Theoretical molecular spectroscopy of actinide compounds: The ThO molecule

The tiny-core generalized (Gatchina) relativistic pseudopotential (GRPP) model provides an accurate approximation for many-electron Hamiltonians of molecules containing heavy atoms, ensuring a proper description of the effects of non-Coulombian electron-electron interactions, electronic self-energy and vacuum polarization. Combining this model with electron correlation treatment in the frames of the intermediate Hamiltonian Fock space coupled cluster theory employing incomplete main model spaces, one obtains a reliable and economical tool for excited state modeling. The performance of this method is assessed in applications to \textit{ab initio} modeling of excited electronic states of the thorium monoxide molecule with term energies below 20000 cm$^{-1}$. Radiative lifetimes of excited states are estimated using truncated expansions of effective and metric operators in powers of cluster amplitudes

Relativistic coupled cluster calculation of Mossbauer isomer shifts of iodine compounds

Mossbauer isomer shifts of 129I and127I in the ICl, IBr and I 2 molecules are studied. Filatov's formulation is used, based on calculating the electronic energy change of the two systems involved in the Mossbauer. transition, the source and absorber. The energy difference between the transitions in the two systems determines the shift. The effects of relativity and electron correlation on the shifts are investigated. The exact two-component (X2C) and the four-component relativistic schemes give virtually identical results; the non-relativistic approach yields about 50% of the relativistic shifts. Electron correlation is included by coupled-cluster singles-and-doubles with perturbative triples [CCSD(T)]; it reduces Hartree-Fock shifts by 15%-20%. Basis sets are increased until the isomer shifts converge. The final results, calculated with the converged basis in the framework of the X2C Hamiltonian and CCSD(T) correlation, give an agreement of 10% or better with experimental data. [GRAPHICS

Ionization potentials and electron affinity of oganesson with relativistic coupled cluster method

We present high accuracy relativistic coupled cluster calculations of the first and second ionisation potentials and the electron affinity of the heaviest element in the Periodic Table, Og. The results were extrapolated to the basis set limit and augmented with the higher order excitations (up to perturbative quadruples), the Breit contribution, and the QED self energy and vacuum polarisation corrections. We have performed an extensive investigation of the effect of the various computational parameters on the calculated properties, which allowed us to assign realistic uncertainties on our predictions. Similar study on the lighter homologue of Og, Rn, yields excellent agreement with experiment for the first ionisation potential and a reliable prediction for the second ionisation potential

Ionization potentials and electron affinity of oganesson

We present high accuracy relativistic coupled cluster calculations of the first and second ionisation potentials and the electron affinity of the heaviest element in the Periodic Table, Og. The results were extrapolated to the basis set limit and augmented with the higher order excitations (up to perturbative quadruples), the Breit contribution, and the QED self energy and vacuum polarisation corrections. We have performed an extensive investigation of the effect of the various computational parameters on the calculated properties, which allowed us to assign realistic uncertainties on our predictions. Similar study on the lighter homologue of Og, Rn, yields excellent agreement with experiment for the first ionisation potential and a reliable prediction for the second ionisation potential

Generalized relativistic small-core pseudopotentials accounting for quantum electrodynamic effects: construction and pilot applications

A simple procedure to incorporate one-loop quantum electrodynamic (QED) corrections into the generalized (Gatchina) nonlocal shape-consistent relativistic pseudopotential model is described. The pseudopotentials for Lu, Tl, and Ra replacing only inner core shells (with principal quantum numbers $n\le 3$ for the two former elements and $n\le 4$ for the latter one) are derived from the solutions of reference atomic SCF problems with the Dirac-Coulomb-Breit Hamiltonian to which the model Lamb shift operator added. QED contributions to atomic valence excitation energies evaluated at the SCF level are demonstrated to exceed the errors introduced by the pseudopotential approximation itself by an order of magnitude. Pilot applications of the new model to calculations of excitation energies of two-valence-electron atomic systems using the intermediate-Hamiltonian relativistic Fock space coupled cluster method reformulated here for incomplete main model spaces are reported. Implications for high-accuracy molecular excited state calculations are discussed

