Two-dimensional spectroscopy and harmonically coupled anharmonic oscillators

Experimentally it is established that the fourth-order anharmonicity plays significant roles in many molecules. In high resolution spectroscopy, it is known that a picture of local (anharmonic) modes with harmonic couplings between modes gives rise to a quartic Darling-Dennison coupling between normal modes. It has been shown that this order of anharmonicity can be selectively studied via seventh-order off-resonant spectroscopy, which probes the three-time response function (J. Chem. Phys. 106 (1997) 1687). In this paper, we further explore the effect of the fourth-order anharmonicity in the seventh-order signal, or in the three-time response function (which can be complementary investigated via third-order infrared spectroscopy), when the anharmonicity causes mode mixing; we obtain a fairly compact analytical result and numerically present the signal from CH stretch vibrations in methylene chloride as two-dimensional (2D) contour maps. It is found that purely kinetic coupling between anharmonic local oscillators can give rise to cross-peaks in the 2D spectra. (C) 2001 Elsevier Science B.V. All rights reserved.