Extended multi-configuration quasi-degenerate perturbation theory: The new approach to multi-state multi-reference perturbation theory

Abstract

The distinctive desirable features, both mathematically and physically meaningful, for all partially contracted multi-state multi-reference perturbation theories (MS-MR-PT) are explicitly formulated. The original approach to MS-MR-PT theory, called extended multi-configuration quasi-degenerate perturbation theory (XMCQDPT), having most, if not all, of the desirable properties is introduced. The new method is applied at the second order of perturbation theory (XMCQDPT2) to the 1(1)A(')-2(1)A(') conical intersection in allene molecule, the avoided crossing in LiF molecule, and the 1(1)A(1) to 2(1)A(1) electronic transition in cis-1,3-butadiene. The new theory has several advantages compared to those of well-established approaches, such as second order multi-configuration quasi-degenerate perturbation theory and multi-state-second order complete active space perturbation theory. The analysis of the prevalent approaches to the MS-MR-PT theory performed within the framework of the XMCQDPT theory unveils the origin of their common inherent problems. We describe the efficient implementation strategy that makes XMCQDPT2 an especially useful general-purpose tool in the high-level modeling of small to large molecular systems.

Internal conversion outcompetes autodetachment from resonances in the deprotonated tetracene anion continuum

“…56 Briefly, the reference active space considered the three highest energy π orbitals, the p lone pair, and all π * orbitals. That is, a (8,13) complete active space.…”

Nuclear Energy Gradients for Internally Contracted Complete Active Space Second-Order Perturbation Theory: Multistate Extensions

“…This apparent divergence reflects the fact that, when the zeroth-order energies are degenerate, the XMS procedure does not yield a unique set of reference states. However, when they are degenerate, it follows from quasi-degenerate perturbation theory 13 that the final XMS-CASPT2 energies are invariant with respect to any rotations among reference states as well. Therefore, whenever |E (0)…”

“…The XMS procedure 13,14 has recently been proposed to make the MS-CASPT2 theory invariant with respect to rotations among reference states. This invariance has been shown to be essential for accurate description of state crossings.…”

“…This invariance has been shown to be essential for accurate description of state crossings. 13,25 In XMS, the Fock operator is diagonalized within the reference configuration space,…”

“…9,10 When multiple electronic states are nearly degenerate, special care has to be taken, because errors in the state-specific approach may arise as the CASPT2 states are generally a linear combination of the CASSCF reference states and may not be accurately approximated by a single CASSCF state. The multi-state (MS) CASPT2 approach has been derived from quasi-degenerate perturbation theory based on the Bloch wave operator formalism, which mixes different CASPT2 states by forming an effective Hamiltonian and diagonalizing it to obtain the mixing coefficients, 11,12 Recently the "extended" version of MS-CASPT2 (XMS-CASPT2) has been proposed 13,14 to rectify its failure near conical intersections and avoided crossings where its potential energy surfaces are sometimes singular. The XMS-CASPT2 method introduces a rotation of the reference CASSCF states to be used in the CASPT2 theory such that the Fock operator is diagonal within the reference space and reduces to the standard MS-CASPT2 method when this rotation is set to unit.…”