Davydov coupling

There is also the possibility of Davydov coupling, which is likely to appear when there are double or multiple H-bond systems [7,21-23]. It is responsible for cooperative effects between neighboring hydrogen bonds in cyclic hydrogen bonded dimers, or more generally in hydrogen-bonded chains in solids [ 10,24—34]. 

A. Dimers Involving Davydov Coupling and Direct and Indirect Dampings... 

The Hamiltonian in the Presence of Damping but in the Absence of Davydov Coupling... 

An Approximation for Quantum Indirect Damping [80] when Davydov Coupling Occurring... 

B. Dimer Involving Damping, Davydov Coupling, and Fermi Resonances... 

At last, many H-bonded species may form cyclic dimers. Then, in such situations, there is the possibility of resonance between the two X—H stretching oscillators belonging to each moiety of the dimer. This leads to Davydov coupling that may affect the IR v5(X—H) line shape [18]. 

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]. 

Consider an excitation of the fast mode of one moiety of the dimer. The corresponding excited state is resonant with the state corresponding to the situation where it is the fast mode of the other moiety that is excited. A resonant exchange mechanism must occur when one of the fast modes has been excited. This mechanism, which is of a nonadiabatic nature, is at the origin of the Davydov coupling [74], which has been introduced by Marechal and Witkowski [18] in their pioneering works. 

The Hamiltonian of the cyclic dimer involving Davydov coupling between the first excited state of the high frequency oscillator a of one moiety and the excited state of the oscillator b of the other moiety, and vice versa, is... 

The Davydov coupling Hamiltonian V uav appearing in this equation is... 

As a consequence, for allowed IR absorption, the SD involving both Davydov coupling and direct damping is [75]... 

It may be observed that the two Hamiltonians (269) are those of quantum harmonic oscillators, whereas Hamiltonian (270) is that of a driven damped quantum harmonic oscillator, and Hamiltonians (271) are those of driven undamped quantum harmonic oscillators perturbed by the Davydov coupling... 

Appendix R shows that the ACF (259) of the transition moment operator of the fast mode, involving indirect damping, but without direct damping ignored, takes the form given by Eq. (R.3). Of course, the direct damping may be taken into account with the aid of a damped exponential factor, as performed in the simpler situation without Davydov coupling. Consequently, in the present situation, the... 

Rosch and Ratner [47] in the absence of Davydov coupling and indirect damping. 

Robertson and Yarwood [46], in the semiclassical limit, without Davydov coupling and direct damping. 

Of course, when the Davydov coupling is in turn missing, the SD (282) reduces to that of a monomer involving the anharmonic coupling a° ... 

Damping But Without Davydov Coupling. Now, consider the limit situation in the absence of Davydov coupling, but with direct and indirect damping. Then,... 

Now, we must observe that because of the absence of the Davydov coupling, it is indifferent to consider the symmetry, so that it is possible to come back to the nonsymmetrized ACFs, and thus to write for the nonsymmetrized coordinate ... 

Equation (287) shows that multiplying the a ACF by the b ACF leads to a new ACF of the same structure in which a0 transforms into a°. Besides, when r)° is zero, p° reduces to p0. As a consequence, the full ACF (284) of the dimer in the absence of Davydov coupling becomes... 

Now, in order to get an approach for Davydov coupling susceptible to generalization to more complex situations, it may be suitable, according to Eqs. (208) and (210), to replace the effective Hamiltonians (289) and (291) by the corresponding non-Hermitean ones, where, as above, the zero-point energy... 

Consequently, the Hamiltonian of the dimer that involves Davydov coupling, Fermi resonances between the g excited state of the fast mode and the g first harmonics of the bending mode, together with the damping of is... 

Figure 19. Davydov coupling and 1 Fermi resonance, for centrosymmetric cyclic dimer within the strong anharmonic coupling theory. (The subscripts 1 and 2 refer, respectively, to the a and b moieties of the centrosymmetric cyclic dimer).

In the presence of Davydov coupling and Fermi resonances, the ACF of the dipole moment operator of the fast mode involving both direct and indirect dampings and also damping of the bending modes, has the same structure as Eq. (272), that is,... 

Recently [76], we proposed an approach in which we introduced the quantum indirect damping in the Marechal and Witkowski model involving Davydov coupling. More precisely, this model equally takes into account the strong... 

When the indirect damping is missing, the Hamiltonian (255) of a cyclic dimer involving Davydov coupling reduces to... 

The aim of this appendix is to show that the g ACF (304) involving Davydov coupling, Fermi resonances, and damping, may be viewed, after some simplifications, as formally equivalent to that used by Marechal [83] in his peeling-off approach of Fermi resonances. 

The ACF involving Davydov coupling, without Fermi resonance and without direct and indirect dampings. 

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