Triple zeta contracted functions

The starting point is our previously performed calculations [3] using the Huzinaga basis set [20] (9s) for Be and (4s) for H, triple-zeta contracted, supplemented by the three 2p orbitals proposed for Be by Ahlrichs and Taylor [21] with exponents equal to 1.2, 0.3 and 0.05 respectively. This initial basis set, noted I, includes one s-type bond-function the exponent of which is equal to 0.5647. Several sets of diffuse orbitals have then been added to this basis I. Their corresponding exponents were determined by downward extrapolation from the valence basis set, using the Raffenetti [22] and Ahlrichs [21] procedure. Three supplementary basis sets noted II, III and IV containing respectively one, two and three... 

Using five basis functions optimized for the 3d 4s configuration of Ni, a double zeta (split valence) or triple zeta contraction leads to basis set errors of 4.1 eV in the description of the d state. However, optimizing the basis functions for the 3d states and using a double zeta contraction leads to errors of only 0.07 eV in describing the 3d 4s -3d splitting.For this reason we always use primitive basis sets optimized for the maximum d occupation of the neutral atom. ... 

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. 

The double zeta basis sets, such as the Dunning-Huzinaga basis set (D95), form all molecular orbitals from linear combinations of two sizes of functions for each atomic orbital. Similarly, triple split valence basis sets, like 6-3IIG, use three sizes of contracted functions for each orbital-type. 

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. 

For semiquantitative work, double-zeta or triple-zeta basis sets (in which there are two or three shells of AOs for each fully or partially occupied atomic shell) are needed, at least for the valence shell. For first-row atoms, for example, the popular 6-31G basis has a minimal representation of the l.v core orbital and a double-zeta representation of the valence orbitals. Moreover, each AO is represented by a fixed linear combination of primitive GTOs the l.v core orbital contains six primitive AOs, and each 2s and 2p valence orbital is represented by two contracted orbitals, containing three and one primitive functions. 

Several different sizes of cc basis sets are available in terms of final number of contracted functions. These are known by their acronyms cc-pVDZ, cc-pVTZ, cc-pVQZ, cc-pV5Z and cc-pV6Z correlation consistent polarized Valence Double/Triple/Quadru-ple/Quintuple/Sextuple Zeta). The composition in terms of contracted and primitive (for the s- and p-part) functions is shown in Table 5.3. Note that each step up in terms of quality increases each type of basis function by one, and adds a new type of higher... 

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