Effect of long range and anharmonicity in the minimum energy states of the Davydov-Scott model

The Davydov-Scott model, which describes the states of amide I excitations in a lattice, is extended to include distance dependent nonlocal hopping and/or a nonlinear lattice. Minimum energy one quantum states are determined by numerical minimization. For the parameters which characterize the motion of the amide I excitation in an a-helix it is found that the harmonic terms are a very good approximation of the full Lennard-Jones potential. On the other hand, although the inclusion of distance-independent hopping terms leads to generally broader solitons, surprisingly it also results in the suppression of the transition from localized to delocalized states. A particular way of including of distance dependent terms in the hopping coefficient is also considered which leads to spikes in the lattice distortion and otherwise a rich phase diagram for the corresponding minimum energy states. (C) 1998 Elsevier Science B.V.