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[Licence| Download | New Version Template] acbm_v1_0.gz(27 Kbytes)
Manuscript Title: A set of routines for efficient and accurate computation of lattice sums of 1/r**n-potentials.
Authors: M. Monkenbusch
Program title: FP
Catalogue identifier: ACBM_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 67(1991)343
Programming language: Fortran.
Computer: IBM3081D32.
Operating system: VM/CMS.
RAM: 51K words
Word size: 8
Peripherals: disc.
Keywords: Solid state physics, Lattice dynamics, Lattice sums, Convergence acceleration, Incomplete gamma Function.
Classification: 7.8.

Nature of problem:
Lattice sums over 1/r**n potentials and their FOURIER transforms and derivatives of them are needed for lattice (dynamical) calculations on molecular crystals. The convergence of a naive direct summation is bad for lower n.

Solution method:
Routines for the convergence accelerated computation of lattice sums of 1/r**n-potential terms for general n are given. The sums, their FOURIER transforms and derivatives may be evaluated. Summation parameters and widths are determined automatically for any desired accuracy. By the way an efficient function subprogram for the calculation of the incomplete gamma function as needed by the convergence acceleration algorithm is provided.

Running time:
4 sec for a typical initialisation (delta=10**-7, cubic lattice). 0.05 sec for one summation including first and second derivatives.