Equivalence between the Classical and Quantum IR Spectral Density Approaches of Weak H-Bonds in the Absence of Damping

The aim of this paper is to overhaul the quantum elucidation of the spectral density (SD) of weak H-bonds treated without taking into account any of the damping mechanisms. The reconsideration of the SD is performed within the framework the linear response theory. Working in the setting of the strong anharmonic coupling theory and the adiabatic approximation, the simplified expression of the classical SD, in the absence of dampings, is equated to be I Cl (ω) = Re[∫ 0 ∞ G Cl ( t )e –iΩ t d t ] in which the classical-like autocorrelation function (ACF), G Cl ( t ), is given by G Cl ( t ) = tr{ ρ (β){ μ (0)}{ μ ( t )} † }. With this consideration, we have shown that the classical SD is equivalent to the line shape obtained by F (ω) = Ω I Cl (ω), which in turn is equivalent to the quantum SD given by I Qu (ω) = Re[∫ 0 ∞ G Qu ( t )e –iΩ t d t ], where G Qu ( t ) is the corresponding quantum ACF having for expression G Qu ( t ) = (1/β) tr{ ρ ∫ 0 β [ μ(0)}{ μ ( t + iλℏ)} † dλ}. Thus, we have shown that for weak H-bonds dealt without dampings, the SDs obtained by the quantum approaches are equivalent to the SDs geted by the classical approach in which the incepation ACF is, however, of quantum nature and where the line shape is the Fourier transform of the ACF times the angular frequency. It is further shown that the classical approach dealing with the SD of weak H-bonds leads identically to the result found by Maréchal and Witkowski in their pioneering quantum treatment where they ignored the linear response theory and dampings.

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