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

International Tables for Crystallography (2006). Vol. B. ch. 1.2, p. 21

Table 1.2.8.3 

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 1.2.8.3| top | pdf |
Products of two real spherical harmonic functions [y_{lmp}] in terms of the density functions [d_{lmp}] defined by equation (1.2.7.3b)[link]

y 00 y 00 = 1.0000d 00
y 10 y 00 = 0.43301d 10
y 10 y 10 = 0.38490d 20 + 1.0d 00
y 11± y 00 = 0.43302d 11±
y 11± y 10 = 0.31831d 21±
y 11± y 11± = 0.31831d 22+ − 0.19425d 20 + 1.0d 00
y 11+ y 11− = 0.31831d 22−
y 20 y 00 = 0.43033d 20
y 20 y 10 = 0.37762d 30 + 0.38730d 10
y 20 y 11± = 0.28864d 31± − 0.19365d 11±
y 20 y 20 = 0.36848d 40 + 0.27493d 20 + 1.0d 00
y 21± y 00 = 0.41094d 21±
y 21± y 10 = 0.33329d 31± + 0.33541d 11±
y 21± y 11± = ±0.26691d 32+ − 0.21802d 30 + 0.33541d 10
y 21± y 11∓ = −0.26691d 32−
y 21± y 20 = 0.31155d 41± + 0.13127d 21±
y 21± y 21± = ±0.25791d 42+ ± 0.22736d 22+ − 0.24565d 40 + 0.13747d 20 + 1.0d 00
y 21+ y 21− = 0.25790d 42− + 0.22736d 22−
y 22± y 00 = 0.41094d 22±
y 22± y 10 = 0.26691d 32±
y 22± y 11± = ± 0.31445d 33+ − 0.083323d 31+ + 0.33541d 11+
y 22± y 11∓ = 0.31445d 33− ± 0.083323d 31− ∓ 0.33541d 11−
y 22± y 20 = 0.22335d 42± − 0.26254d 22±
y 22± y 21± = ± 0.23873d 43+ − 0.089938d 41+ + 0.22736d 21+
y 22± y 21∓ = 0.23873d 43− ± 0.089938d 41− ∓ 0.22736d 21−
y 22± y 22± = ± 0.31831d 44+ + 0.061413d 40 − 0.27493d 20 + 1.0d 00
y 22+ y 22− = 0.31831d 44−