N. S. Mosyagin

Enhancement of the electric dipole moment of the electron in the BaF molecule

We report results of ab initio calculation of the spin-rotational Hamiltonian parameters including P- and P,T-odd terms for the BaF molecule. The ground state wave function of BaF molecule is found with the help of the Relativistic Effective Core Potential method followed by the restoration of molecular four-component spinors in the core region of barium in the framework of a non-variational procedure. Core polarization effects are included with the help of the atomic Many Body Perturbation Theory for Barium atom. For the hyperfine constants the accuracy of this method is about 5-10%.

ELECTRIC DIPOLE MOMENT OF THE ELECTRON IN THE YBF MOLECULE

Ab initio calculation of the hyperfine, P-odd, and P,T-odd constants for the YbF molecule was performed with the help of the recently developed technique, which allows to take into account correlations and polarization in the outercore region. The ground state electronic wave function of the YbF molecule is found with the help of the Relativistic Effective Core Potential method followed by the restoration of molecular four-component spinors in the core region of ytterbium in the framework of a non-variational procedure. Core polarization effects are included with the help of the atomic Many Body Perturbation Theory for Yb atom. For the isotropic hyperfine constant A, accuracy of our calculation is about 3% as compared to the experimental datum. The dipole constant Ad (which is much smaller in magnitude), though better than in all previous calculations, is still underestimated by almost 23%. Being corrected within a semiempirical approach for a perturbation of 4f-shell in the core of Yb due to the bond making, this error is reduced to 8%. Our value for the effective electric field on the unpaired electron is 4.9 a.u.=2.5E+10 V/cm.We have performed an ab initio calculation of the hyperfine, P-odd and P,T-odd constants for the YbF molecule using a recently developed technique which allows us to take into account correlations and polarization in the outer-core region. The ground state electronic wavefunction of the YbF molecule is found with the help of the relativistic effective core potential method followed by the restoration of molecular four-component spinors in the core region of ytterbium within the framework of a non-variational procedure. Core polarization effects are included with the help of atomic many-body perturbation theory for the Yb atom. Our calculation of the isotropic hyperfine constant A agrees at the 3% level with the experimental value. The dipole constant (which is much smaller in magnitude), though better than in all previous calculations, is still underestimated by almost 23%. This error is reduced to 8% after a semiempirical correction for perturbation of the -shell in the core of Yb due to the chemical bonding made. Our value for the effective electric field on the unpaired electron is .Ab initio calculation of the hyperfine, P-odd, and P,T-odd constants for the YbF molecule was performed with the help of the recently developed technique, which allows to take into account correlations and polarization in the outercore region. The ground state electronic wave function of the YbF molecule is found with the help of the Relativistic Effective Core Potential method followed by the restoration of molecular four-component spinors in the core region of ytterbium in the framework of a non-variational procedure. Core polarization effects are included with the help of the atomic Many Body Perturbation Theory for Yb atom. For the isotropic hyperfine constant A, accuracy of our calculation is about 3% as compared to the experimental datum. The dipole constant Ad (which is much smaller in magnitude), though better than in all previous calculations, is still underestimated by almost 23%. Being corrected within a semiempirical approach for a perturbation of 4f-shell in the core of Yb due to the bond making, this error is reduced to 8%. Our value for the effective electric field on the unpaired electron is 4.9 a.u.=2.5E+10 V/cm.

Towards relativistic ECP / DFT description of chemical bonding in E112 compounds: spin-orbit and correlation effects in E112X versus HgX (X=H, Au)

The relativistic effective core potential (RECP) approach combined with the spin-orbit DFT electron correlation treatment was applied to the study of the bonding of eka-mercury (E112) and mercury with hydrogen and gold atoms. Highly accurate small-core shape-consistent RECPs derived from Hartree-Fock-Dirac-Breit atomic calculations with Fermi nuclear model were employed. The accuracy of the DFT correlation treatment was checked by comparing the results in the scalar-relativistic (spin-orbit-free) limit with those of high level scalar-relativistic correlation calculations within the same RECP model. E112H was predicted to be slightly more stable than its lighter homologue (HgH). The E112-Au bond energy is expected to be ca. 25–30 % weaker than that of Hg-Au. The role of correlations and magnetic (spin-dependent) interactions in E112-X and Hg-X (X=H, Au) bonding is discussed. The present computational procedure can be readily applied to much larger systems and seems to be a promising tool for simulating E112 adsorption on metal surfaces.

Comparison of relativistic effective core potential and all-electron Dirac-Coulomb calculations of mercury transition energies by the relativistic coupled-cluster method

Relativistic effective core potential (RECP) and all-electron Dirac-Coulomb calculations of transition energies for low-lying states of the mercury atom and its ions are carried out with equivalent basis sets by the relativistic coupled-cluster method. RECP results are compared with corresponding all-electron values to estimate the accuracy of different RECP versions. Contributions from correlations of different electron shells to the calculated transition energies are studied. Effects of different nuclear models and of basis set truncation at different orbital angular momenta as well as errors of the Gaussian approximation of the generalized RECP components are reported. We show that at least 34 external electrons of the mercury atom should be correlated and the one-electron basis set should contain up to h-type functions in order to attain consistent agreement within 200 cm 1 with experimental data.

