Origin of the first Hund rule and the structure of Fermi holes in two-dimensional He-like atoms and two-electron quantum dots

Abstract

The lowest singlet-triplet pair of states of the two-electron twodimensional quantum dots and the corresponding pair of states of the two-dimensional helium-like systems have been studied by the full configuration interaction method focusing on the origin of the first Hund rule. The one-and two-electron components of the singlet-triplet energy gap show distinct trends for the systems studied in the regime of small nuclear charge Z n or of small confinement strength ω. The (0σ g)(1π u) singlet state in quantum dots is characterized by a larger electron repulsion than its counterpart triplet state for all values of ω while this relationship gets inverted for the corresponding (1s)(2p) singlet-triplet pair of He-like systems for small values of Z n , such as Z n = 2 or 3. The internal part of the full configuration interaction wave functions has been extracted and visualised in the three-dimensional internal space (r 1 ,r 2 ,φ −) to rationalize the observed trends. The singlet probability density of Helike systems located originally near the Fermi holes is shown to migrate into regions where either r 1 or r 2 are large while the corresponding singlet probability of quantum dots stays close to the Fermi holes. Their differences and their observed trends are rationalized on the basis of the structure of the genuine and conjugate Fermi holes.

One and two body densities for excited states of the helium confined atom

“…This same happens when the atoms are confined, that is, the interelectronic repulsion energy for the singlet becomes greater than for the triplet as the confinement radius decreases . On the contrary, this such inversion between singlet and triplet does not appear in the study of two electron quantum dots …”

“…[15] On the contrary, this such inversion between singlet and triplet does not appear in the study of two electron quantum dots. [16,17] An analysis of these two properties, level crossing and the interpretation of the Hund's rule, is carried out in the present work in terms of the different contributions to the total energy of the states as well as in terms of the single particle and two body densities of the system. Two-body…”

The change in the nature of bonding in the Li2 dimer under confinement

“…The interest in confined electronic systems has been considerably growing in the last years due to a wide variety of applications in chemistry and physics, such as the modeling of atoms and molecules under extreme pressures [1–6], the study of quantum dots [7–10], defects in crystals [11], and astrophysics [12, 13]. The electronic properties of atoms and molecules under confinement is the result of an interplay between attractive and repulsive terms in the Hamiltonian and Pauli's principle that increases the kinetic energy as the available volume is reduced.…”

“…To compute energetic aspects, a correlated wavefunction is used and changes of bonding patterns are captured by a topological analysis of the electron localization function (ELF). Note that although harmonic potential have been used to model quantum dots [7–10], we choose this potential because its ubiquity in physics and because it is simple enough to use machinery of correlated ab initio methods of quantum chemistry. We do not claim that this model is a realistic case of quantum dot, impurity, molecular cage or whatever specific case of a molecule under confinement.…”

Hund’s rule in open-shell states of two-electron systems: From free through confined and screened atoms, to quantum dots

“…However, unlike atoms, evidence has been presented indicating that these systems do not exhibit a reversal of the magnitudes of the interelectronic repulsion energies. Indeed, such reversal does not take place in the two-electron harmonically confined quantum dot [12,13], a fact that could also be accounted for analytically [11].…”