We present the theory and algorithms for computing analytical energy gradients for explicitly correlated second-order Møller–Plesset perturbation theory (MP2-F12). The main difficulty in F12 gradient theory arises from the large number of two-electron integrals for which effective two-body density matrices and integral derivatives need to be calculated. For efficiency, the density fitting approximation is used for evaluating all two-electron integrals and their derivatives. The accuracies of various previously proposed MP2-F12 approximations [3C, 3C(HY1), 3*C(HY1), and 3*A] are demonstrated by computing equilibrium geometries for a set of molecules containing first- and second-row elements, using double-ζ to quintuple-ζ basis sets. Generally, the convergence of the bond lengths and angles with respect to the basis set size is strongly improved by the F12 treatment, and augmented triple-ζ basis sets are sufficient to closely approach the basis set limit. The results obtained with the different approximations differ only very slightly. This paper is the first step towards analytical gradients for coupled-cluster singles and doubles with perturbative treatment of triple excitations, which will be presented in the second part of this series.
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7 December 2017
Research Article|
December 04 2017
Analytical energy gradients for explicitly correlated wave functions. I. Explicitly correlated second-order Møller-Plesset perturbation theory
Werner Győrffy;
Werner Győrffy
1
Institut für Theoretische Chemie, Universität Stuttgart
, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
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Gerald Knizia;
Gerald Knizia
1
Institut für Theoretische Chemie, Universität Stuttgart
, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
2
Department of Chemistry, Pennsylvania State University
, 401A Chemistry Building, University Park, Pennsylvania 16802, USA
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Hans-Joachim Werner
Hans-Joachim Werner
a)
1
Institut für Theoretische Chemie, Universität Stuttgart
, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
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Werner Győrffy
1
Gerald Knizia
1,2
Hans-Joachim Werner
1,a)
1
Institut für Theoretische Chemie, Universität Stuttgart
, Pfaffenwaldring 55, D-70569 Stuttgart, Germany
2
Department of Chemistry, Pennsylvania State University
, 401A Chemistry Building, University Park, Pennsylvania 16802, USA
a)
Electronic mail: [email protected]
J. Chem. Phys. 147, 214101 (2017)
Article history
Received:
September 02 2017
Accepted:
November 06 2017
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Citation
Werner Győrffy, Gerald Knizia, Hans-Joachim Werner; Analytical energy gradients for explicitly correlated wave functions. I. Explicitly correlated second-order Møller-Plesset perturbation theory. J. Chem. Phys. 7 December 2017; 147 (21): 214101. https://doi.org/10.1063/1.5003065
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