NORMAL MODE TREATMENT OF OPTICAL-PROPERTIES OF A CLASSICAL COUPLED DIPOLE OSCILLATOR SYSTEM WITH LORENTZIAN BAND SHAPES

DeVoe's classical coupled dipole oscillator model for molecular optical properties is specialized for the case where the individual oscillators have complex polarizabilities with Lorentzian band shapes. The optical properties of this system are derived in terms of a set of eigenvectors and eigenvalues which describe the normal modes of the system. When the real and imaginary parts of the interaction matrix can be diagonalized by the same transformation, the properties are expressed as explicit functions of frequency and do not require a matrix inversion at each frequency. This condition is met by a system in which all oscillators have the same bandwidth. For such a case the computation time is much less than that required by the more general method involving point-by-point matrix inversion. A further simplification is achieved for a system in which a subset of the oscillators have natural frequencies so high that their polarizabilities may be regarded as nondispersive. For this case the order of the eigenvalue problem is reduced to the number of dispersive oscillators. Sum rules are derived for the mixed dispersive/nondispersive system. The normal mode method is illustrated by calculations for a 12-residue right-handed α-helix in which oscillators at 52 000 and 67 600 cm -1 are assigned to each residue. The predicted absorption and circular dichroic spectra are similar to those predicted using Gaussian band shapes for the individual oscillators by the matrix inversion method, while a 40-fold saving in computer time was achieved by the normal mode method. © 1979 American Institute of Physics.