Core-valence Electron Correlation Research Articles

Precision investigations of clock transitions and metastable lifetimes in highly charged Te-like ions

This study utilizes the multi-configuration Dirac-Hartree-Fock method to accurately calculate the lifetime and atomic parameters for the metastable state S01 of the 5s25p4 configuration, pertinent to clock transitions in Te-like highly charged ions. We systematically account for Valence–Valence, Core-Valence, and Core-Core electron correlations, alongside Breit interaction and quantum electrodynamics effects. Addressing the contingency problem regarding the lifetime of metastable state S01 of Xe2+ ion, as highlighted by E.Träbert (Phys. Scr. 85, 048101, 2012, https://doi.org/10.1088/0031-8949/85/04/048101) and K.G.Bhushan et al. (Phys. Rev A, 62, 012504, 2000, https://doi.org/10.1103/PhysRevA.62.012504) in early experiments and theories, we present theoretically calculated lifetime results. Our reasonable electron correlation model predicts a lifetime of 4.44 ms, which agrees with the experimentally measured lifetime of 4.46 ± 0.08 ms. Furthermore, we investigate the energy level crossing between 3P0 and 3P1 in Te-like systems near atomic number Z=52, where 3P→03P2 transition serves as a clock transition. We have calculated the atomic parameters related to the clock transition and hope that these results will provide valuable insights for the development of future highly charge ion clocks.

Rovibrational Line Lists of Triplet and Singlet Methylene.

The methylene molecule (CH2) is a short-lived radical with lacking data on its spectral line intensities. Although the lifetime of CH2 is extremely short under Earth's conditions, it exists in a free form in interstellar media. CH2 is an important intermediate species in chemical reactions associated with the formation and destruction of complex hydrocarbons. We present the first rovibrational line lists of CH2 in its ground triplet and first excited singlet electronic state. To this end, our previously developed accurate ab initio potential energy surface (PES) was used for the ground electronic triplet state [Egorov et al. J. Comp. Chem. 2024. V. 45. (2). P. 83] while a new PES for the singlet state was constructed in this work using the single-reference coupled cluster approach [CCSD(T)] combined with the extrapolation to the complete basis set (CBS) limit based on the correlation-consistent orbital basis sets with the core-valence electron correlation effects [aug-cc-pCVXZ, X = T, Q, 5, and 6]. In addition, the contributions to the correlation energy from highly excited Slater determinants [CC(n), n = 3-5] were included as well as the scalar relativistic effects and DBOC. The most accurate description of the infrared band origins of singlet CH2 was thus achieved for the energy range where the impact of the nonadiabatic coupling due to the Renner-Teller effect can be neglected. To obtain the probabilities of the rovibrational transitions, new ab initio DMSs were constructed both for the triplet and singlet CH2 using the CCSD(T)/aug-cc-pCVQZ approach. Finally, the absorption spectra of triplet and singlet methylene were predicted from the variationally computed line lists.

High-Temperature Line List of Phosphaethyne (HCP).

Phosphaethyne (HCP) has been detected in circumstellar envelopes; its spectroscopic line list is helpful for modeling the relevant atmospheric opacity. We present the first comprehensive line list for HCP(X1Σ+) using robust first-principles methods. The analytical potential energy surface and dipole moment surface were constructed based on 26478 ab initio points from coupled-cluster calculations, along with the considerations of core-valence electron correlation and scalar relativistic effects. The variational nuclear motion program TROVE was used to obtain the ro-vibrational energy levels, Einstein A coefficients, and so on. The J-dependent Coriolis-decoupled Hamiltonian was adopted in the variational calculations with k ≤ 20, and the linear molecule treatment was applied to consider the l-type doubling of the bending vibration. The line list contains almost 0.45 billion transitions between 1.21 million levels with rotational excitation up to J = 200. It covers the wavenumber range of 0-9000 cm-1 (wavelengths above 1.11 μm) and is suitable for temperatures up to 3000 K. The millimeter wave spectra agree well with the experiments, and the Fermi resonance between 2v2 and v3 bands has been reproduced.

