The confined diatomic molecule problem

Пупышев, В.И.; Bobrikov, Vladimir V.

doi:10.1002/qua.20079

Cited by 17 publications

(10 citation statements)

References 18 publications

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“…In recent years, there has been increased interest in the study of confined systems because of the great variety of their applications. A primary area of interest has been atoms and molecules subjected to high pressure 1–29. Here, we should draw attention to models in which the atoms are confined at the center of spherical penetrable 16, 17 and impenetrable boxes 1–15 and those in which the atoms are confined off‐center in the spherical box and inside boxes of diverse geometry.…”

Section: Introductionmentioning

confidence: 99%

Highly accurate solutions for the confined hydrogen atom

Aquino¹,

Campoy²,

Montgomery³

2007

Int J of Quantum Chemistry

118

122

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ABSTRACT:The model of the confined hydrogen atom (CHA) was developed by Michels et al. [1] in the mid-1930s to study matter subject to extreme pressure. However, since the eigenvalues cannot be obtained analytically, even the most accurate calculations have yielded little more than 10 figure accuracy. In this work, we show that it is possible to obtain the CHA eigenvalues with extremely high accuracy (up to 100 decimal digits) and we do that using two completely different methods. The first is based on formal solution of the confluent hypergeometric function while the second uses a series method. We also compare radial expectation values obtained by both methods and conclude that the wave functions obtained by these two different approaches are of high quality. In addition, we compute the hyperfine splitting constant, magnetic screening constant, polarizability in the Kirkwood approximation, and pressure as a function of the box radius.

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Section: Introductionmentioning

confidence: 99%

Highly accurate solutions for the confined hydrogen atom

Aquino¹,

Campoy²,

Montgomery³

2007

Int J of Quantum Chemistry

118

122

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“…Because of impenetrability a Dirichlet boundary condition is imposed on the wave function at the sphere surface. Since 1937, such a confinement model has often been utilized to simulate spatial compression on various quantum systems …”

Section: Introductionmentioning

confidence: 99%

Fine structure in the hydrogen atom boxed in a spherical impenetrable cavity

Rojas

Aquino

Flores-Riveros

2018

Int J of Quantum Chemistry

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The spectrum of the hydrogen atom confined in a spherical impenetrable box of radius Rc has been investigated by many authors up to date, but not at the level of relativistic corrections. It is well known that, as Rc diminishes, all energy levels and the pressure increase very rapidly, whereas the polarizability goes to zero. In this report, we have computed the relativistic corrections that underlie the fine structure of the confined hydrogen atom, as a function of Rc. Such corrections correspond to relativistic kinetic energy, spin‐orbit coupling and the Darwin term, which are calculated in the frame of time‐independent perturbation theory, for which, use was made of the exact confined hydrogen atom wave functions. We show that for a confinement radius of 0.5 au the relativistic corrections increase up to three orders of magnitude with respect to those corresponding to the free atom. As Rc decreases, the kinetic energy correction and the spin‐orbit coupling for j=1/2 become negative whereas their absolute value and the Darwin term, which is positive, increase very rapidly.

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“…The thickness of this layer is of the same order of magnitude as the equilibrium internuclear distance, R e , in the molecule, i.e., the center of mass moves in the effective cavity of a smaller size. 12 Neverthe less, the energy ratios for transitions from the ground state to the (0,1) and (0,2) states, calculated by both methods using the model of free motion of a particle in a box are very similar to 8/3. As R increases, the energies of the (0,v c ) states tend to zero at any v c .…”

Section: States Of Hydrogen Molecule In the Cavitymentioning

confidence: 87%

“…After discretization the system of these equations permits estimation of the energies of stationary states by dichotomy (for more de tails, see Ref. 12). In this approximation it is convenient to use spherical coordinates for the Jacoby variables, which allows the problem of the molecule in a cavity to be re lated to the free molecule problem.…”

Section: Methods B Complete Adiabatic Separation Of Nuclear Vari Ablesmentioning

confidence: 99%

“…The sign of expression (11) is determined by the sign of the difference δ i -δ j . By esti mating δ i -δ j using the Lagrange formula we get (12) where ∂ denotes the derivative with respect to R and θ is a point from the segment [1, m 1/(n+2) ]. Since the energy of the higher lying level i decreases to a greater extent com pared to the energy of the level j with an increase in R,…”

Section: Transition Energiesmentioning

confidence: 99%

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Isotope effects for molecules in a cavity

Bobrikov

Пупышев

2005

Russ Chem Bull

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A model problem of the motion of a particle in an impenetrable cavity is considered in order to establish how the energy levels and transition energies between them depend on the linear size, R, of the cavity and on the particle mass. In the case of one particle problem with a uniform potential inside the cavity there exists a simple qualitative solution that describes the effect of the cavity size and shows that a decrease in R can cause the isotopic frequency shift to increase as compared to the free system. The estimates obtained were used to interpret the results of numerical calculations of low lying energy states of hydrogen molecule and its isotopomers confined within impenetrable spherical cavity. The effect of the cavity radius on the structure of the low lying part of the energy spectra of H 2 , D 2 , and HD molecules and on the reliability of adiabatic separation of nuclear variables are considered. The approach pro vides a qualitatively correct description of the changes in the energy level positions but the behavior of the isotopic frequency ratio is too smooth compared with results of more accurate calculations.Key words: hydrogen molecule, molecule in cavity, isotopic frequency shift, rovibrational energy levels, separation of variables.Analysis of the influence of isotopic substitution on the spectral characteristics of molecules is an important and efficient tool of investigation of the structure of mo lecular systems. In the framework of a simple harmonic model the frequency ratio of two isotopomers can be esti mated as the square root of the inverse ratio of their masses. However, experiments also give abnormally large isotopic shifts. For instance, considerations of vibrational motions of entire hydrogen molecule confined in an octahedral cavity between fullerene molecules in solid C 60 shows that H-D substitution leads to a frequency ratio of about , 1 which means that the model mentioned above is inapplicable in this case.When studying motions of molecular systems in cavi ties of solids or cage structures (e.g., a fullerene or zeolite) or in a crystal or matrix defect, one must take into ac count a variety of different type factors among which constraints on the region of free motion of particles de serves particular attention. The model of a system placed in a cavity with impenetrable walls is often used in studies of complex physicochemical systems (see, e.g., Refs 2-12 and references cited therein). In this work we considered the influence of the cavity size on the magnitude of isoto pic frequency shift. First, we performed a qualitative study of a model problem of the motion of a particle in a uni form potential; some of the results obtained were found to be valid for any potential. The estimates obtained make it possible to interpret the results of numerical calculations of the lowest part of rovibrational spectra of hydrogen molecule isotopomers in a spherical cavity, which corre sponds to the motions of the system as a whole. The model systemConsider a model problem of the motion of a...

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The confined diatomic molecule problem

Cited by 17 publications

References 18 publications

Highly accurate solutions for the confined hydrogen atom

Highly accurate solutions for the confined hydrogen atom

Fine structure in the hydrogen atom boxed in a spherical impenetrable cavity

Isotope effects for molecules in a cavity

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