Slater-type atomic orbitals

Hehre, W.J. Stewart, R.F. Pople, J.A. Self-consistent molecular-orbital methods. I. Use of Gaussian expressions of Slater-Type Atomic Orbitals 7 Chem. 51 2657-2664, 1969. 

Self Consistent Molecular-Orbital Methods I. Use of Gaussian Expansions of Slater-Type Atomic Orbitals W. J. Hehre, R. F. Stewart and J. A. Pople The Journal of Chemical Physics 51 (1969) 2657-2665... 

Least squares representations of Slater-type atomic orbitals as a sum of Gaussian-type orbitals are presented. These have the special feature that... 

The term STO-3G denotes a minimal Gaussian basis set in which each Slater-type atomic orbital (s, p or d) is approximated by a fixed block of three Gaussian functions189,... 

The molecular orbitals x are most commonly written as linear combinations of atomic orbitals and T is then described as a LCAO wavefunction. The atomic orbitals are usually represented by Slater-type atomic orbitals (STO)... 

F. LCAO Self-consistent Field (Hartree-Fock) Molecular Orbitals I. Slater-type atomic orbitals... 

The first SCF wavefunctions for the ground state of N3 were calculated by Clementi. Initially he used the minimal basis set (Table 16) with Slater-type atomic orbitals (STO) The orbital exponents C (equation 20) were chosen as the best free-atom values and the internuclear distance was taken as 1T2A. (As already discussed, section II.A, this distance is erroneous.) The total electronic energy of N3 was calculated as — 162 5422// (I // = 27 209 eV/atom). 

It is in the definition of the integrals or the lack of it, that most m.o. methods differ. The overlap integrals are easy to compute and were, indeed, tabulated for Slater-type atomic orbitals a long time ago (ref. 79). In some simple calculations, namely extended Huckel-type calculations a rough estimation of Hmn is as follows (see also page 79). 

In brief, the CNDO (the acronym stands for complete neglect of differential overlap) approach is an all valence electron, self-consistent field calculation in which multicenter integrals have been neglected and some of the two electron integrals parameterized using atomic data. Slater type atomic orbitals are used as the basis 2s, 2px, 2p, 2p for carbon and oxygen. In these calculations two-electron in egrafs are approximated as... 

The one-electron Kohn-Sham equations were solved using the Vosko-Wilk-Nusair (VWN) functional [27] to obtain the local potential. Gradient correlations for the exchange (Becke fimctional) [28] and correlation (Perdew functional) [29] energy terms were included self-consistently. ADF represents molecular orbitals as linear combinations of Slater-type atomic orbitals. The double- basis set was employed and all calculations were spin unrestricted. Integration accuracies of 10 -10 and 10 were used during the single-point and vibrational frequency calculations, respectively. The cluster size chosen for Ag or any bimetallic was... 

When calculating the wavefunction it is important to make a choice of basis set J. t that is suitable for the available computing power and the accuracy desired. A straightforward early approach to basis set construction was to fit an accurate Slater-type atomic orbital (STO) with n gaussians,called STO- G. The quality of STO- G wavefunctions increases as n increases. It was determined that = 3 was a good starting point, and the STO-3G basis set has been widely used, particularly where computing resources were limited or for lai er molecules. 

The standard extended Huckel Hamiltonian (23) with a minimum basis set of Slater-type atomic orbitals were used in all calculations. The overlap and Hamiltonian matrices were computed for the RC fragment in the light conformation (12), which included Bph Qa Qb, the iron ion and the relevant protein environment Met , Met , His ,... 

Hehre W J, Stewart R F and Pople J A 1969 Self-consistent molecular-orbital method I. Use of Gaussian expansions of Slater-type atomic orbitals J. Chem. Phys. 51 2657-64... 

Hall G G 1951 The Molecular Orbital Theory of Chemical Valency VIII A Method for Calculating lomsation Potentials. Proceedings of the Royal Society (London) A205 541-552 Hehre W J, R F Stewart and J A Pople 1%9 Self-Consistent Molecular-Orbital Methods I Use of Gaussian Expansions of Slater-Type Atomic Orbitals. Journal of Chemical Physics 51 2657-2664 Hehre W J, L Radom, P v R Schleyer and J A Pople 1986 Ah initio Molecular Orbital Theory New York, John Wiley Sons. 

In [710] a 65-atom molecular cluster is used that was treated semiempiricaUy at the INDO level and embedded in the electrostatic field generated by multipoles. To model the F and F+ centers in corundum additional 2s and 2p Slater-type atomic orbitals were placed in the vacancy after removing one O atom. The relaxation of the four aluminum atoms nearest to the vacancy resulted in an outward displacement by 2-3% and 5-6% for the F and F+ center, respectively. Prom the 12 next-nearest oxygen atoms only two were allowed to relax. In contrast to the results of [709] the two oxygen atoms moved toward the vacancy by about -2.2% and -4.6% for the F and F+ center, respectively. Defect-formation energies were not calculated. 

Fig. 2.8 Contour plots of the wavefunction amplitudes for the highest occupied molecular orbital HOMO) and lowest unoccupied molecular orbital (LUMO) of 3-methylindole. Positive amplitudes are indicated by solid lines, negative amplitudes by dotted lines, and zero by dot-dashed lines. The plane of the map is parallel to the plane of the indole ring and is above the ring by o as in Fig. 2.7, panels D and E. The contour intervals for the amplitude are 0.05ao. Small contributions from the carbon and hydrogen atoms of the methyl group are neglected. The straight black lines indicate the carbon and nitrogen skeleton of the molecule. The atomic coefficients for the molecular orbitals were obtained as described by Callis [37-39]. Slater-type atomic orbitals (Eq. 2.40) with with f = 3.071/A (1.625/ao) and 3.685/A (1.949/ o) were used to represent C and N, respectively...

---