The 3d 2 D 5/2−2 D 3/2 magnetic dipole transition in potassium-like ions

Spectral lines of the magnetic-dipole transition between the 3d2D3/2,5/2 levels of K-like Kr17+, Zr21+, Nb22+, Mo23+, and Ru25+ ions were measured in a compact electron beam ion trap. By means of dedicated calibration methods, the transition wavelengths of Kr17+, Zr21+, and Mo23+ ions reduce uncertainties by at least one order of magnitude and the wavelengths of Nb22+ and Ru25+ ions are measured for the first time at a few ppm level. In addition, the fine-structure energy splittings were systematically calculated using the multiconfiguration Dirac–Hartree–Fock method combined with the relativistic configuration interaction approach. The contributions of the core-valence and core-core electron correlations, the Breit interaction and QED effect were discussed in detail. The results show that it is essential to include deep core-valence correlation of L-shell and core-core valence correlation of 3p subshell to obtain an agreement better than 0.15% with existing experimental values. The calculation model can be performed to predict the wavelength within a high accuracy for a wide range of potassium-like ions.

Accurate and experimentally validated transition data for Si I and Si II

Aims. The aim of this study is to provide radiative data for neutral and singly ionised silicon, in particular for the first experimental oscillator strengths for near-infrared Si I lines. In addition, we aim to perform atomic structure calculations both for neutral and singly ionised silicon while including lines from highly excited levels. Methods. We performed large-scale atomic structure calculations with the relativistic multiconfiguration Dirac-Hartree-Fock method using the GRASP2K package to determine log(𝑔ƒ) values of Si I and Si II lines, taking into account valence-valence and core-valence electron correlation. In addition, we derived oscillator strengths of near-infrared Si I lines by combining the experimental branching fractions with radiative lifetimes from our calculations. The silicon plasma was obtained from a hollow cathode discharge lamp, and the intensity-calibrated high-resolution spectra between 1037 and 2655 nm were recorded by a Fourier transform spectrometer. Results. We provide an extensive set of accurate experimental and theoretical log(𝑔ƒ) values. For the first time, we derived 17 log(𝑔ƒ) values of Si I lines in the infrared from experimental measurements. We report data for 1500 Si I lines and 500 Si II lines. The experimental uncertainties of our ƒ-values vary between 5% for the strong lines and 25% for the weak lines. The theoretical log(𝑔ƒ) values for Si I lines in the range 161 nm to 6340 nm agree very well with the experimental values of this study and complete the missing transitions involving levels up to 3s23p7s (61 970 cm−1). In addition, we provide accurate calculated log(𝑔ƒ) values of Si II lines from the levels up to 3s27f (122 483 cm−1) in the range 81 nm to 7324 nm.

Single-photon ionization of SiC in the gas phase: experimental and ab initio characterization of SiC.

We report the first experimental observation of single-photon ionization transitions of the SiC radical between 8.0 and 11.0 eV performed on the DESIRS beamline at the SOLEIL synchrotron facility. The SiC radical, very difficult to synthesize in the gas phase, was produced through chemical reactions between CHx (x = 0-3) and SiHy (y = 0-3) in a continuous microwave discharge flow tube, the CHx and SiHy species being formed by successive hydrogen-atom abstractions induced by fluorine atoms on methane and silane, respectively. Mass-selected ion yield and photoelectron spectra were recorded as a function of photon energy using a double imaging photoelectron/photoion coincidence spectrometer. The photoelectron spectrum enables the first direct experimental determinations of the X+ 4Σ- ← X 3Π and 1+ 2Π ← X 3Π adiabatic ionization energies of SiC (8.978(10) eV and 10.216(24) eV, respectively). Calculated spectra based on Franck-Condon factors are compared with the experimental spectra. These spectra were obtained by solving the rovibrational Hamiltonian, using the potential energy curves calculated at the multireference single and double configuration interaction level with Davidson correction (MRCI + Q) and the aug-cc-pV5Z basis set. MRCI + Q calculations including the core and core-valence electron correlation were performed using the aug-cc-pCV6Z basis set to predict the spectroscopic properties of the six lowest electronic states of SiC+. Complete basis set extrapolations and relativistic energy corrections were also included in the determination of the energy differences characterizing the photoionization process. Using our experimental and theoretical results, we derived semi-experimental values for the five lowest ionization energies of SiC.

