Spectra and correlated wave functions of two electrons confined in a quasi-one-dimensional nanostructure

The energy spectra and wave functions of two electrons confined by a quasi-one-dimensional Gaussian potential have been calculated for different strengths of confinement, ωz, and anharmonicity by using the quantum chemical full configuration interaction method employing a Cartesian anisotropic Gaussian basis set. The energy spectra for a nearly harmonic Gaussian potential have been studied and analyzed in three regimes of ωz: namely, large (ωz=5.0), medium (ωz=1.0), and small (ωz=0.1). For large and medium ωz the energy spectrum shows a band structure which is characterized by the polyad quantum number vₚ while for small ωz it is characterized by the extended polyad quantum number vₚ*. The energy levels for small ωz form doublet pairs each of which consists of a pair of singlet and triplet states. The nodal patterns of their wave functions are almost identical to each other except for their phases. The energy spectra for the strongly anharmonic Gaussian potential look quite similar to those of the nearly harmonic case except that an irregular level structure appears in the high-energy region for ωz=0.1. The wave functions of the states in this high-energy region have curved nodal lines which align along a pair of bent nodal coordinates. Two types of pairs of bent nodal coordinates have been identified: namely, those passing through the valley of the confining potential and the others passing on the hillside. It is shown that the wave functions with these nodal coordinates correspond to new types of classical local-mode motions of electrons.