Relativistic Coupled-cluster Calculations Research Articles

Spectroscopy of the 5s5p3P0→5s5d3D1 transition of strontium using laser cooled atoms

This article presents spectroscopy results of the 5s5p3P0→5s5d3D1 transition in all isotopes of laser cooled Sr atoms and the utility of this transition for repumping application. By employing the 5s5p3P0→5s5d3D1 (483 nm) transition in combination with the excitation of 5s5p3P2→5s6s3S1 (707 nm) transition, we observe a significant increase (∼13 fold) in the steady state number of atoms in the magneto-optic trap. This enhancement is attributed to the efficient repumping of Sr atoms that have decayed into the dark 5s5p3P2 state by returning them to the ground state 5s21S0 without any loss into the other states. The absolute transition frequencies were measured with an absolute accuracy of 30 MHz. To support our measurements, we performed Fock-space relativistic coupled-cluster calculations of the relevant parameters in Sr To further increase the accuracy of the calculated properties, corrections from the Breit, quantum electrodynamical and perturbative triples were also included. The calculated branching ratio for the repumping state confirms the significantly increased population in the 3P1 state. Thereby, leading to an increase of population of atoms trapped due to the enhanced repumping. Our calculated hyperfine-splitting energies are in excellent agreement with the measured values. Moreover, our calculated isotope shifts in the transition frequencies are in good agreement with our measured values.

Ab initio study of electronic states and radiative properties of the AcF molecule.

Relativistic coupled-cluster calculations of the ionization potential, dissociation energy, and excited electronic states under 35 000 cm-1 are presented for the actinium monofluoride (AcF) molecule. The ionization potential is calculated to be IPe = 48 866 cm-1, and the ground state is confirmed to be a closed-shell singlet and thus strongly sensitive to the T,P-violating nuclear Schiff moment of the Ac nucleus. Radiative properties and transition dipole moments from the ground state are identified for several excited states, achieving a mean uncertainty estimate of ∼450 cm-1 for the excitation energies. For higher-lying states that are not directly accessible from the ground state, possible two-step excitation pathways are proposed. The calculated branching ratios and Franck-Condon factors are used to investigate the suitability of AcF for direct laser cooling. The lifetime of the metastable (1)3Δ1 state, which can be used in experimental searches of the electric dipole moment of the electron, is estimated to be of order 1ms.

Relativistic coupled-cluster calculations of RaOH pertinent to spectroscopic detection and laser cooling.

A relativistic coupled-cluster study of the low-lying electronic states in the radium monohydroxide molecule (RaOH), a radioactive polyatomic molecule of interest to laser cooling and to the search of new physics beyond the Standard Model, is reported. The level positions of the A2Π1/2 and C2Σ states have been computed with an accuracy of around 200 cm-1 to facilitate spectroscopic observation of RaOH using laser induced fluorescence spectroscopy, thereby exploiting the systematic convergence of electron-correlation and basis-set effects in relativistic coupled-cluster calculations. The energy level for the B2Δ3/2 state has also been calculated accurately to conclude that the B2Δ3/2 state lies above the A2Π1/2 state. This confirms X2Σ ↔ A2Π1/2 as a promising optical cycling transition for laser cooling RaOH.

Route to Chemical Accuracy for Computational Uranium Thermochemistry.

Benchmark spinor-based relativistic coupled-cluster calculations for the ionization energies of the uranium atom, the uranium monoxide molecule (UO), and the uranium dioxide molecule (UO2) and for the bond dissociation energies of UO and UO2 are reported. The accuracy of these calculations in the treatments of relativistic, electron-correlation, and basis-set effects is analyzed. The intrinsic convergence of the computed results and the favorable comparison with the experimental values demonstrate the unique applicability of the spinor representation of quantum-chemical methods to open-shell uranium-containing atomic and molecular species with uranium oxidation states ranging from U(0) to U(V).

Relativistic exact two-component coupled-cluster calculations of electronic g-factors for heavy-atom-containing molecules pertinent to search of new physics

Exact two-component (X2C) coupled-cluster calculations of electronic g-factors for heavy-atom-containing small molecules pertinent to search of new physics beyond the standard model (BSM) is reported. A magnetic-field-dependent unitary transformation of the Dirac Hamiltonian has been adopted to enable a simple inclusion of the quantum electrodynamics correction to the free-electron g-factor in the four-component formulation. The X2C transformation is subsequently employed to eliminate the positronic degrees of freedom to enhance computational efficiency without significant loss of accuracy. The relationship of the present scheme to alternative four- and two-component formulations is discussed. To demonstrate the accuracy and usefulness of the present X2C scheme, we report coupled-cluster calculations for electronic g-factors of representative heavy-metal-containing small molecules including those relevant to precision spectroscopic search of BSM physics.

