Slater atomic orbitals

Ch em uses Slater atom ic orbitals to con struct sent i-em pirical molecular orbitals. I he complete set of Slater atomic orbitals is called the basis set. Core orbitals are assumed to be chemically inactive and arc not treated explicitly. Core orbitals and the atomic nucleus form the atomic core. 

Having the Slater atomic orbitals, the linear combination approximation to molecular orbitals, and the SCF method as applied to the Fock matrix, we are in a position to calculate properties of atoms and molecules ab initio, at the Hartree-Fock level of accuracy. Before doing that, however, we shall continue in the spirit of semiempirical calculations by postponing the ab initio method to Chapter 10 and invoking a rather sophisticated set of approximations and empirical substitutions... 

So called Hydrogenic atomic orbitals (exact solutions for the hydrogen atom) have radial nodes (values of the distance r where the orbital s value goes to zero) that make them somewhat inconvenient for computation. Results are not sensitive to these nodes and most simple calculations use Slater atomic orbitals of the form... 

The next step was to represent each Slater atomic orbital as a fixed linear combination of Gaussian orbitals so a Slater-type orbital with exponent f is written as a sum of GTOs with exponents a, q 2, and so on. For example, in the case of three primitive GTOs we might write... 

The next fundamental hypothesis in the CNDO procedure concerns the values of the Coulomb integrals which are all approximated as Coulomb integrals over 2s Slater atomic orbitals. If p. and v are on the same atom A ... 

Our main reason for introducing the Slater atomic orbitals, however, is that linear combinations of them have often been used to approximate the SCF Hartree-Fock numerical orbitals. If x represents a set of analytical orbitals, such as the STOs of equation (6.56), then we may expand 0 in the Slater determinant (6.36) in terms of x,... 

E is calculated by summing and integrating the forces on the nuclei as the atoms approach each other due to the superposition of rigid atom density functions using Slater atomic orbitals. Eq is approximated by the change in one-electron molecular orbital energy, A mo> calculated using... 

The o-components can also be obtained by calculation of all o-moments according to the approach suggested by Mulliken and Coulson [86,87], with the inclusion of homopolar and atomic dipoles and using Slater atomic orbitals [88-90]. Other possibilities are to calculate the o-electronic charges on the individual atoms [91-93] or the Del Re approach [94,95]. Some of the eariy papers devoted to dipole moments calculated by the PPP method were later subjected to a criticism by Exner [18], In one of the older studies, satisfactory dipole moments were obtained for pyridine and pyrrole using the variable electronegativity SCF method [96],... 

The parameters for MINDO/3 were obtained in an entirely different way from previous semi-empirical methods. Some of the values that were fixed in CNDO, INDO and NNDO were permitted to vary during the MINDO/3 parametrisation procedure. For example, the exponents of the Slater atomic orbitals were allowed to vary from the values given by Slater s rules, and indeed the exponents for s and p orbitals were not required to be the... 

MINN and KARPLUS /32a/. An extended basis set of Slater atomic orbitals (double basis set of s-orbitals + 2p orbitals) was used. Account is taken for the electronic interactions by a variation of the weight factors of the configurations and the parameters X of the Slater atomic wave functions... 

Although atomic functions do not need to be atomic orbitals (e.g., they may be placed between nuclei), in most cases, tiiey are centered directiy on the nuclei of the atoms belonging to the molecule under consideration. If M is small (in the less precise calculations), die Slater atomic orbitals discussed above are often used as the expansion functions Xr - for laiger M (in more accurate calculations), the relation between Xr und the orbitals of the isolated atoms is lost, and Xr are chosen based on the numerical experience gathered from the literature. ... 

The forms for and implicitly assume that the potentials are spherically symmetric about the perturbing nuclei, that the wave functions for the shielding electrons may be approximated by Slater atomic orbitals and that the Is electrons of carbon shield... 

We estimate the bond potential V, = V di) - V( ) corresponding to bond i of length di by considering the electron as being in a Slater atomic orbital (f>siater exp(-Zsiater /2 o) whcrc ao is the Bohr radius. The ef-... 

As with the pi-electron model we want to treat the orbital coefficients as variation variables and use something like the Clementi-Raimondi-Slater atomic orbitals for the basis functions, or at least something like them which are easy to integrate. We want to minimize the energy by varying the values of the but we also want to maintain the orthonormality of the linear combination of basis functions as orthonormal one-electron orbitals. They are formed from linear combinations of basis... 

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