Triple zeta double polarization

G. K.-L. Chan and M. Head-Gordon, Exact solution (within a triple-zeta, double polarization basis set) of the electronic Schrodinger equation for water. J. Chem. Phys. 118, 8551 (2003). 

One advantage of Ax is its relatively low cost. The cc-pVTZ basis set may still be out of reach for many practical problems, however, and therefore, the basis set dependence of the diagnostic is of interest. Table 3 lists correlation coefficients and deviation statistics (from near-basis-set-limit values with Jensen s pc-3 polarization consistent basis set [49-55]) for the LANL2DZ, 6-3IG, and 6-3IIG basis sets. It is shown there that > 0.98 for basis sets of at least polarized double-zeta quality, while > 0.995 can be reached for triple-zeta double polarization or better basis sets. Only for small double-zeta basis sets like LANL2DZ or SDD could basis set dependence potentially become an issue. 

Four basis sets were examined BSl and BS3 are based on the Couty-Hall modification of the Hay and Wadt ECP, and BS2 and BS4 are based on the Stuttgart ECP. Two basis sets, BSl and BS2, are used to optimize the geometries of species in the OA reaction, [CpIr(PH3)(CH3)]++ CH4 [CpIr(PH3)(H)(CH3)2]+, at the B3LYP level, while the other basis sets, BS3 and BS4, are used only to calculate energies at the previously optimized B3LYP/BS1 geometries. BSl is double-zeta with polarization functions on every atom except the metal atom. BS2 is triple-zeta with polarization on metal and double-zeta correlation consistent basis set (with polarization functions) on other atoms. BS3 is similar to BSl but is triple-zeta with polarization on the metal. BS4 is similar to BS2 but is triple-zeta with polarization on the C and H that are involved in the reaction. The basis set details are described in the Computational Details section at the end of this chapter. 

The full Cl is impractical except as a reference because the number of determinants is asymptotically N . That means its application is possible only for small molecules and small basis sets. In praaice, calculations using 25 x 10 determinants for H O in a double zeta plus polarization (DZP) basis have been made and —10 determinants for CH3 in a triple zeta plus polarization (TZP) basis. ... 

These comparisons, and additional comparisons with other ab initio calculations, indicate that the harmonic frequencies for benzene have not been pinned down at the 10-20 cm 1 level by the previously mentioned ab initio calculations. In order to reduce inaccuracies in the harmonic force field, we have performed relatively large scale calculations using a valence triple zeta plus polarization basis set (pVTZ) in coupled-cluster calculations with single and double excitations (CCSD). These results, as well as comparisons with previous ab initio and recent density functional (156-157) results, are described elsewhere (108). 

Here, we should comment on the inconsistency of the basis sets employed for geometries and magnetic interactionism and LC-coPBE/LACVP //LC-coPBE/chem. A most remarkable error in optimization calculations of LC-coPBE/chem is for the double-protonated state, in which the error is approximately 0.1 A as described above. This must be caused by the different levels of the basis sets for the Mn atoms triple-zeta + diffuse + polarization (TZ + d + p) quality function in the chem basis set and LANL-DZ in the LACVP basis set. Obviously, the interatomic (Mn-Mn) distances of chem are larger than the corresponding values of LACVP not only for LC-coPBE but also for all other XC functionals as shown in Fig. 26.3. A noteworthy point is that the chem basis set is a typical different basis... 

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) ... 

As already anticipated, one of advantages of using TD-DFT is that this method does not exhibit any dramatic dependence on the size of the basis set. For valence transitions, many studies indicate that a medium-size basis set (valence double-zeta or triple-zeta adding polarization and diffuse functions) provides VEE close to convergence [53-58]. 

The cluster structures were optimized at the corresponding level of theory employing a double zeta valence polarization (DZVP) basis set (Godbout et al. 1992). For the polarizability calculations a triple zeta valence polarization (TZVP) basis set augmented with field induced polarization (FIP) function was used (Calaminid et al. 1999). All calculations were performed in the framework of auxiliary density fimctional theory (ADFT) (Koster et al. 2004b) with A2 or GEN-A2 auxiliary function sets (Calaminici et al. 2007a). The latter was used in the analytical calculation of the cluster polarizabilities (Flores-Moreno and Koster 2008). 

