IR SPECTRAL DENSITY OF WEAK H-BONDED COMPLEXES INVOLVING DAMPED FERMIRESONANCES - I - QUANTUM-THEORY

The IR spectral density of the high frequency stretching mode of weak H-bonded complexes involving Fermi resonances is studied within the li near response theory from a full quantum mechanical point of view: the anharmonic coupling between the high frequency X-H and the low freque ncy X-H ... Y modes is treated inside the strong anharmonic coupling t heory. Following Witkowski and Wojcik [A. Witkowski, M. Wojcik, Chem. Phys. 1 (1973) 9.], the Fermi resonance between the first excited stat e of the fast mode and the first harmonic of single or several bending modes is introduced. Besides, the direct relaxation involved by the f ast and bending modes are incorporated, in the spirit of the reduced G reen formalism, by aid of imaginary damping terms. The spectral densit y is obtained by the Fourier transform of the autocorrelation function of the dipole moment operator of the fast mode, in which time depende nt terms appear that are solution of a set of coupled linear different ial equations. It reduces in the special situation where the Fermi cou pling is ignored to that obtained by Rosch and Ratner [N. Rosch, M. Ra tner, J. Chem. Phys. 61 (1974) 3344.]. Furthermore, when the anharmoni c coupling between the slow and fast modes is neglected, it reduces to the spectral density that may be obtained in the framework of the Gir y et al. [M. Giry, B. Boulil, O. Henri-Rousseau, C.R. Acad. Sci. Paris 316 s.II (1993) 455; B. Boulil, M. Giry, O. Henri-Rousseau, Phys. sta tus solidi (b) 158 (1990) 629.] approach. At last, it reduces to the W itkowski and Wojcik [A. Witkowski, M. Wojcik, Chem. Phys. 1 (1973) 9.] approach, when the relaxation disappears. A generalization to several Fermi resonances is also proposed. Numerical tests of the theory and physical discussions are reported in the following paper [D. Chamma, O . Henri-Rousseau, Chem. Phys. 229 (1998) 51]. (C) 1998 Elsevier Scienc e B.V.