Atomic quadrupole moment definition

The operators for the potential, the electric field, and the electric field gradient have the same symmetry, respectively, as those for the atomic charge, the dipole moment, and the quadrupole moment discussed in chapter 7. In analogy with the moments, only the spherical components on the density give a central contribution to the electrostatic potential, while the dipolar components are the sole central contributors to the electric field, and only quadrupolar components contribute to the electric field gradient in its traceless definition. 

The quadrupole-dipole interaction differs by a factor of 2 from the usual definition of this term.48 However, the effect of this difference on the overall results of the simulation that it was used in is thought to be small. The sign of Q was taken as positive and the dipole moment direction was from the oxygen atom to the carbon atom.50... 

Finally starting from the usual definitions of atomic electric dipole and quadrupole and magnetic dipole moments fAkel, qfcel, and jnkm... 

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