Basis sets Slater-type atomic orbital

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,... 

Consistent Molecular-Orbital Methods. I. Use of Gaussian Expansions of Slater-Type Atomic Orbitals. See also D. Feller and E. R. Davidson, in Reviews in Computational Chemistry, K. B. Lipkowitz and D. B. Boyd, Eds., VCH Publishers, New York, 1990, Vol. 1, pp. 1-43. Basis Sets for Ab Initio Molecular Orbital Calculations and Intermolecular Interactions. 

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). 

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 ,... 

The simplest basis sets are those used in the simple Hiickel and the extended Hiickel methods (SHM and EHM, Chapter 4). As applied to conjugated organic compounds (its usual domain), the simple Hiickel basis set consists of just p atomic orbitals (or geometrically p-type atomic orbitals, like a lone-pair orbital which can be considered not to interact with the er framework). The extended Hiickel basis set consists of only the atomic valence orbitals. In the SHM we don t worry about the mathematical form of the basis functions, reducing the interactions between them to 0 or —1 in the SHM Fock matrix (e.g. Eqs. 4.64 and 4.65). In the EHM the valence atomic orbitals are represented as Slater functions (Sections 4.4.1.2 and 4.4.2). 

For both types of orbitals, the coordinates r, 0, and (j) refer to the position of the electron relative to a set of axes attached to the center on which the basis orbital is located. Although Slater-type orbitals (STOs) are preferred on fundamental grounds (e.g., as demonstrated in Appendices A and B, the hydrogen atom orbitals are of this form and the exact solution of the many-electron Schrodinger equation can be shown to be of this form (in each of its coordinates) near the nuclear centers), STOs are used primarily for atomic and linear-molecule calculations because the multi-center integrals < XaXbl g I XcXd > (each... 

These atomic orbitals, called Slater Type Orbitals (STOs), are a simplification of exact solutions of the Schrodinger equation for the hydrogen atom (or any one-electron atom, such as Li" ). Hyper-Chem uses Slater atomic orbitals to construct semi-empirical molecular orbitals. The complete set of Slater atomic orbitals is called the basis set. Core orbitals are assumed to be chemically inactive and are not treated explicitly. Core orbitals and the atomic nucleus form the atomic core. 

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. ... 

The self-consistent field function for atoms with 2 to 36 electrons are computed with a minimum basis set of Slater-type orbitals. The orbital exponents of the atomic orbitals are optimized so as to ensure the energy minimum. The analysis of the optimized orbital exponents allows us to obtain simple and accurate rules for the 1 s, 2s, 3s, 4s, 2p, 3p, 4p and 3d electronic screening constants. These rules are compared with those proposed by Slater and reveal the need for the screening due to the outside electrons. The analysis of the screening constants (and orbital exponents) is extended to the excited states of the ground state configuration and the positive ions. 

The first step in reducing the computational problem is to consider only the valence electrons explicitly, the core electrons are accounted for by reducing the nuclear charge or introducing functions to model the combined repulsion due to the nuclei and core electrons. Furthermore, only a minimum basis set (the minimum number of functions necessary for accommodating the electrons in the neutral atom) is used for the valence electrons. Hydrogen thus has one basis function, and all atoms in the second and third rows of the periodic table have four basis functions (one s- and one set of p-orbitals, pj, , Pj, and Pj). The large majority of semi-empirical methods to date use only s- and p-functions, and the basis functions are taken to be Slater type orbitals (see Chapter 5), i.e. exponential functions. 

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