Complete active space second-order perturbation theory with cumulant approximation for extended active-space wavefunction from density matrix renormalization group. 2014

Yuki Kurashige, and Jakub Chalupský, and Tran Nguyen Lan, and Takeshi Yanai
Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan.

We report an extension of our previous development that incorporated quantum-chemical density matrix renormalization group (DMRG) into the complete active space second-order perturbation theory (CASPT2) [Y. Kurashige and T. Yanai, J. Chem. Phys. 135, 094104 (2011)]. In the previous study, the combined theory, referred to as DMRG-CASPT2, was built upon the use of pseudo-canonical molecular orbitals (PCMOs) for one-electron basis. Within the PCMO basis, the construction of the four-particle reduced density matrix (4-RDM) using DMRG can be greatly facilitated because of simplicity in the multiplication of 4-RDM and diagonal Fock matrix in the CASPT2 equation. In this work, we develop an approach to use more suited orbital basis in DMRG-CASPT2 calculations, e.g., localized molecular orbitals, in order to extend the domain of applicability. Because the multiplication of 4-RDM and generalized Fock matrix is no longer simple in general orbitals, an approximation is made to it using the cumulant reconstruction neglecting higher-particle cumulants. Also, we present the details of the algorithm to compute 3-RDM of the DMRG wavefunction as an extension of the 2-RDM algorithm of Zgid et al. [J. Chem. Phys. 128, 144115 (2008)] and Chan et al. [J. Chem. Phys. 128, 144117 (2008)]. The performance of the extended DMRG-CASPT2 approach was examined for large-scale multireference systems, such as low-lying excited states of long-chain polyenes and isomerization potential of {[Cu(NH3)3]2O2}(2+).

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