Theoretical studies of bound configuration levels and their radiative lifetimes in Pd− and Pt−

We performed multiconfiguration Dirac-Hartree-Fock and relativistic configuration-interaction calculations for states of the $4{d}^{9}5{s}^{2}$ and $4{d}^{10}5s$ configurations in ${\mathrm{Pd}}^{\ensuremath{-}}$ and for states of the $5{d}^{9}6{s}^{2}$ and $5{d}^{10}6s$ configurations in ${\mathrm{Pt}}^{\ensuremath{-}}$. Valence-valence, core-valence, and core-core electron correlation effects are accounted for in the present studies. The calculated excited energy levels agree within 2.5% with the available experimental values for both ${\mathrm{Pd}}^{\ensuremath{-}}$ and ${\mathrm{Pt}}^{\ensuremath{-}}$ and we confirm that ${\mathrm{Pd}}^{\ensuremath{-}}$ only has one bound excited state. We report a more precise value for the radiative lifetime of $5{d}^{9}6{s}^{2}{\phantom{\rule{4pt}{0ex}}}^{2}{D}_{3/2}$ in ${\mathrm{Pt}}^{\ensuremath{-}}$ ($67.0\ifmmode\pm\else\textpm\fi{}0.3$ ms), which agrees within the experimental range (50--200 ms), but the radiative lifetime of $5{d}^{10}6s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}$ ($4.00\ifmmode\pm\else\textpm\fi{}0.16$ s) in ${\mathrm{Pt}}^{\ensuremath{-}}$ is 50% longer than the experimental measurement ($2.54\ifmmode\pm\else\textpm\fi{}0.10$ s). The radiative lifetimes for $4{d}^{9}5{s}^{2}{\phantom{\rule{4pt}{0ex}}}^{2}{D}_{3/2,5/2}$ in ${\mathrm{Pd}}^{\ensuremath{-}}$ are also discussed in detail.

New Theoretical Infrared Line List for the Methyl Radical with Accurate Vibrational Band Origins from High-Level Ab Initio Calculations.

In the present work, high-level ab initio calculations were carried out for the ground electronic state of the methyl radical (CH3). Dunning's augmented correlation-consistent orbital basis sets were employed up to the quintuple-ζ valence quality with the core-valence electron correlation [aug-cc-pCV5Z] combined with the single- and double-excitation unrestricted coupled-cluster approach with a perturbative treatment of triple excitations [RHF-UCCSD(T)]. The explicitly correlated version of the coupled-cluster approach [RHF-UCCSD(T)-F12x{x = a, b}] was additionally applied with the core-valence cc-pCVQZ-F12 basis set in order to study convergence with respect to the basis set size. The contributions beyond the coupled-cluster level of the theory like Douglas-Kroll-Hess scalar relativistic Hamiltonian, diabatic Born-Oppenheimer corrections, and high-order electronic correlations have been included into the ab initio potential energy surfaces (PESs). It is shown that the theoretical band origins of CH3 converge gradually to the experimental values when applying the ab initio PESs using the aug-cc-pCVXZ [X = T, Q, and 5] basis sets. For the first time, all available experimental band origins of the gaseous CH3 are reproduced within an accuracy of 0.2 cm-1 using a newly developed PES extrapolated to the complete basis set limit [CBS(TQ5Z)]. The reached accuracy is one order of magnitude better than that of the best available calculations. A new theoretical infrared line list was generated for astrophysical applications using an ab initio dipole moment surface computed at the RHF-UCCSD(T)/aug-cc-pCVQZ level of the theory. The manifestation of a large-amplitude motion in CH3 is also discussed.

Ab initio potential energy functions, spectroscopy and thermal physics for krypton-contained rare gas dimers

Three state-of-the-art ab initio interatomic potential energy functions (PEFs) for the Kr-Ne, Kr-Ar, Kr-Xe rare gas dimers are presented. These PEFs are based upon extrapolation to complete basis set (CBS) limit results of supermolecular computations at the coupled-cluster level with single, double, and perturbative triple excitations (CCSD(T)) and correlation-consistent basis sets up to sextuple-zeta quality, augmented with mid-bond functions. Core-core and core-valence electron correlation, higher-order coupled-cluster excitations up to perturbative quadruple excitations, CCSDT(Q), and scalar relativistic corrections have also been taken into account. We have employed Morse/Long Range (MLR) potential energy functions (PEFs) to fit the total interaction energies as a function of the internuclear separation, followed by the calculation of spectroscopic parameters, vibrational and rotational energy levels, absorption spectra, and thermophysical properties over an extensive temperature range. Good agreement with experimental data and an empirical potential energy function shows that our ab initio MLR PEFs are superior not only to previous PEFs, but also to most empirical PEFs.

