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Symmetric and antisymmetric terms have been obtained in the framework of thevariational approach for two-dimensional (2D) Coulomb systems of symmetrictrions XXY. Stability diagrams and certain anomalies arising in the 2D spaceare explained qualitatively in the framework of the Born--Oppenheimer adiabaticapproximation. The asymptotics of energy terms at large distances obtained foran arbitrary space dimensionality are analyzed, and some approximation formulasfor 2D terms are proposed. An anomalous dependence of multipole moments on thespace dimensionality has been found in the case of a spherically symmetricfield. The main results obtained for the 2D and 3D problems of two Coulombcenters are compared.

Energy terms and stability diagrams for the 2D problem of three charged particles