Relativistic coupled cluster calculations of the electron affinity and ionization potential of Nh(113)

Theoretical calculations based on the Dirac–Coulomb–Breit relativistic coupled cluster method have been carried out for the electron affinities and ionization potentials (IPs) of the superheavy element nihonium (Nh) and its lighter homologues In and Tl. The In and Tl calculations are in agreement with measurement within uncertainties. For Nh, where experiment is yet unknown, we predict the IP of 7.569(48) eV and electron affinity of 0.776(30) eV.

Relativistic coupled-cluster calculations of the energies, Landé g factors, radiative transition properties including line strengths, oscillator strengths, and transition rates for Th3+

Energies, Landé g factors, line strengths, transition probabilities, and oscillator strengths for electric dipole (E1), electric quadrupole (E2), and magnetic dipole (M1) transitions arising from the nS1/2 (n=7-10), nP1/2,3/2 (n=7-9), nD3/2,5/2 (n=6-9), nF5/2,7/2 (n=5-8), and nG7/2,9/2 (n=5,6) energy levels in Th3+, are calculated using the singles and doubles approximation of the relativistic coupled-cluster (CCSD) method. The data are compared with available experimental and theoretical results, showing a good agreement. To the best of our knowledge, many results are reported for the first time. This work reports a high-precision atomic property calculation of Th3+ and is of great significance for future spectral analysis and precision experiments targeting various applications.

Calculations of time-reversal-symmetry-violation sensitivity parameters based on analytic relativistic coupled-cluster gradient theory

We develop an analytic-gradient based method for relativistic coupled-cluster calculations of effective electric field, $\mathcal{E}_{\text{eff}}$, with improved efficiency and robustness over the previous state of the art. The enhanced capability to calculate this time-reversal symmetry violation sensitivity parameter enables efficient screening of candidate molecules for the electron electric dipole moment (eEDM) search. As examples, the |$\mathcal{E}_{\text{eff}}$| values of metal methoxides including BaOCH$_3$, YbOCH$_3$, and RaOCH$_3$ are shown to be as large as those of the corresponding fluorides and hydroxides, which supports the recent proposal of using these symmetric-top molecules to improve the sensitivity of eEDM measurements. The computational results also show that molecules containing late actinide elements, NoF, NoOH, LrO, and LrOH$^+$, exhibit particularly large |$\mathcal{E}_{\text{eff}}$| values of around 200 GV/cm.

The electron affinity of the uranium atom.

The results of a combined experimental and computational study of the uranium atom are presented with the aim of determining its electron affinity. Experimentally, the electron affinity of uranium was measured via negative ion photoelectron spectroscopy of the uranium atomic anion, U-. Computationally, the electron affinities of both thorium and uranium were calculated by conducting relativistic coupled-cluster and multi-reference configuration interaction calculations. The experimentally determined value of the electron affinity of the uranium atom was determined to be 0.309 ± 0.025eV. The computationally predicted electron affinity of uranium based on composite coupled cluster calculations and full four-component spin-orbit coupling was found to be 0.232eV. Predominately due to a better convergence of the coupled cluster sequence for Th and Th-, the final calculated electron affinity of Th, 0.565eV, was in much better agreement with the accurate experimental value of 0.608eV. In both cases, the ground state of the anion corresponds to electron attachment to the 6d orbital.

Relativistic coupled-cluster calculation of the electric dipole polarizability and correlation energy of Cn, Nh+ , and Og: Correlation effects from lighter to superheavy elements

We employ a fully relativistic coupled-cluster theory to calculate the ground-state electric dipole polarizability and electron correlation energy of superheavy elements Cn, Nh$^+$ and Og. To assess the trend of electron correlation as function of $Z$, we also calculate the correlation energies for three lighter homologs--Zn, Cd and Hg; Ga$^+$, In$^+$ and Tl$^+$; Kr, Xe and Rn--for each superheavy elements. The relativistic effects and quantum electrodynamical corrections are included using the Dirac-Coulomb-Breit Hamiltonian with the corrections from the Uehling potential and the self-energy. The effects of triple excitations are considered perturbatively in the theory. Furthermore, large bases are used to test the convergence of results. Our recommended values of polarizability are in good agreement with previous theoretical results for all SHEs. From our calculations we find that the dominant contribution to polarizability is from the valence electrons in all superheavy elements. Except for Cn and Og, we observe a decreasing contribution from lighter to superheavy elements from the Breit interaction. For the corrections from the vacuum polarization and self-energy, we observe a trend of increasing contributions with $Z$. From energy calculations, we find that the second-order many-body perturbation theory overestimates the electron correlation energy for all the elements considered in this work.