Benchmarking calculations of wavelengths and transition rates with spectroscopic accuracy for W xlviii through W lvi tungsten ions

Atomic properties of $n=3$ levels for ${\mathrm{W}}^{47+}\ensuremath{-}{\mathrm{W}}^{55+}$ ions ($Z=74$) are systematically calculated using two different and independent methods, namely, the second-order many-body perturbation theory and the multiconfiguration Dirac-Hartree-Fock method combined with the relativistic configuration interaction approach. Wavelengths and transition rates for electric- and magnetic-dipole transitions involving the $n=3$ levels of ${\mathrm{W}}^{47+}\ensuremath{-}{\mathrm{W}}^{55+}$ are calculated. In addition, we discuss in detail the importance of the valence and core-valence electron correlations, the Breit interaction, the higher-order frequency-dependent retardation correction, and the leading quantum electrodynamical corrections for transition wavelengths. Spectroscopic accuracy is achieved for the present calculated wavelengths, and most of them agree with experimental values within $0.05%$. Our calculated wavelengths, combined with collisional radiative model simulations, are used to identify the yet unidentified 25 observed lines in the extremely complex spectrum between $27\phantom{\rule{0.16em}{0ex}}\AA{}$ and $34\phantom{\rule{0.16em}{0ex}}\AA{}$ measured by Lennartsson $et\phantom{\rule{4pt}{0ex}}al.$ [Phys. Rev. A 87, 062505 (2013)]. We provide additional data for 472 strong electric-dipole transitions in the wavelength range of 17--50 \AA{}, and 185 strong magnetic-dipole transitions between $36\phantom{\rule{0.16em}{0ex}}\AA{}$ and $4384\phantom{\rule{0.16em}{0ex}}\AA{}$, with a line intensity greater than $1\phantom{\rule{0.16em}{0ex}}\mathrm{photon}/\mathrm{s}$. These can provide benchmark data for future experiments and theoretical calculations.

Highly accurate theoretical study on spectroscopic properties of SH including spin–orbit coupling* *Project supported by the National Natural Science Foundation of China (Grant No. 11874177), the Postdoctoral Scientific Research Developmental Fund of Heilongjiang Province, China (Grant No. LBH-Q20189), the Natural Science Research Project of the Education Department of Anhui Province, China (Grant Nos. KJ2020A0544 and KJ2018A0335), and the Excellent Youth

The multi-reference configuration interaction method plus Davidson correction (MRCI+Q) are adopted to study the low-lying states of SH with consideration of scalar relativistic effect, core-valence (CV) electron correlation, and spin–orbit coupling (SOC) effect. The SOC effect on the low-lying states is considered by utilizing the full Breit–Pauli operator. The potential energy curves (PECs) of 10 Λ–S states and 18 Ω states are calculated. The dipole moments of 10 Λ–S states are calculated, and the variation along the internuclear distance is explained by the electronic configurations. With the help of calculated SO matrix elements, the possible predissociation channels of A2Σ+, c4Σ− and F2Σ− are discussed. The Franck–Condon factors of A2Σ+–X2Π, F2Σ−–X2Π and E2Σ+–X2Π transitions are determined, and the radiative lifetimes of A2Σ+ and F2Σ− states are evaluated, which are in good agreement with previous experimental results.

