Calculation of Araki-Sucher correction for many-electron systems

Abstract

In this paper we consider the evaluation of the Araki-Sucher correction for arbitrary many-electron atomic and molecular systems. This contribution appears in the leading order quantum electrodynamics corrections to the energy of a bound state. The conventional one-electron basis set of Gaussian-type orbitals (GTOs) is adopted; this leads to two-electron matrix elements which are evaluated with help of generalised the McMurchie-Davidson scheme. We also consider the convergence of the results towards the complete basis set. A rigorous analytic result for the convergence rate is obtained and verified by comparing with independent numerical values for the helium atom. Finally, we present a selection of numerical examples and compare our results with the available reference data for small systems. In contrast with other methods used for the evaluation of the Araki-Sucher correction, our method is not restricted to few-electron atoms or molecules. This is illustrated by calculations for several many-electron atoms and molecules.

Weakly bound molecules as sensors of new gravitylike forces

“…18 ), as it excels for Yukawa ranges of several nanometers, complementing the range of ∼0.1 nm probed in the latter. In the future, with the development of next-generation optical molecular clocks 25,35 and with improved theoretical description of long range interactions 32,34 , our technique could constrain new gravitylike forces at unprecedented levels and provide a valuable means of testing new physics beyond the Standard Model 1–6 .…”

“…For instance, the current limits for nm to nm could be surpassed by about 1.5–2 orders of magnitude. This, however, will also require the inclusion of several subtle QED and relativistic effects 26,32,34 in the theoretical description of long range atomic interactions. If data for many isotopes are to be used 35,36 an ab initio calculation of isotope-dependent corrections, like the adiabatic, nonadiabatic or nuclear volume corrections 28 may prove necessary.…”

Second virial coefficients for helium-4 and helium-3 from accurate relativistic interaction potential

“…where a, b are numerical constants, see Ref. [43]. Combining results from three consecutive basis sets, we find the following expression for the CBS limit in this case…”

“…In the latter case, the Hartree-Fock orbitals, the standard one-and twoelectron integrals, and integrals involving the relativistic operators were generated using the local version of the Dalton 2.0 package [37,39,42], while integrals involving the AS operator were computed using the computer code developed in Ref. [43].…”

Complete Basis Set Extrapolation of Electronic Correlation Energies Using the Riemann Zeta Function

“…For example, separate treatment of singlet and triplet electron pairs can be invoked, and an analogous separation can be performed for core/valence electron pairs. It is also possible to generalize the zeta-function method to extrapolate relativistic and quantum electrodynamics corrections in light systems that are known to converge pathologically slowly [16,44] calculated at the FCI level of theory. All values are given in the atomic units and the abbreviations are the same as in Table II.…”