Relativistic Coupled-Cluster Calculations of Isotope Shifts for the Low-Lying States of Ca II in the Finite-Field Approach

We have evaluated the isotope shift (IS) constants of the first five low-lying fine-structure states of the singly charged calcium ion (Ca II) by adopting a finite-field (FF) approach in the relativistic coupled-cluster (RCC), a method developed by us and by using a code also developed by us. A similar previous calculation using singles and doubles approximation RCC theory (RCCSD method), gives results for the individual states in the FF approach that deviate substantially, while the differential values (the shifts of the spectral lines) agree reasonably well with other theoretical results and with experiments. However, we find a contrasting trend from the FF approach using our RCCSD method although calculations with the Dirac–Hartree–Fock (DHF) method shows good agreement. Our results also show that inclusion of partial triple excitations in the perturbative approach (RCCSD(T) method) through energy derivation lessens accuracy, but these results can be improved when triple excitations are included in the wave function that determines the RCC equations. The differences between the RCCSD and RCCSD(T) results demonstrate the importance of triple excitations in evaluating energies and IS constants for Ca II. Finally, we also present ab initio values of IS’s between the S–P, S–D, and D–P transitions in the DHF, and RCCSD and RCCSD(T) approximations and this is compared to the previously reported values (theoretical as well as experimental).

Relativistic coupled-cluster calculation of hyperfine-structure constants of La 2+

Using the singles and doubles approximated relativistic coupled-cluster method, we calculate hyperfine-structure constant A and B of 24 low-lying states of La2+. The results of the lowest four states 5d 3/2,5/2 and 4f 5/2,7/2 are compared with recently measured values (Olmschenk et al 2017 Phys. Rev. A 96 032502). Reasonable agreement is found for hyperfine-structure constant A of 5d 3/2 and 4f 5/2,7/2 states, but the hyperfine-structure constant A of 5d 5/2 and the hyperfine-structure constant B have a large deviation. To understand the role of the electron correlation effect, the intermediate results from lower-order many-body perturbation-theory and the linear version of coupled-cluster with single and double approximation are also presented. In the framework of coupled-cluster theory, the contribution trends from individual correlation effects are also investigated.

Photoelectron Spectroscopic and ab Initio Computational Studies of the Anion, HThO.

The synergetic combination of anion photoelectron spectroscopy and high-level relativistic coupled-cluster calculations was employed to study the anion, HThO-. The atomic connectivity of this anion was found to be HThO- and not ThOH-. Vibrational and electronic energy spacings in the HThO- photoelectron spectrum were measured and calculated, with good agreement between them being found. Computations yielded electronic energies and equilibrium structures as well as enabling orbital analyses. The adiabatic electron affinity (EAa) of HThO was determined to be 1.297 ± 0.035 eV.

Nuclear moments of germanium isotopes near N=40

Collinear laser spectroscopy measurements were performed on $^{69,71,73}$Ge isotopes ($Z = 32$) at ISOLDE-CERN. The hyperfine structure of the $4s^2 4p^2 \, ^3P_1 \rightarrow 4s^2 4p 5s \, ^3P_1^o$ transition of the germanium atom was probed with laser light of 269 nm, produced by combining the frequency-mixing and frequency-doubling techniques. The hyperfine fields for both atomic levels were calculated using state-of-the-art atomic relativistic Fock-space coupled-cluster calculations. A new $^{73}$Ge quadrupole moment was determined from these calculations and previously measured precision hyperfine parameters, yielding $Q_{\rm s}$ = $-$0.198(4) b, in excellent agreement with the literature value from molecular calculations. The moments of $^{69}$Ge have been revised: $\mu$ = +0.920(5) $\mu_{N}$ and $Q_{\rm s}$= +0.114(8) b, and those of $^{71}$Ge have been confirmed. The experimental moments around $N = 40$ are interpreted with large-scale shell-model calculations using the JUN45 interaction, revealing rather mixed wave function configurations, although their $g$-factors are lying close to the effective single-particle values. Through a comparison with neighboring isotones, the structural change from the single-particle nature of nickel to deformation in germanium is further investigated around $N = 40$.

