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

Abstract

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. ̂= ̂̂̂+ ̂̂ĤPf P Q f Q (0) SA SA(2)

Analytic gradients for restricted active space second-order perturbation theory (RASPT2)

“…In addition, the use of the state-averaged density matrix in the Fock matrix may cause an observable difference. 47,48 Nevertheless, the present numerical result demonstrates that geometry optimizations with the (20e,20o) active space can be performed using MRPT, and the predicted gap is rather reasonable.…”

Extended Dynamically Weighted CASPT2: The Best of Two Worlds

“…From a theoretical standpoint, XDW-CASPT2 corresponds to a new and somewhat sophisticated partitioning of the Hamiltonian, thus retaining the underlying structure of the parent theory. Recently, an analogous attempt to find a zeroth-order Hamiltonian that coincides with the canonical MS-CASPT2 one, but that at the same time is invariant as in XMS-CASPT2 was carried out by Park 25 . XDW-CASPT2 also shares some similarities with the recently introduced dynamically weighted driven similarity renormalization group (DW-DSRG) 26 as well as the dynamically weighted complete active space self-consisted field method.…”

“…For a thorough comparison between them in the context of CASPT2 see e.g. the recent work by Park25 .…”

Analytical Gradient Theory for Strongly Contracted (SC) and Partially Contracted (PC) N-Electron Valence State Perturbation Theory (NEVPT2)

“…For CASPT2, the nuclear gradient theory was first formulated for the partially internally contracted variant, 25,37,38 and then it was expanded to the fully internally contracted variant using the automatic code generation technique. [39][40][41][42][43][44] Because of these developments, carrying out geometry optimizations and molecular dynamics (MD) simulations using CASPT2 is now routine and has moderate computational costs. 41,[45][46][47] Other uncontracted multireference perturbation methods, such as MCQDPT2 and GVVPT2, have algorithms for nuclear gradient as well.…”