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

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+).