Reaction dynamics, hyperspherical coordinates

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

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. 

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

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

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

Clapp and Delves rediscovered them for the field of nucJear physics (1949) [4] and within the last two decades the set of hyperspherical coordinates was introduced to the theory of molecular dynamics (i.e. molecular collisions (1960) [5], collision induced dissociation (1971) [6], photolysis of molecules (1974) [7], chemical reactions (1973)... 

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... 

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. 

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]. 

---