Correlated exponential functions in high precision calculations for diatomic molecules

Various properties of the general two-center two-electron integral over the explicitly correlated exponential function are analyzed for the potential use in high precision calculations for diatomic molecules. A compact one dimensional integral representation is found, which is suited for the numerical evaluation. Together with recurrence relations, it makes possible the calculation of the two-center two-electron integral with arbitrary powers of electron distances. Alternative approach via the Taylor series in the internuclear distance is also investigated. Although numerically slower, it can be used in cases when recurrences lose stability. Separate analysis is devoted to molecular integrals with integer powers of interelectronic distances $r_{12}$ and the vanishing corresponding nonlinear parameter. Several methods of their evaluation are proposed.Comment: 26 pages, includes two tables with exemplary calculation

Analytical two-center integrals over Slater geminal functions

We present analytical formulas for the calculation of the two-center two-electron integrals in the basis of Slater geminals and products of Slater orbitals. Our derivation starts with establishing a inhomogeneous fourth-order ordinary differential equation that is obeyed by the master integral, the simplest integral with inverse powers of all interparticle distances. To solve this equation it was necessary to introduce a new family of special functions which are defined through their series expansions around regular singular points of the differential equation. To increase the power of the interparticle distances under the sign of the integral we developed a family of open-ended recursion relations. A handful of special cases of the integrals is also analysed with some remarks on simplifications that occur. Additionally, we present some numerical examples of the master integral that validate the usefulness and correctness of the key equations derived in this paper. In particular, we compare our results with the calculations based on the series expansion of the exp(-\gamma r12) term in the master integral.Comment: 28 pages, 0 figures, 7 table

Bounds on fifth forces from precision measurements on molecules

Highly accurate results from frequency measurements on neutral hydrogen molecules H_2, HD and D_2 as well as the HD^+ ion can be interpreted in terms of constraints on possible fifth-force interactions. Where the hydrogen atom is a probe for yet unknown lepton-hadron interactions, and the helium atom is sensitive for lepton-lepton interactions, molecules open the domain to search for additional long-range hadron-hadron forces. First principles calculations in the framework of quantum electrodynamics have now advanced to the level that hydrogen molecules and hydrogen molecular ions have become calculable systems, making them a search-ground for fifth forces. Following a phenomenological treatment of unknown hadron-hadron interactions written in terms of a Yukawa potential of the form V_5(r)=\beta exp(-r/\lambda)/r current precision measurements on hydrogenic molecules yield a constraint \beta < 1 \times 10^{-7} eV\AA for long-range hadron-hadron interactions at typical force ranges commensurate with separations of a chemical bond, i.e. \lambda ~1 \AA and beyond.Comment: 7 pages, 3 figures, 1 tabl

Properties of the triplet metastable states of the alkaline-earth-metal atoms

A configuration interaction approach with a semiempirical model potential for the core was used to study the static and dynamic properties of the alkaline-earth-metal atoms. The alkaline-earth-metal atoms properties determined were the scalar and tensor polarizabilities, the quadrupole moment, some of the oscillator strengths and the dispersion coefficents of the van der Waals intearaction. It was observed that the use of a polarization potential to the experimental binding energy consider the influence of relativistic effects upon the core electron distribution. The resulting polarizabilities, and dispersion parameters for homonuclear pairs of atoms were within 0.1% and within 1-2 % for heavier atoms

Dispersion coefficients of the excited states of lithium atoms

The dispersion coefficients of a number of the low-lying states of Li are determined for the homonuclear case. The Li wave functions and energies were computed in a frozen core Hamiltonian with a semiempirical polarization potential. Besides computing the dispersion coefficients, the scalar and tensor polarizabilities and oscillator strengths are computed and generally seen to be in good agreement with other accurate calculations

Configuration-interaction calculations of positron binding to group-II elements

The configuration-interaction (CI) method is applied to the study of positronic magnesium (e+Mg), positronic calcium (e+Ca), and positronic strontium (e+Sr). The CI expansion was seen to converge slowly with respect to Lmax, the maximum angular momentum of any orbital used to construct the CI basis. Despite doing explicit calculations with Lmax=10, extrapolation corrections to the binding energies for the Lmax&rarr;&infin; limit were substantial in the case of e+Ca (25%) and e+Sr (50%). The extrapolated binding energies were 0.0162 hartree for e+Mg, 0.0165 hartree for e+Ca, and 0.0101 hartree for e+Sr. The static-dipole polarizabilities for the neutral parent atoms were computed as a by-product, giving 71.7a03, 162a03, and 204a03 for Mg, Ca, and Sr, respectively