Research carried out in part during the author's stay as a visiting professor at the University of Delaware, Newark, DE, 1987-88.
New algorithms for calculating 3n-j symbols
Article first published online: 19 OCT 2004
Copyright © 1993 John Wiley & Sons, Inc.
International Journal of Quantum Chemistry
Supplement: Proceedings of the International Syposium on Atomic, Molecular, and Condensed Matter Theory and Computational Methods
Volume 48, Issue Supplement 27, pages 13–24, 13/20 March 1993
How to Cite
Roothaan, C. C. J. (1993), New algorithms for calculating 3n-j symbols. Int. J. Quantum Chem., 48: 13–24. doi: 10.1002/qua.560480805
- Issue published online: 19 OCT 2004
- Article first published online: 19 OCT 2004
- Manuscript Received: 23 JUN 1993
Compact expressions are presented for the 3n-j symbols, where 1 ⩽ n ⩽ 4, which feature sums over products of binomial coefficients, and certain integer triangular coefficients. The triangular coefficients in turn can be expressed as products of binomial coefficients. Thus in the formulas presented for the 3n-j symbols, the dependence on numerous factorials, formally as well as computationally, has been completely eliminated. While formulas which incorporate summations over products of binomial coefficients have been known for the 3- j and 6- j symbols, the introduction of the triangular coefficients, and the application of the binomial/triangular scheme to 3n-j symbols with n > 2, provide important new results. The new formulas are simpler, and they permit more efficient computations of the 3n-j symbols, both in exact and in floating point format, than most schemes which are currently in use. © 1993 John Wiley & Sons, Inc.