Benchmarking calculations with spectroscopic accuracy of level energies and wavelengths in W LVII–W LXII tungsten ions

Atomic properties of n=3 states of the W56+ - W61+ ions are systematically investigated through two state-of-the-art methods, namely, the second-order many-body perturbation theory, and the multi-configuration Dirac–Hartree–Fock method combined with the relativistic configuration interaction approach. The contributions of valence-valence and core-valence electron correlations, the Breit interaction, the higher-order retardation correction beyond the Breit interaction through the transverse photon interaction, and the quantum electrodynamical corrections to the excitation energies are studied in detail. The excitation energies and wavelengths obtained with the two methods agree with each other within ≈0.01%. The present results achieve spectroscopic accuracy and provide a benchmark test for various applications and other theoretical calculations of W56+ - W61+ ions. They will assist spectroscopists in their assignment and direct identification of observed lines in complex spectra.

Model potential study of Rydberg one-electron spectrum of thallium

Semi-empirical model potential calculations of excitation energies, fine structure splittings, oscillator strengths and line strengths ratios were computed for high Rydberg transitions in principal, sharp and diffuse series of thallium one-electron spectrum with allowance for core–valence electron correlations in core polarization picture. Relativistic effects are fully included through solving Dirac equations and core–valence electron correlation is represented in core polarization picture by appropriate term in model potential optimized to reproduce ionization energies of the system for lowest states of given |nlj〉 symmetry. The dipole-moment operator of transition is modified in accordance. Systematic trends are investigated in line strength ratios and oscillator strengths along the spectral series, the latter showing hydrogen-like behavior for large n* effective quantum number of upper states of transition. The influence of core–valence correlation (core polarization) on line strength ratios and oscillator strengths along the spectral series is studied in detail demonstrating its importance even for transitions to highly excited Rydberg states with n=20. The strong effect of cancellation of positive and negative contributions to transition matrix element was observed for oscillator strengths and line strength ratios in principal series of thallium spectrum.

Benchmarking calculations with spectroscopic accuracy of excitation energies and wavelengths in sulfur-like tungsten

Atomic properties of S-like W are evaluated through a state-of-the-art method, namely, the multi-configuration Dirac-Hartree-Fock (MCDHF) method combined with the relativistic configuration interaction (RCI) approach. The level energies, wavelengths, and transition parameters involving the 88 lowest levels of W$^{+58}$ (W LIX) are calculated. We discuss in detail the relative importance of the valence- and core-valence electron correlation effects, the Breit interaction, the higher order retardation correction beyond the Breit interaction through the transverse photon interaction, and the quantum electrodynamical (QED) corrections. The present level energies are highly accurate, with uncertainties close to what can be achieved from spectroscopy. As such, they provide benchmark tests for other theoretical calculations of S-like W and should assist the spectroscopists in their assignment/identification of observed lines in complex spectra.

Semi-empirical model potential study of Rydberg transitions in gold one-electron spectrum

Semi-empirical model potential calculations of oscillator strengths for Rydberg transitions in principal, sharp and diffuse series of gold one-electron spectrum are presented. Relativistic effects are fully included through solving Dirac equations and core–valence electron correlation is represented in core polarization picture by appropriate part in model potential. The dipole-moment operator of transition is modified in accordance. Systematic trends are investigated in oscillator strengths along the spectral series showing hydrogen-like behavior for large n∗ effective quantum number of upper states of transitions. The so-called Cooper minimum in oscillator strengths is observed for principal series transitions. The influence of core–valence correlation (core polarization) on oscillator strengths along the spectral series is studied in detail​ demonstrating its importance even for transitions to rather highly excited Rydberg states with n≈18. In addition, excitation energies for some levels which positions in the neutral gold spectrum is unknown so far, are also predicted.

Equilibrium Structures of the Phosphorus Trihalides PF3 and PCl3, and the Phosphoranes PH3F2, PF5, PCl3F2, and PCl5.

