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 overtone vibrational frequencies of near infrared (NIR) spectra for molecules and polymers. According to the theory, the transition frequency between two quantum states, n and m, may be found from the relation ω_nm=(m-n)ω(n̄), where n̄ = (n+m)/2. The variable n̄ is a semi-classical eigenvalue associated with the action of a vibrational mode, and ω(n̄) is the vibrational frequency of a dynamical trajectory which has an action J=(n̄+1/2)ℏ in the mode of interest. Frequencies are calculated from a classical trajectory using the MUSIC frequency estimator. A normal mode analysis is not able to calculate overtone frequencies because that approach does not allow for a variable such as n̄. The accuracy and significance of the method is demonstrated by two examples. First, the method is applied to the Morse potential, which is an analytical function with exact solutions. Second, it is applied to a model of polyethylene in order to calculate the overtone spectra of the CH₂ anti-symmetric and symmetric stretching vibrations.