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Analytic Calculation of First-order Molecular Properties at the
Explicitly-correlated Second-order Møller-Plesset Level

By Sebastian Höfener^{1}, Christof Hättig^{2},
and Wim Klopper^{1}

^{1}*
Karlsruhe Institue of Technology (KIT), Theoretical Chemistry Group,
Kaiserstraße 12, 76131 Karlruhe, Germany*

^{2}*
Ruhr-Universität Bochum, Lehrstuhl für Theoretische Chemie,
Universitätstraße 150, 44801 Bochum, Germany
*

* Z. Phys. Chem. - Int. J. Res. Phys. Chem. & Chem. Phys.***224**, 695-708 (2010)

(Received July 29, 2009; accepted October 12, 2009)

Formulae are derived and implemented for the analytic calculation of
first-order molecular properties at the level of explicitly-correlated
second-order Møller-Plesset perturbation theory. In this theory, which
is denoted as MP2-F12 theory, Slater-type geminals are used to expand
the first-order wave function. A second-order perturbation theory
correction for single excitations into a complementary auxliary basis
set is also included. At the MP2-F12 level, it seems sufficient to
restrict the analytic calculation of energy derivatives to the level of
standard approximation A of MP2-F12 theory and to assume the extended
Brillouin condition to hold. Smooth and rapid convergence towards the
basis-set limit is observed for the dipole moments of a selection of
small closed- and open-shell molecules when calculated at the
RI-MP2-F12/2A*[T+V] + CABS singles level in augmented
correlation-consistent polarized valence double-, triple-, and
quadruple-zeta basis sets that have been optimized especially for use
in MP2-F12 theory.

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