DZ and TZ basis sets

WsOig]"-, [WjOigf- and [WsOig]"- UV-Vis Several DFT methods/ DZ and TZ basis sets COSMO 88... 

The basis sets employed in the MCQR calculations are the DZ and TZ gaussian basis sets of Dunning [177, 178] augmented with Rydberg-like functions (R), DZR and... 

A double-zeta (DZ) basis set is obtained by replacing each STO of a minimal basis set by two STOs that differ in their orbital exponents ((zeta). (Recall that a single STO is not an accurate representation of an AO use of two STOs gives substantial improvement.) For example, for QHa a double-zeta set consists of two Is STOs on each H, two Is STOs, two 2s STOs, two 2p two 2py, and two 2p STOs on each carbon, for a total of 24 basis functions this is a (4s /2s) basis set. (Recall that we did a double-zeta SCF calculation on He in Section 13.16.) Since each basis function Xr in < i = 2, CriXr has its own independently determined variational coefficient c , the number of variational parameters in a double-zeta-basis-set wave function is twice that in a minimal-basis-set wave function. A triple-zeta (TZ) basis set replaces each STO of a minimal basis set by three STOs that differ in their orbital exponents. 

After the completion of the present research, a beautiful paper by de Oliveira-Filho et al. [43] appeared on the same reaction. The methodology used by Oliveira-Filho is somewhat different from ours. First, they used the CCSD(T)-F12a/cc-pVTZ-F12 method for their most reliable structural predictions. Our most reliable stractural predictions were made with CCSD(T)/cc-pV5Z(-PP), with the analogous DZ, TZ, and QZ basis set results included test convergence. Thus, our stmctural predictions include scalar relativistic effects, while those of Bowman do not. 

Additional ab initio SCF energies are collected in the following table. The orbitals, for which E, were given in the original publications, are indicated as well as the geometry and the basis set (GTO = Gaussian-type orbital, DZ or TZ = double or triple zeta, P = polarization) ... 

McLean and Chandler developed a similar set of contracted basis sets from Huzinaga s primitive optimized set for second row elements. A DZ type basis is derived by contracting (12s8p) —> [5s3p], and a TZ type is derived by contracting (13s9p) —> [6s4p]. The latter contraction is 6,3,1,1,1,1 for tlie s-functions and 4,2,1,1,1 for the p-functions, and is often used in connection with the Pople 6-3IG when second row elements are present. 

Each CGTO can be considered as an approximation to a single Slater-type orbital (STO) with effective nuclear charge f (zeta). The composition of the basis set can therefore be described in terms of the number of such effective zeta values (or STOs) for each electron. A double-zeta (DZ) basis includes twice as many effective STOs per electron as a single-zeta minimal basis (MB) set, a triple-zeta (TZ) basis three times as many, and so forth. A popular choice, of so-called split-valence type, is to describe core electrons with a minimal set and valence electrons with a more flexible DZ (or higher) set. 

The ECP basis sets include basis functions only for the outermost one or two shells, whereas the remaining inner core electrons are replaced by an effective core or pseudopotential. The ECP basis keyword consists of a source identifier (such as LANL for Los Alamos National Laboratory ), the number of outer shells retained (1 or 2), and a conventional label for the number of sets for each shell (MB, DZ, TZ,...). For example, LANL1MB denotes the minimal LANL basis with minimal basis functions for the outermost shell only, whereas LANL2DZ is the set with double-zeta functions for each of the two outermost shells. The ECP basis set employed throughout Chapter 4 (denoted LACV3P in Jaguar terminology) is also of Los Alamos type, but with full triple-zeta valence flexibility and polarization and diffuse functions on all atoms (comparable to the 6-311+- -G++ all-electron basis used elsewhere in this book). 

From the data provided by the systematic experimental study at standardized conditions the free energy of activation (AG exp.) was calculated from the experimental rate constant and compared to calculated AG values. Two different basis sets have been employed in the DFT calculations the split valence double- (DZ) basis set 6-31G(d) with a triple- (TZ) [44, 45] valence basis set for manganese (we will refer to this combination as basis set I (BS1)) and the triple- basis set 6-311+G(d,p), which will be denoted basis set n (BS2). The BSl-results for transition states and intermediates are shown in Table 5, a comparison of the free activation energies is shown in Figure 8 [46],... 

A more sequential approach to the analysis of the systematic error of ab initio methods has been proposed in [14]. The same set of molecules as in [10] has been analyzed there. For this set the series of calculations using the basis sets aug-cc-pVxZ containing both polarization and diffuse functions with the number of exponents x in their respective radial parts up to x = 6 (single zeta x = 1, double zeta - DZ -x = 2, triple zeta - TZ - x = 3, etc.) and with the account of correlation effects in the range of methods from MP2 up to CCSD(T) had been performed and then fitted to the formulae [15-18] ... 

The average phosphorescence radiative lifetime calculated with different basis sets vary between 23 (DZ) and 96 (TZ) seconds. The DZ and DZR results overestimate the T — So transition probability in unsaturated hydrocarbons their r values are too small. Discussion of these results has sense only in context of comparison with other molecules, but the absolute DZ values have no credit this basis set produces bad energies for a — 7T excitations, which are highly important for the T-S intensity borrowing. The best quality basis set (TZR) gives 64 seconds, which is much more credible. The so-called best experimental value is 30 seconds [154], but the proper estimation of non-radiative channels and the quantum yields still presents an open problem. From... 

The minimum basis set is usually inadequate, failing to allow the core electrons to get close enough to the nucleus and the valence electrons to delocalize. An obvious solution is to double the size of the basis set, creating a double zeta (DZ) basis. So for carbon, the DZ basis set has four s basis functions and two p basis functions (recognizing that the term p basis functions refers here to the full set—Pj, p, and p functions), for a total of 10 basis functions. Further improvement can be made by choosing a triple zeta (TZ) or even larger basis set. 

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