Dipole-dipole forces act between the molecules possessing permanent dipole. Ends of the dipoles possess “partial charges” and these charges are shown by Greek letter delta (δ). Partial charges are always less than the unit electronic charge ($\pu{1.610e–19 C}$). The polar molecules interact with neighbouring molecules. The figure shows electron cloud distribution in the dipole of hydrogen chloride and thereby shows dipole-dipole interaction between two HCl molecules

Partial charges on different HCl molecules highlighted by white-blue colour gradients

I want to know how partial charges can exist as it would go against the quantization of charge?

  • 1
    $\begingroup$ It is simple: partial charge = measured dipole moment / measured distance of the dipole centers ( e.g. atom distance with a polar bond ). $\endgroup$
    – Poutnik
    Nov 17, 2021 at 16:51
  • $\begingroup$ Partial charge is a formal, not quantized charge, that would cause for the given displacement the given value of dipole moment. // By other words, if there is probability 0.5 of occurance of charge 1 e, it is equivalent of probability 1.0 of presence of formal charge 0.5e. $\endgroup$
    – Poutnik
    Nov 17, 2021 at 18:06
  • $\begingroup$ The title of the question and the question within the body are different. It would be nice to clarify which one is to be answered. $\endgroup$
    – Ian Bush
    Nov 18, 2021 at 9:26

2 Answers 2


Think about the probability of finding an electron is a specific region and it will be clearer

To understand where partial charges come from remember that electrons are not located in one specific place (Heisenberg!) but spread around in a cloud. In molecules, those clouds are called molecular orbitals which are more complex in shape and distribution than the atomic orbitals in isolated atoms.

In simple molecules with different atoms those orbitals are not, in general, symmetric around the two atoms. So in hydrogen chloride, for example, the electrons in the bonding orbital are more likely to be found near the chlorine. The bond still only contains 2 electrons each of charge -1. But the probability weighted distribution shows more negative charge around the chlorine.

So the partial charge is a function of the probability distribution of electron density which is dependent on the 3D shape of the bonding orbital. It isn't a violation of quantisation of charge, just a consequence of the quantum mechanics of bound electrons which can't be nailed down to being in a single specific place because of the uncertainty principle.

From the outside, this looks like a dipole with a partial charge and that simplification is good enough for most systems and avoids excessively complex quantum mechanical calculations that would add little to the picture.


Very good question but keep in mind that partial charge concept is a gross oversimplification. The very first sentence on Wikipedia on partial charge Partial charge is not fully correct either. Consider the partial charge as a book-keeping "number". Just like the oxidation state concept, a "partial" charge can be estimated for a diatomic molecule AB, on the basis of electronegativities

$\delta_A = G_A -L_A - B[\chi_A/(\chi_A+\chi_B)]$

where, $\delta_A$ is the partial charge, $G_A$ is the group number, $L_A$ is the unshared electron number on A, B is the number of bonding electrons, and $\chi$ is the electronegativity value proposed by Allen. Allen avoids the term "partial charge" and calls it this number "Lewis-Langmuir Atomic Charges." So don't treat this number as a fraction of an elementary charge.

The following references will help:

Ionization Energies, Electronegativity, Polar Bonds, and Partial Charges Ronald J. Gillespie, James N. Spencer, and Richard S. Moog, J. Chem. Educ. 1996, 73, 7, 627.

"Lewis-Langmuir atomic charges." Allen, Leland C., Journal of the American Chemical Society 111.25 (1989): 9115-9116.

And finally if you are interested in who came up with this $\delta$ symbol see...

Jensen, W. B. (2009). The Origin of the" Delta" Symbol for Fractional Charges. Journal of Chemical Education, 86(5), 545.

An old 1959 article in the Journal of Chemical Education addresses this idea. See Models for demonstrating electronegativity and "partial charge" R. T. Sanderson, J. Chem. Educ. 1959, 36, 507.

Knowing molecules to be composed of two or more “point” positive charges in relatively fixed positions, imbedded in a diffuse cloud of electrons, one can recognize that the assignment of partial charges to the individual atoms must at best be only a deliberate simplification. It is indeed an attempt to describe an exceedingly complex system in terms useful toward reaching a practical understanding of the molecule.

Furthermore he writes,

All these physical data, when considered together with the properties of compounds, strongly support the conclusion that the condition of a combined atom does indeed depend on its environment, which to a large and usually dominant extent results from electronegativities. One may call this contribution “partial charge” or by any other name, as long as its true significance is clearly understood: “Partial charge’ is a quantitative estimate of the relative extent to which differences in electronegativity of the atoms before compound formation have altered the electronic field about the nucleus of an atom in a compound. In the following discussion it will become apparent that as an index of the condition of a combined atom, partial charge provides a uniquely useful and satisfactorily reliable basis for explaining much of chemistry


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