Recently, I have been reading up on articles relating to the dipole moments of different molecules (specifically this). I see how they can get bond lengths and experimental dipole moments with reasonable accuracy and compare that to the theoretically predicted values.
What I don't get is the how theoretical prediction of dipole moment happens. I know that dipole moment equals the charge times the separation distance (u=q*d). So I must be able to predict the dipole (making sure its a vector) of any molecule given its distance of separation and partial charge on the molecules. The partial charge on the molecule depends on the electronegativity values. But then you can't put the electronegativity values (Pauling or Sanderson or others) directly as charge in the formula. Now, I know that Pauling or any other electronegativity scale is only arbitrarily chosen and is relative to the most electronegative element.
But then, how do we make theoretical estimates of dipole moments? Is there any way of relating the electronegativity values to partial charge on each atom? Or is there an entirely different approach?
I have already read these StackExchange answers - this which answers the 'how' but not by 'how much'