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

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.