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Symmetry
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Relativistic and QED Effects in Atoms and Molecules
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Relativistic and QED Effects in Atoms and Molecules

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (1 July 2021) | Viewed by 11940

Special Issue Editor

Prof. Dr. Ephraim Eliav

E-Mail Website
Guest Editor
The School of Chemistry, Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel
Interests: benchmarks calculations of atomic and molecular properties; heavy and superheavy elements chemistry and physics; relativistic and QED effects in chemistry; development of high-precision relativistic electron correlation approaches in quantum chemistry and atomic physics; multireference relativistic coupled cluster methods

Special Issue Information

Dear Colleagues,

It is now well established and illustrated by many calculations and experiments that the structure, spectroscopy, and chemical activity of heavy atoms and molecules exhibit large relativistic and non-negligable QED effects, together with a sizeable electron correlation. All the effects, enumerated above, are in many cases of the same order of magnitude, non-additive, and strongly intertwined. In order to be eligable for  benchmark atomic and molecular calculations, these effects should be included into the computational scheme on equal footing, up to high orders and sized consistently. These effects play an important role in lighter element compounds too, showing up in phenomena such as the fine or hyperfine structure of electronic states. Tremendous progress has been achieved recently in the development, computer implementation, and actual application of different levels of approximation treatment of relativistic and QED effects in atomic and molecular systems. Various top-level many-body relativistic approaches are nowadays available in free or open-source software, and are used routinely in high-quality or benchmark calculations of atomic and molecular systems. However, many theoretical and computational challenges still remain. Below, some of them are enumerated:

  1. The development of efficient, multireference, all-order correlation relativistic (and QED) approaches for the treatment of general, open-shell, many-electron-charged, and neutral systems;
  2. The formulation and implementation of QED-based, Lorentz-invariant many-body approaches suitable for practical atomic and molecular applications;
  3. Nuclear structure and weak interaction effects on atomic and molecular spectra and properties;
  4. High-level calculations of the electronic structure and properties of actinide and trans-actinide compounds and a firm prediction of the structure of extended periodic table of elements;
  5. Atomic and molecular evidence for new physics beyond the Standard model.

Prof. Dr. Ephraim Eliav
Guest Editor

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Keywords

  • Relativistic effests
  • QED effects in chemistry
  • Four-component methods
  • Dirac Coulomb Breit Hamiltonian
  • Heavy elements compounds
  • Super-heavy elements
  • Vaccuum polarization and self energy calculations
  • PNC effects in atoms and molecules
  • Multireference relativistic correlation methods
  • Nuclear structure effects.

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Published Papers (4 papers)

