On the Calculations of the Exciton-Phonon Coupling Parameters in the Theory of Davydov Solitons
Davydov soliton (DS) theory2, 3 considers collective amide-1 vibrations (excitons) in the chains of the hydrogen-bonded peptide groups in the peptide α-helix and their coupling with longitudional deformations of the chains (acoustic phonons). The coupling leads to the H-bond length changes, thus resulting, under some conditions, in a self-trapping of the excitation. Due to the exciton-phonon coupling (EPC) the longitudional α-helix deformations affect the exciton Hamiltonian, changing the resonance parameters (which describe the hopping of the excitation between H-bonded peptide groups), and nonresonance (diagonal) parameters (which are the excitation energy of each peptide group). Accordingly, the EPC can be characterized by three parameters: the “resonance” parameter χres defined as the derivative of the hopping integral with the respect to the corresponding H-bond length and two “nonresonance” parameters, χ′ and χ″, which are the derivatives of the amide-1 excitation energy E in the peptide group with the respect to its distances to the “right” and “left” groups in the chain. In other words, χ′ and χ” present the extra forces with which some peptide group acts, when excited, upon its right and left neighbours in the chain.
KeywordsAmide Soliton Polypeptide Formamide Acetanilide
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