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 1.2.8.1 

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 1.2.8.1| top | pdf |
Products of complex spherical harmonics as defined by equation (1.2.7.2a)[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 = 0.30901936Y 22
Y 11 Y 11− = −0.12615663Y 20 + 0.28209479Y 00
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 = 0.26116903Y 32
Y 21 Y 11− = −0.14304817Y 30 + 0.21850969Y 10
Y 21 Y 20 = 0.22072812Y 41 + 0.09011188Y 21
Y 21 Y 21 = 0.25489487Y 42 + 0.22072812Y 22
Y 21 Y 21− = −0.16119702Y 40 + 0.09011188Y 20 + 0.28209479Y 00
Y 22 Y 00 = 0.28209479Y 22
Y 22 Y 10 = 0.18467439Y 32
Y 22 Y 11 = 0.31986543Y 33
Y 22 Y 11− = −0.08258890Y 31 + 0.30901936Y 11
Y 22 Y 20 = 0.15607835Y 42 − 0.18022375Y 22
Y 22 Y 21 = 0.23841361Y 43
Y 22 Y 21− = −0.09011188Y 41 + 0.22072812Y 21
Y 22 Y 22 = 0.33716777Y 44
Y 22 Y 22− = 0.04029926Y 40 − 0.18022375Y 20 + 0.28209479Y 00