Among the title species, a reliable and accurate equilibrium geometry (re structure) is available only for PF3, which has been determined experimentally more than 20 years ago. Here, we report accurate re structures for all title molecules, which were obtained using a composite computational approach based on explicitly correlated coupled-cluster theory (CCSD(T)-F12b) in conjunction with a large correlation-consistent basis set (cc-pCVQZ-F12) to take core–valence electron correlation into account. Additional terms were included to correct for the effects of iterative triple excitations (CCSDT), noniterative quadruple excitations (CCSDT(Q)), and scalar relativistic contributions (DKH2-CCSD(T)). The performance of this computational procedure was established through test calculations on selected small molecules (PH, PF, PCl, PH2, PF2, and PH3). For PF3, PCl3, PH3F2, and PF5 sufficiently accurate experimental ground-state rotational constants from the literature were used to determine semiexperimental re structures, which were found to be in excellent agreement with the corresponding best estimates from the current composite approach. The recommended equilibrium structural parameters are for PCl3, re(PCl) = 203.94 pm and θe(ClPCl) = 100.18°; for PH3F2, re(PHeq) = 138.38 pm and re(PFax) = 164.15 pm; for PF5, re(PFeq) = 153.10 pm and re(PFax) = 157.14 pm; for PCl3F2, re(PCleq) = 200.21 pm and re(PFax) = 159.37 pm; and for PCl5, re(PCleq) = 201.29 pm and re(PClax) = 211.83 pm. The associated uncertainties are estimated to be ±0.10 pm and ±0.10°, respectively.

Core-polarization corrected relativistic model potential energies and oscillator strengths for one-electron spectra of Ce XII through Ho XXI and for the W XXVIII spectrum of the silver isoelectronic sequence

The relativistic core-polarization corrected model potential energy levels and oscillator strengths are computed for highly ionized spectra of silver isoelectronic sequences from Ce XII through Ho XXI and for the W XXVIII spectrum. Calculations were performed altogether for 781 relativistic components of 5s–np, 5p–nd, 5d–nf, 4f–nd transitions with n = 5–9, and for 6s–np and 5p–ns transitions with n = 6–9. This paper presents oscillator strength values only for the 19 lowest transitions for each spectrum compared with other theoretical data available. The remaining data are available in electronic form upon request. It is demonstrated that core polarization (core-valence electron correlation) has a strong influence on oscillator strengths, not only for spectra close to the neutral end of the silver isoelectronic sequence, as believed in the past, but also for highly ionized systems.

Energies, wavelengths, and transition rates for Ge-like Mo, Ru, and Rh ions

The energy levels, wavelengths, transition rates, and oscillator strengths have been calculated for the fine-structure levels of the 4s24p2, 4s4p3, 4s24p4d, and 4p4 configurations in Ge-like Mo, Ru, and Rh ions. The fully relativistic multiconfiguration Dirac–Hartree–Fock method, taking correlations within the n = 8 complex, the Breit interaction and the quantum electrodynamics effects into consideration have been used in the calculations. Valence and core–valence electron correlation effects are accounted for through single–double multireference (SD-MR) expansions to increasing sets of active orbitals. Our results are compared with available experimental and other theoretical results, and a good agreement is obtained.

Radiative Transition Parameters in Atomic Lanthanum from Pseudo-Relativistic Hartree–Fock and Fully Relativistic Dirac–Hartree–Fock Calculations

Calculated radiative transition probabilities and oscillator strengths are reported for 392 lines of neutral lanthanum (La I) atom in the spectral range from the near ultraviolet to the mid infrared. They were obtained using two different theoretical methods based on the pseudo-relativistic Hartree–Fock (HFR) and the fully relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) approaches, both including the most important intravalence and core-valence electron correlations. The quality of these radiative parameters was assessed through detailed comparisons between the results obtained using different physical models and between our theoretical results and the experimental data, where available. Of the total number of La I lines listed in the present work, about 60% have gf- and gA-values determined for the first time.

Continuum wave functions for estimating the electric dipole moment: Calculation based on a multiconfiguration Dirac-Hartree-Fock approximation

The multiconfiguration Dirac-Hartree-Fock method is employed to calculate the continuum electron wave functions, which are then used to estimate their contribution to the atomic electric dipole moment (EDM) of $^{129}\mathrm{Xe}$. The EDM arises from $(P,T)$-odd electron-nucleon tensor-pseudotensor and pseudoscalar-scalar interactions, the nuclear Schiff moment, the interaction of the electron electric dipole moment with nuclear magnetic moments, and atomic electric dipole matrix elements. In addition to being estimated in the continuum states, all of these interactions are also estimated in the ground state, as well as in the Rydberg states of $^{129}\mathrm{Xe}$. Calculations of one-electron atomic orbitals include the interelectronic interactions, through valence and core-valence electron correlation effects. The contribution to the EDM from continuum states is found to be of the same order of magnitude as the contribution from discrete states.