Exploration of interlacing and avoided crossings in a manifold of potential energy curves by a Unitary Group Adapted State Specific Multi-Reference Perturbation Theory (UGA-SSMRPT)

TL;DR

This paper analyzes the UGA-SSMRPT2 method's effectiveness in describing avoided crossings and interlacing in potential energy curves, introducing a rigorous 'projection' version and benchmarking its accuracy against established methods.

Contribution

It introduces a new rigorous 'projection' version of UGA-SSMRPT2 and compares its performance with earlier formulations for complex electronic state interactions.

Findings

Both versions of UGA-SSMRPT2 show high accuracy in various crossing scenarios.

The 'projection' version provides a more rigorous theoretical foundation.

Benchmarking against IC-MRCISD+Q confirms the method's reliability.

Abstract

The Unitary Group Adapted State-Specific Multi-Reference Perturbation Theory (UGA-SSMRPT2) developed by Mukherjee et al [J. Comput. Chem. 2015, 36, 670] has successfully realized the goal of studying bond dissociation in a numerically stable, spin-preserving and size-consistent manner. In this paper, we explore and analyse the UGA-SSMRPT2 theory in the description of avoided crossings and interlacing between a manifold of states belonging to the same space-spin symmetry. In a state-specific formalism, since each state is an eigenstate of its own effective operator, to include the information of the other states requires the theory to be sufficiently accurate. Three different aspects of UGA-SSMRPT2 have been studied: (a) We introduce and develop the most rigorous version of UGA-SSMRPT2 which emerges from the rigorous version of UGA-SSMRCC utilizing a linearly independent virtual manifold; we call this the 'projection' version of UGA-SSMRPT2 denoted as UGA-SSMRPT2 Scheme P. We compare and contrast this approach with our earlier formulation that used extra sufficiency conditions via amplitude equations, which we will denote as UGA-SSMRPT2 Scheme A. (b) We present the results for a variety of electronic states of a set of molecules which display the striking accuracy of both the two versions of UGA-SSMRPT2; with respect to three different situations involving weakly avoided crossings, moderate/strongly avoided crossings and interlacing in a manifold of PECs of same symmetry. Accuracy of our results has been benchmarked against IC-MRCISD+Q. (c) For weakly avoided crossing between states displaying differently charged sectors in the asymptotes, the insufficient inclusion of state-specific orbital relaxation in a second order perturbative theory might lead to an artefact of double crossing between the pair of PECs.