Selected configuration interaction with truncation energy error and application to the Ne atom

Abstract

Selected configuration interaction ͑SCI͒ for atomic and molecular electronic structure calculations is reformulated in a general framework encompassing all CI methods. The linked cluster expansion is used as an intermediate device to approximate CI coefficients B K of disconnected configurations ͑those that can be expressed as products of combinations of singly and doubly excited ones͒ in terms of CI coefficients of lower-excited configurations where each K is a linear combination of configuration-state-functions ͑CSFs͒ over all degenerate elements of K. Disconnected configurations up to sextuply excited ones are selected by Brown's energy formula,with B K determined from coefficients of singly and doubly excited configurations. The truncation energy error from disconnected configurations, ⌬E dis , is approximated by the sum of ⌬E K s of all discarded Ks. The remaining ͑connected͒ configurations are selected by thresholds based on natural orbital concepts. Given a model CI space M, a usual upper bound E S is computed by CI in a selected space S, and E M = E S + ⌬E dis + ␦E, where ␦E is a residual error which can be calculated by well-defined sensitivity analyses. An SCI calculation on Ne ground state featuring 1077 orbitals is presented. Convergence to within near spectroscopic accuracy ͑0.5 cm −1 ͒ is achieved in a model space M of 1.4ϫ 10 9 CSFs ͑1.1ϫ 10 12 determinants͒ containing up to quadruply excited CSFs. Accurate energy contributions of quintuples and sextuples in a model space of 6.5ϫ 10 12 CSFs are obtained. The impact of SCI on various orbital methods is discussed. Since ⌬E dis can readily be calculated for very large basis sets without the need of a CI calculation, it can be used to estimate the orbital basis incompleteness error. A method for precise and efficient evaluation of E S is taken up in a companion paper.

Accurate ab initio potential energy curve of F2. I. Nonrelativistic full valence configuration interaction energies using the correlation energy extrapolation by intrinsic scaling method

“…This would also call, however, for the use of larger basis sets and the possible accounting of smaller physical corrections such as nonadiabatic effects or spin-spin couplings. Such extensions might be revisited when new approaches to the CI problem, such as nonlinear expansions 36 or selection techniques, 32,38,64,65 are further developed. For larger systems, the use of appropriately localized molecular orbitals [146][147][148][149] should prove helpful.…”

“…In this context, the full configuration interaction ͑FCI͒ method 24,25 has as yet remained the benchmark approach because of its variational attributes. [26][27][28][29] However, while considerable strides have been made in CI methodology, [30][31][32][33][34][35][36][37][38] its excessively long configurational expansions still present the challenge of discovering the most efficiently converging reordering of its terms.…”

CI Calculations of the Ground State Ionization Potential and Electron Affinity of Aluminum

“…Disconnected congurations are those that can be expressed as products of combinations of lower excited ones, whereas connected congurations are all others [10].…”

“…where E is any pertinent energy, H K K is the diagonal matrix element which can be well approximated by the expectation value of any determinant belonging to the conguration K, and B K is an approximation to the conguration coecient associated with triple and higher excited disconnected congurations [10]. The selection of q-excited connected congurations are based on modied Brown formula [17]:…”

“…In Sect. 4, the approach of the approximate full conguration interaction (FCI) in the frame work of a priori selected conguration interaction (SCI) with its corresponding truncation energy error [10] and CI by parts CIBP [11] are presented. Results and discussion is presented in Sect.…”