Orbital, Slater

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... 

Most simple empirical or semi-empirical molecular orbital methods. including all ofthose ii sed in IlyperCh em, neglect inner sh ell orbitals and electrons and use a minimal basis se.i r>f valence Slater orbitals. 

Slater exponent for the. t type Slater orbitals on atom A and. s orbital Slater exponent for the s type Slater orbitals on atom li. 

The algorithms in Z[ DO/S are almost the same as those in ZlNDO/1, except of the one-center two-electron integral, b . ZINDO/S uses em pirical value of in stead of ii sin g ah initio vaine in terms of the Slater orbitals. 

The orbitals used for methane, for example, are four Is Slater orbitals of hydrogen and one 2s and three 2p Slater orbitals of carbon, leading to an 8 x 8 secular matrix. Slater orbitals are systematic approximations to atomic orbitals that are widely used in computer applications. We will investigate Slater orbitals in more detail in later chapters. 

There is considerable variation in the values assigned to the election repulsion integrals in Exercise 8.9.1. Salem (1966) points out that calculation using Slater orbitals leads to... 

Minimal basis sets use fixed-size atomic-type orbitals. The STO-3G basis set is a minimal basis set (although it is not the smallest possible basis set). It uses three gaussian primitives per basis function, which accounts for the 3G in its name. STO stands for Slater-type orbitals, and the STO-3G basis set approximates Slater orbitals with gaussian functions. ... 

Slater orbitals have been demonstrated to be more accurate than a similar number of gaussian functions for molecular orbital computations, but they are not as mathematically convenient to use. This is why it is preferable to gaussian fimctions even if larger numbers of functions are required. 

We must now consider the choice of a basis set. I have already made reference to hydrogenic orbitals and Slater orbitals without any real explanation. I have also hinted at the integrals problem variational calculations almost always involve the calculation of a number of two-electron integrals over the basis functions... 

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. 

The calculated perturbed wavefunctions have been rewritten in terms of a combination of normalized Slater orbitals in real form. Ref. 6 gives a detailed illustration for... 

The S overlap expression relies on the general situation where 4 atoms form 2 bonds having their valence electrons involved in spn hybrid Mos. In the context of Slater orbitals, cs et cp are the hybridation coefficients and, for example, S is then formulated for the bond-bond term as ... 

The ground state 9, (0 of the neutral target atom is represented by a Roothan-Hartree-Fock wavefunction that may be expanded in terms of Slater orbitals [45]. Denoting the triply differential cross section by... 

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