Accurate non-Born-Oppenheimer calculations of the complete pure vibrational spectrum of D2 with including relativistic corrections

In this work we report very accurate variational calculations of the complete pure vibrational spectrum of the D(2) molecule performed within the framework where the Born-Oppenheimer (BO) approximation is not assumed. After the elimination of the center-of-mass motion, D(2) becomes a three-particle problem in this framework. As the considered states correspond to the zero total angular momentum, their wave functions are expanded in terms of all-particle, one-center, spherically symmetric explicitly correlated Gaussian functions multiplied by even non-negative powers of the internuclear distance. The nonrelativistic energies of the states obtained in the non-BO calculations are corrected for the relativistic effects of the order of α(2) (where α = 1/c is the fine structure constant) calculated as expectation values of the operators representing these effects.     

An algorithm for calculating atomic D states with explicitly correlated gaussian functions

An algorithm for the variational calculation of atomic D states employing n-electron explicitly correlated gaussians is developed and implemented. The algorithm includes formulas for the first derivatives of the hamiltonian and overlap matrix elements determined with respect to the gaussian nonlinear exponential parameters. The derivatives are used to form the energy gradient which is employed in the variational energy minimization. The algorithm is tested in the calculations of the two lowest D states of the lithium and beryllium atoms. For the lowest D state of Li the present result is lower than the best previously reported result.     

Noncommutative Circle Bundles and New Dirac Operators

We study spectral triples over noncommutative principal U(1) bundles. Basing on the classical situation and the abstract algebraic approach, we propose an operatorial definition for a connection and compatibility between the connection and the Dirac operator on the total space and on the base space of the bundle. We analyze in details the example of the noncommutative three-torus viewed as a U(1) bundle over the noncommutative two-torus and find all connections compatible with an admissible Dirac operator. Conversely, we find a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection.     

Permeation of a solvent mixture through an elastomeric membrane—The case of pervaporation

This article presents a model for the permeation of solvent mixtures through an elastomer in the particular case of pervaporation. An analytical expression for each solvent permeation rate is derived, in the limited case of a membrane that undergoes small swelling, without making any assumptions on the solvent diffusion coefficients and their dependence on solvent concentrations. Applying this analytical expression to different situations, we fitted most of the curves previously published on pervaporation experiments. In particular, we correlated the synergy developed by a mixture of two solvents in the permeation process with the sign of their Flory–Huggins interaction parameter χ_AB. This explains why, in most cases (χ_AB > 0), a molecule permeating easily through a membrane is mixed with a molecule permeating much less easily; the latter can see its permeation flux increase by a factor 10 or 100 because the swelling of the polymer induced by the more permeable molecule “opens the meshes of the network” allowing the less permeable molecule to pass through more easily. Within our analysis, the efficiency of the pervaporation process, expressed through the separation factor, is derived very simply as a function of the interaction coefficients and the viscosities of solvents and exhibits an exponential dependence on the volume fraction of either component as seen in most experiments. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 183–193, 2003     

Polarisation control of light by light in a nonlinear polymer

Received: 11 December 1997/Revised version: 11 May 1998     

Thermal curve interpretation by spectral resolution into a basic set of rectangular pulse curves

An improvement of the algorithm of the spectral resolution method for the determination of thermokinetics is presented. With the aid of the modified computer program and an experimental thermal curve, an analysis of the method has been performed.     

Basis set generation for the SCF calculation

A method for basis set generation for SCF calculations is proposed. Using SCF orbitals and orbital energies obtained in the extended basis set the Fock operator can be expressed as its spectral resolution. The sum of differences between occupied orbital energies and corresponding eigenvalues obtained by the diagonalization of this operator in the new smaller basis set is a criterion of the quality of this new set. The present method consists of the minimization of this sum by changing the parameters that determine the new basis functions. An example of the optimization of the different Gaussian basis sets for the LiH molecule is described.     

Theoretical study of PO and PO−

The diatomic systems, PO and PO^– are studied, using numerical Hartree-Fock (NHF) and coupled-cluster calculations. The latter employs a hybrid NHF and Slater orbital basis set. Highly accurate CCSD methods predict bond lengths accurate to <0.004 Å and frequencies to 60 cm^–1. In addition the electron affinity of PO is computed to be 0.89 eV compared to an experimental value of 1.09±0.01. Comparisons are made with SCF and MBPT(2) results for PO⁺ using conventional basis sets.Dedicated to Professor J. Koutecký on the occasion of his 65th birthdayGuggenheim Fellow     

Operation characteristics of the Au-II 690-nm laser transition in a segmented hollow-cathode discharge

Single-mode operation at the Au-II 690-nm transition was obtained in a segmented hollow-cathode discharge laser without the use of any additional frequency-selective device. The pressure of the helium buffer gas, which is responsible for the significant homogeneous broadening of the laser line, was varied between 10 and 20 mbar. The discharge was excited with rectangular current pulses (up to 3 A) six times exceeding the threshold value. The time dependence of the laser output during the 1-ms-long discharge pulses is explained on the basis of the temperature and pressure changes in the tube. The highest small-signal gain at optimal discharge conditions was 11%m⁻¹. Received: 1 July 1999 / Revised version: 4 November 1999 / Published online: 23 February 2000