Abstract
We present in this paper two new versions of Rayleigh-Schr¨odinger (RS) and the Brillouin-Wigner (BW) state-specific multi-reference perturbative theories (SSMRPT) which stem from our state-specific multi-reference coupled-cluster formalism (SS-MRCC), developed with a complete active space (CAS). They are manifestly sizeextensive and are designed to avoid intruders. The combining coefficients cμ for the model functions φμ are completely relaxed and are obtained by diagonalizing an effective operator in the model space, one root of which is the target eigenvalue of interest. By invoking suitable partitioning of the hamiltonian, very convenient perturbative versions of the formalism in both the RS and the BW forms are developed for the second order energy. The unperturbed hamiltonians for these theories can be chosen to be of both Mφller-Plesset (MP) and Epstein-Nesbet (EN) type. However, we choose the corresponding Fock operator fμ for each model function φμ, whose diagonal elements are used to define the unperturbed hamiltonian in the MP partition. In the EN partition, we additionally include all the diagonal direct and exchange ladders. Our SS-MRPT thus utilizes a multi-partitioning strategy. Illustrative numerical applications are presented for potential energy surfaces (PES) of the ground (1Σ+) and the first delta (1Δ) states of CH+ which possess pronounced multi-reference character. Comparison of the results with the corresponding full CI values indicates the efficacy of our formalisms.
Highlights
One of the prime challenges in quantum chemistry lies in the development of formally rigorous models capable of reliable computations of potential energy surfaces (PES) of systems of arbitrary complexity and generality
The effective hamiltonian based multi-reference (MR) methods [1,2,3,4] are often unsuitable for PES studies due to the perennial intruder state problem [5], though the intruders could be bypassed to a large extent at certain specific geometries by utilizing an incomplete model spaces (IMS) [6,7,8]
We demonstrated that the state-specific multi-reference coupledcluster (SS-MRCC) theory is quite rich in its structure in that it embodies in a natural manner some underlying Rayleigh-Schrodinger (RS) and Brillouin-Wigner (BW) type perturbation expansion with robust denominators, depending on the expansion strategy
Summary
One of the prime challenges in quantum chemistry lies in the development of formally rigorous models capable of reliable computations of potential energy surfaces (PES) of systems of arbitrary complexity and generality. We have recently suggested a specific way to generate such state-specific multireference perturbation theories (SS-MRPT) [12] and demonstrated their usefulness with some preliminary applications [11, 13] This mode of formulation has the limitation that only a very specific partitioning of the hamiltonian H could be supported for a consistent development. Coupled-cluster based IH formalisms [22,23,24], which are size-extensive, were developed Another approach to circumvent the difficulty of intruders is to abandon the idea of partitioning of the CAS into primary and secondary subspaces, and define a wave operator which acts on just one reference function, which is a linear combination of all the functions of the CAS.
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