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Invariance properties of the multipole expansion
Author(s) -
Piecuch Piotr
Publication year - 1982
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560220208
Subject(s) - multipole expansion , spherical multipole moments , convergence (economics) , coordinate system , range (aeronautics) , fast multipole method , physics , classical mechanics , mathematics , geometry , quantum mechanics , materials science , economics , composite material , economic growth
The calculations of long‐range interaction energy are often based on multipole expansion. The truncated multipole expansion and interaction energy calculated with it are noninvariant with respect to an arbitrary choice of local coordinate systems. In this paper we show that truncated multipole expansion of form Σ k = 1 nC k R − k is “numerically” independent on a choice of local coordinate systems, if convergence conditions are satisfied.