Pair-correlated configuration interaction method and its approximate version for solving the electron correlation problem in molecules

Abstract

ABSTRACT:The pair-correlated configuration interaction (PCCI) method has been developed in this work to be an alternative to the traditional CI method for solving the correlation problem in closed-shell, ground-state molecules. The PCCI expansion is well defined on the localized molecular orbital description and can be truncated according to how many electron pairs are explicitly correlated (namely, the PCCI-n expansion includes all configurations up to n-pair correlation). However, PCCI-n calculations are formidable for most of chemical systems, and therefore further approximations are required. After the separated electron pair approximation is adopted, the PCCI method reduces to the simplified PCCI (SPCCI) method, which is computationally feasible for moderate molecular systems by using matrix element expressions presented in this work. We have tested the SPCCI-n method by applying it to solve the ground state of the Pariser-Parr-Pople (PPP) Hamiltonian for π-networks of a series of conjugated polyenes. The most significant features of the SPCCI-n method have been brought to light from our test calculations: (1) The SPCCI-n (n = 2, 3) method can recover more than 90% of the total ground-state correlation energy for conjugated polyenes with up to 30 π-electrons. It is far superior to the conventional configuration interaction that includes all singly and doubly excited configurations (CI-SD) method in systems with more than 6 π-electrons. (2) The SPCCI-n method works well in the moderately and strongly correlated regions but less satisfactorily in the weakly correlated domain. Finally, the size consistency error of the general SPCCI-n method is analyzed and a size-consistent coupled-cluster-like approach is proposed.

Phase diagram of the13-filled extended Hubbard model on the kagome lattice

“…II are presented the model and methods, as well as the physical quantities used to determine the phases. In particular, we briefly introduce the configuration interaction (CI) method [38][39][40][41][42][43] that we combine to an Unrestricted Hartree-Fock in order to partially bring back the correlations lost in the mean-field decoupling. Section III gives an overview of the thermodynamic limit phase diagram and a brief description of the encountered phases, emphasizing two original ones, the pinned metal droplet phase (PMD) and a spin charge density wave (SCDW).…”

A multireference configuration interaction method based on the separated electron pair wave functions

“…Once the number of orbitals for each electron pair is determined, one then minimizes the energy functional 〈Ψ SEP | H |Ψ SEP 〉 to obtain the SEP energy and orbitals. For the computational convenience, the pair function is expressed as a natural expansion20 where, {φ ui , i = 1, 2, … , n u } ( u = 1, 2, … , N ) are the natural orbitals (NOs) of electron pairs, which can be derived from a unitary transformation on a set of predetermined orthogonal LMOs {ϕ ui , i = 1, 2, … , n u } ( u = 1, 2, … , N ) 16b. In fact, the set of natural orbitals of all electron pairs are just the set of natural orbitals defined by Löwdin for the SEP wave function 21.…”

“…The natural orbitals and occupation coefficients are determined as simultaneous solutions of two interdependent sets of equations 16b, 21. The set of coupled eigenvalue equations for the coefficients is solved by an iterative procedure, and a direct energy minimization by using two‐by‐two rotations is applied to obtain the natural orbitals and the SEP energy.…”

“…Recently, we have demonstrated that the separated electron pair (SEP) wave function is a good starting point for treating the quasi‐degenerate effects in bond‐breaking processes 16. Using the SEP wave function as the reference function, we have developed two MR methods, that is, pair‐correlated configuration interaction (PCCI)16a and pair‐correlated coupled cluster (PCCC)16b alternative to traditional MR‐based methods.…”

“…Recently, we have demonstrated that the separated electron pair (SEP) wave function is a good starting point for treating the quasi‐degenerate effects in bond‐breaking processes 16. Using the SEP wave function as the reference function, we have developed two MR methods, that is, pair‐correlated configuration interaction (PCCI)16a and pair‐correlated coupled cluster (PCCC)16b alternative to traditional MR‐based methods. Based on the fact that the orbitals obtained from the optimization of the SEP wave function are reasonably like the corresponding CASSCF orbitals, in the present work we suggest a SEP‐based configuration interaction method (called the SEP‐CI in short) to replace the traditional CASSCF method for describing the ground‐state potential energy surfaces involving the breaking of one or more chemical bonds.…”