Jeppe Olsen

BASIS-SET CONVERGENCE IN CORRELATED CALCULATIONS ON NE, N2, AND H2O

Valence and all-electron correlation energies of Ne, N2, and H2O at fixed experimental geometries are computed at the levels of second-order perturbation theory (MP2) and coupled cluster theory with singles and doubles excitations (CCSD), and singles and doubles excitations with a perturbative triples correction (CCSD(T)). Correlation-consistent polarized valence and core-valence basis sets up to sextuple zeta quality are employed. Guided by basis-set limits established by rij-dependent methods, a number of extrapolation schemes for use with the correlation-consistent basis sets are investigated. Among the schemes considered here, a linear least-squares procedure applied to the quintuple and sextuple zeta results yields the most accurate extrapolations.

Determinant based configuration interaction algorithms for complete and restricted configuration interaction spaces

A restricted active space (RAS) wave function is introduced, which encompasses many commonly used restricted CI expansions. A highly vectorized algorithm is developed for full CI and other RAS calculations. The algorithm is based on Slater determinants expressed as products of alphastrings and betastrings and lends itself to a matrix indexing C(Iα, Iβ ) of the CI vector. The major features are: (1) The intermediate summation over determinants is replaced by two intermediate summations over strings, the number of which is only the square root of the number of determinants. (2) Intermediate summations over strings outside the RAS CI space is avoided and RAS calculations are therefore almost as efficient as full CI calculations with the same number of determinants. (3) An additional simplification is devised for MS =0 states, halving the number of operations. For a case with all single and double replacements out from 415 206 Slater determinants yielding 1 136 838 Slater determinants each CI iteration takes ...

Passing the one-billion limit in full configuration-interaction (FCI) calculations

Abstract Full configuration-interaction calculations have been carried out using more than one-billion determinants. Such large eigenvalue calculations are possible because of advances in the direct CI technology and in the iterative technique used to solve the eigenvalue equations. The CPU time per direct CI iteration varies approximately linearly with the dimension of the matrix from one million to more than one billion. One direct CI iteration is found to take about 1.2-1.4 min per million determinants on an IBM 3090/VF.

The prediction of molecular equilibrium structures by the standard electronic wave functions

A systematic investigation has been carried out of the accuracy of molecular equilibrium structures of 19 small closed-shell molecules containing first-row atoms as predicted by the following standard electronic ab initio models: Hartree–Fock (HF) theory, Mo/ller–Plesset theory to second, third, and fourth orders (MP2, MP3, and MP4), coupled-cluster singles and doubles (CCSD) theory; CCSD theory with perturbational triples corrections [CCSD(T)], and the configuration-interaction singles and doubles (CISD) model. For all models, calculations were carried out using the correlation-consistent polarized valence double-zeta (cc-pVDZ) basis, the correlation-consistent polarized valence triple-zeta (cc-pVTZ) basis, and the correlation-consistent polarized valence quadruple-zeta (cc-pVQZ) basis. Improvements in the basis sets shorten the bond distances at all levels. Going from cc-pVDZ to cc-pVTZ, bond distances are on the average reduced by 0.8 pm at the Hartree–Fock level and by 1.6 pm at the correlated levels....

EXCITATION ENERGIES OF H2O, N2 AND C2 IN FULL CONFIGURATION INTERACTION AND COUPLED CLUSTER THEORY

Abstract Singlet excitation energies of H2O, N2 and C2 have been calculated in full configuration interaction (FCI) and in the coupled cluster model hierarchy CCS, CC2, CCSD and CC3. Excitation energies are improved at each level in the coupled cluster hierarchy, with a decrease in the error compared to FCI of about a factor of three at each level. This decrease is in accordance with the fact that the excitations in CCS, CC2, CCSD and CC3 are correct through higher and higher order in the fluctuation potential, and that more and more completer cluster treatments are used. Non-iterative triples corrections to the CCSD excitation energies are compared with the iterative triples models CC3 and FCI. The CCSDR(3) approach recovers the major part of the correlation improvement obtained in the CC3 model.

Full configuration–interaction and state of the art correlation calculations on water in a valence double‐zeta basis with polarization functions

Using a valence double‐zeta polarization basis, full configuration–interaction (FCI) calculations are carried out on water at its equilibrium geometry and at geometries where the OH bond lengths are stretched until dissociation. At the same geometries and with the same basis set configuration interaction calculations at excitation levels up to hextuples, multireference singles doubles configuration interaction calculations, coupled cluster calculations at excitation levels up to quadruples, Mo/ller–Plesset perturbation theory calculations through order fifteen, and complete active space second‐order perturbation theory calculations are also carried out. The static correlation contribution increase with increasing bond length. The calculations show that the coupled cluster approach has a remarkable ability to describe even relatively large static correlation contributions. The single reference perturbation expansion breaks down for larger OH bond length, while the multireference approach preserves the accu...

Quadratic response functions for a multiconfigurational self-consistent field wave function

We describe an efficient implementation of the quadratic response function for a multiconfiguration self‐consistent field reference wave function. The quadratic response function determines the hyperpolarizability and its residues determine the two‐photon transition matrix elements and the transition matrix elements between excited states. We report sample calculations for the hyperpolarizability of Ne and for the two‐photon transition matrix elements of Ne and H2.

Excitation energies of BH, CH2 and Ne in full configuration interaction and the hierarchy CCS, CC2, CCSD and CC3 of coupled cluster models

Abstract Excitation energies in the coupled cluster model hierarchy CCS, CC2, CCSD and CC3 have been calculated for Ne, BH and CH 2 and compared with full configuration interaction (FCI) results. Single replacement dominated excitations are improved at each level in this hierarchy, with a decrease in the error compared to FCI of about a factor of three at each level. This decrease is in accordance with the fact that the single replacement dominated excitations in CCS, CC2, CCSD and CC3 are correct through respectively first, second and third order in the fluctuation potential. The improvement from CC2 to CCSD is due to the fact that CCSD gives a full coupled cluster treatment in the singles, doubles space. Double replacement dominated excitations can only be described at the CCSD and CC3 levels, and are correct through first and second order, respectively. The CC3 double replacement dominated excitations have similar quality as the single replacement dominated excitations in CC2. The scaling of CCS, CC2, CCSD and CC3 is N 4 , N 5 , N 6 and N 7 , respectively, where N is the number of orbitals.

Linear response calculations for large scale multiconfiguration self‐consistent field wave functions

It is shown that large scale MCSCF linear response (MCLR) calculations can be carried out efficiently using an iterative algorithm where the linear transformations are carried out directly, i.e., without explicitly constructing the MCLR matrices. Calculations are presented on H2O of frequency dependent polarizabilities with configuration spaces containing up to 128 283 determinants.

Surprising cases of divergent behavior in Mo/ller–Plesset perturbation theory

High‐order Mo/ller–Plesset perturbation calculations have been carried out for several small molecules and compared to full configuration interaction (FCI) results. The convergence of the Mo/ller–Plesset series is found to depend crucially on the one‐electron basis sets. Addition of diffuse basis functions leads in some cases to divergent behavior of the Mo/ller–Plesset series, even for highly single reference dominated systems as Ne and HF. The results thus questions the usefulness of higher‐order perturbation calculations as a vehicle for obtaining arbitrary accuracy of quantum chemical calculations and raises the fundamental theoretical question: When does Mo/ller–Plesset perturbation theory converge for many‐electron systems in extended basis sets?