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... 

---