Confined quantum systems: dipole polarizability of the two-electron quantum dot, the hydrogen negative ion and the helium atom

The dipole polarizabilities of the electronic ground state of three two-electron quantum systems, namely the two-electron quantum dot, the hydrogen negative ion and the helium atom, confined by an anisotropic harmonic oscillator potential have been studied for different confinement strengths ω by using the quantum chemical configuration interaction (CI) method employing a Cartesian anisotropic Gaussian basis set supplemented by a quantum-chemical standard Cartesian Gaussian basis set, respectively, and a full CI wavefunction. The dipole polarizability of the harmonic oscillator quantum dot may be calculated analytically. It is proportional to the number of electrons, inversely proportional to the square of ω and has no electron correlation contribution. This is valid for all states including the excited states. The situation is different for quantum systems with a finite nuclear charge, like the hydrogen negative ion and the helium atom. In general the dipole polarizability of the two-electron quantum dot decreases strongly with increasing confinement strength ω, the polarizability of the helium atom varying slowly with increasing ω, while the behaviour of the polarizability of the hydrogen negative ion lies between both. Except for the two-electron quantum dot each component of the dipole polarizability tensor, i.e. α_xx, α_yy and α_zz, depends on the confinement along all axes. The electron correlation contribution to the dipole polarizability of the helium atom and of the hydrogen negative ion behaves differently for the different Cartesian components α_zz and α_xx of the tensor. The different behaviour observed for different Cartesian components may be rationalized by the reduced dimensionality of the systems.