Configuration-Driven Unitary Group Approach for Generalized Van Vleck Variant Multireference Perturbation Theory

Abstract

A new, efficient, configuration-driven algorithm utilizing the unitary group approach (UGA) was developed and implemented for the generalized van Vleck perturbation theory (GVVPT) variant of multireference perturbation theory. The computational speed has been improved by 1 or 2 orders of magnitude compared to the previous implementation based on the Table-CI technique. It is shown that the reformulation is applicable to both the second-order (GVVPT2) and third-order (GVVPT3) approximations. Calculations on model problems and on a chemically realistic description of cyclobutadiene are used to illustrate the performance of the method. The calculations on cyclobutadiene, using over 2.3 billion CSFs, provide results on geometric parameters and the barrier height of the automerization reaction in good agreement with established high accuracy results.

Molecular electric dipole moments using the GVVPT2 variant of multireference perturbation theory

“…It was demonstrated that, despite the complexity of the GVVPT2 resolvent (e.g., the presence of the highly nonlinear hyperbolic tangent function) and the relaxation of the primary subspace, computationally amenable algorithms could be realized. Because the algorithm can use all of the advantages of the GVVPT2 energy calculations (e.g., macroconfiguration-and configuration-based screening and graphical unitary group approach (GUGA) evaluation of matrix elements [17]), efficient computer codes can be developed. In particular, the prototype computer code that realized the Lagrangian-based GVVPT2 dipole formalism described in this Letter was observed to require no more than 2.5 times the amount of computer time than does the GVVPT2 energy code; additional optimizations can be expected.…”

“…Since the GVVPT2 method [3] and its high performance implementation [17] have been described in previous publications, here only salient features critical to the evaluation of the electric dipole are reviewed. In GVVPT2, the configuration space, in which the N Plowest electronic states are sought, is divided into two subspaces: a model MCSCF subspace, L M (dim L M > N P ), specified by a given set of reference electron configurations, and an external subspace, L Q , whose configurations are related to the reference ones through single and double excitations (N.B.…”

Taming the Electronic Structure of Diradicals through the Window of Computationally Cost Effective Multireference Perturbation Theory

“…In order to avoid higher-order reduced density matrices ( and also to simplify the analytical energy gradients), the partially contracted scheme has also been proposed by Werner and coworkers for CASPT2 31,68,69 . Another interesting development is the generalized van Vleck PT (GVVPT) of Hoffmann and coworkers 70,71 . They showed the way to tackle large active spaces via the use of macroconfigurations and also discusses very nicely how to avoid the intruder problem.…”

State-specific complete active space multireference Møller–Plesset perturbation approach for multireference situations: illustrating the bond breaking in hydrogen halides

“…3. The R e , x e , x e x e , B e , D e and D 0 values we obtain for the X 1 R þ HF are of 0.9175 Å , 4133.79, 88, 20.77, 0.00210 cm -1 , and 158.88 (kcal/mol) at the CBS 16 15 In this article, authors study the difference between the various direct perturbation theory and Pauli perturbation method for the HX (X = F,Cl, Br, and I) molecules in order to investigate the relative importance of relativistic effects, higher-order electron correlation effects, and remaining basis sets effects. 16 To obtain the results at CBS limit, we have used the same scheme as done by Hirata et al [68].…”

“…From the previously published data due to Klopper et al [92] 15 (computed at CCSD(T) level including a first-order relativistic correction obtained from an analytical evaluation of the first-order direct perturbation energy at the CCSD level in conjunction with large one-particle basis sets), it is found that the overall accuracy of the spectroscopic constants for the HF system is clearly dominated by electron correlation and basis set truncation effects, while the relativistic effects are of minor importance. Although we observe that the shapes of PESs generated via CASS-CF(2,2) and SS-MRMPPT/CAS(2,2) methods are very similar, as shown in the table, the dynamical correlation effects on the spectroscopic properties of HF are noticeable.…”