We present the theory and algorithms for computing analytical energy gradients for explicitly corre-lated 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 approx-imation 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 treat-ment, 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. Published by AIP Publishing. https://doi.org/10.1063/1.5003065
%0 Journal Article
%1 publ9340464
%A Gyorffy, Werner
%A Knizia, Gerald
%A Werner, Hans Joachim
%D 2017
%J J. Chem. Phys.
%K chemie imported werner from:alexanderdenzel theoretische stuttgart theochem
%N 21
%R 10.1063/1.5003065
%T Analytical energy gradients for explicitly correlated wave functions. I. Explicitly correlated second-order Møller-Plesset perturbation theory
%U http://dx.doi.org/10.1063/1.5003065
%V 147
%X We present the theory and algorithms for computing analytical energy gradients for explicitly corre-lated 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 approx-imation 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 treat-ment, 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. Published by AIP Publishing. https://doi.org/10.1063/1.5003065
@article{publ9340464,
abstract = {We present the theory and algorithms for computing analytical energy gradients for explicitly corre-lated 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 approx-imation 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 treat-ment, 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. Published by AIP Publishing. https://doi.org/10.1063/1.5003065},
added-at = {2019-03-01T15:49:39.000+0100},
author = {Gyorffy, Werner and Knizia, Gerald and Werner, Hans Joachim},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2ddec6e1aba5616127455f7aac8cacdfe/theochem},
doi = {10.1063/1.5003065},
interhash = {32404e567168a305f62b0e7d93e020da},
intrahash = {ddec6e1aba5616127455f7aac8cacdfe},
issn = {00219606},
journal = {J. Chem. Phys.},
keywords = {chemie imported werner from:alexanderdenzel theoretische stuttgart theochem},
number = 21,
timestamp = {2019-03-01T14:49:39.000+0100},
title = {{Analytical energy gradients for explicitly correlated wave functions. I. Explicitly correlated second-order Møller-Plesset perturbation theory}},
url = {http://dx.doi.org/10.1063/1.5003065},
volume = 147,
year = 2017
}
