  Four diabatic states are used to construct a simple model for double proton
transfer in hydrogen bonded complexes. Key parameters in the model are the
proton donor-acceptor separation R and the ratio, D_1/D_2, between the proton
affinity of a donor with one and two protons. Depending on the values of these
two parameters the model describes four qualitatively different ground state
potential energy surfaces, having zero, one, two, or four saddle points. In the
limit D_2=D_1 the model reduces to two decoupled hydrogen bonds. As R decreases
a transition can occur from a concerted to a sequential mechanism for double
proton transfer.
