Classical double-layer atoms: Artificial molecules

The ground-state configuration and the eigenmodes of two parallel two-dimensional classical atoms are obtained as a function of the interatomic distance (d). The classical particles are confined by identical harmonic wells and repel each other through a Coulomb potential. As a function of d we find several structural transitions which are of first or second order. For first (second) order transitions the first (second) derivative of the energy with respect to d is discontinuous, the radial position of the particles changes discontinuously (continuously), and the frequency of the eigenmodes exhibits a jump (one mode becomes soft, i.e., its frequency becomes zero).