IR Spectral Density Research Articles

IR spectral density of weak H-bonds involving indirect damping. Part II: Davydov coupling

Abstract A non-perturbative approach of the quantum indirect damping for cyclic dimers of weak H-bonds susceptible to involve Davydov coupling is proposed. The effective non-Hermitian Hamiltonians describing the damped H-bond bridge obtained in Part I [Chem. Phys. (2003) submitted] following the basic quantum model of the indirect damping [Chem. Phys. 126 (1988) 263], is introduced in the model of Marechal and Witkowski [J. Chem. Phys. 48 (1968) 3637]. A result which is equivalent to an infinite order expansion of a precedent perturbative approach [J. Mol. Struct. (Theochem.) 314 (1994) 101] is obtained. It allows us to obtain, within the linear response theory, the infrared lineshape of the ν X–H stretching mode. The fine structure of the high frequency tail appears to be more smoothed than that of the low frequency one.

Infrared spectra of weak H-bonds: Fermi resonances and intrinsic anharmonicity of the H-bond bridge

The present quantum theory is a new step in our attempt to obtain a flexible tool susceptible to be used by experimentalists working in the realm of the infrared spectra of the ν S ( X– H → ⋯Y) mode of weak strength hydrogen bonds. We take into account the intrinsic anharmonicity of the hydrogen bond stretching mode X ← –H⋯ Y → through a Morse potential by starting from a previous model [Chem. Phys. 248 (1999) 91] which described a weak hydrogen bond subject to a Fermi resonance and which included relaxation phenomena within a quantum treatment, but which considered this mode as an harmonic oscillator. The IR spectral density is studied within the linear response theory by Fourier transform of the autocorrelation function of the transition dipole moment operator of the X–H bond. The main feature brought by the anharmonicity of the H-bond bridge X–H⋯Y is the increase of the average frequency of the ν S ( X– H → ⋯Y) IR band upon a temperature rising. Then, this theory reproduces successfully the experimental behavior of both the first and second moments of this band which is observed when varying the temperature as well as upon isotopic substitution.

Anharmonic effects on theoretical IR line shapes of H-bonds

In the spirit of Y. Maréchal and A. Witkowski's [J. Chem. Phys. 48 (1968) 2697] work, one revisits, for weak H-bonds, the dependence of the angular frequency ω and of the equilibrium position q e of the υ X–H high frequency mode q, on the position coordinate Q of the low frequency υ X–H⋯Y mode. One considers: ω= ω o+ bQ+ cQ 2 and q e= gQ+ fQ 2. That leads to the anharmonic potential U: U= k 1 q 2+∑ k r Q r +∑∑ k nm q n Q m + k 15 qQ 5. Here k r and k mn ( r=2–5, n=1,2 and m=1–4) are interrelated through b, c, g and f. By aid of the Hamiltonian involving U, we find the direct damped auto correlation function of υ X–H, which, by Fourier transform, gives the IR spectral density (SD). When only b≠0, the SD is nothing but that given in a previous paper [P. Blaise, O. Henri-Rousseau, Chem. Phys. 243 (1999) 229]. When the adiabatic approximation is performed, this SD becomes that of N. Rösch and M. Ratner [J. Chem. Phys. 61 (1974) 3444] which reduces in turn to that of Maréchal and Witkowski in the absence of damping. With respect to b≠0, c produces a narrowing of the SD if c>0 and a subtle broadening if c<0. Besides, g induces the same narrowing for g>0 and g<0, while f gives subtle changes very sensitive to the sign of f and to the values of b, c and g. The situation b<0 and f>0 which is physically the most probable, leads to SDs which are the most evoking experimental profiles.

Theory of weak damped H-bonds: relative influence of relaxation mechanisms on IR spectra

We revisit numerically the roles played by relaxation mechanisms on the line shapes of the IR spectral density of weak H-bonds. This is performed by means of three theories already published. The tools common to these theories are the strong anharmonic coupling theory (between the high- and low-frequency stretching modes of the H-bond), and the linear response theory (according to which the spectral density is the Fourier transform of the autocorrelation function). The theories are those of: (1) G. Robertson and J. Yarwood [Chem. Phys. 32 (1978) 267], taking into account (semiclassically) indirect damping; (2) N. Rösch and M. Ratner [J. Chem. Phys. 61 (1974) 3444] dealing (quantum mechanically) with direct damping; and (3) B. Boulil, J.-L. Déjardin, N. El-Ghandour, O. Henri-Rousseau [J. Mol. Struct. (Theochem) 314 (1994) 83] involving (quantum mechanically) slow-mode damping. The quantum direct damping induces a broadening, and the quantum slow-mode damping (in contrast with the semiclassical indirect relaxation) a weak narrowing, when they are both occurring. The direct damped quantum spectral density leads to Lorentzian (fast modulation limit) or Gaussian (slow modulation limit) shapes as does the spectral density of the semiclassical model of indirect relaxation. The dephasing of the fast mode should be predominant for line shapes with broadened sub-bands (obeying the Franck–Condon progression law), or without sub-bands (but with nearly symmetric profiles intermediate between Gaussian and Lorentzian). Both the dephasing of the fast mode and the damping of the slow mode should occur by similar amounts if the line shapes are without sub-bands but with asymmetry, or with sub-bands but with intensity anomalies in the Franck–Condon progression.

