Cumulant Approximated Second-Order Perturbation Theory Based on Density Matrix Renormalization Group for Transition Metal Complexes: A Benchmark Study

Q. M. Phung, S. Wouters, K. Pierloot
Journal of Chemical Theory and Computation
12 (9), 4352–4361


The complete active space second-order perturbation theory (CASPT2) can be extended to larger active spaces by using the density matrix renormalization group (DMRG) as solver. Two variants are commonly used: the costly DMRG-CASPT2 with exact 4-particle reduced density matrix (4-RDM) and the cheaper DMRG-cu(4)-CASPT2 in which the 4-cumulant is discarded. To assess the accuracy and limitations of the latter variant DMRG-cu(4)-CASPT2 we study the spin state energetics of iron porphyrin Fe(P) and its model compound FeL2, a model for the active center of NiFe hydrogenase, and manganese-oxo porphyrin MnO(P)+; a series of excited states of chromium hexacarbonyl Cr(CO)6; and the interconversion of two Cu2O22+ isomers. Our results clearly show that PT2 on top of DMRG is essential in order to obtain quantitative results for transition metal complexes. Good results were obtained with DMRG-cu(4)-CASPT2 as compared to full CASPT2 and DMRG-CASPT2 in calculations with small and medium-sized active spaces. In calculations with large-sized active spaces (~ 30 active orbitals), the performance of DMRG-cu(4)-CASPT2 is less impressive due to the errors originating from both the finite number of renormalized states m and the 4-RDM approximation.