Hyperquantization algorithm

V. Aquilanti, S. Cavalli, D. De Fazio, A. Volpi, A. Aguilar, J.M. Lucas, Benchmark rate constants by the hyperquantization algorithm. The F+H2 reaction for various potential energy surfaces Features of the entrance channel and of the transition state, and low temperature reactivity, Chem. Phys. 308 (2005) 237. 

V. Aquilanti, S. Cavalli, and G. Grossi, Theor. Chim. Acta, 79, 283 (1991). Discrete Analogs of Spherical Harmonics and Their Use in Quantum Mechanics The Hyperquantization Algorithm. 

Exact reaction cross sections and rates by the hyperquantization algorithm Auzinsh M. 

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],... 

For a review of the use of hyperspherical harmonics as orbitals in quantum chemistry, (see [97]). Applications to bound state problems have mainly regarded nuclear physics, and are outside the scope of this article. The hyperquantization algorithm had been successfully applied to the prototype ion-molecule reaction He + IlJ HeH+ + H [98,99] and atom-molecule reaction F + H2 HF + H [100,101]. For the latter, resonances were characterized [102,103] and benchmark state-to-state differential cross sections and rate constants [104,105] were given. 

V. Aquilanti and G. Capecchi, Harmonic analysis and discrete polynomials from semiclassical angular momentum theory to the hyperquantization algorithm. Theor. Chem. Accounts, 104 183-188, 2000. 

D. De Fazio, S. Cavalli, and V. Aquilanti, Orthogonal polynomials of a discrete variable as expansion basis sets in quantum mechanics. The hyperquantization algorithm. Int. J. Quant. Chem., 93 91-111,2003. 

Chem. Phys. 63, 3737-40 Aquilanti, V., Cavalli, S., De Fazio, D. and Volpi, A. (1998) Hyperquantization algorithm. II. Implementation for the F + H2 reaction dynamics including open-shell and spin-orbit interactions, J. Chem. Phys. 109, 3805-18. 

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. 

Aquilanti V, Cavalli S, De Fazio D et al (2002) Exact reaction dynamics by the hyperquantization algorithm integral and differential cross sections for F + H2, including long-range and spin oibit effects. Phys Chem Chem Phys 4 401-415... 

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