Multistate Complete-Active-Space Second-Order Perturbation Theory Based on Density Matrix Renormalization Group Reference States

We
present the development of the multistate multireference second-order
perturbation theory (CASPT2) with multiroot references, which are
described using the density matrix renormalization group (DMRG) method
to handle a large active space. The multistate first-order wave functions
are expanded into the internally contracted (IC) basis of the single-state
single-reference (SS-SR) scheme, which is shown to be the most feasible
variant to use DMRG references. The feasibility of the SS-SR scheme
comes from two factors: first, it formally does not require the fourth-order
transition reduced density matrix (TRDM) and second, the computational
complexity scales linearly with the number of the reference states.
The extended multistate (XMS) treatment is further incorporated, giving
suited treatment of the zeroth-order Hamiltonian despite the fact
that the SS-SR based IC basis is not invariant with respect to the
XMS rotation. In addition, the state-specific fourth-order reduced
density matrix (RDM) is eliminated in an approximate fashion using
the cumulant reconstruction formula, as also done in the previous
state-specific DMRG-cu(4)-CASPT2 approach. The resultant method, referred
to as DMRG-cu(4)-XMS-CASPT2, uses the RDMs and TRDMs of up to third-order
provided by the DMRG calculation. The multistate potential energy
curves of the photoisomerization of diarylethene derivatives with
CAS­(26e,24o) are presented to illustrate the applicability of our
theoretical approach.