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Absorption and rotation of light by helical oligomers: The nearest neighbor approximation
Author(s) -
Bradley D. F.,
Tinoco I.,
Woody R. W.
Publication year - 1963
Publication title -
biopolymers
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.556
H-Index - 125
eISSN - 1097-0282
pISSN - 0006-3525
DOI - 10.1002/bip.360010305
Subject(s) - chemistry , maxima , exciton , excited state , excitation , k nearest neighbors algorithm , perpendicular , monomer , molecular physics , absorption (acoustics) , absorption band , atomic physics , polymer , crystallography , condensed matter physics , physics , quantum mechanics , optics , geometry , mathematics , art , organic chemistry , artificial intelligence , performance art , computer science , art history
Abstract Explicit expressions for the D K and R K associated with the excitation of regular oligomers from their ground states to the K th exciton state as functions of N, P , μ , μ∥, μ t , and μ r have been derived on the assumption that the only perturbation V ij to the N singly excited states results from exciton transfer between adjacent residues, V 12 . The D K relation predicts the occurrence of a perpendicularly polarized absorption band arising from μ⟂ and a parallel polarized band from μ∥ with maxima at K = [2( N + 1)/ P ] and 1, which are shifted from the monomer band by 2 V 12 cos(2π/ P ) and 2 V 12 cos[π/( N + 1)], respectively. Overlapping of the bands, which may occur in oligomers, decreases rapidly with N , leaving two perfectly polarized bands in the polymer. Within each band which includes only a few levels near the maxima, the most probable transition may be associated with all of the intensity for very short chains but only 40.2–50% (⟂) and 80.9% (∥) as N → ∞ (polymer case). A relation was derived by which V 12 may be simply calculated from μ , μ r , μ t , μ∥, a , and z . The nearest neighbor theory was compared with experiment by calculating a reasonable set of the relevant parameters which exactly account for known spectral shifts.