AMBER = assisted model building with energy refinement force field CHARMM = chemistry at Harvard macromolecu-lar mechanics force field MP4SDQ = Mpller-Plesset fourth-order perturbation theory with corrections for single, double, and quadruple excitations OPLS = optimized potentials for liquid simulation force field TZP = triple-zeta -f polarization. 

The next step in iin proving a basis set could be to go to triple zeta, quadruple zeta, etc. Ifone goes in this direction rather than adding functions of higher angular quantum number, the basis set would not be well balanced. With a large number of s and p functions only, one finds, for example, that the equilibrium geometry of am monia actually becomes planar. The next step beyond double z.ela n sit ally in voices addin g polarization fn n ciion s, i.e.. addin g d-... 

An older, but still used, notation specihes how many contractions are present. For example, the acronym TZV stands for triple-zeta valence, meaning that there are three valence contractions, such as in a 6—311G basis. The acronyms SZ and DZ stand for single zeta and double zeta, respectively. A P in this notation indicates the use of polarization functions. Since this notation has been used for describing a number of basis sets, the name of the set creator is usually included in the basis set name (i.e., Ahlrichs VDZ). If the author s name is not included, either the Dunning-Hay set is implied or the set that came with the software package being used is implied. 

Barone also introduces two new basis sets, EPR-Il and EPR-llI. These are optimized for the calculation of hyperfine coupling constants by density functional methods. EPR-Il is a double zeta basis set with a single set of polarization functions and an enhanced s part. EPR-III is a triple zeta set including diffuse functions, double d polarization functions and a single set off functions. 

Details of the extended triple zeta basis set used can be found in previous papers [7,8]. It contains 86 cartesian Gaussian functions with several d- and f-type polarisation functions and s,p diffuse functions. All cartesian components of the d- and f-type polarization functions were used. Cl wave functions were obtained with the MELDF suite of programs [9]. Second order perturbation theory was employed to select the most energetically double excitations, since these are typically too numerous to otherwise handle. All single excitations, which are known to be important for describing certain one-electron properties, were automatically included. Excitations were permitted among all electrons and the full range of virtuals. 

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). 

For the related [CpIr(PH3)(CH3)]+ system, four basis sets were used. Basis set one (BS1) is the same as the ones described above for Ir and P, but the C and H are described as D95. Basis set two (BS2) is the Stuttgart relativistic, small core ECP basis set (49) augmented with a polarization function for Ir, and Dunning s correlation consistent double-zeta basis set with polarization function (50) for P, C and H. Basis set three (BS3) is the same as BS1 except the d-orbital of Ir was described by further splitting into triple-zeta (111) from a previous double-zeta (21) description and augmented with a f-polarization function (51). Basis set four (BS4) is the same as BS2 for Ir, P, and most of the C and H, but the C and H atoms involved in the oxidative addition were described with Dunning s correlation consistent triple-zeta basis set with polarization. 

In general, DFT calculations are known to converge fast with the size of the basis set. Although polarized double-zeta basis sets are a minimum requirement, polarized triple-zeta basis sets are... 

As with the summaries of the other sections, we mention a number of calculation parameters or variables that have been demonstrated to be of critical importance for accurate prediction of aspects of the interactions. Symmetry constraints on the clusters have been shown to introduce arti-factual behavior. Corrections to account for the correlation of electrons have become essential in a calculation, and they must be incorporated self-consistently rather than as postoptimization corrections. Basis sets need to have the flexibility afforded by double- or triple-zeta functionality and polarization functions to reproduce known parameters most accurately. The choice of the model cluster and its size affect the acid strength, and the cluster must be large enough not to spatially constrain reactants or transition states. The choice of cluster is invariably governed by the available resources, but a small cluster can still perform well. Indeed, some of the... 

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