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

International Tables for Crystallography (2006). Vol. B. ch. 1.2, pp. 16-17

## Table 1.2.7.3

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 1.2.7.3| top | pdf | `Kubic Harmonic' functions
 (a) Coefficients in the expression with normalization (Kara & Kurki-Suonio, 1981).
Even l mp
l j0+2+4+6+8+10+
0 1 1
4 1
0.76376   0.64550
6 1
0.35355   −0.93541
6 2
0.82916   −0.55902
8 1
0.71807   0.38188   0.58184
10 1
0.41143   −0.58630   −0.69784
10 2
0.80202   0.15729   0.57622
l j   2− 4− 6− 8−
3 1   1
7 1
0.73598   0.41458
9 1
0.43301   −0.90139
9 2
0.84163   −0.54006
 (b) Coefficients and density normalization factors in the expression where (Su & Coppens, 1994).
Even l mp
l j   0+ 2+ 4+ 6+ 8+ 10+
0 1 1
4 1 0.43454 1
6 1 0.25220 1
6 2 0.020833   1
8 1 0.56292 1   1/5940
10 1 0.36490 1   1/5460
10 2 0.0095165 1
l j     2− 4− 6− 8−
3 1 0.066667   1
7 1 0.014612   1
9 1 0.0059569   1
9 2 0.00014800     1
 (c) Density-normalized Kubic harmonics as linear combinations of density-normalized spherical harmonic functions. Coefficients in the expression . Density-type normalization is defined as .
Even l mp
l j0+2+4+6+8+10+
0 1 1
4 1 0.78245   0.57939
6 1 0.37790   −0.91682
6 2   0.83848   −0.50000
l j 2− 4− 6− 8−
3 1 1
7 1 0.73145   0.63290
 (d) Index rules for cubic symmetries (Kurki-Suonio, 1977; Kara & Kurki-Suonio, 1981).
lj23 432
T O
0 1 × × × × ×
3 1 ×     ×
4 1 × × × × ×
6 1 × × × × ×
6 2 × ×
7 1 ×     ×
8 1 × × × × ×
9 1 ×     ×
9 2 ×   ×
10 1 × × × × ×
10 2 × ×