Tuning mode

Figure 3. Example of Graphical Output from Analysis Mode. Reaction progress for water-jacketted reactor, with Cascade coupled temperature controllers, both in self-tuning mode.

Switch on the microwave bridge to tune mode (and allow two minutes warm-up time). 

FIGURE 2.8 Tuning mode patterns. The scope mode shows a dip when the frequency of the microwave fits into the resonator. This dip has maximal depth when the spectrometer is tuned (with the adjustable iris) to be reflectionless, that is, when the resonator is critically coupled to the bridge. Shown patterns are (a) off resonance, (b) slightly off resonance, (c) either under- or over-coupled, (d) critically coupled, (e) asymmetry from out-of-phase reference. 

When the microwave bridge is in tune mode, the microwave source is at high voltage, and its guaranteed lifetime is ticking away (therefore, switch to off for a lunch break). 

In rough-tuning, the spectrometer is put at the tune mode. A low microwave power (e.g., 25 dB, 0.63 mW) is applied to generate the model pattern , which is the microwave power reflected from the resonator as a function of the microwave frequency. Microwave frequency is adjusted to... 

Figure 3.42 The Cl seam in the (r, z) plane (0 = 90°) for the combined PSB chromophore plus solvent system, comprising the coupling mode Q, tuning mode r, and the solvent coordinate z in the role of an additional tuning mode. The minimum free energy Cl (MECI) is indicated. The (r, z) projection of the Franck-Condon geometry is shown for reference.

The same is approximately true for a plot of the property versus an appropriate geometrical coordinate, in the approximation that the two states have approximately equal force constants and behave harmonically along the coordinate of interest. It should be emphasized that the coordinate discussed in this context is not the coupling coordinate, but rather a totally symmetric coordinate over which the gap between the coupled states varies. Such a coordinate is often called a tuning mode [230],... 

In Eqs. (54c) and (69), the parameters s, g and h are used to determine the energies and derivative couplings near a point of conical intersection. Below we compare these perturbative results with those of ab initio calculations at (trans, p, 2.95). Figures 4 depicts the g h plane for this point. From this figure it is seen that the coupling mode, y, has a" synunetry and therefore is the unique internal a" coordinate. The tuning mode x has a symmetry and tends to decrease i (C-N) and increase ZNCO. 

This one-dimensional vibronic-coupling problem is converted into a conical intersection by the totally symmetric tuning modes (ring stretching) and j/6a (ring bending), which induce symmetry-allowed intersections of... 

Fig. 5. Time evolution of the population probability of the upper (5i) adiabatic electronic state of the photoisomerization model with (a) two degrees of freedom (torsion, coupling mode), (b) three degrees of freedom (torsion, coupling mode, tuning mode), and (c) four degrees of freedom (torsion, coupling mode, two tuning modes).

Here aj(aj) are creation and annihilation operators of the bath mode of frequency ojj and bc(bt) are annihilation operators of a coupling and a tuning mode, respectively. The so-called rotating-wave approximation (RWA) has been invoked in Eq. (17), neglecting terms of the type ba and b a. The effect of the bath on the system dynamics is completely determined by the... 

Fig. 9. Time evolution of the expectation values of (a) position and (b) momentum of the tuning modes ui (solid line) and i 6a(dotted line) of the three-mode pyrazine model.

As discussed in detail in Ref. 34, the vibrational dephasing process represents the origin of the irreversible time evolution of the electronic population (Fig. 2). The initial quasi-periodic recurrences of P it) reflect the driving of electronic population by initially coherent vibrational motion in the tuning modes i/i and z/ga. The vibrational dephasing process destroys the coherence of vibrational motion and thus irreversibly traps the electronic populations. 

Pig. 11. Time-dependent energy content of the torsional mode (solid line), the coupling mode (dashed line), and the tuning mode (dotted line) of the three-dimensional photoisomerization model. 

Fig. 12. Projected probability density of the tuning mode usa in the S2 (upper frame) and Si (lower frame) adiabatic electronic states for the three-dimensional pyrazine model. The normal coordinate axis extends from —7.0 to 7.0, the time axis from zero to 200 fs (from front to back).

The wave-packet dynamics of the coupling mode is very different, as can seen in Fig. 13. In this case the initially prepared wave packet experiences no gradient on the S2 surface. It is rather squeezed (that is, it becomes more localized) as the conical intersection is approached by motion in the tuning modes. When the conical intersection is reached, the wave packet instantaneously appears on the lower surface, where it spreads rapidly as a... 

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