Quantum bottleneck states

The SQ method extracts resonance states for the J = 25 dynamics by using the centrifugally-shifted Hamiltonian. In Fig. 20, the SQ wavefunc-tion for a trapped state at Ec = 1.2 eV is shown. The wavefunction has been sliced perpendicular to the minimum energy path and is plotted in the symmetric stretch and bend normal mode coordinates. As anticipated, the wavefunction shows a combination of one quanta of symmetric stretch excitation and two quanta of bend excitation. The extracted state is barrier state (or quantum bottleneck state) and not a Feshbach resonance. 

Since the submission of this article in 2002, there has been a great deal of new work published on the subject of resonances and quantum bottleneck states in chemical reactions. Unfortunately, a discussion of these exciting new results was not possible here. 

A second scenario is provided by barrier-type resonances (sometimes referred to as quantum bottleneck states [QBS]), which do not rely on the internal excitation of the collision complex for their existence. In fact, barrier resonances are observed even when there is no well in Vad(s n). Collisional time delay occurs near the barrier maximum simply because the motion along the s-coordinate slows down passing over the barrier, as in the lower... 

F.J. Aoiz, V.J. Herrero, M.P. de Miranda, V.S. Ranbanos, Constraints at the transition state of the D+H2 reaction Quantum bottlenecks vs. stereodynamics, Phys. Chem. Chem. Phys. 9 (2007) 5367. 

The photoisomerization of all types of azobenzenes is a very fast reaction on either the singlet or triplet excited-state surfaces according to the preparation of the excited state, with nearly no intersystem crossing. Bottleneck states have lifetimes on the order of 10 ps. The molecules either isomerize or return to their respective ground states with high efficiency. So photoisomerization is the predominant reactive channel, and the azobenKnes are photochemically stable. Only aminoazobenzene-type molecules and pseudo-stilbenes have small quantum yields of photodegradation. 

D.C. Chatfield, S.L. Mielke, T.C. Allison, D.G. Truhlar, Quantum dynamical bottlenecks and transition state control of the reaction of D with H2 Effect of varying the total angular momentum, J. Chem. Phys. 112 (2000) 8387. 

Attempts to take into account both localization and percolation or, in other words, to allow for quantum effects in percolation go back to Khmel-nitskii s pioneer paper [68]. The experimental attempts to study quantum effects in conductivity close to the percolation threshold have been undertaken in Refs. [69-71]. The physical sense of these results is stated in Ref. [71] and could be described as follows. The percolation cluster is non-uniform it includes both big conductive regions ( lakes ) and small regions (weak links or bottlenecks) which connect lakes to each other. On approaching the percolation threshold from the metallic side of the transition, these weak links become thinner and longer, and at x = xc the cluster breaks or tears into pieces just in such areas. As a result, exactly these conditions start to be sufficient for the electron localization. Thus, a percolation provokes an Anderson localization in bottlenecks of the percolation cluster. Sheng and collaborators [36,37,72] tried to take into account the influence of tunneling on conductivity for systems in the vicinity of the percolation transition. Similar attempts have been made in papers [38,56]. The obtained results prove that the possibility of tunneling shifts the percolation threshold toward smaller x values and affects material properties in its vicinity. 

How does the solvent influence a chemical reaction rate There are three ways [1,2]. The first is by affecting the attainment of equilibrium in the phase space (space of coordinates and momenta of all the atoms) or quantum state space of reactants. The second is by affecting the probability that reactants with a given distribution in phase space or quantum state space will reach the dynamical bottleneck of a chemical reaction, which is the variational transition state. The third is by affecting the probability that a system, having reached the dynamical bottleneck, will proceed to products. We will consider these three factors next. 

A.L. Efros, V.A. Kharchenko, M. Rosen, Breaking the phonon bottleneck in nanometer quantum dots Role of Auger-like processes, Solid State Commun. 93 (1995) 281. 

The singlet-singlet energy transfer between the central zinc porphyrin in the antenna of 60 and the free base porphyrin ( 3) is slow (240 ps) compared with that among the zinc porphyrins (ki) (50 ps). Thus, the rate constant is a bottleneck that limits the quantum yield of the final charge-separated state (Pzp)3-Pzc-P -C6o . Structural modifications are envisioned to improve the performance of this antenna-reaction center device. 

Some of the stable states are clearly regular. These include some extreme motion adiabatic states, discussed previously, that have no direct coupling to the doorway channel. In order to decay, such states must undergo multiple quantum transitions (often as many as 10), until they diffuse to the doorway channel. Figures 21 and 22 show that many of the adiabatic states are very resistant to diffusion and serve as bottlenecks for dissociation. 

Appearances of bottlenecks for energy transfer,91 ionization,92 and multiphoton dissociation93 have recently been discussed in great detail. The existence of localization91 in quantum systems, as opposed to free diffusion in classically chaotic systems, is closely related to the appearance of adiabatic states discussed here. 

The quantization of transition state energy levels is not simply a mathematical device to add quantum effects to the partition functions. The quantized levels actually show up as structure in the exact quantum mechanical rate constants as functions of total energy [51]. The interpretation of this structure provides clear evidence for quantized dynamical bottlenecks, both near to and distant from the saddle points, as reviewed elsewhere [52]. Quantized variational transition states have also been observed in molecular beam scattering experiments [53]. Analysis of the reactive flux in state-to-state terms from reactant states to transition state levels to product states provides the ultimate limit of resolution allowed by quantum mechanics [53,54]. Quantized energy levels of the variational transition state have been used to rederive TST using the language of quantum mechanical resonance scattering theory [55]. 

The fit identified 17 features up to 1.9 eV. The width parameter WT generally scales inversely with v, and directly with v2, as expected (14). For many of the states kt is very close to 1.00, and its smallest value is 0.54 (14). Thus many of the quantized transition states are nearly ideal dynamical bottlenecks, and even ones with large bend quantum numbers are quite good. 

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