Nano Science and Technology Institute
Nanotech 2001 Vol. 2
Nanotech 2001 Vol. 2
Technical Proceedings of the 2001 International Conference on Computational Nanoscience and Nanotechnology
Chapter 7: General Theory and Methods

The Distributive Calculation of Unitary Group Recoupling Coefficients

Authors:L.F. McAven, M. Schlesinger and R.D. Kent
Affilation:University of Windsor, CA
Pages:192 - 195
Keywords:block selective, distributed processing, group theory, symmetric groups, unitary groups
Abstract:Symmetries, through group theory, can provide exact information about complex systems. However approximations are often made, for example density functionals are used in quantum chemistry, because it is impractical to obtain group coefficients. Coefficients for the widely applicable unitary group (Un) can be calculated for any case, but not by a general and practical procedure. The block selective method (bsm) of calculating symmetrical group (Sf) coefficients of fractional parentage (cfp), related to Un recoupling coefficients (rcc/6j), makes phase and multiplicity choices systematically in the Sf representation matrices. We have added this algorigh to RACAD v4, a program for the exploitation of group theoretical coefficients which it calculates recursively. We compare the use of the bsm in calculating Un 6j directly, versus applying it to lower Un 6j combined with recursion cost. Either way is costly as larger Sf cfp’s are required so we consider distributive computation.
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