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Auxiliary basis sets for density-fitted correlated wavefunction calculations:
Weighted core-valence and ECP basis sets for post-*d* elements

Christof Hättig,^{*a‡} Gunnar Schmitz,^{a§}
and Jörg Koßmann^{a¶}

*
Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44780 Bochum, Germany
*

*Phys. Chem. Chem. Phys.* **14**, 6549-6555 (2012).

Received 09 Feb 2012, Accepted 11 Mar 2012

First published on the web 13 mar 2012

We report optimised auxiliary basis sets for the resolution-of-the-identity (or density-fitting) approximation of two-electron
integrals in second-order Møller-Plesset perturbation theory (MP2) and similar electronic structure calculations with correlation-consistent
basis sets for the post-*d* elements Ga-Kr, In-Xe, and Tl-Rn. The auxiliary basis sets are optimised such that the
density-fitting error is negligible compared to the one-electron basis set error. To check to which extend this criterion is fulfilled
we estimated for a test set of 80 molecules the basis set limit of the correlation energy at the MP2 level and evaluated the
remaining density-fitting and the one-electron basis set errors. The resulting auxiliary basis sets are only 2-6 times larger than
the corresponding one-electron basis sets and lead in MP2 calculations to speed-ups of the integral evaluation by one to three
orders of magnitude. The density-fitting errors in the correlation energy are at least hundred times smaller than the one-electron
basis set error, i.e. in the order of only 1-100 µH per atom.

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