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

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

Quadratic response functions in the relativistic four-component Kohn-Sham approximation.

International audienceA formulation and implementation of the quadratic response function in the adiabatic four-component Kohn-Sham approximation is presented. The noninteracting reference state is time-reversal symmetric and formed from Kramers pair spinors, and the energy density is gradient corrected. Example calculations are presented for the optical properties of disubstituted halobenzenes in their meta and ortho conformations. It is demonstrated that correlation and relativistic effects are not additive, and it is shown that relativity alone reduces the mubeta-response signal by 62% and 75% for meta- and ortho-bromobenzene, respectively, and enhances the same response by 17% and 21% for meta- and ortho-iodobenzene, respectively. Of the employed functionals, CAM-B3LYP shows the best performance and gives hyperpolarizabilities beta distinctly different from B3LYP

Analytic one-electron properties at the 4-component relativistic coupled cluster level with inclusion of spin-orbit coupling

International audienceArticles you may be interested in Description of spin-orbit coupling in excited states with two-component methods based on approximate coupled-cluster theory An ab initio two-component relativistic method including spin-orbit coupling using the regular approximation We present a formulation and implementation of the calculation of (orbital-unrelaxed) expectation values at the 4-component relativistic coupled cluster level with spin-orbit coupling included from the start. The Lagrangian-based analytical energy derivative technique constitutes the basic theoretical framework of this work. The key algorithms for single reference relativistic coupled cluster have been implemented using routines for general tensor contractions of up to rank-2 tensors in which the direct product decomposition scheme is employed to benefit from double group symmetry. As a sample application, we study the electric field gradient at the bismuth nucleus in the BiX (X = N, P) series of molecules, where the effect of spin-orbit coupling is substantial. Our results clearly indicate that the current reference value for the nuclear quadrupole moment of 209 Bi needs revision. We also have applied our method to the calculation of the parity violating energy shift of chiral molecules. The latter property is strictly zero in the absence of spin-orbit coupling. For the H 2 X 2 (X = O,S,Se,Te) series of molecules the effect of correlation is found to be quite small. Published by AIP Publishing. [http://dx

A simple scheme for magnetic balance in four-component relativistic Kohn-Sham calculations of nuclear magnetic resonance shielding constants in a Gaussian basis

International audienceWe report the implementation of nuclear magnetic resonance (NMR) shielding tensors within the four-component relativistic Kohn-Sham density functional theory including non-collinear spin magnetization and employing London atomic orbitals to ensure gauge origin independent results, together with a new and efficient scheme for assuring correct balance between the large and small components of a molecular four-component spinor in the presence of an external magnetic field (simple magnetic balance). To test our formalism we have carried out calculations of NMR shielding tensors for the HX series (X = F, Cl, Br, I, At), the Xe atom, and the Xe dimer. The advantage of simple magnetic balance scheme combined with the use of London atomic orbitals is the fast convergence of results (when compared with restricted kinetic balance) and elimination of linear dependencies in the basis set (when compared to unrestricted kinetic balance). The effect of including spin magnetization in the description of NMR shielding tensor has been found important for hydrogen atoms in heavy HX molecules, causing an increase of isotropic values of 10%, but negligible for heavy atoms

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