Excitation and decay of a C–H overtone attached to a linear hydrocarbon chain: A simple quantum-mechanical model

The decay of a C–H overtone at one end of a linear chain of identical C–C bonds is investigated. It is assumed that only the C–H and the adjacent C–C bond may be sufficiently excited to exhibit anharmonicity, while the remaining part of the chain behaves harmonically. The limit of an infinite number of C–C bonds is considered and the time decay of the C–H overtone is calculated. The results (quite unexpected on the basis of classical calculations on finite chains) show that two time scales appear in the decay, one much slower than the other. This manifests also in the coexistence of sharp and broad peaks in the absorption spectra. The possible consequences on the reactivity of the terminal part of long-chain molecules are discussed. The mechanism of optical preparation of overtones is also analyzed in some detail.