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

Selected configuration interaction (SCI) 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 ones) in terms of CI coefficients of lower-excited configurations where each K is a linear combination of configuration-state-functions (CSFs) over all degenerate elements of K. Disconnected configurations up to sextuply excited ones are selected by Brown's energy formula, Delta E-K=(E-H-KK)B-K(2)/(1-B-K(2)), with B-K determined from coefficients of singly and doubly excited configurations. The truncation energy error from disconnected configurations, Delta E-dis, is approximated by the sum of Delta E(K)s of all discarded Ks. The remaining (connected) 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+Delta E-dis+delta E, where delta 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 1.4x10(9) CSFs (1.1x10(12) determinants) containing up to quadruply excited CSFs. Accurate energy contributions of quintuples and sextuples in a model space of 6.5x10(12) CSFs are obtained. The impact of SCI on various orbital methods is discussed. Since Delta 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. (c) 2006 American Institute of Physics.