Slater-type orbitals calculations

The application of density functional theory to isolated, organic molecules is still in relative infancy compared with the use of Hartree-Fock methods. There continues to be a steady stream of publications designed to assess the performance of the various approaches to DFT. As we have discussed there is a plethora of ways in which density functional theory can be implemented with different functional forms for the basis set (Gaussians, Slater type orbitals, or numerical), different expressions for the exchange and correlation contributions within the local density approximation, different expressions for the gradient corrections and different ways to solve the Kohn-Sham equations to achieve self-consistency. This contrasts with the situation for Hartree-Fock calculations, wlrich mostly use one of a series of tried and tested Gaussian basis sets and where there is a substantial body of literature to help choose the most appropriate method for incorporating post-Hartree-Fock methods, should that be desired. 

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... 

The complete neglect of differential overlap (CNDO) method is the simplest of the neglect of differential overlap (NDO) methods. This method models valence orbitals only using a minimal basis set of Slater type orbitals. The CNDO method has proven useful for some hydrocarbon results but little else. CNDO is still sometimes used to generate the initial guess for ah initio calculations on hydrocarbons. 

T vo main streams of computational techniques branch out fiom this point. These are referred to as ab initio and semiempirical calculations. In both ab initio and semiempirical treatments, mathematical formulations of the wave functions which describe hydrogen-like orbitals are used. Examples of wave functions that are commonly used are Slater-type orbitals (abbreviated STO) and Gaussian-type orbitals (GTO). There are additional variations which are designated by additions to the abbreviations. Both ab initio and semiempirical calculations treat the linear combination of orbitals by iterative computations that establish a self-consistent electrical field (SCF) and minimize the energy of the system. The minimum-energy combination is taken to describe the molecule. 

There are two types of basis functions (also called Atomic Orbitals, AO, although in general they are not solutions to an atomic Schrodinger equation) commonly used in electronic structure calculations Slater Type Orbitals (STO) and Gaussian Type Orbitals (GTO). Slater type orbitals have die functional form... 

In Table 5, we show the calculated magnetic susceptibilities for AlH and SiH+, and the Lipseomb et al. [7] obtained values for AlH using an extended basis set of field independent Slater type orbitals. 

We have just explained that the wave equation for the helium atom cannot be solved exacdy because of the term involving l/r12. If the repulsion between two electrons prevents a wave equation from being solved, it should be clear that when there are more than two electrons the situation is worse. If there are three electrons present (as in the lithium atom) there will be repulsion terms involving l/r12, l/r13, and l/r23. Although there are a number of types of calculations that can be performed (particularly the self-consistent field calculations), they will not be described here. Fortunately, for some situations, it is not necessary to have an exact wave function that is obtained from the exact solution of a wave equation. In many cases, an approximate wave function is sufficient. The most commonly used approximate wave functions for one electron are those given by J. C. Slater, and they are known as Slater wave functions or Slater-type orbitals (usually referred to as STO orbitals). 

Ab initio calculations are based on first principles using molecular orbital (MO) calculations based on Gaussian functions. Combinations of Gaussian functions yield Slater-type orbitals (STOs), also called Slater determinants. STOs are mathematical functions closely related to exact solutions for the hydrogen atom. In their ultimate applications, ab initio methods would use Gaussian-type wave functions rather than STOs. The ab initio method assumes that from the point of view of the electrons the nuclei are stationary, whereas... 

J. Fernandez Rico, R. Lopez, A. Aguado, I. Ema, and G. Ramirez, Reference program for molecular calculations with Slater-type orbitals. J. Comput. Chem. 19, 1284 (1998). 

Hoffmann introduced the so-called extended Hiickel method. He found that a value for K= 1.75 gave optimal results when using Slater-type orbitals as a basis (and for calculating the Sjll,v)- The diagonal h elements are given, as in the conventional Hiickel method, in terms of valence-state IP s and EA s. Cusachs later proposed a variant of this parameterization of the off-diagonal elements ... 

For first- and second-row atoms, the Is or (2s, 2p) or (3s,3p, 3d) valence-state ionization energies (au s), the number of valence electrons ( Elec.) as well as the orbital exponents (es, ep and ec ) of Slater-type orbitals used to calculate the overlap matrix elements SP V corresponding are given below. 

This problem will be concerned with carrying out an SCF calculation for the HeH+ molecule in the 1Zg+(lo2) ground state. The one- and two-electron integrals (in atomic units) needed to carry out this SCF calculation at R = 1.4 a.u. using Slater type orbitals with orbital exponents of 1.6875 and 1.0 for the He and H, respectively are ... 

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