Basis sets well-tempered

WTBS Well-tempered basis set for high-accuracy results. Available for He(17.v) through Rn(28.v24/ 18dl2/). 

Even-tempered basis sets have the same ratio between exponents over the whole range. From chemical considerations it is usually preferable to cover the valence region better than the core region. This may be achieved by well-tempered basis sets. The idea is similar to the even-tempered basis sets, tire exponents are generated by a suitable formula containing only a few parameters to be optimized. The exponents in a well-tempered basis of size M are generated as ... 

Results for the other open-shell atoms are encouraging. One would expect the P3 method to be considerably less accurate when an unrestricted Hartree-Fock reference state is used. The lowest MAD for B -Ar obtains with the largest of the Dunning sets examined here, i.e. cc-pVQZ. The 6-311++G(3df,3pd) and well-tempered basis sets (WTBS) are roughly equivalent, with MADs of 0.50 eV and 0.57 eV, respectively. 

A well-tempered basis set has four parameters, compared with two for an even-tempered one, and is consequently capable of giving a better result for the same number of functions. Petersson et alJ have proposed a somewhat more general parameterization based on expanding the logarithmic exponents in a polynomial of order K in the basis function number. 

Table 8.2 AE calculated atomic and ionic terms and levels (cm ) employing different correlation spaces for Groups 15 and 13 elements using the uncontracted well-tempered basis sets (WTBS) [22] ...

Huzinaga S and Klohukowski M. 1985. Well-tempered basis sets for the atoms K through Xe. Chem. Phys. Lett. 120, 509-512. 

Of cmcial importance in designing a basis set is the issue of linear dependence, because this affects the numerical stability of the atomic or molecular calculations that use the basis sets. Linear dependence in the primitive set can be controlled by the use of even-tempered or well-tempered basis sets, which minimize the linear dependence by construction. However, such basis sets tend to be larger than energy-optimized basis sets, where linear dependence problems can become significant as the basis set size increases. 

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