Confined quantum systems: a comparison of the spectral properties of thetwo-electron quantum dot, the negative hydrogen ion and the heliumatom

Abstract

The spectrum, the electron density distribution and the character of threetwo-electron quantum systems, namely the two-electron quantum dot, thenegative hydrogen ion and the helium atom, confined by an anisotropic harmonicoscillator potential, have been studied for different confinement strengths, ω,by using the quantum chemical configuration interaction (CI) methodemploying a Cartesian anisotropic Gaussian basis set supplemented by aquantum chemical standard Cartesian Gaussian basis set, respectively,and a full CI wavefunction. Energy level diagrams and electron densitydistributions are displayed for low lying electronic singlet states and selectedconfinement parameters. The results for the three confined quantum systems arecompared with each other: in general, the absolute energies of the states andthe interval between states increase with increasing confinement, ω.The ordering of states may vary for different values of ω.The shape of the electron density distribution differs among the threesystems. Its size increases in the order He < H− < two-electronquantum dot. Electron distributions in prolate type confinement are stretched alongthe zaxis, while those in oblate type are compressed with respect to this axis.The CI wavefunction of most of the low lying states for the helium atomand the negative hydrogen ion is dominated by one configuration, whilesome of the CI wavefunctions corresponding to states of the two-electronquantum dot have more than one leading configuration. The ground state CIwavefunctions of the negative hydrogen ion and the helium atom confined in aspherical potential are dominated by harmonic oscillator functions up to82.4 and 47.1%, respectively, for the smallest confinement of ω = 0.1.These values increase to 98.8 and 89.0%, respectively, for ω = 0.5.