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Research

15 pages, 358 KiB  
Article
Finite-Field Calculations of Transition Properties by the Fock Space Relativistic Coupled Cluster Method: Transitions between Different Fock Space Sectors
by Andréi Zaitsevskii, Alexander V. Oleynichenko and Ephraim Eliav
Symmetry 2020, 12(11), 1845; https://doi.org/10.3390/sym12111845 - 8 Nov 2020
Cited by 15 | Viewed by 2397
Abstract
Reliable information on transition matrix elements of various property operators between molecular electronic states is of crucial importance for predicting spectroscopic, electric, magnetic and radiative properties of molecules. The finite-field technique is a simple and rather accurate tool for evaluating transition matrix elements [...] Read more.
Reliable information on transition matrix elements of various property operators between molecular electronic states is of crucial importance for predicting spectroscopic, electric, magnetic and radiative properties of molecules. The finite-field technique is a simple and rather accurate tool for evaluating transition matrix elements of first-order properties in the frames of the Fock space relativistic coupled cluster approach. We formulate and discuss the extension of this technique to the case of transitions between the electronic states associated with different sectors of the Fock space. Pilot applications to the evaluation of transition dipole moments between the closed-shell-like states (vacuum sector) and those dominated by single excitations of the Fermi vacuum (the 1h1p sector) in heavy atoms (Xe and Hg) and simple molecules of heavy element compounds (I2 and TlF) are reported. Full article
(This article belongs to the Special Issue Relativistic and QED Effects in Atoms and Molecules)
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14 pages, 788 KiB  
Article
Charge Conjugation Symmetry in the Finite Basis Approximation of the Dirac Equation
by Maen Salman and Trond Saue
Symmetry 2020, 12(7), 1121; https://doi.org/10.3390/sym12071121 - 6 Jul 2020
Cited by 3 | Viewed by 2868
Abstract
Four-component relativistic atomic and molecular calculations are typically performed within the no-pair approximation where negative-energy solutions are discarded. These states are, however, needed in QED calculations, wherein, furthermore, charge conjugation symmetry, which connects electronic and positronic solutions, becomes an issue. In this work, [...] Read more.
Four-component relativistic atomic and molecular calculations are typically performed within the no-pair approximation where negative-energy solutions are discarded. These states are, however, needed in QED calculations, wherein, furthermore, charge conjugation symmetry, which connects electronic and positronic solutions, becomes an issue. In this work, we shall discuss the realization of charge conjugation symmetry of the Dirac equation in a central field within the finite basis approximation. Three schemes for basis set construction are considered: restricted, inverse, and dual kinetic balance. We find that charge conjugation symmetry can be realized within the restricted and inverse kinetic balance prescriptions, but only with a special form of basis functions that does not obey the right boundary conditions of the radial wavefunctions. The dual kinetic balance prescription is, on the other hand, compatible with charge conjugation symmetry without restricting the form of the radial basis functions. However, since charge conjugation relates solutions of opposite value of the quantum number κ , this requires the use of basis sets chosen according to total angular momentum j rather than orbital angular momentum ℓ. As a special case, we consider the free-particle Dirac equation, where opposite energy solutions are related by charge conjugation symmetry. We show that there is additional symmetry in that solutions of the same value of κ come in pairs of opposite energy. Full article
(This article belongs to the Special Issue Relativistic and QED Effects in Atoms and Molecules)
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17 pages, 452 KiB  
Article
Relativistic Fock Space Coupled Cluster Method for Many-Electron Systems: Non-Perturbative Account for Connected Triple Excitations
by Alexander V. Oleynichenko, Andréi Zaitsevskii, Leonid V. Skripnikov and Ephraim Eliav
Symmetry 2020, 12(7), 1101; https://doi.org/10.3390/sym12071101 - 2 Jul 2020
Cited by 32 | Viewed by 3443
Abstract
The Fock space relativistic coupled cluster method (FS-RCC) is one of the most promising tools of electronic structure modeling for atomic and molecular systems containing heavy nuclei. Until recently, capabilities of the FS-RCC method were severely restricted by the fact that only single [...] Read more.
The Fock space relativistic coupled cluster method (FS-RCC) is one of the most promising tools of electronic structure modeling for atomic and molecular systems containing heavy nuclei. Until recently, capabilities of the FS-RCC method were severely restricted by the fact that only single and double excitations in the exponential parametrization of the wave operator were considered. We report the design and the first computer implementation of FS-RCC schemes with full and simplified non-perturbative account for triple excitations in the cluster operator. Numerical stability of the new computational scheme and thus its applicability to a wide variety of molecular electronic states is ensured using the dynamic shift technique combined with the extrapolation to zero-shift limit. Pilot applications to atomic (Tl, Pb) and molecular (TlH) systems reported in the paper indicate that the breakthrough in accuracy and predictive power of the electronic structure calculations for heavy-element compounds can be achieved. Moreover, the described approach can provide a firm basis for high-precision modeling of heavy molecular systems with several open shells, including actinide compounds. Full article
(This article belongs to the Special Issue Relativistic and QED Effects in Atoms and Molecules)
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16 pages, 550 KiB  
Article
P , T -Violating and Magnetic Hyperfine Interactions in Atomic Thallium
by Timo Fleig and Leonid V. Skripnikov
Symmetry 2020, 12(4), 498; https://doi.org/10.3390/sym12040498 - 30 Mar 2020
Cited by 16 | Viewed by 2682
Abstract
We present state-of-the-art string-based relativistic general-excitation-rank configuration interaction and coupled cluster calculations of the electron electric dipole moment, the nucleon–electron scalar-pseudoscalar, and the magnetic hyperfine interaction constants ( α d e , α C S , A | | , respectively) for the [...] Read more.
We present state-of-the-art string-based relativistic general-excitation-rank configuration interaction and coupled cluster calculations of the electron electric dipole moment, the nucleon–electron scalar-pseudoscalar, and the magnetic hyperfine interaction constants ( α d e , α C S , A | | , respectively) for the thallium atomic ground state 2 P 1 / 2 . Our present best values are α d e = − 558 ± 28 , α C S = 6.77 ± 0.34 [ 10 − 18 e cm], and A | | = 21172 ± 1059 [MHz]. The central value of the latter constant agrees with the experimental result to within 0.7% and serves as a measurable probe of the P , T -violating interaction constants. Our findings lead to a significant reduction of the theoretical uncertainties for P , T -odd interaction constants for atomic thallium but not to stronger constraints on the electron electric dipole moment, d e , or the nucleon–electron scalar-pseudoscalar coupling constant, C S . Full article
(This article belongs to the Special Issue Relativistic and QED Effects in Atoms and Molecules)
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