Broadband velocity modulation spectroscopy of HfF + : towards a measurement of the electron electric dipole moment

Precision spectroscopy of trapped HfF + will be used in a search for the permanent electric dipole moment of the electron (eEDM). While this dipole moment has yet to be observed, various extensions to the standard model of particle physics (such as supersymmetry) predict values that are close to the current limit. We present extensive survey spectroscopy of 19 bands covering nearly 5000 cm −1 using both frequency-comb and single-frequency laser velocity-modulation spectroscopy. We obtain high-precision rovibrational constants for eight electronic states inclu ding those that will be necessary for state preparation and r eadout in an actual eEDM experiment.

Generalized relativistic effective core potential and relativistic coupled cluster calculation of the spectroscopic constants for the HgH molecule and its cation

Generalized relativistic effective core potential (GRECP) calculations of spectroscopic constants of the HgH molecule ground and low excited states and the HgH+ cation ground state are carried out, with correlation included by the Fock-space relativistic coupled cluster (RCC) method. Basis set superposition errors (BSSE) are estimated and discussed. It is demonstrated that connected triple excitations of the 13 outermost electrons are necessary to obtain accurate results for mercury hydride. Spectroscopic constants derived from potential curves which include these terms are in very good agreement with experiment, with errors of a few mbohr in Re, tens of wave numbers in excitation energies and vibrational frequencies, and proportionately for other properties. Comparison with previous calculations is also presented.

Generalized relativistic effective core potential. I. Numerical calculations for atoms Hg through Bi

A generalization of the shape‐consistent Relativistic Effective Core Potential (RECP) method is developed for the case of pseudospinors that may have nodes. Both valence and outermost core pseudospinors are included in the Generalized RECP generation procedure. The numerical potentials have been constructed and the calculations of transition energies and some other properties have been made for the atoms Hg through Bi in the jj‐coupling scheme in order to study the treatment of relativistic effects in the scope of the two‐component Generalized RECP approach. As compared with the other shape‐consistent RECP variants, significant improvement is reached when 5s, 5p, and 5d shells are included in the pseudovalence space.

GRECP/MRD‐CI calculations of spin‐orbit splitting in ground state of Tl and of spectroscopic properties of TlH

The generalized relativistic effective core potential (GRECP) approach is employed in the framework of multireference single- and double-excitation configuration interaction (MRD-CI) method to calculate the spin-orbit splitting in the 2Po ground state of the Tl atom and spectroscopic constants for the 0+ ground state of TlH. The 21-electron GRECP for Tl is used, and the outer core 5s and 5p pseudospinors are frozen with the help of the level shift technique. The spin-orbit selection scheme with respect to relativistic multireference states and the corresponding code are developed and applied in the calculations. In this procedure both correlation and spin-orbit interactions are taken into account. A [4,4,4,3,2] basis set is optimized for the Tl atom and employed in the TlH calculations. Very good agreement is found for the equilibrium distance, vibrational frequency, and dissociation energy of the TlH ground state (Re=1.870 A, ωe=1420 cm−1, De=2.049 eV) as compared with the experimental data (Re=1.872 A, ωe=1391 cm−1, De=2.06 eV).

Relativistic effective core potential calculations of Hg and eka-Hg (E112) interactions with gold: Spin-orbit density functional theory modeling of Hg–Aun and E112–Aun systems

Interactions of eka-Hg (E112) and Hg atoms with small gold clusters were studied in the frame of the relativistic effective core potential model using the density functional theory (DFT) approach incorporating spin-dependent (magnetic) interactions. The choice of the exchange-correlation functional was based on a comparison of the results of DFT and large-scale coupled cluster calculations for E112Au and HgAu at the scalar relativistic level. A close similarity between the E112Aun and HgAun equilibrium structures was observed. The E112 binding energies on Aun are typically smaller than those for Hg by ca. 25%-32% and the equilibrium E112-Au separations are always slightly larger than their Hg-Au counterparts.

Is E112 a relatively inert element? Benchmark relativistic correlation study of spectroscopic constants in E112H and its cation

We report the first results of relativistic correlation calculation of the spectroscopic properties for the ground state of E112H and its cation in which spin-orbit interaction is taken into account non-perturbatively. Studying the properties of E112 (eka-Hg) is required for chemical identification of its long-lived isotope, (283)112. It is shown that appropriate accounting for spin-orbit effects leads to dramatic impact on the properties of E112H whereas they are not so important for E112H(+). The calculated equilibrium distance, R(e) (calc)=1.662 Angstrom, in E112H is notably smaller than R(e) (expt)=(1.738+/-0.003) Angstrom and R(e) (calc)=1.738 Angstrom in HgH, whereas the dissociation energy, D(e) (calc)=0.42 eV, in E112H is close to D(e) (expt)=0.46 eV and D(e) (calc)=0.41 eV in HgH. These data are quite different from R(e) (NH)=1.829 Angstrom and D(e) (NH)=0.06 eV obtained for E112H within the scalar-relativistic Douglas-Kroll approximation. Our results indicate that E112 should not be expected to behave like a noble gas in contrast to the results by other authors.