Quadruple zeta basis set

DyaU, K.G. Relativistic double-zeta, triple-zeta, and quadruple-zeta basis sets for the 5d elements Hf-Hg, Theor. Ghem. Acc. 2004,112,403. 

The value of C is 1.63 and comes from a study by Halkier and coauthors, where an optimal value for two-point HE CBS extrapolations using triple-zeta and quadruple-zeta basis sets was based on comparison to numerical HE energies [67]. Using this value, HE energies for a test set of nine diatomics were within 1 mEh of the numerical HE limits. The (l//max) CBS fit of Schwartz is expressed as... 

We have shown that the Mo oxo-transfer reactions are unusually sensitive to the QM level of theory with respect to both the DFT method and the size of the basis set. Energies obtained with standard split-valence basis sets (used in many old studies) are totally useless with errors of 70 kJ mol or more. In fact, even triple-zeta basis sets may have sizeable errors and when performing calculations on systems with negatively charged substrates, diffuse functions are mandatory. Therefore, the convergence of the basis sets should always be tested by diffuse quadruple-zeta basis sets (which today is a small problem at the DFT level). However, sometimes we have observed that even geometries obtained with a split-valence basis set may be qualitatively wrong, which is a more severe problem that requires re-optimization of key intermediates with triple-zeta basis sets. 

Double zeta, triple zeta, and quadruple zeta basis sets include additional sets of each basis function (2, 3, or 4 sets respectively), with each additional set having a different size. By varying the relative contribution of the alternative sizes to the overall molecular orbital, one effectively introduces a single function with a variable size (see Fig. 2). 

Split-valence basis sets are a simplification to the double, triple, and quadruple zeta basis sets described above. Since the inner shell orbitals are not usually involved in bonding, and their energies are reasonably independent of their molecular environment, it is usually only necessary to include the extra basis functions for the valence orbitals. Basis sets that include different numbers of basis fimctions for the inner shell and valence electrons are known as split-valence basis sets. 

Dunning basis sets have names such as cc-pVnZ. This notation stands for correlation-consistent polarized valence -zeta. For a double zeta basis set, n is replaced by a D, for a triple zeta basis set, n is replaced by a T, for a quadruple zeta basis set, n is replaced by a Q, for a quintuple basis set we use a 5, and for a sextuple basis set we use a 6. When diffuse functions are included, an aug prefix is included in the name, as in aug-cc-pVTZ. The cc-pVTZ basis set generally has a performance similar to 6-311G(2df,p). A special feature of the Dimning basis sets is that they have been designed so the series DZ, TZ, QZ, 5Z, 6Z... systematically converges on the infinite basis set limit (27). This feature has been exploited in the... 

The most recent and high level computation satisfying both these requirements is the potential energy surfaces by Kurkal et al. [226], at the multireference configuration interaction (MRCI) level with a quadruple zeta basis set. 5000 points were calculated (up to bond length of 8.0 a.u.) and joined with cubic splines, and an ab initio quasi-diabatization method [373] was used to obtain diabatic surfaces. Wavepacket dynamics studies employing this surface has not been published however. 

In Table 9 we report the spectroscopic constants calculated for hydrogen fluoride and molecular nitrogen with the cc-pV/iZ sets. As can be seen, the properties of both these species are nearly converged for the quadruple zeta basis sets - differences between the results obtained with the quadruple and sextuple basis sets are a few tenths of a kcal mol in De, a few thousandths of an angstrom in re, and a few wavenumbers in ct>c- In fact, the errors in the Hartree-Fock calculations are rather small even with the triple zeta basis sets. 

Figure 8.5 Optimalg-type basis functions from the Dyall quadruple zeta basis sets for actinides...

---