Negative imaginary potentials

In the adiabatic bend approximation (ABA) for the same reaction,18 the three radial coordinates are explicitly treated while an adiabatic approximation was used for the three angles. These reduced dimensional studies are dynamically approximate in nature, but nevertheless can provide important information characterizing polyatomic reactions, and they have been reviewed extensively by Clary,19 and Bowman and Schatz.20 However, quantitative determination of reaction probabilities, cross-sections and thermal reaction rates, and their relation to the internal states of the reactants would require explicit treatment of five or the full six degrees-of-freedom in these four-atom reactions, which TI methods could not handle. Other approximate quantum approaches such as the negative imaginary potential method16,21 and mixed classical and quantum time-dependent method have also been used.22... 

A negative imaginary potential in the time-independent Schrodinger equation absorbs the particle flux, thus violating the law of conservation of flux, which is satisfied for real potentials [12,13]. Then, the quantum electrodynamical phenomenon of pair annihilation can be represented by particle loss due to an effective absorption potential H = —zVabs since the exact mechanism of positron loss is totally irrelevant to the study of the atomic processes in consideration [9,10,14-16]. The only important aspect of pair annihilation for the present purpose is the correct description of the loss rate. The absorption potential H is proportional to the delta function 5 (r) of the e+-e distance vector r (Section 4.2). 

Mahapatra, S. and Sathyamurthy, K. (1993) Negative imaginary potentials in time-dcpcndcnl quantum molecular scattering, Chem,. Soc Fu,radu,y Trans. 93, 773-779. 

To understand this unique feature of the negative imaginary potential it is easiest to refer to the time-dependent language, discussed later in the section. Heuristically, note that the time-dependent propagator, essentially contains ae term which decays the wavefunction in regions where is positive. The... 

The negative imaginary potentials can be applied in any scattering formalism. In close coupling, they can be implemented to block any product arrangement [31] (see figure 63.4.2) and this thereby converts the reactive problem to an inelastic one the only cost is the propagation of a complex matrix, rather than a real one. 

The parameter e in equation (31b) usually plays a purely formal role in quantum scattering theory, but it has recently" been pointed out that one may think of it as the absorbing potential used to prevent reflections at the edge of the coordinate space grid. In this latter approach one adds a negative imaginary potential to the true potential energy function. 

DVR = discrete variable representation LEPS = Lon-don-Eyring-Polanyi-Sato NIP = negative imaginary potential PODVR = potential optimized DVR QCT = quasiclassi-cal trajectories RBA = rotating bond approximation TST = transition state theory. 

A useful method that can be used in both time-independent and time-dependent calculations on chemical reactions is to add a negative imaginary potential (NIP) to the overall potential in carefully selected regions. This enables reactive flux into particular channels to be absorbed by the NIP and it is then not necessary to integrate the SchrOdinger equation further in that channel as the total reactive flux into it has been obtained. This is useful when state-to-state information is not needed but an overall reactive cross-section is required. The NIP also obviates the need for complicated coordinate systems in chemical reactions (such as hyperspherical coordinates) but the most appropriate parameters for the NIP have to be carefully tested. 

A very powerful approach for calculating cumulative reaction probabilities involves using a negative imaginary potential ie in a Green s function operator. ... 

An alternative way to simulate the presence of the asymptotic region on a finite-sized grid is to introduce a negative imaginary potential into the Hamiltonian,... 

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