Classical molecules in two dimensions

The ground-state configurations and spectrum of two parallel two-dimensional classical atoms are obtained as a function of the inter-atomic distance ( ). The classical particles are confined by parabolic potentials and repel each other through a Coulomb potential. As a function of we find several configurational transitions which are of first or second order. For first- (second-) order transitions the first (second) derivative of the energy with respect to is discontinuous, the radial position of the particles changes discontinuously (continuously) and the frequency of the eigenmodes exhibit a jump (softening of a mode). In the limit of an infinite number of electrons the Wigner bilayer system is recovered which moves through five different stable crystalline phases as a function of . For unequal strength of parabolic confinement we find that the number of configurational transitions increases.