Absorbing potentials

Figure B3.4.2. (a) A sehematie potential surfaee showing bifiiroation for a triatomio reaotive system, (b) By blooking the produots arrangement with an absorbing potential (shaded area) the reaotive system is reduoed to one arrangement tiiis soheme enables oaloulation of both total reaotivities and state-to-state infomiation. Reprinted from [M] with pemiission.

Alternately, absorbing potentials can also be applied to convert scattering to a bound-state-like problem. One method is to write the Sclirodinger wavefiinction as a sum of two temis where... 

Figure B3.4.12. A schematic ID vibrational pre-dissociation potential curve (wide flill line) with a superimposed plot of the two bound fimctions and the resonance fimction. Note that the resonance wavefiinction is associated with a complex wavevector and is slowly increasing at very large values of R. In practice this increase is avoided by iismg absorbing potentials, complex scaling, or stabilization.

Finally, the simplest approach to extract resonances is to add to the Hamiltonian an absorbing potential [8, 48. 108. 109], and then look for the complex eigenvalues of the Hamiltonian /7-i Vj. The absorbing potential... 

Neuhauser D 1992 Reactive scattering with absorbing potentials in general coordinate systems Chem. 

Riss U V and Meyer H D 1998 The transformative complex absorbing potential method a bridge between complex absorbing potentials and smooth exterior scaling J. Phys. B At. Mol. Opt. Phys. 31 2279... 

Fillers fibreglass, silicas, calcium carbonate, powdered metal pigments some may be absorbed potential primary irritant dust inhalation low toxicity... 

Schrodinger Equation with Absorbing Potential for Quantum Scattering Calculations. 

The need for data in relation to photomutagenicity may be indicated by the structure of a molecule, its light absorbing potential, or its potential to be photoactivated. 

The Grid and the Absorbing Potential The Real Wavepacket Method... 

G. G. Balint-Kurti and A. Vibok, Complex absorbing potentials in time dependent quantum dynamics, in Numerical Grid Methods and Their Application to Schrdinger s Equation, C. Ceijan, ed., NATO ASI series, Series C Mathematical and Physical Sciences, Vol. 412 (Kluwer Academic Publishers, 1993), p. 195. 

In Fig. 9.5, curve (a) is the cyclic voltammogram (CV) for the oxidation of tri-p-anisylamine (TAA) in 0.1 M Et4NCl04-AN, and curves (b) and (c) are the absorbance-potential curve and its derivative curve, respectively. They were obtained using an OTE with a vapor-deposited platinum film [8]. The excellent agreement of curves (a) and (c) shows that the reaction in the CV is purely the oxidation and re-reduction of the TAA. However, the two curves are different in that the peak current for curve (a) is proportional to the square root of the voltage sweep rate, while the peak height of curve (c) is inversely proportional to the square root of the voltage sweep rate. 

Figure 1. Solid lines are contours of the potential energy surface for the H + H2 - H2 + H reaction. Broken lines are contours of the absorbing potential (which is zero in the central part of the interaction region and turned on at the edge) for three possible choices of it. The points are the grid points that constitute the basis set for the evaluation of the quantum trace, Eq. (2.5).

The absorbing potential factor is the only nonstandard feature in Eq. (3.1). Fortunately, it is much simpler to deal with the absorbing potential semiclassically than it is quantum mechanically it cannot cause any unwanted reflections in the above semiclassical expression because we have implicitly made an infinitesimal approximation for it. Thus, it does not affect the dynamics and only causes absorption see also the disscussion by Seide-man et al. [3b]. 

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