Purely linear coupling

The vibrations at 392, 390 cm"1 in the excited state, strong, whose molecular spectrum shows the first and the second harmonics.58 From the oscillator strength of the vibronic 0-392-cm"1 transition, we may roughly derive a purely linear coupling with c,2 0.14. Each one of the principal 1400-cm-1 vibronic transitions is flanked with a vibration at 390cm", building the sequence 1400 + 392, 2 x 1400 + 392,...cm". ... 

Pig. 4. Comparison of exact and approximate Jahn-Teller spectra for k = x/5 and g = 0.4, taken from Ref. 39. The approximate spectrum is obtained by utilizing Eq. (35). The inset shows the corresponding spectrum for purely linear coupling, i.e. 5 = 0. 

Several methods for the determination of -y(R) have been proposed [224,225]. One is the direct computation of the non-adiabatic coupling matrix element ( i l(B 2))(r) by finite difference techniques, which gives the derivative of y (cf. Eq. (10)). Another is by supposing that the diabatic states adiabatic states Xk and Xkt are (almost) pure linear combinations of the two monomer states. This approximation can be made at the orbital level or at the A-electron level (or at both levels simultaneously). Also mixing matrix elements of molecular properties over adiabatic states may be used. 

Fig. 3. The figure shows the behavior of the probability of remaining in the initial diabatic state (i.e. P = TFPTP) for the conical intersection of Fig. 1 (whose parameters are specified in the caption). The initial condition corresponds to the case 1 of Fig. 1(c). The exact results are compared with those obtained using the MTDM for both damped (a = 0.33541, 0 = 0.590397) or purely linear interstate coupling. The VM results (see text) are also shown.

The source mechanisms (also called fault plane solutions and focal mechanisms or, using a more general description, seismic moment tensors) of tectonic earthquakes are generally due to shear faulting on a fault plane. In the moment tensor description, this is a pure double-couple source, i.e., no volume change or other non-shear components (such as a compensated linear vector dipole) are present at the source. The earthquake mechanisms that correspond to extension, compression, and lateral motion are normal, thrust (reverse), and strike-slip fault plane solutions basic examples are shown in Fig. 1. Normal faults strike perpendicular to the extension direction, and fault dips commonly found from the analysis... 

The requirement I > 2 can be understood from the symmetry considerations. The case of no restoring force, 1=1, corresponds to a domain translation. Within our picture, this mode corresponds to the tunneling transition itself. The translation of the defects center of mass violates momentum conservation and thus must be accompanied by absorbing a phonon. Such resonant processes couple linearly to the lattice strain and contribute the most to the phonon absorption at the low temperatures, dominated by one-phonon processes. On the other hand, I = 0 corresponds to a uniform dilation of the shell. This mode is formally related to the domain growth at T>Tg and is described by the theory in Xia and Wolynes [ 1 ]. It is thus possible, in principle, to interpret our formalism as a multipole expansion of the interaction of the domain with the rest of the sample. Harmonics with I > 2 correspond to pure shape modulations of the membrane. 

A comparahve analysis of coefficients and descriptors clarifies the relationship between lipophilicity and hydrophobicity (Y in Eq. 4 is the molar volume which assesses the solute s capacity to elicit nonpolar interactions (i.e. hydrophobic forces) which, as also clearly stated in the International Union of Pure and Applied Chemistry definitions [3] are not synonyms but, when only neutral species are concerned, may be considered as interchangeable. In the majority of partitioning systems, the lipophilicity is chiefly due to the hydrophobicity, as is clearly indicated by the finding that the product of numerical values of the descriptors V and of the coefficient v is larger in absolute value than the corresponding product of other couples of descriptors/coefficients [9]. This explains the very common linear rela-... 

A specific and sensitive fluorimetric method was proposed by Al-Majed for the determination of (7))-penicillamine in its pure state and in its dosage forms [24], The method is based on the coupling between (/))-penicillamine and 4-fluoro-7-nitroben-zo-2-oxa-1,3-diazole, and analysis of the fluorescent product was measured at an excitation wavelength of 465 nm and an emission wavelength of 530 nm. The fluorescence intensity was found to be a linear function of the drug concentration over the range of 0.6-3 pg/mL, and the detection limit was 2 ng/mL (13 nM). 

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