Table of spherical harmonics

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This is a table of orthonormalized spherical harmonics that employ the Condon-Shortley phase up to degree l = 10. Some of these formulas give the "Cartesian" version. This assumes x, y, z, and r are related to and through the usual spherical-to-Cartesian coordinate transformation:

Spherical harmonics[edit]

l = 0[1][edit]

l = 1[1][edit]

l = 2[1][edit]

l = 3[1][edit]

l = 4[1][edit]

l = 5[1][edit]

l = 6[edit]

l = 7[edit]

l = 8[edit]

l = 9[edit]

l = 10[edit]

Real spherical harmonics[edit]

For each real spherical harmonic, the corresponding atomic orbital symbol (s, p, d, f, g) is reported as well.

l = 0[2][3][edit]

l = 1[2][3][edit]

l = 2[2][3][edit]

l = 3[2][edit]

l = 4[edit]

See also[edit]

External links[edit]

References[edit]

Cited references
  1. ^ a b c d e f D. A. Varshalovich; A. N. Moskalev; V. K. Khersonskii (1988). Quantum theory of angular momentum : irreducible tensors, spherical harmonics, vector coupling coefficients, 3nj symbols (1. repr. ed.). Singapore: World Scientific Pub. pp. 155–156. ISBN 9971-50-107-4. 
  2. ^ a b c d C.D.H. Chisholm (1976). Group theoretical techniques in quantum chemistry. New York: Academic Press. ISBN 0-12-172950-8. 
  3. ^ a b c Blanco, Miguel A.; Flórez, M.; Bermejo, M. (1 December 1997). "Evaluation of the rotation matrices in the basis of real spherical harmonics". Journal of Molecular Structure: THEOCHEM. 419 (1–3): 19–27. doi:10.1016/S0166-1280(97)00185-1. 
General references