Highly correlated configuration interaction calculations on water with large orbital bases

Abstract

A priori selected configuration interaction (SCI) with truncation energy error [C. F. Bunge, J. Chem. Phys. 125, 014107 (2006)] and CI by parts [C. F. Bunge and R. Carbó-Dorca, J. Chem. Phys. 125, 014108 (2006)] are used to approximate the total nonrelativistic electronic ground state energy of water at fixed experimental geometry with CI up to sextuple excitations. Correlation-consistent polarized core-valence basis sets (cc-pCVnZ) up to sextuple zeta and augmented correlation-consistent polarized core-valence basis sets (aug-cc-pCVnZ) up to quintuple zeta quality are employed. Truncation energy errors range between less than 1 μhartree, and 100 μhartree for the largest orbital set. Coupled cluster CCSD and CCSD(T) calculations are also obtained for comparison. Our best upper bound, -76.4343 hartree, obtained by SCI with up to sextuple excitations with a cc-pCV6Z basis recovers more than 98.8% of the correlation energy of the system, and it is only about 3 kcal/mol above the "experimental" value. Despite that the present energy upper bounds are far below all previous ones, comparatively large dispersion errors in the determination of the extrapolated energies to the complete basis set do not allow to determine a reliable estimation of the full CI energy with an accuracy better than 0.6 mhartree (0.4 kcal/mol).

Communication: Toward an improved control of the fixed-node error in quantum Monte Carlo: The case of the water molecule

“…Results are presented in Table I and compared to the recent benchmark CI calculations of Almora-Dìaz including up to sextuple excitations. [27] As we shall see below, truncated versions of these one-and two milliondeterminant CIPSI expansions will actually be used in DMC, results are thus presented for these shorter expansions. A remarkable point is the high efficiency of CIPSI in obtaining accurate CI expansion with a small number of determinants.…”

“…Number of determinants and corresponding variational energies for CIPSI expansions used in DMC for each cc-pCVnZ (n=2 to 5) basis set. Last column: Deviations of the variational energy to the best FCI estimates of Almora-Dìaz[27]. Energies in atomic units.…”

Seniority based energy renormalization group (Ω-ERG) approach in quantum chemistry: Initial formulation and application to potential energy surfaces

“…Since FCI approach is associated with exponential computational scaling, much research has been focused on the development of less computationally demanding ab initio methods for strongly correlated molecular systems. Examples of such methods include: truncated (limited) CI methods and CI methods with various extrapolations [63][64][65][66][67][68][69][70][71][72][73][74], multireference coupled cluster (CC) methods [75][76][77][78][79][80], iterative variational approaches [81][82][83][84][85][86], various methods based on density-matrices [87][88][89][90], matrix product states (MPS) and tensor product states (TPS)-based approaches [91][92][93][94][95] which include popular density-matrix renormalization group (DMRG) method [96][97][98][99][100][101][102][103][104][105][106][107]…”

The Integral Screened Configuration Interaction Method

“…Furthermore there is still a great interest in the full configuration interaction (FCI) for benchmarking methods [5]. The interest in tractable FCI methods for slightly larger systems has lead to stochastic CI methods, like diffusion Quantum Monte Carlo (QMC) [27,28], configuration selecting CI methods [29][30][31][32] where higher excitations are selected based on the size of lower excitations or the multifacet graphically contracted function method [33,34]. Another interesting new CI development is the configuration interaction generalized singles and doubles (CIGSD) by Nakatsuji [35,36] which in principle is exact but unfortunately suffers from divergences of the integrals [37].…”