Strong anharmonic coupling theory

The cornerstone of the strong anharmonic coupling theory relies on the assumption of a modulation of the fast mode frequency by the intermonomer distance. This behavior is correlated by many experimental observations, and it is undoubtly one of the main mechanisms that take place in a hydrogen bond. Because the intermonomer distance is, in the quantum model, represented by the dimensionless position coordinate Q of the slow mode, the effective angular frequency of the fast mode may be written [52,53]... 

There are two kinds of damping that are considered within the strong anharmonic coupling theory the direct and the indirect. In the direct mechanism the excited state of the high-frequency mode relaxes directly toward the medium, whereas in the indirect mechanism it relaxes toward the slow mode to which it is anharmonically coupled, which relaxes in turn toward the medium. 

The pure quantum approach of the strong anharmonic coupling theory performed by Marechal and Witkowski [7] gives the most satisfactorily zeroth-order physical description of weak H-bond IR lineshapes. 

The Full Hamiltonian Within the Strong Anharmonic Coupling Theory... 

The Adiabatic Approximation [51] Dealing With the Strong Anharmonic Coupling Theory of Weak H-Bonds Partition of the Full Hamiltonian into Diabatic and Adiabatic Parts Weakness of the Diabatic Hamiltonian [122]... 

Now, let us look at the incorporation of the quantum indirect damping in the quantum representation // of the H-bond bridge. It is necessary to introduce in the model of the weak H-bond working within the strong anharmonic coupling theory, an hypothesis on the nature and on the irreversible action of... 

In Section III, we obtained within the strong anharmonic coupling theory and within the adiabatic approximation, an expression for the ACF of the dipole moment operator that takes into account the irreversible influence of the surrounding on the H-bond bridge. In quantum representation II, this ACF is given by Eq. (124), which is a consequence of Eq. (123) after performing the trace over the slow mode, that is,... 

As a consequence of the above equations, the full Hamiltonian describing the fast mode coupled to the H-bond bridge (via the strong anharmonic coupling theory) and to the bending mode (via the Fermi resonance process) may be written within the tensorial basis (222) according to [24] ... 

Fig. 10. Fermi resonance within the strong anharmonic coupling theory.

In Section IE, a theoretical approach of the quantum indirect damping of the H-bond bridge was exposed within the strong anharmonic coupling theory, with the aid of the adiabatic approximation. In Section III, this theory was shown to reduce to the Marechal and Witkowski and Rosch and Ratner quantum approaches. In Section IV, this quantum theory of indirect damping was shown to admit as an approximate semiclassical limit the approach of Robertson and Yarwood. 

Figure 15. Davydov effect within strong anharmonic coupling theory. (The subscripts 1 and 2 refer, respectively, to the a and b moieties of the centrosymmetric cyclic dimer)...

APPENDIX B THE ADIABATIC APPROXIMATION [51] DEALING WITH THE STRONG ANHARMONIC COUPLING THEORY OF WEAK H-BONDS... 

In this section we shall give the connections between the nonadiabatic and damped treatments of Fermi resonances [53,73] within the strong anharmonic coupling framework and the former theory of Witkowski and Wojcik [74] which is adiabatic and undamped, involving implicitly the exchange approximation (approximation later defined in Section IV.C). 

This section now deals with H-bonded species, where together with the strong anharmonic coupling and the quantum indirect damping, Davydov coupling and Fermi resonances may occur, that is, centrosymmetric H-bonded cyclic dimers the theory of which, for situations without damping,was first performed by Marechal and Witkowski [18]. 

B. The Main Mechanism Strong Coupling Theory of Anharmonicity... 

Rather strong temperature variation has been seen in the infrared spectra of CO/Ni(l 11) . Figure 7 shows the peak width and position as a function of substrate temperature for the c(4 x 2) structure, where all molecules are chemisorbed in the bridge position. As seen in the figure the peak width increases strongly with increasing temperature and there is also a small upward shift of the peak position. We observe that both the peak width and position reaches a constant value for very low temperatures, so it could be possible that the behaviour can be explained in terms of an anharmonic coupling. Persson et developed a new theory for this problem, partly... 

From the point of view of statistical mechanics there are many problems, such as strongly anharmonic lattices, to which the theory can be applied.14 It appears as a natural generalization of Landau s theory of quasi-particles in the case when dissipation can no longer be neglected. The most interesting feature is that equilibrium and nonequilibrium properties appear linked. The very definition of the strongly coupled anharmonic phonons depends on their lifetime. 

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