The Distributive Calculation of Unitary Group Recoupling Coefficients

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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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Journal: TechConnect Briefs
Volume: 2, Technical Proceedings of the 2001 International Conference on Computational Nanoscience and Nanotechnology
Published: March 19, 2001
Pages: 192 - 195
Industry sector: Advanced Materials & Manufacturing
Topic: Informatics, Modeling & Simulation
ISBN: 0-9708275-3-9