Relativistic coupled-cluster study of BaF in search of violation

BaF is one of the potential candidates for the experimental search of the electric dipole moment of the electron (eEDM). The NL-eEDM collaboration is building a new experimental set up to measure the eEDM using the BaF molecule (The NL-eEDM collaboration, 2018 Eur. Phys. J. D 72: 197). To analyze the results of such an experiment, one would require the accurate value of the molecular -odd interaction parameters that cannot be measured from any experiment. In this work, we report the precise value of the -odd interaction parameters of the BaF molecule obtained from the four-component relativistic coupled-cluster calculations. We also calculate the hyperfine structure (HFS) constants of the same molecule to assess the reliability of the reported molecular parameters. The calculated HFS constants show good agreement with the available experimental values. Further, the systematic effects of electron-correlation along with the roles of inner-core electrons and the virtual energy functions in the calculation of the studied properties of BaF are investigated.

Role of electron correlation in the P,T -odd effects of CdH: A relativistic coupled-cluster investigation

We investigate the parity ($\mathcal{P}$) and time-reversal ($\mathcal{T}$) symmetry violating effects in the CdH molecule and perform the relativistic coupled-cluster calculation of the molecular parameters- $E_\text{eff}$, $W_\text{s}$ and $W_\text{M}$ related to the electric dipole moment of electron (eEDM) interaction, the scalar-pseudoscalar (S-PS) nucleus-electron neutral current coupling and the nuclear magnetic quadrupole moment (MQM) interaction with electrons, respectively. We also compute the molecular dipole moment and the magnetic hyperfine structure coupling constant of CdH. The value of $E_\text{eff}$, $W_\text{s}$ and $W_\text{M}$ obtained by us in the said molecule are 12.2 GV/cm, 14.0 kHz and $0.82\times$10$^{33}$ Hz/e cm$^2$, respectively, within an uncertainty of 10\%. Furthermore, we study the trend of electron-correlation in the computed properties of CdH and that of the $\mathcal{P,T}$-odd parameters in the group-12 monohydrides (i.e., ZnH, CdH, and HgH).

Enhanced P,T-violating nuclear magnetic quadrupole moment effects in laser-coolable molecules.

Nuclear magnetic quadrupole moments (MQMs), such as intrinsic electric dipole moments of elementary particles, violate both parity and time-reversal symmetry and, therefore, probe physics beyond the standard model. We report on accurate relativistic coupled cluster calculations of the nuclear MQM interaction constants in BaF, YbF, BaOH, and YbOH. We elaborate on estimates of the uncertainty of our results. The implications of experiments searching for nonzero nuclear MQMs are discussed.

Towards accurate prediction for laser-coolable molecules: relativistic coupled-cluster calculations for yttrium monoxide and prospects for improving its laser cooling efficiencies.

Benchmark relativistic coupled-cluster calculations for yttrium monoxide (YO) with accurate treatment of relativistic and electron correlation effects are reported. The spin-orbit mixing of 2Π and 2Δ is found to be an order of magnitude smaller than previously reported in the literature. Together with the measurement of the lifetime of the A'2Δ3/2 state, it implies an enhanced capability of a narrow-line cooling scheme to bring YO to sub-recoil temperature. The computed electronic transition properties also support a four-photon scheme to close the leakage of the A2Π1/2 ↔ X2Σ1/2+ cycle through the A'2Δ3/2 state by repumping the A'2Δ3/2 state to the B2Σ1/2+ state, which subsequently decays back to X2Σ1/2+. Relativistic coupled-cluster methods, capable of providing accurate spectroscopic parameters that characterize the local potential curves and hence of providing accurate Franck-Condon factors, appear to be promising candidates for accurate calculation of properties for laser-coolable molecules.

Accurate Predictions of Volatile Plutonium Thermodynamic Properties.

The ability to predict the nature and amounts of plutonium emissions in industrial accidents, such as in solvent fires at PUREX nuclear reprocessing facilities, is a key concern of nuclear safety agencies. In accident conditions and in the presence of oxygen and water vapor, plutonium is expected to form the three major volatile species PuO2, PuO3, and PuO2(OH)2, for which the thermodynamic data necessary for predictions (enthalpies of formation and heat capacities) presently show either large uncertainties or are lacking. In this work we aim to alleviate such shortcomings by obtaining the aforementioned data via relativistic correlated electronic structure calculations employing the multi-state complete active space with second-order perturbation theory (MS-CASPT2) with a state-interaction RASSI spin-orbit coupling approach, which is able to describe the multireference character of the ground-state wave functions of PuO3 and PuO2(OH2). We benchmark this approach by comparing it to relativistic coupled cluster calculations for the ground, ionized, and excited states of PuO2. Our results allow us to predict enthalpies of formation ΔfH⊖(298.15 K) of PuO2, PuO3, and PuO2(OH)2 to be -449.5 ± 8.8, -553.2 ± 27.5, and -1012.6 ± 38.1 kJ mol-1, respectively, which confirm the predominance of plutonium dioxide but also reveal the existence of plutonium trioxide in the gaseous phase under oxidative conditions, though the partial pressures of PuO3 and PuO2(OH)2 are nonetheless always rather low under a wet atmosphere. Our calculations also permit us to reassess prior results for PuO2, establishing that the ground state of the PuO2 molecule is mainly of 5Σg+ character, as well as to confirm the experimental value for the adiabatic ionization energy of PuO2.

