Reaction dynamics, hyperspherical

Clary, D.C. (1994) Four-atom reaction dynamics, J. Phys. Chem. 98, 10678-10688. Pack, R.T. and Parker, G.A. (1987) Quantum reactive scattering in three dimensions using hyperspherical (APH) coordinates. Theory, J. Chem. Phys. 87, 3888-3921. Truhlar, D.G., Mead, C.A. and Brandt, 5I.A. (1975) Time-Reversal Invariance, Representations for Scattering Wavcfunctions, Symmetry of the Scattering Matrix, and Differential Cross-Sections, Adv. Chem. Phys. 33, 295-344. 

Gallina et al. [20] introduced the hyperspherical symmetrical parametrization in a particle-physics context, as did Zickendraht later [21, 22], At the same time, F.T. Smith [23] gave the definitions of internal coordinates following Fock s work already mentioned [16], Clapp [24, 25] and others and established, for the symmetrical and asymmetrical parametrization, the basic properties and the notation we follow. Since then, applications have been extensive, especially for bound states. For example, the symmetrical coordinates have often been used in atomic [26], nuclear [27] and molecular [28-31] physics. This paper accounts for modem applications, with particular reference to the field of reaction dynamics, in view of the prominent role played by these coordinates for dealing with rearrangement problems. 

The full three-body problem in the physical three-dimensional space required development of hyperspherical harmonic expansions [39]. Crucial for further progress was the introduction of discrete analogues for the latter [40-43], based on hyperangular momentum theory [44,45] and leading to the efficient hyperquantization algorithm [46 19]. For other hyperspherical approaches to reaction dynamics, see [50-63],... 

V. Aquilanti, G. Capecchi, and S. Cavalli, Hyperspherical coordinates for chemical reaction dynamics. Adv. Quant. Chem., 36 341-361, 1999. 

A. Kuppermann, Quantum reaction dynamics and hyperspherical harmonics. Isr. J. Chem., 43 229-241,2003. 

Lepetit B., Launay. J.-M. and M. Le Dourneuf (1986) Quantum mechanical study of electronically non-adiabatic collinear reactions. I. Hyperspherical description of the electronuclear dynamics Chern. Phys. 106, 103-110. 

J. Romelt, Calculations on collinear reactions using hyperspherical coordinates, Theory of Chemical Reaction Dynamics (D. C. Clary, ed.), Reidel, Dordrecht, 1986, p. 77. 

Hyperspherical Coordinates for Chemical Reaction Dynamics only one representation visualized by the tree in fig. 2. 

Finally, time dependent methods are yielding interesting views on polyatomic reaction dynamics, although not actually leading to the full state-to-state information. Most promising for the future will be the blending of these methods with the hyperspherical approach under focus in the present paper. 

ABSTRACT. A number of new effects in reaction dynamics discovered by theoretical investigations using hyperspherical coordinates, e.g. 

In this section we describe those features of the potential energy surfaces in hyperspherical coordinates which are important from the point of view of reaction dynamics. We look for... 

In this contribution, we will describe the essential features of the hyperspherical body-frame method (section 2) and of its numerical implementation (section 3). We will then present in section 4 selected recent results obtained for the three insertion reactions 0( D) + Ho, N( D) + H2 and C( D) + Ho. Our tiine-independent quariturn-dynamical results will be compared with experiment. 

V. Aquilanti, S. Cavalli, G. Grossi, and A. Lagana, A semiclassical approach to the dynamics of chemical reactions within the hyperspherical formalism. J. Mol. Struct., 93 319-323, 1983. 

The recent application of hyperspherical and related coordinates to treat the dynamics on a reactive potential energy surface offers, in fact, the possibility of exploring also those regions where reaction paths present sharp curvatures or bifurcations, taking into account of dynamical quantum effects like tunneling and resonances. Several reviews available [4-10] provide a useful introduction to various aspects of the hyperspherical approach. 

In the final section we briefiy describe some recent developments of the hypersphericeil approach, such as the hyperquantization algorithm as an important computational tool for the solution of dynamical problems and the extensions of the hyperspherical method to treat the dynamics of reactions involving polyatomic systems. 

Being the exact quantum medianical treatment of the dynamics of systems containing more than four atoms presently computationally out of question, only particular cases or approximate methods are nowadays being developed in order to extend the hyperspherical method to complex reactions. Proper formulations of the coordinate systems and relevant hamiltonians have already been referred to [27,28,45], see also [51]. 

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