Gauge origin independent calculations of molecular magnetisabilities in relativistic four-component theory

International audienceThe use of magnetic-field dependent London atomic orbitals, also called gauge including atomic orbitals, is known to be an efficient choice for accurate non-relativistic calculations of magnetisabilities. In this work, the appropriate formulas were extended and implemented in the framework of the four-component relativistic linear response method at the self-consistent field single reference level. Benefits of employing the London atomic orbitals in relativistic calculations are illustrated with Hartree-Fock wave functions on the XF3 (X = N, P, As, Sb, Bi) series of molecules. Significantly better convergence of magnetisabilities with respect to the basis set size is observed compared to calculations employing a common gauge origin. In fact, it is mandatory to use London atomic orbitals unless you want to use ridiculously large basis sets. Relativistic effects on magnetisabilities are found to be quite small (<5%) for this particular set of molecules, but should be investigated on a larger set of molecules. We emphasise the breakdown of the connection between the paramagnetic contribution to magnetisabilities and rotational g tensors in the relativistic domain and discuss its origin. Finally, we visualise the magnetisability density which shows markedly atomic features evocative of Pascal's rules

Generating and grading 34 Optimised Norm-Conserving Vanderbilt Pseudopotentials for Actinides and Super Heavy Elements in the PseudoDojo

In the last decades, material discovery has been a very active research field driven by the necessity of new materials for different applications. This has also included materials incorporating heavy elements, beyond the stable isotopes of lead. Most of actinides exhibit unique properties that make them useful in various applications. Further, new heavy elements, taking the name of super-heavy elements, have been synthesized, filling previously empty space of Mendeleev periodic table. Their chemical bonding behaviour, of academic interest at present, would also benefit of state-of-the-art modelling approaches. In particular, in order to perform first-principles calculations with planewave basis sets, one needs corresponding pseudopotentials. In this work, we present a series of fully-relativistic optimised norm-conserving Vanderbilt pseudopotentials (ONCVPs) for thirty-four actinides and super-heavy elements. The scalar relativistic version of these ONCVPs is tested by comparing equations of states for crystals, obtained with \textsc{abinit} 9.6, with those obtained by all-electron zeroth-order regular approximation (ZORA) calculations performed with the Amsterdam Modelling Suite BAND code. $\Delta$-Gauge and $\Delta_1$-Gauge indicators are used to validate these pseudopotentials. This work is a contribution to the PseudoDojo project, in which pseudopotentials for the whole periodic table are developed and systematically tested. The fully-relativistic pseudopotential files (i.e. including spin-orbit coupling) are available on the PseudoDojo web-interface pseudo-dojo.org under the name NC FR (ONCVPSP) v4.x. Pseudopotentials are made available in psp8 and UPF2 formats, both convenient for \textsc{abinit}, the latter being also suitable for Quantum ESPRESSO

Nuclear spin-dependent parity-violating effects in light polyatomic molecules

Measurements of nuclear spin-dependent parity-violating (NSD-PV) effects provide an excellent opportunity to test nuclear models and to search for physics beyond the Standard Model. Molecules possess closely-spaced states with opposite parity which may be easily tuned to degeneracy to greatly enhance the observed parity-violating effects. A high-sensitivity measurement of NSD-PV effects using light triatomic molecules is in preparation [E. B. Norrgard, et al., Commun. Phys. 2, 77 (2019)]. Importantly, by comparing these measurements in light nuclei with prior and ongoing measurements in heavier systems, the contribution to NSD-PV from $Z^0$-boson exchange between the electrons and the nuclei may be separated from the contribution of the nuclear anapole moment. Furthermore, light triatomic molecules offer the possibility to search for new particles, such as the postulated $Z^{\prime}$ boson. In this work, we detail a sensitive measurement scheme and present high-accuracy molecular and nuclear calculations needed for interpretation of NSD-PV experiments on triatomic molecules composed of light elements Be, Mg, N, and C. The ab initio nuclear structure calculations, performed within the No-Core Shell Model (NCSM) provide a reliable prediction of the magnitude of different contributions to the NSD-PV effects in the four nuclei. These results differ significantly from the predictions of the standard single-particle model and highlight the importance of including many-body effects in such calculations. In order to extract the NSD-PV contributions from measurements, a parity-violating interaction parameter $W_{\text{PV}}$, which depends on molecular structure, needs to be known with high accuracy. We have calculated these parameters for the triatomic molecules of interest using the relativistic coupled-cluster approach.Comment: 16 pages, 4 figures, and 6 table

Systematic study and uncertainty evaluation of P, T-odd molecular enhancement factors in BaF

A measurement of the magnitude of the electric dipole moment of the electron (eEDM) larger than that predicted by the Standard Model (SM) of particle physics is expected to have a huge impact on the search for physics beyond the SM. Polar diatomic molecules containing heavy elements experience enhanced sensitivity to parity (P) and time-reversal (T)-violating phenomena, such as the eEDM and the scalar-pseudoscalar (S-PS) interaction between the nucleons and the electrons, and are thus promising candidates for measurements. The NL-eEDM collaboration is preparing an experiment to measure the eEDM and S-PS interaction in a slow beam of cold BaF molecules [P. Aggarwal et al., Eur. Phys. J. D 72, 197 (2018)]. Accurate knowledge of the electronic structure parameters, Wd and Ws, connecting the eEDM and the S-PS interaction to the measurable energy shifts is crucial for the interpretation of these measurements. In this work, we use the finite field relativistic coupled cluster approach to calculate the Wd and Ws parameters in the ground state of the BaF molecule. Special attention was paid to providing a reliable theoretical uncertainty estimate based on investigations of the basis set, electron correlation, relativistic effects, and geometry. Our recommended values of the two parameters, including conservative uncertainty estimates, are 3.13 ±0.12×1024Hzecm for Wd and 8.29 ± 0.12 kHz for W

Hyperfine Structure Constants on the Relativistic Coupled Cluster Level with Associated Uncertainties

Accurate predictions of hyperfine structure (HFS) constants are important in many areas of chemistry and physics, from the determination of nuclear electric and magnetic moments to benchmarking of new theoretical methods. We present a detailed investigation of the performance of the relativistic coupled cluster method for calculating HFS constants within the finite-field scheme. The two selected test systems are 133Cs and 137BaF. Special attention has been paid to construct a theoretical uncertainty estimate based on investigations on basis set, electron correlation and relativistic effects. The largest contribution to the uncertainty estimate comes from higher order correlation contributions. Our conservative uncertainty estimate for the calculated HFS constants is ∼5.5%, while the actual deviation of our results from experimental values is <1% in all cases

The molecular mean-field approach for correlated relativistic calculations

A new approach for relativistic correlated electron structure calculations is proposed by which a transformation to a two-spinor basis is carried out after solving the four-component relativistic Hartree-Fock equations. The method is shown to be more accurate than approaches that apply an a priori transformation to a two-spinor basis. We also demonstrate how the two-component relativistic calculations with properly transformed two-electron interaction can be simulated at the four-component level by projection techniques, thus allowing an assessment of errors introduced by more approximate schemes. © 2009 American Institute of Physics