International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B. ch. 1.2, p. 20

Table 1.2.8.2 

P. Coppensa*

aDepartment of Chemistry, Natural Sciences & Mathematics Complex, State University of New York at Buffalo, Buffalo, New York 14260-3000, USA
Correspondence e-mail: coppens@acsu.buffalo.edu

Table 1.2.8.2| top | pdf |
Products of real spherical harmonics as defined by equations (1.2.7.2b)[link] and (1.2.7.2c)[link]

y 00 y 00 = 0.28209479y 00
y 10 y 00 = 0.28209479y 10
y 10 y 10 = 0.25231325y 20 + 0.28209479y 00
y 11± y 00 = 0.28209479y 11±
y 11± y 10 = 0.21850969y 21±
y 11± y 11± = 0.21850969y 22+ − 0.12615663y 20 + 0.28209479y 00
y 11+ y 11− = 0.21850969y 22−
y 20 y 00 = 0.28209479y 20
y 20 y 10 = 0.24776669y 30 + 0.25231325y 10
y 20 y 11± = 0.20230066y 31± − 0.12615663y 11±
y 20 y 20 = 0.24179554y 40 + 0.18022375y 20 + 0.28209479y 00
y 21± y 00 = 0.28209479y 21±
y 21± y 10 = 0.23359668y 31± + 0.21850969y 11±
y 21± y 11± = ± 0.18467439y 32+ − 0.14304817y 30 + 0.21850969y 10
y 21± y 11∓ = 0.18467469y 32−
y 21± y 20 = 0.22072812y 41± + 0.09011188y 21±
y 21± y 21± = ± 0.18022375y 42+ ± 0.15607835y 22+ − 0.16119702y 40 + 0.09011188y 20 + 0.28209479y 00
y 21+ y 21− = −0.18022375y 42− + 0.15607835y 22−
y 22± y 00 = 0.28209479y 22±
y 22± y 10 = 0.18467439y 32±
y 22± y 11± = ± 0.22617901y 33+ − 0.05839917y 31+ + 0.21850969y 11+
y 22± y 11∓ = 0.22617901y 33− ± 0.05839917y 31− ∓ 0.21850969y 11−
y 22± y 20 = 0.15607835y 42± − 0.18022375y 22±
y 22± y 21± = ± 0.16858388y 43+ − 0.06371872y 41+ + 0.15607835y 21+
y 22± y 21∓ = 0.16858388y 43− ± 0.06371872y 41− ∓ 0.15607835y 21−
y 22± y 22± = ± 0.23841361y 44+ + 0.04029926y 40 − 0.18022375y 20 + 0.28209479y 00
y 22+ y 22− = 0.23841361y 44−