State‐specific multireference perturbation theory: development and present status

Abstract

The state-specific multireference perturbation theory (SSMRPT), which provides one state at a time may now gradually become a new useful ab initio tool for studying electronic states with strong configurational quasidegeneracy owing primarily to its suitability toward numerical implementation in the presence of intruders and also to a great extent for its firm theoretical construct and the scope of a systematic and hierarchical improvement. The method works with a complete active space, and treats each of the model space functions on the same footing by exploiting Jeziorski-Monkhorst parametrization of the wavefunction. The SSMRPT is size-extensive and size-consistent (with the orbitals localized). The real challenge remains in developing MRPT methods capable of maintaining explicit size-extensivity and avoiding intruders over a vast range of molecular geometries. Recently developed relativistic SSMRPT for the four-component spinors is very promising to describe the near-degenerate states of molecules containing heavy atoms. The analysis of the formal aspects and practical utility of the SSMRPT method vis-à-vis the other MRPT formalisms that bear kinship with the SSMRPT formulation is also presented. Illustrative results show high accuracy of the SSMRPT method in describing quasidegenerate situations such as those appearing when one or more covalent bonds in the molecule become stretched or broken. While actively pursuing SSMRPT method, it became apparent to us that this method encounters two major limitations: (1) the scaling of the computational cost with respect to the number of active orbitals and (2) the lack of invariance of the energy with respect to a unitary transformation of the active orbitals. The future will tell whether the SSMRPT method will be able to acquire the same faith as other widely used single-root MRPT methods.

Driven similarity renormalization group: Third-order multireference perturbation theory

“…In this study we also develop relaxed DSRG-MRPT2 and MRPT3 approaches in which the reference wave function is optimized under the effects of dynamic electron correlation. Most statespecific MRPT2 approaches, including CASPT2 and NEVPT2, do not account for reference relaxation effects, with the notable exception of Mukherjee's state-specific MRPT2, [65][66][67][68][69] generalized Van Vleck PT2, [70][71][72][73] and multiconfigurational PT2. 68,74,75 We begin our discussion of DSRG-MRPT3 by providing a brief overview of the general MR-DSRG ansatz in Sec.…”

Multireference perturbation theory with improved virtual orbitals for radicals: More degeneracies, more problems

“…Reviews of various MRPT methods can be found in Ref. . It is known that they have different strengths and weaknesses.…”

“…Designing methods which can accurately treat MR‐systems at an affordable computational price present a challenge to the practitioners of electronic structure theory . Various workers in the realm of electronic structure theory have suggested different approaches to address these problems .…”

Excitation Energies of Canonical Nucleobases Computed by Multiconfigurational Perturbation Theories

“…In addition to the well‐established MRPT2 methods, there has been recent development of new emerging approaches to add dynamic correlation effects to multiconfigurational wave functions. Among them are the Van Vleck perturbation theory , the canonical transformation theory , the GASPT2 (second‐order perturbation theory for generalized active‐space self‐consistent‐field wave functions) , the SplitGAS and new developments of state‐specific MRPT . In addition, efficient approximations have been introduced to reduce the computational cost and provide favorable scalability, for example the frozen natural orbital complete active‐space second‐order perturbation theory method (FNO‐CASPT2) and the domain‐based local pair natural orbital theory applied to the NEVPT2 method .…”