Absorption spectra of a cosine potential in an excited state: Time-dependent wavepacket calculations

The absorption spectra of various cosine potentials in an excited state are calculated by a time-dependent wavepacket method. The spectra are compared with the spectra of an inverted harmonic potential, the negative harmonicity of which matches the curvature of the excited cosine potential. Control of the flatness or the sharpness of the potential near the Franck-Condon region by inclusion of cos(4θ) for the cosine potential makes the vibrational spacing narrower or wider. However, manipulation of the cosine potential can not give any drastic intensity change in the absorption, as seen in the experimental absorption spectra of ethylene. The difference between the absorption spectra of an cyclic potential and that of an infinite periodic potential is analyzed and discussed.