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

The adiabatic approximation (AA) involved in the quantum theory of the IR lineshapes (νX–H stretching mode) of weak H-bonds, is revisited. This is performed directly by looking at the spectral density obtained by Fourier transform of the direct damped autocorrelation function of the transition dipole moment. The spectral densities computed according to the AA are compared to those obtained directly through the diagonalization of the representative matrix of the Hamiltonian involving the anharmonic coupling between the high- and low-frequency modes. At 300 K, when the anharmonic parameter remains small (α°≤1), the AA lineshape reduces to the exact one, whereas beyond (α°≥1), the AA is less and less satisfied since its spectral density differs progressively from the exact. Introduction in the AA of effective angular frequency and effective anharmonic parameter, allows us for α°≈1.5 to fit sensitively the exact curve except for the spectrum tails. Connection between the two approaches is established through effective Hamiltonians (operators and matrices) by means of the wave operator.