Analytical evaluation of the short-range interaction energy for ground state H<sup>+</sup><sub>2</sub>

Battezzati, M.; Magnasco, Valerio

doi:10.1088/0305-4470/37/44/012

Cited by 6 publications

(25 citation statements)

References 17 publications

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“…The separation of the 3-dimensional Schroedinger equation for + H 2 in confocal elliptic (spheroidal) coordinates x h j ( ) , , of the electron, with nuclei kept in fixed position [1][2][3][4][5][6][7][8][9][10][11][12][13], originates three one-dimensional differential equations, the outer ξ−equation, the inner η-equation and the j-equation. The subsequent variable transformation:…”

Section: Methodsmentioning

confidence: 99%

“…The evaluation of the coefficients arising in the short-range expansion of the interaction in ground state + H 2 has been the object of many investigations [1][2][3][4][5][6][7][8][9][10][11]. In this paper we extend the calculations to the evaluation of the C 10 coefficient using our previous techniques.…”

Section: Introductionmentioning

confidence: 99%

“…The main principles and assumptions on which they are founded are examined and refined calculations are presented. In [7] perturbation theory was applied in conjunction with first-passage time techniques in order to solve both the so-called [4] inner and outer equations, while in subsequent work [8,10] it was found more suitable to make recourse to Hylleraas tridiagonal determinantal method [1] applied to the inner equation. This led straightforwardly to useful analytical results, although the physical picture of an electron stabilized by resonance in a double-well potential, which results from our transformed equations (2), (2ʹ) below, was somewhat hidden in that approach.…”

Section: Introductionmentioning

confidence: 99%

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Short-range interaction energy for ground-state ${{\bf{H}}}_{2}^{+}$

Battezzati

Magnasco

2018

J. Phys. Commun.

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The analytical procedures previously developed by the authors (see references) in order to evaluate the short-range interaction energy of two protons bound by one electron are briefly reviewed. The Hamilton-Jacobi-Riccati outer equation is solved perturbatively up to fifth order in the perturbation parameter, where the zero-order function is the He + ground-state function. The inner equation is solved by expanding Hylleraas determinant. The results are consistent with those of similar treatments and with accurate numerical calculations.J. Phys. Commun. 2 (2018) 045018 M Battezzati and V Magnasco Recently analytical methods for evaluation of + H 2 interaction energies were used extensively with the help of computer algebra and combined with highly accurate numerical calculations [12,17]. They contribute to shed light on the structure and properties of the solutions. In [17] a variant of the present approach was developed in order to check numerical data, from which exact values of h.o. coefficients of the expansion were inferred by numerical interpolation.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Short-range interaction energy for ground-state ${{\bf{H}}}_{2}^{+}$

Battezzati

Magnasco

2018

J. Phys. Commun.

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“…framework, the Schrodinger equation (SE) for the protons inside the cavity takes the form (6) Here, a is the vector that connects the nuclei, m and r are the electron mass and radius, and μ = M/2, where M is the proton mass. Hereafter, we use the universal units ប = c = 1.…”

Section: A Molecular Hydrogen Ion In a Cavity With Robin's Boundary Cmentioning

confidence: 99%

“…The molecular hydrogen ion has always been the starting point in studying the properties of diatomic molecules [1][2][3][4][5][6][7][8][9][10][11][12]. At the same time, the development of modern technologies has stimulated theoretical studies of atoms and molecules in vacuum microcavi ties [13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

H 2 + in a lattice of cavities: Ammonia-like splitting of the lowest level

Sveshnikov

Tolokonnikov

2015

Moscow Univ. Phys.

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It is shown that reconstruction of the low lying energy levels of the ion under conditions of confinement in a given spatial volume is substantially more significant as compared to the confinement by simple potential barrier. Depending on the cavity parameters, the ground state binding energy of could be significantly greater than that of the free ion, while the behavior of the lowest molecular term of the ion turns out to be quite different when considered as a function of the internuclear distance. In particular, two minima might occur in , while the relationship between them could be sufficiently different depend ing on the cavity parameters, which is shown on the phase diagram that was obtained in the work. We studied the case of a "mexican hat" structure of the effective ion potential in detail. As a result, the lowest electronic level of ion splits into the ground state level and the first excited one, with difference between them being as small as ~10 -4 eV. As in the NH 3 molecule, in the last case the lowest level gives rise to an effective two level system that is separated from the vibrational and rotational modes by a wide energy gap. More concretely, cal culation using the Neumann conditions that actually reproduce the confinement on a lattice of similar cavi ties shows that the splitting of ~10 -4 eV occurs for the linear sizes of the confinement area of the order of some a B and a shell potential magnitude of ~10 eV.

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Simple analytical relation between vibrational frequencies of linear $$XY_2$$ X Y 2 -type molecules

Damljanović

2016

Opt Quant Electron

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Analytical evaluation of the short-range interaction energy for ground state H⁺₂

Cited by 6 publications

References 17 publications

Short-range interaction energy for ground-state ${{\bf{H}}}_{2}^{+}$

Short-range interaction energy for ground-state ${{\bf{H}}}_{2}^{+}$

H 2 + in a lattice of cavities: Ammonia-like splitting of the lowest level

Simple analytical relation between vibrational frequencies of linear $$XY_2$$ X Y 2 -type molecules

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Analytical evaluation of the short-range interaction energy for ground state H+2

Cited by 6 publications

References 17 publications

Short-range interaction energy for ground-state ${{\bf{H}}}_{2}^{+}$

Short-range interaction energy for ground-state ${{\bf{H}}}_{2}^{+}$

H 2 + in a lattice of cavities: Ammonia-like splitting of the lowest level

Simple analytical relation between vibrational frequencies of linear $$XY_2$$ X Y 2 -type molecules

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Product

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Analytical evaluation of the short-range interaction energy for ground state H⁺₂