Ionization potentials and radii of atoms and ions of element 104 (unnilquadium) and of hafnium (2+) derived from multiconfiguration Dirac-Fock calculations

Multiconfiguration relativistic Dirac-Fock (MCDF) values have been computed for the first four ionization potentials (IPs) of element 104 (unnilquadium) and of the other group 4 elements (Ti, Zr, and Hf). Factors were calculated that allowed correction of the systematic errors between the MCDF IPs and the experimental IPs. Single "experimental" IPs evaluated in eV (to ± 0.1 eV) for element 104 are: [104(0),6.5]; [104( 1 + ),14.8]; [104(2 + ),23.8]; [104(3 + ),31.9]. Multiple experimental IPs evaluated in eV for element 104 are: [(0-2+ ),21.2±0.2]; [(0-3+ ),45.1 ±0.2]; [(0-4+ ),76.8±0.3].Our MCDF results track 11 of the 12 experimental single IPs studied for group 4 atoms and ions. The exception is Hf( 2 + ). We submit our calculated IP of 22.4 ± 0.2 eV as much more accurate than the value of 23.3 eV derived from experiment.

Relativistic molecular calculations of superheavy molecules

Relativistic molecular calculations within the Dirac-Slater scheme have been used in a study of the electronic structure of 6d-metal superheavy hexafluorides. The theoretical results are compared with calculations and measurements of the homolog 4d- and 5d-metal hexafluorides. Large spin-orbit splitting dominates the electronic structure and even has the same order of magnitude as the crystal-field splitting for the valence electrons for the superheavy molecules. Ionization energies have been calculated using a transition state procedure.

Self-consistent relativistic molecular calculations of superheavy molecules: (_110 X)F_6

Using new relativistic molecular calculations within the Dirac-Slater scheme it is now feasible to study theoretically molecules containing superheavy elements. This opens a new era for the prediction of the physics and chemistry of superheavy elements. As an example we present the results for (_110 X) F_6, where it is shown that relativistic effects are nearly of the same order of magnitude as the crystal-field splitting.

Precise calculations of atomic electron binding energies in fermium

The comparison between the experimental binding energies for the K, L, and M electrons for fermium and the results of our Dirac-Fock calculation, taking into account all tractable corrections, leads to agreement within about 20 eV. This shows that the present method of calculation is an adequate description of this problem and that nonlinear electrodynamical effects will not be present in nature or will be smaller than 1% compared to the values recently proposed. It is found that the energies of electronic transitions can now be used to estimate the nuclear radius.

Test for basis-set errors in relativistic Dirac-Fock-Slater calculations with a numerical AO-DFS-basis

A fully relativistic four-component Dirac-Fock-Slater program for diatomics, with numerically given AO's as basis functions is presented. We discuss the problem of the errors due to the finite basis-set, and due to the influence of the negative energy solutions of the Dirac Hamiltonian. The negative continuum contributions are found to be very small.

Realistic many electron coupled channel calculations in heavy ion scattering

The time dependent Dirac equation which describes a heavy ion-atom collision system is solved via a set of coupled channel equations with energy eigenvalues and matrix elements which are given by a selfconsistent field many electron calculation. After a brief discussion of the theoretical approximations and the connection of the many particle with the one particle interpretation we discuss first results for the systems F{^8+} - Ne and F{^6+} - Ne. The resulting P(b) curves for the creation of a Ne K-hole are in good agreement with the experimental results.

Many electron coupled channel calculations for the system F{^8+} - Ne

To describe the time dependence of an atomic collision system the Dirac equation usually is rewritten in a coupled channel equation. We first discuss part of the approximation used in this approach and the connection of the many particle with the one particle interpretation. The coupled channel equations are solved for the system F{^8+} - Ne using static selfconsistent many electron Dirac-Fock-Slater wavefunctions as basis. The resulting P(b) curves for the creation of a Ne K-hole are in reasonable agreement with the experimental results.

Non-relativistic and relativistic molecular calculations for the chalcogen hexafluorides: SF_6, SeF_6, TeF_6, PoF_6

Non-relativistic Hartree-Fock-Slater and relativistic Dirac-Slater self-consistent orbital models are applied for the analysis of the electronic structure of the chalcogen hexafluorides: SF_6, SeF_6, TeF_6 and PoF_6. The molecular eigenfunctions and eigenvalues are generated using the discrete variational method (DVM) with numerical basis functions. The results obtained for SF_6 are compared with other ab initio calculations. Information about relativistic level shifts and spin-orbit splitting has been obtained by comparison between the non-relativistic and relativistic results.

