Nuclear size effects in rotational spectra: A tale with a twist

International audienceWe report a 4-component relativistic benchmark study of the isotopic field shift in the rotational spectrum of three diatomic molecules: TlI, PbTe and PtSi. A central quantity in the theory is the derivative with respect to internuclear distance of an effective electron density associated with a given nucleus, calculated at the equilibrium distance. The effective density, which is related to the mean electron density within the nuclear volume, is usually replaced with the contact density, that is, the electron density at the origin of the nucleus. Our computational study shows that for the chosen systems this induces errors on the order of 10%, which is not acceptable for high-precision work. On the other hand, the systematic nature of the error suggests that it can be handled by an atom-specific correction factor. Our calibration study reveals that relativistic effects increase the contact density gradient by about an order of magnitude, and that the proper transformation of the associated property operator is mandatory in 1- and 2-component relativistic calculations. Our results show very good agreement with the experimental data presented by Schlembach and Tiemann [Chem. Phys. 68 (1982) 21], but disagree completely with the revised results given by the same group in a later paper [Chem. Phys. 93 (1985) 349]. We have carefully re-derived the relevant formulas and cannot see that the rescaling of results is justified. Curiously previous DFT calculations agree quite well with the revised results for TlI and PbTe, but we demonstrate that this is because the authors inadvertently employed a non-relativistic Hamiltonian, which by chance induces an error of the same magnitude as the suggested scaling. For the PtSi molecule our results for the correction term due to nuclear volume disagree with experiment by a factor five, and we recommend a re-examination of the experimental data

Towards highly accurate calculations of parity violation in chiral molecules: relativistic coupled-cluster theory including QED-effects

Parity-violating energies $E_{PV}$ of the $H_2X_2$ X = O, S, Se, Te, Po) molecules are reported, calculated as analytical expectation values at the relativistic coupled-cluster singles-and-doubles (CCSD) level using property-optimized basis sets. Radiative corrections to the $E_{PV}$ was investigated using effective QED-potentials and found to reach a maximal value of 2.38% for $H_2Po_2$ . However, this result depends on the choice of effective self-energy potential and may indicate limitations to their domain of validity.Comment: 15 page

Calculating the many-potential vacuum polarization density of the Dirac equation in the finite-basis approximation

In this work, we propose an efficient and accurate computational method to evaluate the many-potential $\alpha\left(Z\alpha\right)^{n\ge3}$ vacuum polarization density of hydrogen-like atoms within the finite-basis approximation of the Dirac equation. To prove the performance of our computational method, we choose to work with the one-electron $_{\,\,\,92}^{238}\text{U}$ atom. In summary, we find that compliance with charge conjugation symmetry is a priori required to obtain physical results that are in line with our knowledge of the analytical problem. We also note that the final numerical results are found to be in excellent agreement with previous formal analytical (and numerical) evaluations that are limited to a few simple nuclear distribution models. Our technique can be efficiently implemented and evaluated in codes that solve the radial Dirac equation in the finite basis set framework and allows the use of arbitrary (radial) nuclear charge distribution. The obtained numerical results of the non-perturbative vacuum polarization density automatically account for the extended nuclear size effect. This method is hence of special importance for atomic Dirac problems whose analytical Green's functions expressions are not at hand or have relatively complicated analytical forms. Furthermore, we propose a vacuum polarization density formula that forces compliance with charge conjugation symmetry and can be used in cases where the relativistic basis violates this symmetry, as is the case in most relativistic basis set programs. In addition, we have shown that vector components of the vacuum polarization four-current vanish in the case where the Dirac Hamiltonian is symmetric under time-reversal symmetry.Comment: 14 page, 12 figure

Relativistic four- and two-component calculations of parity violation effects in chiral tungsten molecules of the form NWXYZ (X, Y, Z = H, F, Cl, Br, or I).

International audienceParity violation (PV) effects to the electronic ground state structure for a series of chiral tungsten molecules of the type NWXYZ (X, Y, Z = H, F, Cl, Br, or I) are compared using four- (Dirac) and two- (X2C) component relativistic Hartree-Fock and density functional theories. The results show the computationally more affordable two-component X2C approach yields accurate results for all molecules investigated. The PV energy differences between the two enantiomers range from as little as 0.4 Hz for NWClBrI to 140 Hz for NWHClI using a generalized gradient approximation including exact exchange (B3LYP). The W-N stretching mode in these molecules lies in the experimentally favorable CO(2) laser frequency range, and we therefore investigated PV effects in vibrational transitions using a single normal mode analysis. Here the PV frequency shift between the two enantiomers ranges from 1.6 mHz for NWFBrI to 710 mHz for NWHClI. Thus these types of molecules could be useful for the future detection of PV effects in chiral molecules

Employee Development Through Group Coaching and Its Applications in Organisations

The aim of the paper is to analyse one particular group coaching method and its implementation; to generalize the results of the authors’ research on the use of group coaching in order to evaluate its impact on employee characteristics, performance and development. We analyse the method and implementation of group coaching to help develop an evidence-based approach to this method. Economic point developing of organizations and teams has led us to pay main attention to intra-organizational cooperation and problem solving. That is crucial to achieving economic results of private and public organizationst. In 2017–2019, trainings and studies were carried out in group coaching with 445 leaders and specialists from the private and public sector in Estonia. The authors conducted interviews and questionnaires after group coaching sessions and used the results of the group coaching participants’ reports. An analysis of the data indicates that group coaching enables many benefits including problem solving, self-awareness, self-confidence and other person skills. It has also shown to strengthen employee self-reflection and develop cooperation skills and a better understanding of the aims and nature of their organization

Dipole allowed transitions in GdF: A four-component relativistic general open-shell configuration interaction study.

International audienceA four-component relativistic study of electronic transitions in the gadolinium monofluoride molecule (GdF) is presented. The electronic spectra of GdF have been investigated with a general open-shell configuration interaction method, where active electrons are distributed among molecular spinors mainly consisting of the Gd 4f, 5d, and 6s atomic spinors. The near-degeneracy effects of these spinors on the molecular electronic structure are considered by the valence full-CI-like approach. By the magnitudes of calculated transition dipole moments, the candidates for the observable transitions were selected. The present result is complementary to our previous study based on multireference configuration interaction singles and doubles calculations, which identified the electronic excited states of GdF by comparing the calculated excitation energies and angular momenta with those given by the laser spectroscopy. The spectra of the excited states less than 3.0 eV have been refined with the help of the calculated transition probabilities. The transitions between the excited states are newly analyzed and a rearrangement is proposed

Linear complex polarization propagator in a four-component Kohn-Sham framework.

International audienceAn algorithm for the solution of the linear response equation in the random phase approximation is presented. All entities including frequency arguments, matrices, and vectors, are assumed to be complex, and it represents the core equation solver needed in complex polarization propagator approaches where nonstimulated relaxation channels are taken into account. Stability and robustness of the algorithm are demonstrated in applications regarding visible, ultraviolet, and x-ray spectroscopies. An implementation of the algorithm at the level of four-component relativistic, noncollinear, density functional theory for imaginary (but not complex) frequency arguments has been achieved and is used to determine the electric dipole dispersion interaction coefficients for the rubidium and cesium dimers. Our best estimates for the C(6) coefficients of Rb(2) and Cs(2) are equal to 14.0x10(3) and 21.9x10(3) a.u., respectively