Symmetric dissociation of the water molecule with truncation energy error. A benchmark study.

We use selected configuration interaction with truncation energy error (SCI-TEE) and CI by parts (CIBP) to study the symmetric dissociation of the water molecule with Roos' triple-ζ double polarization basis set and with the Dunning cc-pVTZ basis. The calculations comprise CISDTQ (CI-4x) through CI-8x for H2O at its equilibrium geometry (Req) and up to fifteen times Req. With the Dunning basis our SCI-TEE-8x energies differ from full CI by less than 0.01 mHartree (0.006 kcal mol-1) at all O-H distances, representing the best upper bounds for this system outside Req. We compare our results with those of other relevant ab initio methods finding good agreement with recent DMRG calculations. The non-parallelity error (NPE) for SCI-TEE-6x remains stable below 0.1 mHartree when moving from the Roos to the Dunning orbitals. For the present system, CBS energy errors at the experimental equilibrium geometry and at dissociation can accurately be evaluated as the difference between non-relativistic total electronic energies taken from the literature, and our SCI-TEE-8x energies obtained with Dunning's or Roos' orbitals. In both cases, the difference between CBS energy errors at the equilibrium geometry and dissociation is not smaller than 10 mH, showing that chemically accurate NPE values do not guarantee a chemically accurate potential energy surface.

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 1.4 x 10(9) CSFs (1.1 x 10(12) determinants) containing up to quadruply excited CSFs. Accurate energy contributions of quintuples and sextuples in a model space of 6.5 x 10(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.

Select-divide-and-conquer method for large-scale configuration interaction.

A select-divide-and-conquer variational method to approximate configuration interaction (CI) is presented. Given an orthonormal set made up of occupied orbitals (Hartree-Fock or similar) and suitable correlation orbitals (natural or localized orbitals), a large N-electron target space S is split into subspaces S0,S1,S2,...,S(R). S0, of dimension d0, contains all configurations K with attributes (energy contributions, etc.) above thresholds tao 0 identical with{Tao 0(egy),Tao 0(etc.)}; the CI coefficients in S0 remain always free to vary. S1 accommodates Ks with attributes above tao 1 < or = tao 0. An eigenproblem of dimension d0 + d1 for S0 + S1 is solved first, after which the last d1 rows and columns are contracted into a single row and column, thus freezing the last d1 CI coefficients hereinafter. The process is repeated with successive Sj(j > or = 2) chosen so that corresponding CI matrices fit random access memory (RAM). Davidson's eigensolver is used R times. The final energy eigenvalue (lowest or excited one) is always above the corresponding exact eigenvalue in S. Threshold values {tao j;j = 0,1,2,...,R} regulate accuracy; for large-dimensional S, high accuracy requires S0 + S1 to be solved outside RAM. From there on, however, usually a few Davidson iterations in RAM are needed for each step, so that Hamiltonian matrix-element evaluation becomes rate determining. One mu hartree accuracy is achieved for an eigenproblem of order 24 x 10(6), involving 1.2 x 10(12) nonzero matrix elements, and 8.4 x 10(9) Slater determinants.