I think there might be a typo in the equation for the Cartesian electric field gradient integrals for

, and that the prefactor of (1/3) should not be present.

Ignoring symmetry and their prefactors, each component of the EFG integrals should be the same as for the spin-dipole integrals. That is, when I divide the matrix representation of

by the matrix representation of

, for example, each entry should be 1 after the prefactors are divided out as well. However, this is only true when (g_e/2) is divided out of the SD integrals, and not (1/3) from the EFG integrals.

I did not check the spherical EFG integrals.