Interacting electrons in a magnetic field in a center-of-mass free basis

We present an extension of the spin-adapted configuration-interaction method (SACI) for the computation of four electrons in a quasi two-dimensional quantum dot. By a group-theoretical decomposition of the basis set and working with relative and center-of-mass (cm) coordinates we obtain an analytical identification of all spurious cm states of the Coulomb-interacting electrons. We find a substantial reduction in the basis set used for numerical computations. At the same time we increase the accuracy compared to the standard SACI due to the absence of distortions caused by an unbalanced cut-off of cm excitations.