Coupling strengths

Such electronic excitation processes can be made very fast with sufficiently intense laser fields. For example, if one considers monochromatic excitation with a wavenumber in the UV region (60 000 cm ) and a coupling strength / he 4000 (e.g. 1 Debye in equation (A3.13.59), / 50 TW cm ),... 

As written, Eq. (52) depends on all the (infinite number of) adiabatic electi onic states. Fortunately, the inverse dependence of the coupling strength on energy separation means that it is possible to separate the complete set of states into manifolds that effeetively do not interact with one another. In particular, Baer has recendy shown [54] that Eq. (57), and hence Eq. (58) also holds in the subset of mutually coupled states. This finding has important consequences for the use of diabatic states explored below. 

In fig. 26 the Arrhenius plot ln[k(r)/coo] versus TojT = Pl2n is shown for V /(Oo = 3, co = 0.1, C = 0.0357. The disconnected points are the data from Hontscha et al. [1990]. The solid line was obtained with the two-dimensional instanton method. One sees that the agreement between the instanton result and the exact quantal calculations is perfect. The low-temperature limit found with the use of the periodic-orbit theory expression for kio (dashed line) also excellently agrees with the exact result. Figure 27 presents the dependence ln(/Cc/( o) on the coupling strength defined as C fQ. The dashed line corresponds to the exact result from Hontscha et al. [1990], and the disconnected points are obtained with the instanton method. For most practical purposes the instanton results may be considered exact. 

Fig. 27. Logarithm of normalized rate constant ln(fc/nto) versus dimensionless coupling strength C /Q for PES (4.28) with Q = 0.1, n = 1, F /a>o = 3. Separate points and dashed line correspond to instanton result and numerical data [Hontscha et al. 1990].

At low temperatures, when the bath is quantum (icoj P 1), the rate expression, expanded in series over the coupling strength, breaks up into the contributions from the various processes involving the bath phonons... 

In Fig. 4 we show how the interlayer coupling strength is decreasing continuously as a function of the intermixing concentration. The behaviour is very similar to the case of interface intermixing in Fe/Cu/" trilayers shown in Fig. 2. 

Internal Yield Pressure for Couplings. Internal yield pressure for threaded and coupled pipe is the same as for plain end pipe, except where a lower pressure is required to avoid leakage due to insufficient coupling strength. The lower pressure is based on... 

In earlier works (4), we and others (5) have formulated and computed such non BO coupling strengths for several of the anion systems that have been studied experimentally including ... 

Figure 23. Arrhenius plot of the electron transfer rate. The electronic coupling strength is TIad = 0.0001 a.u. Solid line-Bixon-Jortner perturbation theory Ref. [109]. FuU-circle present results of Eq. (26 ). Dashed line-results of Marcus s high temperature theory [Eq.(129)]. Taken from Ref. [28].

Figure 25. Electron-transfer rate the electronic coupling strength at T = 500 K for the asymmetric reaction (AG = —3ffl2, oh = 749 cm ). Solid line-present full dimensional results with use of the ZN formulas. Dotted line-full dimensional results obtained from the Bixon-Jortner formula. Filled dotts-effective ID results of the quantum mechanical flux-flux correlation function. Dashed line-effective ID results with use of the ZN formulas. Taken from Ref. [28].

Although energy conservation constraints dictate which VP channels are open, it is the nature of the intermolecular interactions, the density of states and the coupling strengths between the states that ultimately dictate the nature of the dynamics and the onset of IVR. These factors are dependent on the particular combinations of rare gas atom and dihalogen molecule species constituting the complex. For example, Cline et al. showed that, in contrast to He Bra, Av = 2 VP in the He Cla and Ne Cla complexes proceeds via a direct... 

For the explicit calculations presented below, we have chosen a width wq = 10 e V for the ip-band, and a coupling strength A p =0.2 eV, and have varied the parameters for the (i-band. The level shift A(e) is obtained from the second part of (2.7). The resulting functions are illustrated in Fig. 2.12. 

Figure 2.19 The energy of activation of the reduction reaction for various interactions with the d-band (a) as a function of the position of the d-band center (b) as a function of the coupling strength. The parameters are = 0.1 eV, Wd = 1 eV, A = 0.5eV, and A = 4eV in (a), = 2.0eV in (b), = —0.5 eV. The horizontal line indicates the value in the absence of...

FIG. 10 The calculated internal energy of a one-component plasma as a function of coupling strength is compared with corresponding simulation results (open circles) by Brush, Sahlin, and Teller (J. Chem. Phys. 45 2102 (1966). The Debye-Huckel (DH) and hole-corrected Debye-Huckel (DHH) theories were used with results as shown (indicated lines). 

Fig. 19. Calculated coupling strength f (in cm-1, thin line) (Torri and Tasumi, 1998) and angle 0 (in degrees, thick line) between the two amide I transition dipoles as a function of the dihedral angles 0 and 0. From Woutersen and Hamm (2001)./. Chem. Phys. 114, 2727-2737, 2001, Reprinted with permission from American Institute of Physics.

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