Finite-Basis-Set Approach to the Two-Center Heteronuclear Dirac Problem

Kotov, Artem A.; Glazov, D. A.; Malyshev, A. V.; Shabaev, V. M.; Plunien, G.

doi:10.3390/atoms10040145

Cited by 2 publications

(3 citation statements)

References 46 publications

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“…We estimated the accuracy of our values at 10 −8 by comparing them with numerical results performed within the framework of the nonrelativistic approach [37,38]. Although the A-DKB method was initially adapted to study quasi-molecules with heavy nuclei [28][29][30], the results obtained for light systems show sufficient accuracy with the data presented in the literature and are comparable to those for heavy compounds [12]. While this question is not crucial for this work, the A-DKB approach is capable of high-precision calculations using the methods described in [18,19].…”

Section: Discussionmentioning

confidence: 99%

“…The multipolar partial-wave decomposition in the center-of-mass system is usually used as the solution of equation (1), see, for example, [13,17]. We use a method which permits to carry out calculations without such approximation and has shown its efficiency for completely relativistic calculations of heavy quasi-molecules [28][29][30]. The method is based on the decomposition of the required wave function over a finite basis set of B-splines [25,35] with the imposed dual-kinetic-balance conditions [26] generalized to the case of axially symmetric systems [27].…”

Section: The Dual Kinetic Balance Methods For Systems With Axial Symm...mentioning

confidence: 99%

“…Recently, the A-DKB method has been adapted to one-and two-electron systems consisting of two heavy nuclei [28][29][30]. In [31] it has been applied to the light atom-antiproton compounds.…”

Section: Introductionmentioning

confidence: 99%

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Light one-electron molecular ions within the finite-basis-set method for the two-center Dirac equation

Solovyev,

Anikin,

Danilov

et al. 2024

Phys. Scr.

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During the last decades outstanding results on the precision description of light diatomic molecular compounds have been achieved. The most advanced calculations of electron binding energies have been realized mainly in the framework of the nonrelativistic approach with a consistent account of relativistic and radiative QED corrections. Recently, it has been shown that methods based on the Dirac equation are also suitable for obtaining highly accurate results in simple light molecules. In this paper, we present a completely relativistic method and discuss its application to the description of diatomic systems. In particular, the electronic spectra of the light one-electron quasi-molecular compounds H-H$^+$, He$^+$-He$^{2+}$ and He$^+$-H$^+$ are analyzed. For this purpose, the two-center Dirac equation is solved by a dual-kinetic balanced finite-basis-set method for axially symmetric systems, called A-DKB. This method allows for a complete relativistic consideration of the electron at fixed inter-nuclear distances. A comparison of the obtained results with the nonrelativistic and relativistic calculations presented in the literature is performed. Without pursuing the goal of high accuracy calculations, the advantages and disadvantages of the approach, as well as possible applications of the method, are discussed in detail.

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Section: Discussionmentioning

confidence: 99%

Section: The Dual Kinetic Balance Methods For Systems With Axial Symm...mentioning

confidence: 99%

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Light one-electron molecular ions within the finite-basis-set method for the two-center Dirac equation

Solovyev,

Anikin,

Danilov

et al. 2024

Phys. Scr.

Self Cite

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Light antiproton one-electron quasi-molecular ions within the relativistic A-DKB method

Anikin,

Danilov,

Glazov

et al. 2023

The Journal of Chemical Physics

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In the present work, two quasi-molecular compounds each involving one antiproton and one electron (p̄), He+−p̄ and H−p̄, are investigated. Using completely relativistic calculations within the finite-basis method adapted to systems with axial symmetry, the adiabatic potential curves are constructed by numerically solving the two-center Dirac equation. The binding energies of electron are obtained as a function of the inter-nuclear distance and compared with the corresponding nonrelativistic values and relativistic leading-order corrections calculated in the framework of other approaches. A semantic analysis of antiproton quasi-molecular ions with compounds containing a proton (p) instead of an antiproton is given. The advantages of the A-DKB method are demonstrated.

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Finite-Basis-Set Approach to the Two-Center Heteronuclear Dirac Problem

Cited by 2 publications

References 46 publications

Light one-electron molecular ions within the finite-basis-set method for the two-center Dirac equation

Light one-electron molecular ions within the finite-basis-set method for the two-center Dirac equation

Light antiproton one-electron quasi-molecular ions within the relativistic A-DKB method

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