Applicability of multi‐reference many‐body perturbation theory to the determination of potential energy surfaces: A model study

Abstract

The recently written cI-based multi-reference many-body perturbation theory (MR-MBPT) program package is exploited to study a simple ab initio minimum basis set model involving four hydrogen atoms in a rectangular configuration. This model was examined earlier by several authors using both coupled cluster (cc) and finite-order MBPT approaches. Here we present the MR-MBPT results up to the 50th order and examine the effect of various shifting techniques on the convergence behavior of this approach. It is shown that in contrast with cc methods, both single and MR finite-order MBPT potential energy calculations are plagued with convergency and intruder state problems, which can be particularly severe when the latter approach is employed for nondegenerate situations.

Appendix to “Studies in Perturbation Theory”: The Problem of Partitioning

“…Level shift parameters have been applied in a number of works with various purposes [26,[88][89][90][91][92][93], among which the removal of (quasi)degeneracies from the zero order spectrum is an important issue.…”

“…For the perturbation of wave functions consisting of several Slaterdeterminants various MRPT approaches have been proposed [21][22][23][24][25][26][27][28][29][30][31][32][33]. We discuss here the one developed in our laboratory [147] which was termed multi-configurational perturbation theory (MCPT).…”

“…To name a few, we do not know the necessary and sufficient conditions for the convergence of the PT series, we do not have a general and robust method to deal with the case of quasidegenerate zero order, and there is no established method to fix the best partitioning. In addition, in many-body PT (MBPT), the handling of multi-reference zero order state(s) is an open issue [21][22][23][24][25][26][27][28][29][30][31][32][33], just like a clear and general theory to correct coupled-cluster type wave functions perturbatively [34][35][36][37][38][39][40][41][42][43][44][45]. The handling of symmetry in PT can also be a difficult task, especially when the zero order problem has lower symmetry than the perturbed problem, a situation one meets e.g.…”

New classes of non-iterative energy corrections to multi-reference coupled-cluster energies

“…As in the single-reference case, where the appropriate use of higher-than-two-body clusters helps to extend the applicability of the single-reference CC approximations to bond breaking and some types of quasi-degenerate and excited states that cannot be handled by the basic CCSD (CC singles and doubles) approximation [8,[60][61][62], the incorporation of higher-than-twobody clusters in the SUMRCC method may help to reduce the severity of the intruder-state problem in 2426 K. Kowalski and P. Piecuch SUMRCCSD calculations, while improving the description of dynamic correlation effects. Historically, the intruder-state problem was first discovered in the context of MRMBPT calculations, causing the divergent behaviour of the MRMBPT series when the model spaces were inadequate for the electronic states under consideration [143][144][145][146][147][148]. In the context of the SUMRCC calculations, the intruder-state problem has been shown to be closely related to the intrudersolution problem [131] and the existence of multiple [121,131] and singular [114,[120][121][122][123]131] solutions of SUMRCCSD equations.…”

Comparison of the open-shell state-universal and state-selective coupled-cluster theories: H4 and H8 models

“…An attractive feature of these models, in addition to their simplicity, is the fact that the degree of quasidegeneracy can be continuously varied using a single structural parameter and the dissociation of one or several single bonds can be modeled in this way. Consequently, these models were extensively studied using various manybody theories, including MR CC methods, namely the SU CCSD, [25][26][27][28][29][30] VU CCSD 31 and SR CC theories involving higher order excitations ͑i.e., the CCSDT, CCSDTQ or MR CCSD methods relying on the SR formulation͒, 30,32,33 as well as the MR perturbation theory 34 and various approximate SR CC theories. 22,23,35 Although no such quasidegeneracy effects arise in the low-lying excited states of these systems, our interest in them was aroused by the availability of the spin orbital formalism based SU CCSD results 29,30 and by their relatively poor agreement with the exact FCI results.…”