4-component relativistic Hamiltonian with effective QED potentials for molecular calculations

TL;DR

This paper implements effective QED potentials in relativistic molecular calculations, enabling the observation of QED effects in molecules and reactions, with applications to gold compounds, van der Waals dimers, and superheavy elements.

Contribution

The authors developed and integrated effective QED potentials into the DIRAC code for 4-component relativistic molecular calculations, including vacuum polarization and electron self-energy effects.

Findings

QED effects are observable in AuCN molecules, improving agreement with experimental bond lengths.

QED contributes significantly to reaction energies, reducing their magnitude by about 1%.

Electronic structures of superheavy element hydrides are similar, with comparable QED contributions.

Abstract

We report the implementation of effective QED potentials for all-electron 4-component relativistic molecular calculations using the DIRAC code. The potentials are also available for 2-component calculations, proper picture-change being mandatory. Specificially, we have implemented the Uehling potential [E. A. Uehling, Phys. Rev. 48 , 55 (1935)] for vacuum polarization and two effective potentials [P. Pyykk\"o and L.-B. Zhao, J. Phys. B 36 , 1469 (2003); V. V. Flambaum and J. S. M. Ginges, Phys. Rev. A 72 , 052115 (2005)] for electron self-energy. We provide extensive theoretical background for these potentials. We report the following sample applications: i) we confirm the conjecture of Pyykk\"o that QED effects are observable for the AuCN molecule by directly calculating ground-state rotational constants $B_0$ of the three isotopomers studied by MW spectroscopy; QED brings the corresponding substitution Au-C bond length $r_s$ from 0.23 to 0.04 pm agreement with experiment, ii) spectroscopic constants of van der Waals dimers M$_2$ (M=Hg, Rn, Cn, Og) iii) there is a significant change of valence s population of Pb in the reaction PbH$_4$ -> PbH$_2$ + H$_2$, which is thereby a good candidate for observing QED effects in chemical reactions, as proposed in [K. G. Dyall et al., Chem. Phys. Lett. 348 , 497 (2001)]. QED contributes 0.32 kcal/mol to the reaction energy, thereby reducing its magnitude by -1.27 %. For corresponding hydrides of superheavy flerovium, the electronic structures are quite similar. Interestingly, the QED contribution to the reaction energy is of quite similar magnitude (0.35 kcal/mol), whereas the relative change is significantly smaller (-0.50 %). This curious observation can be explained by the faster increase of negative vacuum polarization over positive electron self-energy contributions as a function of nuclear charge.