Linear response theory and IR spectral density of direct damped weak H-bonds: validity of adiabatic approximation

The adiabatic approximation (AA) involved in the quantum theory of the IR l ineshapes (nu(X-H) stretching mode) of weak H-bonds, is revisited. This is performed directly by looking at the spectral density obtained by Fourier t ransform of the direct damped autocorrelation function of the transition di pole moment. The spectral densities computed according to the AA are compar ed to those obtained directly through the diagonalization of the representa tive matrix of the Hamiltonian involving the anharmonic coupling between th e high- and low-frequency modes. At 300 K, when the anharmonic parameter re mains small (alpha degrees less than or equal to 1), the AA lineshape reduc es to the exact one, whereas beyond (alpha degrees greater than or equal to 1), the AA is less and less satisfied since its spectral density differs p rogressively from the exact. Introduction in the AA of effective angular fr equency and effective anharmonic parameter, allows us for alpha degrees app roximate to 1.5 to fit sensitively the exact curve except for the spectrum tails. Connection between the two approaches is established through effecti ve Hamiltonians (operators and matrices) by means of the wave operator. (C) 1999 Elsevier Science B.V. All rights reserved.