IR theory of weak H-bonds: Davydov coupling, Fermi resonances and direct relaxations. I. Basis equations within the linear response theory

Abstract

Infrared and Raman spectral densities of cyclic H-bonded dimers, such as encountered in carboxylic acids, are obtained in a full quantum mechanical way by introducing relaxation effects towards the surroundings in the model of Wójcik [Mol. Phys. 36 (1978) 1757] which accounts for the possibility of simultaneous Davydov coupling (between the two hydrogen bonds involved in a cyclic dimer) and Fermi coupling (between each hydrogen bond and one or several bending modes). The relaxations of the fast stretching modes of the H-bonds and of the bending modes are assumed to be of direct type, and are taken into account in the spirit of the Green formalism by insertion of imaginary damping parameters in the effective hamiltonians. Then, the spectral density is obtained within the framework of the linear response theory by Fourier transform of the time-dependent autocorrelation function either of the dipole moment operator, in the infrared case, or of the tensor of the polarizabilities in the Raman case. Extension to non-resonant fast stretching and bending modes, and to several Fermi resonances is also performed according to Henri-Rousseau and Chamma [Chem. Phys. 229 (1998) 37]. In the undamped case, the equivalence of the present work is established with the theory of Maréchal and Witkowski [J. Chem. Phys. 48 (1968) 3697] by neglecting the Fermi resonances. Moreover, one-to-one correspondences are also shown with the work of Henri-Rousseau and Chamma [Chem. Phys. 229 (1998) 37] by ignoring Davydov coupling, and with that of Rösch and Ratner [J. Chem. Phys. 61 (1974) 3344] by neglecting both Davydov and Fermi couplings. Finally, the use of the symmetry properties which appear in cyclic dimers when neglecting the Fermi resonances, initially performed by Maréchal and Witkowski [J. Chem. Phys. 48 (1968) 3697], is discussed, showing the equivalence with the results of the non-symmetrized treatment.