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The influence of the intramolecular anharmonicity and the strongvibron-phonon coupling on the two-vibron dynamics in an $\alpha$-helix proteinis studied within a modified Davydov model. The intramolecular anharmonicity ofeach amide-I vibration is considered and the vibron dynamics is describedaccording to the small polaron approach. A unitary transformation is performedto remove the intramolecular anharmonicity and a modified Lang-Firsovtransformation is applied to renormalize the vibron-phonon interaction. Then, amean field procedure is realized to obtain the dressed anharmonic vibronHamiltonian. It is shown that the anharmonicity modifies the vibron-phononinteraction which results in an enhancement of the dressing effect. Inaddition, both the anharmonicity and the dressing favor the occurrence of twodifferent bound states which the properties strongly depend on the interplaybetween the anharmonicity and the dressing. Such a dependence was summarized ina phase diagram which characterizes the number and the nature of the boundstates as a function of the relevant parameters of the problem. For asignificant anharmonicity, the low frequency bound states describe two vibronstrapped onto the same amide-I vibration whereas the high frequency bound statesrefer to the trapping of the two vibrons onto nearest neighbor amide-Ivibrations.Comment: may 2003 submitted to Phys. Rev.

Two-vibron bound states in α-helix proteins: The interplay between the intramolecular anharmonicity and the strong vibron–phonon coupling