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We model quasi-two-dimensional two-electron Quantum Dots in a parabolicconfinement potential with rovibrational and purely vibrational effectiveHamiltonian operators. These are optimized by non-linear least-square fits tothe exact energy levels. We find, that the vibrational Hamiltonian describesthe energy levels well and reveals how relative contributions change on varyingthe confinement strength. The rovibrational model suggests the formation of arigid two-electron molecule in weak confinement and we further present amodified model, that allows a very accurate transition from weak to strongconfinement regimes.

Effective Hamiltonian for two-electron Quantum Dots from weak to strong parabolic confinement