Confined H(1s) and H(2p) under different geometries

Abstract

In this paper the diffusion Monte Carlo method is applied to the confined hydrogen atom with different confinement geometries. This approach is validated using the much studied spherical and cylindrical confinements and then applied to cubical and squared ones, for which data are not available, as new applications of the method relevant to solid state physics. The energy eigenvalues of the ground state and one low-lying excited state are reported as a function of the characteristic confinement length.

Monte Carlo calculation of the potential energy surface for octahedral confined H$$_2^+$$2+

“…in [2]). As expected much attention has been devoted to H + 2 , the simplest molecular system [3][4][5][6][7][8][9][10][11][12][13]. Also this particular case, apart from its value as fundamental issue, may find several applications.…”

The H, H2+, and HeH2+ systems confined by an impenetrable spheroidal cavity: Revisited study via the Lagrange‐mesh approach

“…Most of these studies consider the impurity position at the center of the QD whereby the corresponding Schrödinger problem allows an exact treatment, thus rendering an accurate construction of the energy spectrum. A lesser number of studies have been devoted to the more general case where the impurity is located off‐center within the spherical QD . Conversely, the effect of deviations from the spherical to an ovoidal shape of the QD on the hydrogenic donor states has been scarcely reported by considering the impurity within a prolate spheroidal box .…”

“…[1-7].Box models of quantum confinement have shown to be appropriate to survey the effect of spatial limitation on the electronic properties of caged atoms and molecules to mimic high pressure conditions [2,[8][9][10][11][12][13][14][15] as well as to explain the behavior of donor states in semiconductor quantum dots (QD's). [16][17][18][19][20][21][22][23][24][25][26][27] In the latter case, the spectroscopic techniques used to characterize the optical properties of hydrogenic donor impurities embedded in semiconductor QD's pose the need of appropriate theoretical treatments to account for differences in the electronic level structure due to changes in the shape of the QD as well as in the enclosed impurity position. A good deal of theoretical work has been addressed to study the behavior of hydrogenic donor states in spherical QD's.…”

“…A lesser number of studies have been devoted to the more general case where the impurity is located off-center within the spherical QD. [19,20,[23][24][25] Conversely, the effect of deviations from the spherical to an ovoidal shape of the QD on the hydrogenic donor states has been scarcely reported by considering the impurity within a prolate spheroidal box. [26,27] In this context, theoretical modeling of the simple system confined by prolate spheroidal boxes keeps renewed interest to explore the electronic and optical properties of hydrogenic donor impurities trapped in ovoidal QD's.The first exact solutions to the Schr€ odinger problem-within the Born-Oppenheimer approximation-for the H atom, the H 1 2 , and HeH 21 molecular ions inside a hard [28] and soft [29] prolate spheroidal cavity have been commonly used as benchmark reference to validate the numerical assessment of other alternative approaches.…”

“…A lesser number of studies have been devoted to the more general case where the impurity is located off-center within the spherical QD. [19,20,[23][24][25] Conversely, the effect of deviations from the spherical to an ovoidal shape of the QD on the hydrogenic donor states has been scarcely reported by considering the impurity within a prolate spheroidal box. [26,27] In this context, theoretical modeling of the simple system confined by prolate spheroidal boxes keeps renewed interest to explore the electronic and optical properties of hydrogenic donor impurities trapped in ovoidal QD's.…”