A simplified singles-and-doubles linear-r(12) corrected coupled-cluster model, denoted CCSD(R12), is proposed and compared with the complete singles-and-doubles linear-r(12) coupled-cluster method CCSD-R12. An orthonormal auxiliary basis set is used for the resolution-of-the-identity approximation to calculate three-electron integrals needed in the linear-r(12) Ansatz. Basis-set convergence is investigated for a selected set of atoms and small molecules. In a large basis, the CCSD(R12) model provides an excellent approximation to the full linear-r(12) energy contribution, whereas the magnitude of this contribution is significantly overestimated at the level of second-order perturbation theory.
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http://dx.doi.org/10.1063/1.1850094 | DOI Listing |
J Chem Phys
August 2009
Lehrstuhl für Theoretische Chemie Ruhr, Universität Bochum, Universitatsstrasse 150, D-44801 Bochum, Germany.
Coupled-cluster response theory for frequency-dependent optical properties within the coupled-cluster singles-and-doubles model (CCSD) has been derived and implemented for ansatz 2 of the explicitly correlated CCSD(R12) and CCSD(F12) methods as part of the program package DALTON. The basis set convergence of static dipole moments, polarizabilities, and parallel averages of first and second hyperpolarizabilities has been investigated for Ne, BH, N(2), CO, and BF. The frequency-dependent results are presented for the electronic second-harmonic generation of N(2).
View Article and Find Full Text PDFJ Chem Phys
March 2009
Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, Universitatsstrasse 150 D-44801 Bochum, Germany.
The equation-of-motion coupled-cluster method for excited states with the singles-and-doubles model (CCSD) has been implemented for ansatz 2 of the explicitly correlated CCSD(R12) and CCSD(F12) methods as part of the program package Dalton. In this model, an orthonormal complementary auxiliary basis set is used for the resolution-of-identity approximation in order to calculate the three-electron integrals needed for CCSD(R12) and CCSD(F12). The additional CCSD(R12) or CCSD(F12) terms introduced within ansatz 2, which are not present in ansatz 1, are derived and discussed with regard to the extra costs needed for their computation.
View Article and Find Full Text PDFPhys Chem Chem Phys
January 2008
Department of Chemistry, Virginia Tech, Blacksburg, VA 24061, USA.
We propose to account for the large basis-set error of a conventional coupled-cluster energy and wave function by a simple perturbative correction. The perturbation expansion is constructed by Löwdin partitioning of the similarity-transformed Hamiltonian in a space that includes explicitly correlated basis functions. To test this idea, we investigate the second-order explicitly correlated correction to the coupled-cluster singles and doubles (CCSD) energy, denoted here as the CCSD(2)(R12) method.
View Article and Find Full Text PDFJ Chem Phys
August 2007
Laboratory of Physical Chemistry, ETH Zürich, CH 8093 Zürich, Switzerland.
The electron correlation energy of two-electron atoms is known to converge asymptotically as approximately (L+1)(-3) to the complete basis set limit, where L is the maximum angular momentum quantum number included in the basis set. Numerical evidence has established a similar asymptotic convergence approximately X(-3) with the cardinal number X of correlation-consistent basis sets cc-pVXZ for coupled cluster singles and doubles (CCSD) and second order perturbation theory (MP2) calculations of molecules. The main focus of this article is to probe for deviations from asymptotic convergence behavior for practical values of X by defining a trial function X(-beta) that for an effective exponent beta=beta(eff)(X,X+1,X+N) provides the correct energy E(X+N), when extrapolating from results for two smaller basis sets, E(X) and E(X+1).
View Article and Find Full Text PDFJ Chem Phys
April 2007
Institut für Nanotechnologie, Forschungszentrum Karlsruhe, P.O. Box 3640, D-76021 Karlsruhe, Germany.
Response theory up to infinite order is combined with the explicitly correlated coupled-cluster singles and doubles model including linear-r(12) corrections, CCSD(R12). The additional terms introduced by the linear-r(12) contributions, not present in the conventional CCSD calculation, are derived and discussed with respect to the extra costs required for their evaluation. An implementation is presented up to the cubic response function for one-electron perturbations, i.
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