Quadruple zeta valence basis sets

The next step up in basis set size is a Triple Zeta (TZ). Such a basis contains three times as many functions as tire minimum basis, i.e. six s-functions and three p-functions for the first row elements. Some of the core orbitals may again be saved by only splitting the valence, producing a triple split valence basis set. Again the term TZ is used to cover both cases. The names Quadruple Zeta (QZ) and Quintuple Zeta (5Z, not QZ) for the next levels of basis sets are also used, but large sets are often given explicitly in terms of the number of basis functions of each type. 

Weigend, R Ahhichs, R. Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn design and assessment of accuracy, Phys. Chem. Chem. Phys. 2005, 7, 3297-3305. 

Augmented Gaussian basis sets of triple and quadruple zeta valence quality for the atoms H and from Li to Ar applications, in HF, MP2, and DFT calculations-of molecular dipole moment and dipole (h5q)er)polarizability ... 

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. 

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. 

When going to the larger quadruple-zeta valence (QZV) basis sets, the results change only marginally, but the computation times increase substantially. In density functional theory, these basis sets are mainly used for benchmarks and calibration. 

Weigend, F., Furche, F., and Ahlrichs, R. (2003). Gaussian basis sets of quadruple zeta valence quality for atoms H to Kr. J. Chem. Phys., 119, 12753-12762. 

A relatively large basis set has to be used for a reasonable description of correlation effects. Minimal basis sets or split valence basis sets are not suitable for carrying out MP or other correlation corrected ab initio calculations. One needs at least a DZ + P(VDZ -I- P) or TZ + 2P basis set to get reasonable energies, geometries and first-order properties. For second-order properties, TZ -I- 2P or QZ + 3P basis sets are needed. (DZ -I- P = double-zeta plus polarization VDZ = valence DZ TZ = triple-zeta QZ = quadruple-zeta.)... 

Guide R, Poliak P, and Weigend F. 2012. Error-Balanced Segmented Contracted Basis Sets of Double-zeta to Quadruple-zeta Valence QuaUty for the Lanthanides. 7. Chem. Theor. Comput. 8, 4062-4068. 

Dunning has developed a series of correlation-consistent polarized valence n-zeta basis sets (denoted cc-pVnZ ) in which polarization functions are systematically added to all atoms with each increase in n. (Corresponding diffuse sets are also added for each n if the prefix aug- is included.) These sets are optimized for use in correlated calculations and are chosen to insure a smooth and rapid (exponential-like) convergence pattern with increasing n. For example, the keyword label aug-cc-pVDZ denotes a valence double-zeta set with polarization and diffuse functions on all atoms (approximately equivalent to the 6-311++G set), whereas aug-cc-pVQZ is the corresponding quadruple-zeta basis which includes (3d2flg,2pld) polarization sets. 

Examining the results given in these two tables, it is seen that, for this small molecule, very advanced calculations can be carried out. In the tables, all the methods employed have been introduced in the previous sections. For the basis sets, aug-cc-pVnZ stands for augmented correlation consistent polarized valence n zeta, with n = 2-5 referring to double, triple, quadruple, and quintuple, respectively. Clearly, these basis functions are specially designed for... 

There are other aspects of the application of the MCSCF method that have not been discussed in this review. The most notable of these probably is the lack of a discussion of orbital basis sets. Although the orbital basis set choice is very important in determining the quality of the MCSCF wavefunction, the general principles determined from other electronic structure methods also hold for the MCSCF method with very little change. For example, the description of Rydberg states requires diffuse basis functions in the MCSCF method just as any other method. The description of charge-transfer states requires a flexible description of the valence orbital space, triple or quadruple zeta quality, in the MCSCF method just as in other methods. Similarly, the efficient transformation of the two-electron integrals is crucial to the overall efficiency of the MCSCF optimization procedure. However, this is a relatively well understood problem (if not always well implemented) and has been described adequately in previous discussions of the MCSCF method and other electronic structure methods . ... 

A triple-zeta (TZ) basis in which three times as many STOs or CGTOs are used as the number of core and valence AOs (and, yes, there now are quadruple-zeta (QZ) and higher-zeta basis sets appearing in the literature). 

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