Slater orbital exponent

ZINDO/1 IS based on a modified version of the in termediate neglect of differen tial overlap (IXDO), which was developed by Michael Zerner of the Quantum Theory Project at the University of Florida. Zerner s original INDO/1 used the Slater orbital exponents with a distance dependence for the first row transition metals only. Ilow ever. in HyperChein constant orbital expon en ts are used for all the available elein en ts, as recommended by Anderson. Friwards, and Zerner. Inorg. Chem. 2H, 2728-2732.iyH6. 

Once the least-squares fits to Slater functions with orbital exponents e = 1.0 are available, fits to Slater function s with oth er orbital expon cn ts can be obtained by siin ply m ii Itiplyin g th e cc s in th e above three equations by It remains to be determined what Slater orbital exponents to use in electronic structure calculation s. The two possibilities may be to use the "best atom" exponents (e = 1. f) for II. for exam pie) or to opiim i/e exponents in each calculation. The "best atom expon en ts m igh t be a rather poor ch oicc for mo lecular en viron men ts, and optirn i/.at ion of non linear exponents is not practical for large molecules, where the dimension of the space to be searched is very large.. 4 com prom isc is to use a set of standard exponents where the average values of expon en ts are optirn i/ed for a set of sin all rn olecules, fh e recom -mended STO-3G exponents are... 

In honour of J. C. Slater, we refer to such basis functions as Slater-type orbitals (STOs). Slater orbital exponents ( = (Z — s)/n ) for atoms through neon are given in Table 9.2. 

Here Z is the core charge on A (e. g. the nuclear charge less the number of inner core electrons), Pu is the total charge on atom A, is the cartesian coordinate of atom A, and Z x is the Slater orbital exponent for 2 s and 2 p orbitals of atom A. 

Many calculations for atoms have led to the development of a number of recipes for deciding the best values of and n. A further important issue is the size of the basis set. A minimal basis set of STOs for an atom would include one function for each SCF occupied orbital with different n and / quantum numbers in equation (6.56) for the chlorine atom, therefore, the minimal basis set would include s, 2s, 2p, 3s and 3p functions, each with an optimised Slater orbital exponent . A higher order of approximation would be to double the number of STOs (the double zeta basis set), with orbital exponents optimised ultimately the Hartree-Fock limit is reached, as it has been for all atoms from He to Xe [13]. 

The equilibrium VSIP values were evaluated by the method proposed by Anderson and Hoffmann [22]. Benzoate adsorption on iron can involve Fe—C interactions through the carbon atoms of the >C=C< (from the aromatic ring) or >C=0 moieties and the resulting geometries imply a different polarization of the surface. However, in each case, the original VSIP and Slater orbital exponents define the open-circuit potential of the adsorbed ensembles, and all of them are compared through a parameterization based on the Fe—C bond. The open-circuit potential can be correlated to the experimental open-circuit value of the interface, that is, the electrode potential that results from the interaction between benzoate and iron. 

Here L is a correction of the Mulliken approximation for the kinetic energy and All is entirely empirical and contains adjustable bond parameters. These are optimized in order to minimize the deviation from experiment for a set of reference compounds. In a way similar to INDO/S [Eq. (45)], two sets of Slater orbital exponents are used one K(0)] for intra-atomic integrals and the other (0 for molecular integrals. For comparison with experimental heats of formation, the calculated binding energies Eb [Eq. (4)] are corrected by the zero-point energies obtained from vibration analyses. Later, a substantially modified version of SINDOl, MSINDO, was developed and reparameterized for the elements H, C F, Na-Cl, Sc-Zn, and Ga-Br [63-65],... 

SAMI differs from AMI in derivation of the one-center TERIs. At the first stage of the parametrization. Slater orbital exponent values are derived using atomic data. These orbital exponents are then used to calculate all the one-center two-electron integrals in the spd basis and these values are then fixed. The second stage is a molecular parametrization where the usual parameters from the NDDO models are augmented with the needed parameters for SAMI. 

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