A dynamical method for calculating the near infrared spectra of molecules and macromolecules

The Semi-classical Spectral Method (SSM) may be used to calculate the overt one vibrational frequencies of near infrared (NIR spectra for molecules and polymers, According to the theory, the transition frequency between two qu antum states, n and m, may be found from the relation omega(nm) = (m-n)omeg a((n) over bar), where (n) over bar = (n+m)/2, The variable (n) over bar is a semi-classical eigenvalue associated with the action of a vibrational mo de, and omega((n) over bar) is the vibrational frequency of a dynamical tra jectory which has an action J = ((n) over bar + 1/2)(h) over bar in the mod e of interest. Frequencies are calculated from a classical trajectory using the MUSIC frequency estimator, A normal mode analysis is not able to calcu late overtone frequencies because that approach does not allow for a variab le such as (n) over bar. The accuracy and significance of the method is dem onstrated by two examples. First, the method is applied to the Morse potent ial, which is an analytical function with exact solutions. Second, it is ap plied to a model of polyethylene in order to calculate the overtone spectra of the CH2 anti-symmetric and symmetric stretching vibrations.