Explicit expressions for totally symmetric spherical functions and symmetry-dependent properties of multipoles

Journal Article · Wed Sep 03 00:00:00 EDT 2014 · Proceedings of the Royal Society. A. Mathematical, Physical and Engineering Sciences

DOI:https://doi.org/10.1098/rspa.2014.0435· OSTI ID:1376713

Zapol, B.; Zapol, P.

Closed expressions for matrix elements < lm'|A(G)|lm >, where |lm > are spherical functions and A(G) is the average of all symmetry operators of point group G, are derived for all point groups (PGs) and then used to obtain linear combinations of spherical functions that are totally symmetric under all symmetry operations of G. In the derivation, we exploit the product structure of the groups. The obtained expressions are used to explore properties of multipoles of symmetric charge distributions. We produce complete lists of selection rules for multipoles Q(l) and their moments Q(lm), as well as of numbers of independent moments in a multipole, for any l and m and for all PGs. Periodicities and other trends in these properties are revealed.

• Research Organization: Argonne National Lab. (ANL), Argonne, IL (United States)
• Sponsoring Organization: USDOE Office of Science - Office of Basic Energy Sciences - Materials Sciences and Engineering Division
• DOE Contract Number: AC02-06CH11357
• OSTI ID: 1376713
• Journal Information: Proceedings of the Royal Society. A. Mathematical, Physical and Engineering Sciences, Vol. 470, Issue 2171; ISSN 1364-5021
• Publisher: The Royal Society Publishing
• Country of Publication: United States
• Language: English