High-accuracy calculation of nuclear quadrupole moments of atomic halogens,

Electric field gradients at the nuclei of halogen atoms are calculated using a finite field approach. The four-component Dirac-Coulomb Hamiltonian serves as the framework, all electrons are correlated by the relativistic Fock-space coupled cluster method with single and double excitations, and the Gaunt term, the main part of the Breit interaction, is included. Large basis sets (e.g., 28s24p21d9f4g2h Gaussian-type functions for I) are used. Combined with experimental nuclear quadrupole coupling constants, accurate estimates of the nuclear quadrupole moments are obtained. The calculated values are Q (Cl35) =-81.1 (1.2) mb, Q (Br79) =302 (5) mb, and Q (I127) =-680 (10) mb. Currently accepted reference values [Pyykkö, Mol. Phys. 99, 1617 (2001)] are -81.65 (80), 313(3), and -710 (10) mb, respectively. Our values are lower for the heavier halogens, corroborating the recent work of van Stralen and Visscher [Mol. Phys. 101, 2115 (2003)], who obtained Q (I127) =-696 (12) mb in a series of molecular calculations. © 2007 American Institute of Physics

The nuclear anapole moment interaction in BaF from relativistic coupled cluster theory

We present high accuracy relativistic coupled cluster calculations of the P-odd interaction coefficient $W_A$ describing the nuclear anapole moment effect on the molecular electronic structure. The molecule under study, BaF, is considered a promising candidate for the measurement of the nuclear anapole moment, and the preparation for the experiment is now underway [Altunas et al., Phys. Rev. Lett. 120, 142501 (2018)]. Influence of various computational parameters (size of the basis set, treatment of relativistic effects, and treatment of electron correlation) on the calculated $W_A$ coefficient is investigated and a recommended value of 147.7 Hz with an estimated uncertainty of 1.5% is proposed.Comment: 9 pages, 3 figures, 3 tables, minor changes, the published versio

Molecular enhancement factors for P, T-violating eEDM in BaCH3_3 and YbCH3_3 symmetric top molecules

High-precision tests of fundamental symmetries are looking for the parity- (P), time-reversal- (T) violating electric dipole moment of the electron (eEDM) as proof of physics beyond the Standard Model. Particularly, in polyatomic molecules, the complex vibrational and rotational structure gives the possibility to reach high enhancement of the P, T-odd effects in moderate electric fields. Additionally, it is possible to increase the statistical sensitivity by using laser cooling. In this work, we calculate the P, T-odd electronic structure parameters $W_\mathrm{d}$ and $W_\mathrm{s}$ for the promising candidates BaCH$_3$ and YbCH$_3$ for the interpretation of future experiments. We employ high-accuracy relativistic coupled cluster methods and systematically evaluate the uncertainties of our computational approach. Compared to other Ba- and Yb-containing molecules, BaCH$_3$ and YbCH$_3$ exhibit larger $W_\mathrm{d}$ and $W_\mathrm{s}$ associated to increased covalent character of the M--C bond. The calculated values are $3.22\pm 0.11 \times 10^{24}\frac{h\text{Hz}}{e\text{cm}}$ and $13.80\pm 0.35 \times 10^{24}\frac{h\text{Hz}}{e\text{cm}}$ for $W_\mathrm{d}$, and $8.42\pm0.29$~$h$kHz and $45.35\pm1.15$~$h$kHz for $W_\mathrm{s}$, in BaCH$_3$ and YbCH$_3$, respectively. The robust, accurate, and cost-effective computational scheme reported in this work makes our results suitable for extracting the relevant fundamental properties from future measurements and also can be used to explore other polyatomic molecules sensitive to various violations of fundamental symmetries

The electronic structure of the triiodide ion from relativistic correlated calculations: a comparison of different methodologies.

International audienceThe triiodide ion I(3)(-) exhibits a complex photodissociation behavior, the dynamics of which are not yet fully understood. As a first step toward determining the full potential energy surfaces of this species for subsequent simulations of its dissociation processes, we investigate the performance of different electronic structure methods [time-dependent density functional theory, complete active space perturbation theory to second order (CASPT2), Fock-space coupled cluster and multireference configuration interaction] in describing the ground and excited states of the triiodide ion along the symmetrical dissociation path. All methods apart from CASPT2 include scalar relativity and spin-orbit coupling in the orbital optimization, providing useful benchmark data for the more common two-step approaches in which spin-orbit coupling is introduced in the configuration interaction. Time-dependent density functional theory with the statistical averaging of model orbital potential functional is off the mark for this system. Another choice of functional may improve performance with respect to vertical excitation energies and spectroscopic constants, but all functionals are likely to face instability problems away from the equilibrium region. The Fock-space coupled cluster method was shown to perform clearly best in regions not too far from equilibrium but is plagued by convergence problems toward the dissociation limit due to intruder states. CASPT2 shows good performance at significantly lower computational cost, but is quite sensitive to symmetry breaking. We furthermore observe spikes in the CASPT2 potential curves away from equilibrium, signaling intruder state problems that we were unable to curb through the use of level shifts. Multireference configuration interaction is, in principle, a viable option, but its computational cost in the present case prohibits use other than for benchmarking purposes