Localized curve crossing

The second variant is designed for solid state reactants to the exclusion of liquid or gas. This powder variant of Thermostar is described by the Fig. 1.19 (right). The microwave applicator is the same as for the device for liquids heating but the reactant transport is ensured by a metallic screw set within the dielectric pipe. This specific traveling metallic screw crosses all the microwave applicators. The coexistence of this metallic screw with the electric field is ensured by the fact that the major electric field direction is parallel to the major direction and perpendicular to the local curving of the screw. A typical industrial unit for solid or liquid reactants is powered with microwave generators units of 2 or 6 kW for a total microwave power close to 20 or 60 kW. 

Right Histograms of the olg(3II) population vs the iodine-iodine separation at 2 time points. Shown are the first two exits for such points in time that the dissociative population has reached an average intramolecular separation of —4 A (This distance is about the upper limit of the experimental probing window.) [16] The localized nature of the dissociative population is a direct result of the vibrational localization on the parent 6 state, as an exit to the a state occurs only when there is population in the curve-crossing region. 

Within a local complex potential curve crossing model, the cross section for the simple DEA reaction e + AB AB A + B, where AB is a diatomic molecule, may be expressed as [18]... 

The HCP case exhibits one additional signal of the onset of rapid change in vibrational resonance structure. This is the sudden onset of vibrational perturbations at (0, 32, 0) [5]. Local perturbations, where one rotational term curve crosses another, are manifest as level shifts, extra lines, and intensity anomalies [18]. Such perturbations are typically rare at low vib and... 

In the projection operator formalism, which leads to a rigorous basis for the optical potential, the absorptive imaginary part is associated with transitions out of the elastic channel from which no return occurs. Whereas Pgl transitions are in this category, excitation transfer (ET) transitions are not, since return ( virtual excitation ) can occur during the ET collision. In the event that a localized avoided curve crossing with one other state dominates the inelastic process (expected for many endoergic transfers), the total absorption probability (opacity) can still be defined ... 

The basic assumptions of the Landau-Zener theory need to be satisfied. These involve the applicability of classical mechanics (e.g. the neglect of tunneling) for the nuclear dynamics and the locality of the curve crossing event. 

The dissociation has been studied photochemically by exciting the dipole active HN stretch with infrared multiphoton pumping and with one-photon local mode overtone excitation. From the discussions above, it is clear that we are primarily concerned in this chapter with the vibrational events which produce the activation of the N-N reaction coordinate and not with the electronic events which determine whether the curve crossing occurs. Hence, we have focused on the events on the ground electronic surface of the parent molecule which lead to an extension of the N-N bond to 3.5a . 

The point at which each couple of curves crosses indicates where an order has a smaller local error than the other one with the same integration step. Consequently, Figure 2.7 shows that if the acceptable error is larger than Ci2, the first-order method is preferred if it is within ei2 and 623, the second-order method is preferred and if it is smaller than 623, the third-order method is preferred. 

We conclude that the QCL description represents a promising approach to the treatment of multidimensional curve-crossing problems. The density-matrix formulation yields a consistent treatment of electronic populations and coherences, and the momentum changes associated with an electronic transition can be directly derived from the formalism without the need of ad hoc assumptions. Employing a Monte-Carlo sampling scheme of local classical trajectories, however, we have to face two major complications, that is, the representation of nonlocal phase-space operators and the sampling problem caused by rapidly varying phases. At the present time, the... 

However, irrespective of the method used to treat the collision dynamics, there remains a fundamental difficulty with the molecular model, arising from the incapacity of a finite adiabatic (or diabatic) basis set to represent correctly the asymptotic conditions. In practice, the effect (the so-called translation effect) is not serious at low eV energies when the transition is well localized at the curve crossing. 

FIGURE 2.1 Valence bond curve-crossing diagram, for the Jt-component, interconversion of two Kekule structural forms along the bond alternation coordinate (bj mode). VG and QMRE correspond to vertical gap and quantum mechanical resonance energy, respectively. The two putative possibilities represent that in one case (a) the vertical gap is high and therefore a localized structure is preferred in the other ease (b) a small vertical gap results in bringing the stability to a fully delocalized symmetric structure. 

The simplest case for discussing a localized non-adiabatic transition with a small gap is the model of curve crossing. Section 3.2.4, when there is just one nuclear coordinate. We turn now to a more quantitative analysis of this model. 

Atoms in Molecules Electron Transfer Calculations Electronic Wavefunctions Analysis Hyperconjugation Intermolecular Interactions by Perturbation Theory Localized MO SCF Methods Natural Orbitals NMR Chemical Shift Computation Ab Initio Rotational Barriers Barrier Origins Valence Bond Curve Crossing Models. 

The stabilization energy, of the transition state relative to the localized structure at the crossing point in the VB state correlation diagram, due to resonance mixing of the VB curves. VB curve crossing diagrams... 

---