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. WIREs Comput Mol Sci 2016, 6:266–291. doi: 10.1002/wcms.1248This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods