Derived properties from the dipole and generalized oscillator strength distributions of an endohedral confined hydrogen atom

Abstract

We report the electronic properties of a hydrogen atom confined by a fullerene molecule by obtaining the eigenvalues and eigenfunctions of the time-independent Schrödinger equation by means of a finite-differences approach. The hydrogen atom confinement by a C 60 fullerene cavity is accounted for by two model potentials: a square-well and a Woods-Saxon. The Woods-Saxon potential is implemented to study the role of a smooth cavity on the hydrogen atom generalized oscillator strength distribution. Both models characterize the cavity by an inner radius R 0 , thickness Δ, and well depth V 0 . We use two different values for R 0 and Δ, found in the literature, that characterize H@C 60 to analyze the role of the fullerene cage size and width. The electronic properties of the confined hydrogen atom are reported as a function of the well depth V 0 , emulating different electronic configurations of the endohedral cavity. We report results for the hyper-fine splitting, nuclear magnetic screening, dipole oscillator strength, the static and dynamic polarizability, mean excitation energy, photo-ionization, and stopping cross section for the confined hydrogen atom. We find that there is a critical potential well depth value around V 0 = 0.7 a.u. for the first set of parameters and around V 0 = 0.9 a.u. for the second set of parameters, which produce a drastic change in the electronic properties of the endohedral hydrogen system. These values correspond to the first avoided crossing on the energy levels. Furthermore, a clear discrepancy is found between the square-well and Woods-Saxon model potential results on the hydrogen atom generalized oscillator strength due to the square-well discontinuity. These differences are reflected in the stopping cross section for protons colliding with H@C 60 .

An off-center endohedrally confined hydrogen molecule

“…In this work, we use a combination of two Woods–Saxon potentials to model a C 60 fullerene cage as the confining cavity 58,59 where R 0 is the inner radius of the potential, Δ is its width, U 0 represents the depth of the potential, and η is the smoothing parameter. Here, we have used fixed values of the potential height U 0 = −0.422 a.u., width Δ = 1.25 a.u., inner radius R 0 = 6.01 a.u.…”

“…In this work, we use a combination of two Woods-Saxon potentials to model a C 60 fullerene cage as the confining cavity 58,59 V c ðrÞ ¼…”

“…in order to model a C 60 fullerene cage. 58,59,62 Fig. 1 shows the schematic representation of the approaches and confinement used here.…”

“…Different potentials have been employed for fullerene cages, mainly the square-well potential or the combination of two Woods-Saxon potentials, [55][56][57][58] with the latter being more suitable because its diffuse but compact borders are more realistic than the infinitely sharp edges of the former; therefore, we use the combination of two Woods-Saxon potentials to model a C 60 fullerene cage as the confining cavity. 58,59 The convergence of the partial wave expansion in two different reference systems is studied: (a) the one associated with the confining cavity and (b) the one related to one of the molecule's Coulomb centers. The solution of the Schro ¨dinger equation is computed using a configuration-interaction approach with generalized Sturmian functions.…”

Polarization of the C$_{60}$ cage by the photoelectron, interior static polarization of C$_{60}$ by the ion-remainder and atomic-core relaxation in $A$@C$_{60}$ photoionization

“…Many of theoretical results on this topic have been obtained in the framework of a model potential where the C 60 carbon cage is modelled by a Dirac δ-like potential [2,7,8] (and references therein), or a U C (r) spherical attractive potential of a certain inner radius, thickness and depth [9-14, 17, 18, 21, 24-27], or Woods-Saxon potential [15,16,26], or other potentials [3]. However, all of these studies have overlooked to account for polarization of C 60 by the outgoing photoelectron (to be referred to as "αpolarization", α being dipole static polarizabity).…”