Thursday, June 17, 2010

Spin-state-corrected GTOs

One of the fundamental basic tools in quantum chemistry is formed by the basis set, where Gaussian-type orbitals (GTOs) are fast (because of analytical integrals) but not so good, and Slater-type orbitals (STOs) are excellent but have not all analytical integrals. The latter is not a problem for density functional theory (DFT), because one needs to a numerical integration for the exchange-correlation potential anyway, so one might as well use STOs (as in done in the Amsterdam Density Functional program).

The results obtained depend critically on the quality and size of the basis set, where more is better. This is however not true for spin-state energies as shown by us recently in J. Phys. Chem. A 2008, 112, 6384-6391. There we showed that STOs work fine, already with small basis sets, i.e. they converge fast. Large GTOs give the same result, but the convergence is much slower. And basis sets containing effective core potentials (ECPs) give systematically different (wrong!!) answers, so should not be used for spin-state energies.


Small Pople-type GTO basis sets (like 6-31G* etc.) are in particular very poor. We have studied in this paper (J. Phys. Chem. A 2010, 114, 7191-7197) these basis sets, and showed that their faulty behavior can be largely corrected by increasing the [2d] contraction scheme to a [3d] contraction. In particular what is needed is an additional diffuse d-function. The resulting spin-state-corrected GTO (J. Phys. Chem. A 2010, 114, 7191-7197) basis sets give good results, and are available from the Basis Set Exchange online database.

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