Triple-zeta polarization functions

The calculations shown in this work have been performed using the Amsterdam Density Functional (ADF) code [20,21]. All of them are spin not polarized. The influence of the quality of the basis set on the Re value has been explored taking as a guide the case of Mn in fluoroperovskites. For this goal two types of basis sets have been employed. Firstly calculations have been carried out by means of functions of quality IV (which are implemented in the ADF code) involving triple zeta basis functions plus a polarization function. In a second step Re has also been computed using double zeta functions of quality II for F and ions. 

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. 

Calculations at the 6-31G and 6-31G level provide, in many cases, quantitative results considerably superior to those at the lower STO-3G and 3-21G levels. Even these basis sets, however, have deficiencies that can only be remedied by going to triple zeta (6-31IG basis sets in HyperChem) or quadruple zeta, adding more than one set of polarization functions, adding f-type functions to heavy atoms and d-type functions to hydrogen, improving the basis function descriptions of inner shell electrons, etc. As technology improves, it will be possible to use more and more accurate basis sets. 

Even larger basis sets are now practical for many systems. Such basis sets add multiple polarization functions per atom to the triple zeta basis set. For example, the 6-31G(2d) basis set adds two d functions per heavy atom instead of just one, while the 6-311++G(3df,3pd) basis set contains three sets of valence region functions, diffuse functions on both heavy atoms and hydrogens, and multiple polarization functions 3 d functions and 1 f function on heavy atoms and 3 p functions and 1 d function on hydrogen atoms. Such basis sets are useful for describing the interactions between... 

The experimental bond length is 1.476. Both the triple zeta basis set and multiple polarization functions are needed to produce a very accurate structure for this molecule. 

Electron correlation studies demand basis sets that are capable of very high accuracy, and the 6-31IG set I used for the examples above is not truly adequate. A number of basis sets have been carefully designed for correlation studies, for example the correlation consistent basis sets of Dunning. These go by the acronyms cc-pVDZ, cc-pVTZ, cc-pVQZ, cc-pV5Z and cc-pV6Z (double, triple, quadruple, quintuple and sextuple-zeta respectively). They include polarization functions by definition, and (for example) the cc-pV6Z set consists of 8. 6p, 4d, 3f, 2g and Ih basis functions. 

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. 

The Veillard basis set [23] (1 ls,9p) has been used for A1 and Si, and the (1 ls,6p) basis of the same author has been retained for Mg. However, three p orbitals have been added to this last basis set, their exponents beeing calculated by downward extrapolation. The basis sets for Al, Si and Mg have been contracted in a triple-zeta type. For the hydrogen atom, the Dunning [24] triple-zeta basis set has been used. We have extended these basis sets by mean of a s-type bond function. We have optimized the exponents a and locations d of these eccentric polarization functions, and the internuclear distance R of each of the studied molecules. These optimized parameters are given in Table 3. 

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. 

In terms of basis sets, there is compelling evidence that sets smaller than polarized triple-zeta quality significantly reduce the accuracy that can be obtained with modem hybrid functionals and cannot be recommended if quantitative energetic results are the prime target. 

Dickson and Becke, 1996, use a basis set free numerical approach for obtaining their LDA dipole moments, which defines the complete basis set limit. In all other investigations basis sets of at least polarized triple-zeta quality were employed. Some of these basis sets have been designed explicitly for electric field response properties, albeit in the wave function domain. In this category belong the POL basis sets designed by Sadlej and used by many authors as well as basis sets augmented by field-induced polarization (FTP) func-... 

G minimal 6G (nc = 6) core and triple-zeta 3G (nv = 3), lG(nv" = 1) valence sp sets, with polarization functions on heavy atoms... 

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). 

---