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On efficient integration techniques for oscillatory integrals in periodic system calculations

✍ Scribed by W. J. Schneider; J. J. Ladik

Publisher
John Wiley and Sons
Year
1981
Tongue
English
Weight
693 KB
Volume
2
Category
Article
ISSN
0192-8651

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✦ Synopsis

Abstract

Quantum chemical calculations of polymers and solids, especially on an ab initio level, represent a large computational task and therefore necessitate efficient computing methods. This is particularly true for the oscillatory integrals appearing in such calculations. For these integrals efficient integration methods based both on the Chebyshev series and the spline representation of the nonoscillatory part of the integrand are considered; they are found far superior compared with more standard integration rules. In two‐ and three‐dimensional systems, directions with maximum oscillatory behavior can be selected along which these new efficient integration techniques can be used advantageously. The ideas are illustrated by Hückel crystal orbital (HCO) bond orders for the polyacetylene chain and the graphite layer. In the latter example, also, a method for the integration of oscillatory integrands with a singularity is given.

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