Ionization potentials and radii of atoms and ions of element 105 (unnilpentium) and ions of tantalum derived from multiconfiguration Dirac-Fock calculations

Multiconfiguration relativistic Dirac-Fock (MCDF) values were calculated for the first five ionization potentials of element 105 (unnilpentium) and of the other group 5b elements (V, Nb, and Ta). Some of these ionization potentials in electron volts (eV) with uncertainties are: 105(0), 7.4±0.4; 105(1 +), 16.3 ±0.2; 105(2 +), 24.3 ± 0.2; 105(3 + ), 34.9 ± 0.5; and 105(4 + ), 44.9 ± 0.1. Ionization potentials for Ta(1+), Ta(2 +), and Ta(3 + ) were also calculated. Accurate experimental values for these ionization potentials are not available. Ionic radii are presented for the 2+, 3+, 4 +, and 5+ ions of element 105 and for the + 2 ions of vanadium and niobium. These radii for vanadium and niobium are not available elsewhere. The ionization potentials and ionic radii obtained are used to determine some standard electrode potentials for element 105. Born-Haber cycles and a form of the Born equation for the Gibbs free energy of hydration of ions were used to calculate the standard electrode potentials.

Model Calculations and Implementation of Filters and Hybrid Green VCSELs based on Optical Thin Film Stacks

This work introduced the novel conception of complex coupled hybrid VCSELs for the first time. Alternating organic and inorganic layers in the lasers provide periodic variation of refractive index and optical gain, which enable single mode operation and low threshold of the VCSELs. Model calculations revealed great reduction of the lasing threshold with factors over 30, in comparison with the existing micro-cavity lasers. Tunable green VCSEL has been also designed, implemented and analyzed taking advantage of the broad photoluminescence spectra of the organics. Free standing optical thin films without compressive stress are technologically implemented. Multiple membrane stacks with air gap in between have been fabricated for the implementation of complex coupled VCSEL structures. Complex coupled hybrid VCSEL is a very promising approach to fill the gaps in the green spectral range of the semiconductor lasers.

A unified approach for representing rows and columns in contingency tables

By using suitable parameters, we present a uni¯ed aproach for describing four methods for representing categorical data in a contingency table. These methods include: correspondence analysis (CA), the alternative approach using Hellinger distance (HD), the log-ratio (LR) alternative, which is appropriate for compositional data, and the so-called non-symmetrical correspondence analysis (NSCA). We then make an appropriate comparison among these four methods and some illustrative examples are given. Some approaches based on cumulative frequencies are also linked and studied using matrices. Key words: Correspondence analysis, Hellinger distance, Non-symmetrical correspondence analysis, log-ratio analysis, Taguchi inertia

Bandwidth allocation based on real time calculations using the convolution approach

This paper focuses on one of the methods for bandwidth allocation in an ATM network: the convolution approach. The convolution approach permits an accurate study of the system load in statistical terms by accumulated calculations, since probabilistic results of the bandwidth allocation can be obtained. Nevertheless, the convolution approach has a high cost in terms of calculation and storage requirements. This aspect makes real-time calculations difficult, so many authors do not consider this approach. With the aim of reducing the cost we propose to use the multinomial distribution function: the enhanced convolution approach (ECA). This permits direct computation of the associated probabilities of the instantaneous bandwidth requirements and makes a simple deconvolution process possible. The ECA is used in connection acceptance control, and some results are presented

An introduction to Authentic World drug calculations

This 8 minute video provides a brief introduction to Authentic World, a website available to students in Health Sciences that enables them to practice drug calculations, get feedback on their performance and be formally assessed.

Physics : calculations for A-level.

Manual diseñado para ayudar al alumno a obtener el máximo provecho y garantizar que se cumplan los objetivos necesarios de As y A Level de Física. Teoría relevante es descrita en cada capítulo y se le acompaña ejemplos de trabajo. Al final de cada capítulo hay una serie de ejercicios de examen para los cuales hay respuestas y consejos. Los temas del libro son: la forma de abordar un cálculo, matemáticas esenciales (fracciones, porcentaje, ecuaciones, exponentes, logaritmos), unidades y dimensiones, mecánica (velocidad, aceleración y fuerza, trabajo y energía), oscilaciones y ondas, instrumentos ópticos (microscopio, telescopio), electricidad y magnetismo, física atómica y nuclear, astronomía (distancias de las estrellas, los planetas y sus órbitas).

Automatic generation of active coordinates for quantum dynamics calculations: application to the dynamics of benzene photochemistry

A new practical method to generate a subspace of active coordinates for quantum dynamics calculations is presented. These reduced coordinates are obtained as the normal modes of an analytical quadratic representation of the energy difference between excited and ground states within the complete active space self-consistent field method. At the Franck-Condon point, the largest negative eigenvalues of this Hessian correspond to the photoactive modes: those that reduce the energy difference and lead to the conical intersection; eigenvalues close to 0 correspond to bath modes, while modes with large positive eigenvalues are photoinactive vibrations, which increase the energy difference. The efficacy of quantum dynamics run in the subspace of the photoactive modes is illustrated with the photochemistry of benzene, where theoretical simulations are designed to assist optimal control experiments