Born-Oppenheimer potential for H2_2

The Born-Oppenheimer potential for the $^1\Sigma_g^+$ state of H$_2$ is obtained in the range of 0.1 -- 20 au, using analytic formulas and recursion relations for two-center two-electron integrals with exponential functions. For small distances James-Coolidge basis is used, while for large distances the Heitler-London functions with arbitrary polynomial in electron variables. In the whole range of internuclear distance about $10^{-15}$ precision is achieved, as an example at the equilibrium distance $r=1.4011$ au the Born-Oppenheimer potential amounts to $-1.174\,475\,931\,400\,216\,7(3)$. Results for the exchange energy verify the formula of Herring and Flicker [Phys. Rev. {\bf 134}, A362 (1964)] for the large internuclear distance asymptotics. The presented analytic approach to Slater integrals opens a window for the high precision calculations in an arbitrary diatomic molecule.Comment: 14 pages, 5 tables, 1 figure, corrected numeric

Solution of the Dirac-Coulomb equation using the Rayleigh-Ritz method. Results for He-like atoms

The Dirac-Coulomb equation for helium-like ions is solved using the iterative self-consistent field method, with Slater-type spinor orbitals as the basis. These orbitals inherently satisfy the kinetic-balance condition due to their coupling for both large- and small-components. The $1/r_{12}$ Coulomb interaction is treated without constraints. Computations are carried out for total energies of atoms with nuclear charges up to $Z \leq 80$ using both minimal and extended basis sets. Variationally optimal values for orbital parameters are determined through the Rayleigh-Ritz variational principle. No manifestations related to the Brown-Ravenhall disease are found

I. Complete and orthonormal sets of exponential-type orbitals with noninteger principal quantum numbers

The definition for the Slater-type orbitals is generalized. Transformation between an orthonormal basis function and the Slater-type orbital with non-integer principal quantum numbers is investigated. Analytical expressions for the linear combination coefficients are derived. In order to test the accuracy of the formulas, the numerical Gram-Schmidt procedure is performed for the non-integer Slater-type orbitals. A closed form expression for the orthogonalized Slater-type orbitals is achieved. It is used to generalize complete orthonormal sets of exponential-type orbitals obtained by Guseinov in [Int. J. Quant. Chem. 90, 114 (2002)] to non-integer values of principal quantum numbers. Riemann-Liouville type fractional calculus operators are considered to be use in atomic and molecular physics. It is shown that the relativistic molecular auxiliary functions and their analytical solutions for positive real values of parameters on arbitrary range are the natural Riemann-Liouville type fractional operators

Management of Groundwater Recharge Areas in the Mouth of Weber Canyon

Proper management of surface and groundwater resources is important for their prolonged and a beneficial use. Within the Weber Delta area there has existed a continual decline in the piezometric surface of the deep confined aquifer over the last 40 years. This decline ranges from approximately 20 feet along the eastern shore of the Great Salt Lake to 50 feet along in the vicinity of Hill Air Force Base. Declines in the piezometric surface are undesirable because of the increased well installation costs, increased pumping costs, decreased aquifer storage, increased risk of salt water intrusion, and the possibility of land subsidence. Declines in the piezometric surface can be prevented or reduced by utilizing artificial groundwater recharge. The purpose of this study was to develop and operate a basin groundwater model with stochastic recharge inputs to determine the feasibility of utilizing available Weber River water for the improvement of the groundwater availability. This was accomplished by preparing auxiliary computer models which generated statistically similar river flows from which river water rights were subtracted. The feasibility of utilizing this type of recharge input was examined by comparing the economic benefit gained by reducing area wide pumping lifts through artificial recharge with the costs of the recharge operations. Institutions for implementing a recharge program were examined. Through this process a greater understanding of the geohydrologic conditions of the area was obtained. Piezometric surface contour maps, geologic profiles, calibrated values for geologic and hydrologic variables, as well as system response to change were quantified

Considering a mixed atomic basis set composed of only 1s STO and 1s GTO in molecular calculations

An atomic basis set composed of only 1s orbitals is introduced, for molecular calculations in the HartreeFock-LCAO approximation. The 1s Slater Type Orbitals are located at the nuclei and the 1s Gaussian Type Orbitals can be used both in fixed locations and as Floating Orbitals. Surprisingly, despite the simplicity of the orbitals, this basis set provides an accurate description of molecular systems containing atoms with two shells such as oxygen and carbon, used as case studies in this work. From a numerical perspective, the basis set is first optimized for the free atoms and then they are introduced into the molecular environment. The molecular calculations for OH_2 and CH_2 show validating results for the energy and the molecular geometry. From the description of the inner atomic and the valence shells achieved with this particular basis set, we can assign a charge to the bonds and the lone pairs by using the Löwdin population analysis, with excellent result from the molecular point of view.Fil: Pérez, Jorge Eduardo. Universidad Nacional de Rio Cuarto. Facultad de Cs.exactas Fisicoquímicas y Naturales. Departamento de Física; ArgentinaFil: Cesco, Juan Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; ArgentinaFil: Alturria Lanzardo, Carmina José. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Zaccari, Daniel Gustavo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas Fisicoquímicas y Naturales. Departamento de Química; ArgentinaFil: Ortiz, Félix. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas Fisicoquímicas y Naturales. Departamento de Química; ArgentinaFil: Soltermann, Arnaldo Teseo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas Fisicoquímicas y Naturales. Departamento de Química; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Hoggan, P. E.. Université Clermont Auvergne. Institut Pascal; Franci