Ahlrichs basis

Alternatively, the Ahlrichs style split-valence basis sets (Schaefer et al. 1992) are also ubiquitous in computational chemistry. Practically, extended AO basis sets of polarized TZV or QZV quality should be employed. Because the Ahlrichs basis sets have been carefully optimized vari-ationally, the basis set superposition error (described below) is much smaller than with Pople or Dunning sets of about the same size. These expansions are consistently available for all elements of the periodic table. 

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 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... 

Schaefer, A. Huher, C. Ahlrichs, R. Fully optimized contracted Gaussian basis sets of triple zeta valence quality for atoms Li to Kr. J. Chem. Phys. 1994, 100, 5829-5835. 

Eichkorn, K., Treutler, O., Ohm, H., Haser, M., Ahlrichs, R., 1995, Auxiliary Basis Sets to Approximate Coulomb Potentials , Chem. Phys. Lett., 240, 283. 

Schafer, A., Horn, H., Ahlrichs, R., 1992, Fully Optimized Contracted Gaussian Basis Sets for Atoms Li to Kr , J. Chem. Phys., 97, 2571. 

All electron calculations were carried out with the DFT program suite Turbomole (152,153). The clusters were treated as open-shell systems in the unrestricted Kohn-Sham framework. For the calculations we used the Becke-Perdew exchange-correlation functional dubbed BP86 (154,155) and the hybrid B3LYP functional (156,157). For BP86 we invoked the resolution-of-the-iden-tity (RI) approximation as implemented in Turbomole. For all atoms included in our models we employed Ahlrichs valence triple-C TZVP basis set with polarization functions on all atoms (158). If not noted otherwise, initial guess orbitals were obtained by extended Hiickel theory. Local spin analyses were performed with our local Turbomole version, where either Lowdin (131) or Mulliken (132) pseudo-projection operators were employed. Broken-symmetry determinants were obtained with our restrained optimization tool (136). Pictures of molecular structures were created with Pymol (159). 

Neither of these basis set families is satisfactory for accurate calculations without the addition of polarization functions. Various ad hoc rules have been developed over the years for polarization exponents. Since SCF polarization is less sensitive to exponent choice than correlation, it is reasonable to let the latter determine the exponents. By fitting the results of correlated calculations on closed-shell hydrides, Ahlrichs and Taylor [47] arrived at the following formulas for d exponents (ay)... 

Basis sets [23] For the Sc-Cu metal atoms the Ahlrichs VTZ basis sets [24] were used with extra polarization and diffuse functions (two p-functions, one d-function) from the Wachters basis set [25] and (one f-function) from ref. [26]. For Zn the Ahlrichs VTZ basis set was used with addition of two p-functions, one d-function and one f-function [27]. For the oxygen atom Ahlrichs TZV basis set [28] was used with two polarization d-functions and one diffuse s and... 

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