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. Pyykkö 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 Pyykkö 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.

arXiv comment27 pages, 4 figures. The following article has been submitted to The Journal of Chemical Physics. After it is published, it will be found at https://aip.scitation.org/toc/jcp/current

References in corpus (18)

• Intrinsic atomic orbitals: An unbiased bridge between quantum theory and chemical concepts
• Tenth-Order QED Contribution to the Electron g-2 and an Improved Value of the Fine Structure Constant
• The DIRAC code for relativistic molecular calculations
• The radiative potential method for calculations of QED radiative corrections to energy levels and electromagnetic amplitudes in many-electron atoms
• Model operator approach to the Lamb shift calculations in relativistic many-electron atoms
• Relativity and the lead-acid battery
• Equation-of-Motion Coupled-Cluster Theory based on the 4-component Dirac-Coulomb(-Gaunt) Hamiltonian. Energies for single electron detachment, attachment and electronically excited states
• AMBiT: A program for high-precision relativistic atomic structure calculations
• Atomic many-body effects and Lamb shifts in alkali metals
• 4-component relativistic Hamiltonian with effective QED potentials for molecular calculations
• Approaching meV level for transition energies in the radium monofluoride molecule RaF and radium cation Ra${}^{+}$ by including quantum-electrodynamics effects
• Ground state hyperfine splitting in ^6,7Li atoms and the nuclear structure
• NRQED approach to the fine and hyperfine structure corrections of order $m{\alpha }^6$ and $m{\alpha }^6(m/M)$ -- Application to the hydrogen atom
• Model-QED operator for superheavy elements
• Analytical formula for the Uehling potential
• The role of QED effects in transition energies of heavy-atom alkaline earth monofluoride molecules: a theoretical study of Ba${}^{+}$, BaF, RaF and E120F
• Accurate \textit{ab initio} calculations of RaF electronic structure indicate the need for more laser-spectroscopical measurements
• Towards highly accurate calculations of parity violation in chiral molecules: relativistic coupled-cluster theory including QED-effects

Cited by in corpus (19)

• 4-component relativistic Hamiltonian with effective QED potentials for molecular calculations
• Generalized relativistic small-core pseudopotentials accounting for quantum electrodynamic effects: construction and pilot applications
• Theoretical molecular spectroscopy of actinide compounds: The ThO molecule
• Ground state of superheavy elements with $120\le Z\le 170$: systematic study of the electron-correlation, Breit, and QED effects
• Accurate theoretical determination of the ionization potentials of CaF, SrF, and BaF
• QED radiative corrections to electric dipole amplitudes in heavy atoms
• Radiative Decay Rate and Branching Fractions of MgF
• Atomic Bethe logarithm in the mean-field approximation
• Isotope-shift factors with quantum electrodynamics effects for many-electron systems: A study of the nuclear charge radius of ${}^{26m}$Al
• Relativistic coupled cluster calculations of the electron affinity and ionization potentials of lawrencium
• Generating coupled cluster code for modern distributed memory tensor software
• Relativistic atomic structure calculations in support of spectroscopy
• Relativistic effects on electronic pair densities: a perspective from the radial intracule and extracule probability densities
• Effective quantum electrodynamics: One-dimensional model of the relativistic hydrogen-like atom
• Ionization potential of radium monofluoride
• Theoretical determination of the ionization potentials of ScF, YF, LaF and AcF
• Vacuum polarization corrections to hyperfine structure in many-electron atoms
• Ab Initio Calculations of the Static and Dynamic Polarizability of BaOH
• On the bottom-up construction of many-electron relativistic QED Hamiltonian