Table of Spherical Harmonics
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Table of Spherical Harmonics

This is a table of orthonormalized spherical harmonics that employ the Condon-Shortley phase up to degree = 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

= 0[1]

= 1[1]

= 2[1]

= 3[1]

= 4[1]

= 5[1]

= 6

= 7

= 8

= 9

= 10

Real spherical harmonics

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

= 0[2][3]

= 1[2][3]

= 2[2][3]

= 3[2]

= 4

See also

External links


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

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