Observation of an Inner-Shell Orbital Clock Transition in Neutral Ytterbium Atoms.

We observe a weakly allowed optical transition of atomic ytterbium from the ground state to the metastable state 4f^{13}5d6s^{2} (J=2) for all five bosonic and two fermionic isotopes with resolved Zeeman and hyperfine structures. This inner-shell orbital transition has been proposed as a new frequency standard as well as a quantum sensor for new physics. We find magic wavelengths through the measurement of the scalar and tensor polarizabilities and reveal that the measured trap lifetime in a three-dimensional optical lattice is 1.9(1) s, which is crucial for precision measurements. We also determine the g factor by an interleaved measurement, consistent with our relativistic atomic calculation. This work opens the possibility of an optical lattice clock with improved stability and accuracy as well as novel approaches for physics beyond the standard model.

Diffuse Basis Functions for Relativistic s and d Block Gaussian Basis Sets.

Diffuse s, p, and d functions have been optimized for use with previously reported relativistic basis sets for the s and d blocks of the periodic table. The functions were optimized on the 4:1 weighted average of the s2 and p2 configurations of the anion, with the d shell in the dn+1 configuration for the d blocks. Exponents were extrapolated for groups 2 and 12, which have unstable or weakly bound anions. The diffuse basis sets have been tested by application to calculations of electron affinities of the group 11 elements (Cu, Ag, and Au), double electron affinities of the group 11 monocations, and potential energy curves of Mg2 and Ca2 van der Waals dimers, as well as some response properties of the group 1 anions (Rb-, Cs-, and Fr-), the group 2 elements (Sr, Ba, and Ra), and RbLi, CsLi, and FrLi molecules.

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 rs 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 6s1/2 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.

Linearity and Chemical Bond of UO22+ Revisited: A Comparison Study with UN2 and UE22+ (E = S, Se, and Te) Based on Relativistic Calculations.

The stability and electronic structure of UO22+ are compared with those of UN2 and UE22+ (E = S, Se, and Te) based on four- and two-component relativistic Hamiltonians. We observed that the Hartree-Fock method overestimates the stability of the linear structures of UO22+ and UN2. In addition to the conventional mechanism based on valence orbitals, we proposed another mechanism wherein the small energy difference between U's 6p3/2 and O's σ(2s) orbitals destabilizes the bent structure of UO22+. The validity of the analysis based on the DFT method was evaluated using the coupled-cluster method. The slightly bent structures of UO22+ and UN2 are feasible from the viewpoint of energetic stability: the destabilized energy at 160° is 0.144 and 0.059 eV for UO22+ and UN2, respectively. The U-X bond (X = N,O) is rigid in the slightly bent structure, and it corresponds to the conservation of the feature of the chemical bond. For UE22+, core-valence orbitals mainly affect the stability of these molecules, like UO22+ and UN2. In UE22+, the 6p hole is fairly modest, and the 6p hole in UO22+ is a unique feature in uranium-chalcogen systems.

Sr(ii) extraction by crown ether in HFC: entropy driven mechanism through H2PFTOUD.

The solvent extraction of Sr(ii) was carried out using dicyclohexano-18-crown-6 (DCH18C6) and two HFC mixed solvents MS1 and MS2, where MS1 was composed of 30/60 (w/w)% trans-1,2-dichloroethylene/HFC-43 (HFC-43: 1,1,1,2,2,3,4,5,5,5-decafluoropentane) and MS2 was 5/95 (w/w)% heptane/HFC-43. Nitric acid and perfuruoro-3-6-9-trioxaundecane-1,11-dioic acid (H2PFTOUD) were used to study the effect of acid on the extraction. The maximum distribution ratio of Sr(ii) (D Sr) observed for H2PFTOUD conditions was ∼180, and >10 times larger than aqueous nitric acid conditions. The D Sr value was influenced by concentrations of the DCH18C6, Sr(ii), and acid, and by temperature. The composition of extracted complexes was estimated using slope analysis as an Sr(ii)-anion-DCH18C6 ratio of ∼1 : 2 : 1. From the extended X-ray absorption fine structure (EXAFS) measurements of Sr(ii) in the aqueous and organic phases, it is inferred that regardless of the acid used, DCH18C6 coordinates to the first coordination sphere of the Sr(ii) extracted complexes and Sr(ii) is hydrated (complexation with H2PFTOUD cannot be distinguished) in the aqueous phase. Thermodynamic data were significantly changed by choice of acid, i.e., both enthalpy and entropy values were negative for nitric acid conditions, on the other hand, entropy values were large and positive for H2PFTOUD conditions. These results have demonstrated that the combination of HFC solvent and crown ether is applicable for metal extraction.

The DIRAC code for relativistic molecular calculations.

DIRAC is a freely distributed general-purpose program system for one-, two-, and four-component relativistic molecular calculations at the level of Hartree-Fock, Kohn-Sham (including range-separated theory), multiconfigurational self-consistent-field, multireference configuration interaction, electron propagator, and various flavors of coupled cluster theory. At the self-consistent-field level, a highly original scheme, based on quaternion algebra, is implemented for the treatment of both spatial and time reversal symmetry. DIRAC features a very general module for the calculation of molecular properties that to a large extent may be defined by the user and further analyzed through a powerful visualization module. It allows for the inclusion of environmental effects through three different classes of increasingly sophisticated embedding approaches: the implicit solvation polarizable continuum model, the explicit polarizable embedding model, and the frozen density embedding model.