Assessment of Perturbative Explicitly Correlated Methods for Prototypes of Multiconfiguration Electronic Structure.

The performance of the [2]S and [2]R12 universal perturbative corrections that account for oneand many-body basis set errors of singleand multiconfiguration electronic structure methods is assessed. A new formulation of the [2]R12 methods is used in which only strongly occupied orbitals are correlated, making the approach more amenable for larger computations. Three model problems are considered using the aug-cc-pVXZ (X = D,T,Q) basis sets: the electron affinity of fluorine atom, a conformational analysis of two Si2H4 structures, and a description of the potential energy surfaces of the X Σg, a Πu, b Σg , and A Πu states of C2. In general, the [2]R12 and [2]S corrections enhance energy convergence for conventional multireference configuration interaction (MRCI) and multireference perturbation theory (MRMP2) calculations compared to their complete basis set limits. For the electron affinity of the F atom, [2]R12 electron affinities are within 0.001 eV of the experimental value. The [2]R12 conformer relative energy error for Si2H4 is less than 0.1 kcal/mol compared to the complete basis set limit. The C2 potential energy surfaces show nonparallelity errors that are within 0.7 kcal/mol compared to the complete basis set limit. The perturbative nature of the [2]R12 and [2]S methods facilitates the development of a straightforward text-based data exchange standard that connects an electronic structure code that can produce a two-particle density matrix with a code that computes the corrections. This data exchange standard was used to implement the interface between the GAMESS MRCI and MRMP2 codes and the MPQC [2]R12 and [2]S capabilities. ■ INTRODUCTION Explicitly correlated R12/F12 methods are an effective approach to reduce the basis set incompleteness error (BSIE) of the conventional (i.e., based on Slater determinants) ab initio many-body methods. The primary source of the BSIE is the slow convergence of the atomic basis set within Slater determinant based expansions near the singularities of the interelectronic potential. Although Slater determinants are computationally convenient because of factorization of n-electron matrix elements (Slater−Condon rules), they describe an interelectronic potential that is smooth everywhere, whereas the exact wave functions are known to have cusps wherever the interelectronic potential is singular. When electrons approach one another, the exact wave function is linear in the interparticle distance (rij) with the coefficient dependent on how the spins of the electrons are coupled: γ ∂Ψ̂ ∂ = Ψ = = r r ( / ) ( 0) ij r ij 0 ij (1) where Ψ̂ is the spherically averaged wave function Ψ about the point of coalescence (rij = 0), and γ = 1/2 for a singlet spin coupled electron pair. The description of the cusp in terms of Slater determinants requires the use of high angular momentum basis functions that causes a steep rise of the computational expense with an increase in the accuracy. An alternative is to augment the Slater determinants with basis functions that describe the cusp directly in terms of the interelectronic distances, rij, as is done in R12 methods. All R12 methods involve n-electron (n > 1) basis functions that depend on the correlation factor, f(rij), a function of the interelectronic coordinate rij that is used to capture the essential shape of the wave function at short rij. The threeand fourelectron integrals that appear in R12 methods are handled approximately by factorization into two-electron integrals only. Robust R12 methods for the single-configurational ground-state wave functions, such as the coupled-cluster singles and doubles (CCSD) approach, have become well-established in the past decade. However, R12 methods for multireference (MR) wave functions have not been as thoroughly tested; although several such methods have been introduced, as discussed in the following paragraphs. A better understanding of the strengths and weaknesses of explicitly correlated MR methods is important since MR wave functions are essential for reliable descriptions of chemical species that exhibit near degeneracies which occur in the vicinity of conical intersections, in bond breaking, in free radical chemistry, in electronic excited states, and in unsaturated transition metal compounds. An early adaptation of single reference R12 methodology to MR wave functions (MR-R12) resulted in the linear R12 multireference configuration interaction (R12-MRCI) method and the linear multireference averaged coupled-pair functional (R12-ACPF) method. These methods augmented the conventional MRCI and ACPF expansions with many terms that Received: July 29, 2013 Published: November 12, 2013 Article