Three-dimensional doorway-state theory for analyses of absorption bands of many-oscillator systems

A three-dimensional doorway-state theory is worked out for the purpose of analyzing absorption bands of many-oscillator systems, such as the amide-I infrared (ir) bands of globular proteins. An appropriate basis set of the doorway-state subspace is defined, so that the complication in interpretation of computational results, which may arise from the interference among the transition dipoles of the basis states, is avoided. As an example of application of the formulation, calculations of the doorway states are given for the ir band of a model system consisting of 400 oscillators. It is shown that the doorway-state formalism provides band assignments based on the origin of ir intensity, even in the case where the molecule has an irregular structure or irregular force constants and the molecular-eigenstate picture is not appropriate to describe vibrational motions responsible for the ir intensity. Possibility of applying this formalism to problems in other energy regions (such as electronic absorption of molecular aggregates) is also pointed out.