Profiles of the νs(XH) mode in IR spectra of hydrogen-bonded complexes. Theoretical approach

The Analytical Possibilities of FT-IR Spectroscopy Powered by Vibrating Molecules

This paper discusses the state of advancement in the development of spectroscopic methods based on the use of mid (proper) infrared radiation in the context of applications in various fields of science and technology. The authors drew attention to the most important solutions specific to both spectroscopy itself (ATR technique) and chemometric data processing tools (PCA and PLS models). The objective of the current paper is to collect and consistently present information on various aspects of FT-IR spectroscopy, which is not only a well-known and well-established method but is also continuously developing. The innovative aspect of the current review is to show FT-IR's great versatility that allows its applications to solve and explain issues from both the scientific domain (e.g., hydrogen bonds) and practical ones (e.g., technological processes, medicine, environmental protection, and food analysis). Particular attention was paid to the issue of hydrogen bonds as key non-covalent interactions, conditioning the existence of living matter and determining the number of physicochemical properties of various materials. Since the role of FT-IR spectroscopy in the field of hydrogen bond research has great significance, a historical outline of the most important qualitative and quantitative hydrogen bond theories is provided. In addition, research on selected unconventional spectral effects resulting from the substitution of protons with deuterons in hydrogen bridges is presented. The state-of-the-art and originality of the current review are that it presents a combination of uses of FT-IR spectroscopy to explain the way molecules vibrate and the effects of those vibrations on macroscopic properties, hence practical applications of given substances.

Towards accurate infrared spectral density of weak H-bonds in absence of relaxation mechanisms

Following the previous theoretical developments to completely reproduce the IR spectra of weak hydrogen bond complexes within the framework of the linear response theory (LRT), the quantum theory of the high stretching mode spectral density (SD) of weak H-bonds is reconsidered. Within the LRT theory, the SD is the one sided Fourier transform of the autocorrelation function (ACF) of the high stretching mode dipole moment operator. In order to provide more accurate theoretical bandshapes, we have explored the equivalence between the SDs given in previous studies with respect to a new quantum one, and revealed that in place of the basic equations used in the precedent works for which the SD I_Old(ω)=2Re∫₀^∞G_Old(t)e^-iωtdt where the ACF G_Old(t) = ⟨μ(0)μ(t)⁺⟩ = tr {ρ {μ(0)} {μ(t)}⁺}, one can use a new expression for the SD, given by I_New(ω)=2ωRe∫₀^∞G_New(t)e^-iωtdt where G_New(t)=μ(0)μ(t)⁺=1βtrρ_B∫₀^βμ(0)μ(t+iλℏ)⁺dλ. Here ρ_B is the Boltzmann density operator, μ(0) the dipole moment operator at initial time and μ(t) the dipole moment operator at time t in the Heisenberg picture, ℏ is the Planck constant, β is the inverse of the Boltzmann factor k_BT where T is the absolute temperature and k_B the Boltzmann constant. Using this formalism, we demonstrated that the new quantum approach gives the same final SD as used by previous models, and reduces to the Franck-Condon progression appearing in the Maréchal and Witkowski's pioneering approach when the relaxation mechanisms are ignored. Results of this approach shed light on the equivalence between the quantum and classical IR SD approaches for weak H-bonds in absence of medium surroundings effect, which has been a subject of debate for decades.

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^-iΩt dt] 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) = ΩI_Cl(ω), which in turn is equivalent to the quantum SD given by I_Qu(ω) = Re[∫₀^∞G_Qu(t)e^-iΩt dt], 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.

Theoretical interpretation of the line shape of crystalline adipic acid

A general quantum theoretical approach of the upsilon(X-H) IR line shape of cyclic dimers of weakly H-bonded species in the crystal state is proposed. In this model, the adiabatic approximation (allowing to separate the high-frequency motion from the slow one of the H-bond bridge) is performed for each separate H-bond bridge of the dimer and a strong nonadiabatic correction is introduced into the model via the resonant exchange between the fast-mode excited states of the two moieties. Quantum indirect damping and Fermi resonances are taken into account. The present model reduces satisfactorily to many models in the literature dealing with more special situations. It has been applied to the cyclic dimers of adipic acid in the crystal phase. It correctly fits the experimental line shape of the hydrogenated compound and predicts satisfactorily the evolution in the line shapes with temperature and the change in the line shape with isotopic substitution.

Theoretical interpretation of the line shape of the gaseous acetic acid cyclic dimer

A general quantum theoretical approach of the nu(X-H) IR line shape of cyclic dimers of weakly H-bonded species in the gas phase is proposed. In this model, the adiabatic approximation (allowing to separate the high frequency motion from the slow one of the H-bond bridge), is performed for each separate H-bond bridge of the dimer and a strong nonadiabatic correction is introduced into the model via the resonant exchange between the fast mode excited states of the two moieties. The present model reduces satisfactorily to many models in the literature dealing with more special situations. It has been applied to the cyclic dimers (CD(3)CO(2)H)(2) and (CD(3)CO(2)D)(2) in the gas phase. It correctly fits the experimental line shape of the hydrogenated compound and predict satisfactorily the evolution in the line shapes, to the deuterated one by reducing simply the angular frequency of the H-bond bridge and the anharmonic coupling parameter by the factor 1/ square root of 2.