Eigenvalues calculations using Slater orbitals

The pre-exponential factors in the equation 1.12 normalize the Slater approximations to the radial components of atomic orbitals. Normality is not an inherent property of linear combinations of Slater orbitals, for example, as in Table 1.3, and it is important to check any published coefficients to determine whether normalization is included. In addition, the Slater orbitals for a set of atomic orbitals in an atom are not mutually orthogonal. The results of atomic structure calculations using Slater orbitals, either as single functions or in linear combinations, as in double-zeta sets, of course, are mutually orthogonal, since this property of the eigenfunctions, is mirrored in the final linear combinations returned by the calculations for the eigenvalues. 

The non-relativistic DV-Xa calculation [21] was performed with the Slater exchange parameter, a = 0.7, for all atoms and with 50,000 DV sampling points, which provided a precision of less than 0.1 eV for valence electron energy eigenvalues. We employed the basis functions of the central nickel atom ls-4p orbitals, while those of the nitrogen and carbon atoms were used ls-2p orbitals. The calculations were carried out self-consistently until the difference in the orbital populations between the initial and final states of the iteration was less... 

The wave eigenfunctions and energy eigenvalues were obtained by real space electronic state calculations, which were performed by the use of the program code SCAT of the DV-Xx molecular orbital (MO) cluster method with the Hartree-Fock-Slater approximation [8,9]. In the method, the exchange-correlation term Vxc in the one-electron Hamiltonian was expressed in terms of the statistical local potential (1),... 

Figure 4.9 Application of the canonical orthonormalization procedure of Section 3.6 to the calculation of the 1 s and 2s eigenfunctions and eigenvalues approximations for the Is and 2s orbitals in hydrogen over Slater functions. Note the exact fit of the Is Slater, which is an eigenfunction of the Fock matrix for the hydrogen atom and the relatively close agreement of the ls/2s linear combinations based on simple canonical orthogonalization and also direct orthonormalization using the matrix procedure of Section 3.7.

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