QUANTUM-THEORY OF THE SPECTRAL DENSITY OF THE HYDROGEN-BOND IN SOLUTION .1. A CLOSED AUTOCORRELATION FUNCTION

A novel formulation of the quantum theory of the spectral density of t he hydrogen bond in solution is proposed. It leads to a compact form f or the autocorrelation function to be Fourier transformed in order to get the spectral density. An approximation concerning the modelization of the damping that was performed in our initial approach is avoided, leading to an autocorrelation function that is more physical. The com pact form of the autocorrelation function provides an understanding of how our model reduces to that of Witkowski and Marechal in the absenc e of relaxation and what the differences are between our model and the classical model of Robertson which involves damping. It is also shown that it is not possible to find an equivalent formulation of the spec tral density in terms of the density operator formalism, which elimina tes the possibility of treating more complex hydrogen bonds with the a id of the perturbation theory using the density operator formalism. Fi nally, we underline the importance of the recent work of Witkowski on the coupling between slow and fast movements which gives a physical ba sis for understanding the unexplained coupling between the slow and fa st modes of hydrogen bonds, which is at the basis of all the explanati ons of the features of hydrogen bonds.