Observing pre-edgeK-shell resonances in Kr, Xe, andXeF2

The $1s\phantom{\rule{4pt}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{4pt}{0ex}}np$ Rydberg transitions below the $1s$ ionization thresholds of Kr and Xe are obscured in x-ray absorption spectra due to core-hole lifetime broadening. However, the $np$ spectator electrons associated with those resonances can affect the core-hole decay spectra. We report on ion charge-state distributions of Kr and Xe measured in coincidence with ${KL}_{2,3}$ ($K{\ensuremath{\alpha}}_{1,2}$), ${KM}_{2,3}$ ($K{\ensuremath{\beta}}_{1,3}$), and ${\mathrm{KN}}_{2,3}$ ($K{\ensuremath{\beta}}_{2}$) x-ray fluorescence as the incident x-ray energy is scanned through pre-edge resonances and ionization thresholds. The coincidence measurements select vacancy cascades that begin with a radiative transition that transfers $1s$ holes to the $2p$, $3p$, and $4p$ shells followed by emission of Auger electrons. We observe shifts of ion yields from higher to lower charge states that we attribute to $np$ spectator electrons. For the special case of ${\mathrm{Kr}}^{1+}$ that is produced in coincidence with $K{\ensuremath{\beta}}_{2}$ x rays, the ion yield decreases in the pre-edge region. This is attributed to production of neutral, metastable Kr $4{p}^{\ensuremath{-}1}np$ states that reduce the ${\mathrm{Kr}}^{1+}$ yield. Model fits to the x-ray absorption spectra are presented to show the lifetime broadened pre-edge resonances and ionization thresholds. High-level relativistic coupled-cluster calculations that treat relativistic, electron correlation, and wave function relaxation effects on the same footing obtain agreement with the experimental $1s$ ionization energies of Kr and Xe to $<2$ eV. The Xe $K$-edge x-ray absorption spectrum and ion charge-state distributions of ${\mathrm{XeF}}_{2}$ were also recorded. Excitation of the $7{\ensuremath{\sigma}}_{u}$ lowest unoccupied molecular orbital (LUMO) in ${\mathrm{XeF}}_{2}$ is observed in the pre-edge region. Our ab initio calculations find that the $6{p}_{z}$ Rydberg state is strongly perturbed by the presence of the $7{\ensuremath{\sigma}}_{u}$ LUMO. A fit to the measured LUMO, $6{p}_{x}$, $6{p}_{y}$, $6{p}_{z}$ Rydberg states, and ionization threshold is guided by the relativistic coupled-cluster calculations. The F ligands modify the valence electron charge distribution and result in a $\ensuremath{\sim}2.3$ eV chemical shift of the Xe $1s$ ionization energy relative to atomic Xe. Xe $1{s}^{\ensuremath{-}1}$ core-hole decay in ${\mathrm{XeF}}_{2}$ results in ionization of the F ligands and energetic fragmentation into atomic ions. Ion charge-state spectra of ${\mathrm{XeF}}_{2}$ were recorded in coincidence with x-ray fluorescence for excitation on the LUMO resonance and above the Xe $1s$ ionization threshold. For the ion time of flight spectra recorded on the LUMO resonance, the ${\mathrm{F}}^{q+}$ ($q=1$--4) peaks are split into two peaks along the linear polarization direction of the incident x-ray beam. This effect is attributed to spatial alignment of ${\mathrm{XeF}}_{2}$ molecules by resonant x-ray absorption, and the peak splittings are used to measure the F ion fragmentation energies following $K{\ensuremath{\alpha}}_{1,2}$, $K{\ensuremath{\beta}}_{1,3}$, and $K{\ensuremath{\beta}}_{2}$ x-ray fluorescence. We observe variations of the F ion charge state yields and fragmentation energies for the three fluorescence pathways that leave the molecule in different outer-shell hole states.