Multireference configuration interaction theory using cumulant reconstruction with internal contraction of density matrix renormalization group wave function

We report development of the multireference configuration interaction (MRCI) method that can use active space scalable to much larger size references than has previously been possible. The recent development of the density matrix renormalization group (DMRG) method in multireference quantum chemistry offers the ability to describe static correlation in a large active space. The present MRCI method provides a critical correction to the DMRG reference by including high-level dynamic correlation through the CI treatment. When the DMRG and MRCI theories are combined (DMRG-MRCI), the full internal contraction of the reference in the MRCI ansatz, including contraction of semi-internal states, plays a central role. However, it is thought to involve formidable complexity because of the presence of the five-particle rank reduced-density matrix (RDM) in the Hamiltonian matrix elements. To address this complexity, we express the Hamiltonian matrix using commutators, which allows the five-particle rank RDM to be canceled out without any approximation. Then we introduce an approximation to the four-particle rank RDM by using a cumulant reconstruction from lower-particle rank RDMs. A computer-aided approach is employed to derive the exceedingly complex equations of the MRCI in tensor-contracted form and to implement them into an efficient parallel computer code. This approach extends to the size-consistency-corrected variants of MRCI, such as the MRCI+Q, MR-ACPF, and MR-AQCC methods. We demonstrate the capability of the DMRG-MRCI method in several benchmark applications, including the evaluation of single-triplet gap of free-base porphyrin using 24 active orbitals.