Multireference Rayleigh–Schrödinger perturbation theory and its application

Abstract

Based on the complete active space multireference wavefunction, multireference Rayleigh–Schrödinger perturbation theory (MRSPT) is derived with the assumption that the orbital energies of active orbitals are the same as ε¯, an unknown parameter. In this work, ε¯ is optimized at the MRSPT2 level. The second and third order perturbation theories are shown numerically to be size extensive. The second order perturbation theory is exploited to compute the ground state energies of F2, AlH, HCl, and P2 and to optimize the equilibrium bond lengths and harmonic vibrational frequencies of BH, BF, P2, HF, and F2. The dissociation behaviors of NH3 and OH− have also been investigated. Comparisons with other theoretical models as well as the experimental data have been made to show advantages of the present theory.

Block Effective Hamiltonian Theory and Its Application

“…The CCSD­(T) curve however bends down to the horizontal axis with the biggest RBA value 0.84° at R C–H = 3.0 Å, which is possibly due to the poor performance of the perturbative triple correction at a relatively large bond length. This typical bending behavior of the CCSD­(T) curve was also observed previously for the ground state of the OH – molecule …”

“…Because of difficulties in treating molecular dissociations, chemical reactions, and the quasi-degenerate excited states with the single-reference perturbation theories, multireference approaches are needed. Multireference perturbation theory (MRPT) − has been proven to be a powerful method. Among them, to list a few, there are Hylleraas variational perturbation theory of Davidson et al., CASPT2 and CASPT3, multireference Møller–Plesset perturbation theory of Hirao, , the MRPT of Davidson et al, , the state-specific MRPT, ,,,, the n -electron valence perturbation theory (NVPT2 and NVPT3), MRPT of Chen, Davidson, and Iwata, , the multiconfiguration perturbation theories of Surján et al., ,, the generalized Van Vleck perturbation theory of Hoffmann et al, , the size extensive and orbital invariant MRPT of Chen et al, valence bond perturbation theory of Wu et al, , the block correlated second-order perturbation theory of Li et al, , the multireference Rayleigh–Schrödinger perturbation theory of Chen et al, and the iCIPT2 for strongly correlated electrons by Liu et al , More studies on the MRPT can also be found from refs and .…”

Investigation of Multiple-Bond Dissociation Using Brillouin–Wigner Perturbation with Improved Virtual Orbitals

“…In recent years, tremendous efforts have been made to extend the domain of application of multireference perturbation theory (MRPT) − to treat strongly correlated states that require multiple determinants for a qualitative description. Like other MR ab initio methods, the MR generalization of the perturbation theory is not obvious and a multitude of versions exist. − The development of various MRPT methods have contributed greatly to our understanding of molecular electronic spectra and other properties.…”

Simplified Treatment of Electronic Structures of the Lowest Singlet and Triplet States of Didehydropyrazines

“…A large number of successful use of the IVO-CASCI ,,− to a wide range of chemical systems has demonstrated that IVO-CASCI provides very faithful findings and estimates with low computational cost compared to the complete active space self-consistent field (CASSCF) method, although neither of the methods are efficient at capturing all of the correlation effects. In passing, it should be mentioned that since the advent of the MRPT protocol, a considerable amount of effort has been dedicated to enhancing the accuracy and efficacy of the MRPT scheme, ,,− ,− many of which have been compared in refs and . It has been exhibited that the electronic structure of diradicals can accurately be described by the spin-flip methods of Krylov and co-workers …”