Single-State Single-Reference and Multistate Multireference Zeroth-Order Hamiltonians in MS-CASPT2 and Conical Intersections.

Multistate complete active space second-order perturbation theory (MS-CASPT2) is one of the most successful quantum chemical methods for both static and dynamical correlations in photochemistry. In the literature, there are two definitions of the zeroth-order Hamiltonian depending on the form of the one-electron operator: multistate multireference MS-CASPT2 (MS-MR-MS-CASPT2) and single-state single-reference MS-CASPT2 (SS-SR-MS-CASPT2). Here, we implement an analytical gradient and derivative coupling for SS-SR-MS-CASPT2 and test SS-SR-MS-CASPT2 against MS-MR-(X)MS-CASPT2 in optimizing the molecular geometry critical points [the most stable geometries and minimum energy conical intersections (MECIs)] of a rhodopsin protein chromophore model (PSB3) and a green fluorescent protein chromophore model. In both cases, the MECIs in MS-MR-XMS-CASPT2 tend to have bridge hydrogen bonds that are more out-of-plane than those in SS-SR-MS-CASPT2, and for PSB3, the topology of potential energy surfaces (PESs) near the conical intersections is different. This result implies that caution is needed in analyzing the simulation results with different zeroth-order Hamiltonians and state-averaging schemes. The MS-MR-XMS-CASPT2 theory yields smooth PESs near the MECIs in all the tested cases, while the SS-SR-MS-CASPT2 theory does not. Therefore, we recommend using MS-MR-XMS-CASPT2 in conical intersection simulations, which require smooth PESs.