Orthogonal Linear Combinations of Gaussian Type Orbitals

The set of Gaussian Type Orbitals g(n1,n2,n3) of order (n+1)(n+2)/2, of common n=n1+n2+n3<=7, common center and exponential, is customized to define a set of 2n+1 linear combinations t(n,m) (-n<=m<=n) such that each t(n,m) depends on the azimuthal and polar angle of the spherical coordinate system like the real or imaginary part of the associated Spherical Harmonic. (Results cover both Hermite and Cartesian Gaussian Type Orbitals.) Overlap, kinetic energy and Coulomb energy matrix elements are presented for generalized basis functions of the type r^s*t(n,m) (s=0,2,4,...). In addition, normalization integrals int |g(n1,n2,n3)|d^3r are calculated up to n=7 and normalization integrals int |r^s*t(n,m)|d^3r up to n=5.Comment: 13 pages, no figures, REVTeX4. Corrected eqs. (23) and (C4

Roothaan aita Juan Jesu Lagundiko lenengo-buru zanak egindako Gogalben-erakasbidea

Dialecto : texto en euskera central -- guipuzcoanoS. XX -- Periodo : último euskera modernoEuskalkia : erdialdekoa -- gipuzkeraXX. md. -- Aroa : azken euskara modernoaDigitalización. Vitoria-Gasteiz : Fundación Sancho el Sabio, 2008Carton

Método para la meditación

Port. con esc. xil. de los Jesuítas.Texto con apostillas marginales.Copia digital : Junta de Castilla y León. Consejería de Cultura y Turismo, 201

Analytic Energy Gradients for Multiconfigurational Self-Consistent Field Second-Order Quasidegenerate Perturbation Theory (MC-QDPT)

An analytic energy gradient method for second-order quasidegenerate perturbation theory with multiconfigurational self-consistent field reference functions (MC-QDPT) is derived along the lines of the response function formalism (RFF). According to the RFF, the gradients are calculated without solving coupled perturbed equations. Instead, it is necessary to solve seven sets of linear equations in order to determine Lagrangian multipliers, corresponding to four sets of parameter constraining conditions and three sets of additional parameter defining conditions in the Lagrangian. Just one of these linear equations is a large scale linear equation; the others are reducible to just partial differentiations or simple equations solvable by straightforward subroutines

Interaction and Localization of One-electron Orbitals in an Organic Molecule: Fictitious Parameter Analysis for Multi-physics Simulations

We present a new methodology to analyze complicated multi-physics simulations by introducing a fictitious parameter. Using the method, we study quantum mechanical aspects of an organic molecule in water. The simulation is variationally constructed from the ab initio molecular orbital method and the classical statistical mechanics with the fictitious parameter representing the coupling strength between solute and solvent. We obtain a number of one-electron orbital energies of the solute molecule derived from the Hartree-Fock approximation, and eigenvalue-statistical analysis developed in the study of nonintegrable systems is applied to them. Based on the results, we analyze localization properties of the electronic wavefunctions under the influence of the solvent.Comment: 4 pages, 5 figures, the revised version will appear in J. Phys. Soc. Jpn. Vol.76 (No.1

Quantum mechanical ab-initio simulation of the electron screening effect in metal deuteride crystals

In antecedent experiments the electron screening energies of the d+d reactions in metallic environments have been determined to be enhanced by an order of magnitude in comparison to the case of gaseous deuterium targets. The analytical models describing averaged material properties have not been able to explain the experimental results so far. Therefore, a first effort has been undertaken to simulate the dynamics of reacting deuterons in a metallic lattice by means of an ab-initio Hartree-Fock calculation of the total electrostatic force between the lattice and the successively approaching deuterons via path integration. The calculations have been performed for Li and Ta, clearly showing a migration of electrons from host metallic to the deuterium atoms. However, in order to avoid more of the necessary simplifications in the model the utilization of a massive parallel supercomputer would be required.Comment: 11 pages, 12 figures, svjour class. To be published in Eur. Phys. J.

Spectral data for doubly excited states of helium with non-zero total angular momentum

A spectral approach is used to evaluate energies and widths for a wide range of singlet and triplet resonance states of helium. Data for total angular momentum $L=1,...,4$ is presented for resonances up to below the 5th single ionization threshold. In addition the expectation value of $\cos(\theta_{12})$ is given for the calculated resonances.Comment: 35 pages, 16 tables, to be published in Atomic Data and Nuclear Data Table