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 lineshapes ( ν X–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.

IR spectral density of weak H-bonded complexes involving damped Fermi resonances. II. Numerical experiments and physical discussion

The IR absorption band profile of the X–H stretching mode of weak H-bonded complexes involving Fermi resonances between the high frequency mode and some bending modes, all these modes being damped, have been computed within the linear response theory, by aid of the Fourier transform of the autocorrelation function of the dipole moment operator of the high frequency mode [O. Henri-Rousseau, D. Chamma, Chem. Phys. 229 (1998) 37]. As it appears the probability to observe realistic and noticeable modifications of the experimental lineshapes by Fermi resonances is strongly enhanced by the presence of an hydrogen bond, leading to the conclusion that Fermi resonances must play a very general role in the lineshapes of H-bonds.

IR spectral density of weak H-bonded complexes involving damped Fermi resonances. I. Quantum theory

The IR spectral density of the high frequency stretching mode of weak H-bonded complexes involving Fermi resonances is studied within the linear response theory from a full quantum mechanical point of view: the anharmonic coupling between the high frequency X–H and the low frequency X–H⋯Y modes is treated inside the strong anharmonic coupling theory. Following Witkowski and Wójcik [A. Witkowski, M. Wójcik, Chem. Phys. 1 (1973) 9.], the Fermi resonance between the first excited state of the fast mode and the first harmonic of single or several bending modes is introduced. Besides, the direct relaxation involved by the fast and bending modes are incorporated, in the spirit of the reduced Green formalism, by aid of imaginary damping terms. The spectral density is obtained by the Fourier transform of the autocorrelation function of the dipole moment operator of the fast mode, in which time dependent terms appear that are solution of a set of coupled linear differential equations. It reduces in the special situation where the Fermi coupling is ignored to that obtained by Rösch and Ratner [N. Rösch, M. Ratner, J. Chem. Phys. 61 (1974) 3344.]. Furthermore, when the anharmonic coupling between the slow and fast modes is neglected, it reduces to the spectral density that may be obtained in the framework of the Giry et al. [M. Giry, B. Boulil, O. Henri-Rousseau, C.R. Acad. Sci. Paris 316 s.II (1993) 455; B. Boulil, M. Giry, O. Henri-Rousseau, Phys. status solidi (b) 158 (1990) 629.] approach. At last, it reduces to the Witkowski and Wójcik [A. Witkowski, M. Wójcik, Chem. Phys. 1 (1973) 9.] approach, when the relaxation disappears. A generalization to several Fermi resonances is also proposed. Numerical tests of the theory and physical discussions are reported in the following paper [D. Chamma, O. Henri-Rousseau, Chem. Phys. 229 (1998) 51].

Effect of nonuniform spectral dome transmittance on the accuracy of infrared radiation measurements using shielded pyrradiometers and pyrgeometers

We discuss the problem arising from the nonuniform distribution of spectral transmittance of the instrument's shielding dome. Recently, by using high-resolution atmospheric radiation software, itbecame possible to evaluate both the real downward IR spectral flux density and the transmitted spectral flux density of the instrument's dome. By using a simplified model we obtained a theoretical formula that describes the effect of dome transmittance on the instrument's response. By the formula, the effective dome transmittance (average dome transmittance weighted by the spectral flux density) is directly proportional to the calibration constant of the instrument. In order to obtain a quantitative relationship we computed the effective dome transmittance for several domes and model atmospheres. ccording to our results the maximum difference in effective dome transmittance of individual domes is 20% for Eppley-type silicon domes and 10% for polyethylene domes. These relatively large differencesmust be corrected when the domes are replaced. The effective dome transmittance shows strongcorrelation with precipitable water and the total downward IR flux density. The combined effect on thecalibration factor is a maximum 2% for the Eppley domes and 5% for the polyethylene domes. By usingthe linear regression method these types of error can be minimized.