Table 6.1.1.8

International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

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International Tables for Crystallography (2006). Vol. C. ch. 6.1, p. 585

E. N. Maslen,^e ^‡ A. G. Fox^b and M. A. O'Keefe^c

Table 6.1.1.8 | top | pdf |
Cubic harmonics $[K_{lj}(\theta,\,\varphi)]$ for cubic site symmetries

$[K_{lj}(\theta,\varphi)]$	$[N_{l^{2}j}]$	Site symmetry
$[K_{lj}(\theta,\varphi)]$	$[N_{l^{2}j}]$	23	m3	432	$[{\bar 4}3m]$	m3m
$[K_0 = Y_{00+} = 1]$	$[4\pi]$	×	×	×	×	×
$[K_3 = Y_{32-}]$	$[\displaystyle{{240\pi}\over{7}}]$	×			×
$[K_4 = Y_{40+} + {{1}\over{168}} \, Y_{44+}]$	$[\displaystyle{{16\pi}\over{21}}]$	×	×	×	×	×
$[K_{6,1} = Y_{60+} - {{1}\over{360}}\,Y_{64+}]$	$[\displaystyle{{32\pi}\over{13}}]$	×	×	×	×	×
$[K_{6,2} = Y_{62+} - {{1}\over{792}}Y_{66+}]$	$[\displaystyle{{512\pi}\over{13}} \cdot {{105}\over{11}}]$	×	×
$[K_7 = Y_{72-} + {{1}\over{1560}}Y_{76-}]$	$[\displaystyle{{256\pi}\over{15}} \cdot {{567}\over{13}}]$	×			×
$[K_8 = Y_{80+} + {{1}\over{5940}}\,\,(Y_{84+} + {{1}\over{672}}Y_{88+})]$	$[\displaystyle{{256\pi}\over{17 \cdot 33}}]$	×	×	×	×	×
$[K_{9,1} = Y_{92-} - {{1}\over{2520}}Y_{96-}]$	$[\displaystyle{{512\pi}\over{19}} \cdot 165]$	×			×
$[K_{9,2} = Y_{94-} - {{1}\over{4080}}Y_{98-}]$	$[\displaystyle{{2048\pi}\over{19}} \cdot {{243 \cdot 5005}\over{17}}]$	×		×
$[K_{10,1} = Y_{10,0+} - {{1}\over{5460}}(Y_{10,4} + {{1}\over{4320}}Y_{10,8+})]$	$[\displaystyle{{512\pi}\over{21}} \cdot {{3}\over{65}}]$	×	×	×	×	×
$[K_{10,2} = Y_{10,2+} + {{1}\over{43680}} (Y_{10,6+} + {{1}\over{456}}Y_{10,10+})]$	$[\displaystyle{{2048\pi}\over{21}} \cdot {{4455}\over{247}}]$	×	×