Interpretation of the Hyperfine Matrix

The general form of the dipolar contribution to the hyperfine term of the Hamiltonian is  

P has been computed using Hartree-Fock atomic orbital wavefunctions and can be found in several published tabulations14 17 and in Appendix 1. Because of the (r 3) dependence of P, dipolar coupling of a nuclear spin with electron spin density on another atom is usually negligible. 

The factor of 2/5 and the weighting of the orbital coefficients is determined by the angular factors.14 Equations (4.17-4.19) can therefore be combined in matrix notation to write the dipolar hyperfine matrix for p-orbitals as  

Similarly, if an atom contributes d atomic orbitals to the SOMO, 

The dipolar contribution to the hyperfine matrix for a pure d-orbital is  

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