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

We report the implementation of effective quantum electrodynamics (QED) potentials for all-electron four-component relativistic molecular calculations using the DIRAC code. The potentials are also available for two-component calculations, being properly picture-change transformed. The latter point is important; we demonstrate through atomic calculations that picture-change errors are sizable. Specifically, we have implemented the Uehling potential [E. A. Uehling, Phys. Rev. 48, 55 (1935)] for vacuum polarization and two effective potentials [P. Pyykkö and L.-B. Zhao, J. Phys. B: At., Mol. Opt. Phys. 36, 1469 (2003) and 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, hopefully reaching an audience beyond QED specialists. We report the following sample applications: (i) We first confirm the conjecture of P. Pyykkö that QED effects are observable for the AuCN molecule by directly calculating ground-state rotational constants B₀ of the three isotopomers studied by microwave spectroscopy; QED brings the corresponding substitution Au–C bond length r_s from 0.23 to 0.04 pm agreement with experiment. (ii) In regard to spectroscopic constants of van der Waals dimers M₂ (M = Hg, Rn, Cn, Og), QED induces bond length expansions on the order of 0.15(0.30) pm for row 6(7) dimers. (iii) We confirm that there is a significant change of valence s population of Pb in the reaction PbH₄ → PbH₂ + H₂, 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)]. We also find that whereas in PbH₄ the valence 6s_1/2 population resides in bonding orbitals, it is mainly found in nonbonding orbitals in PbH₂. 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 in negative vacuum polarization over positive electron self-energy contributions as a function of nuclear charge.