitals (3d4s), and also is oversensitive to the choice of the zeroth-order Hamiltonian.
In multi-reference (MR) methods, addressing systems with large active spaces remains a challenge in the field. In Papers I and II of this series, we demonstrated that full rank N-electron valence state second-order perturbation theory (FR-NEVPT2) is a robust MR perturbation theory capable of computing strongly correlated systems with approximate density matrices. However, the previous FR-NEVPT2 implementation requires the computation and storage of fifth-order reduced density matrices (RDMs), limiting the usage of FR-NEVPT2 for systems with large active spaces. In the present work, as Paper III of the series, we report a new FR-NEVPT2 algorithm to handle systems with large active spaces. In the new algorithm, an approximate complete active space (CAS) self-consistent field (SCF) method, iterative configuration expansion (ICE) SCF, is employed to compute the reference wave functions for FR-NEVPT2. Then, the necessary Koopmans matrices of FR-NEVPT2 involving various RDMs are constructed using the intermediates designed by Kollmar et al. [J. Chem. Phys. 155, 234104 (2021)] to avoid storage bottlenecks. The performance of the new FR-NEVPT2 algorithm for systems with large active spaces is evaluated. Our results show that even with aggressive truncation parameters to truncate the ICE-SCF reference wave function, FR-NEVPT2 effectively recovers the missing static correlations of ICE-SCF. Several interesting systems with active spaces up to CAS(34,34) are studied using FR-NEVPT2 with ICE-SCF reference.
Abstract An algorithm that accelerates the convergence of the iterative optimization of the complete active space self‐consistent field (CASSCF) wavefunction so as to find a optimum solution in fewer macroiterations is described. The algorithm is oriented to large‐scale CASSCF problems that are to be solved with a combination of density matrix renormalization group (DMRG) method for the configuration interaction (CI) process. The algorithm is based on the alternating (or two‐step) CASSCF optimization in which the CI and molecular orbital (MO) parameters are optimized separately. Convergence ratio is improved by finding further optimized MOs from a linear extrapolation of the MO sets of the iteration history. The acceleration results in fewer diagonalizations in a total CASSCF calculation to save a considerable computational cost. The convergence performance is examined in a couple of realistic applications on SiC 3 and poly(phenyl)carbenes. For poly(phenyl)carbenes, the large‐size CASSCF calculations with CAS(30e,30o) that entails full π valence space as well as sp 2 orbital space of carbenes are performed by using the practical implementation of DMRG‐CASSCF in conjunction with the acceleration technique. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009