# Why does electronegativity increase as effective nuclear charge increases?

I know that electronegativity is the ability to attract shared electrons and that effective nuclear charge is the pull of the nucleus on outer electrons based on my notes.

I would like to point out that electronegativity does not necessarily increase with increasing effective nuclear charge. Take for example, the elements magnesium and calcium. Ptable clearly shows that magnesium has a higher electronegativity than calcium (1.31 vs 1.0), despite its lower effective nuclear charge (Zeff) acting on its valence electrons (3.308e vs 4.398e), as provided by Wikipedia. (Just as a side note, the e in the Zeff values represent the elementary charge of a proton, or 1.60 x 10-19 Coulombs to 3 s.f.)

As Jan mentioned, electrostatic forces are dependent both on the charge of the two bodies in question, as well as their distance of separation. I think it's useful to include the formula for Coulomb's force to better illustrate this point:

$$F=k_e\frac{q_1q_2}{r^2}$$

Because electronegativity, like others have mentioned, is a measure of an atom's tendency to attract external electrons, it is dependent mainly on the net electrostatic force of attraction exerted by the atom. As such, the Coulomb's Force comes in handy to explain the magnesium and calcium disparity; say we take q1 as being the Zeff value (which takes into account inter-electronic repulsion between the electron shells), q2 as being an external electron with charge -e, and r as being the atomic radius (from Ptable, calculated), we can substitute the relevant values for calcium and magnesium, such that:

$$F_\mathrm{Ca}=k_\mathrm{e}\frac{-4.398|e^2|}{(\pu{194E-12})^2}=k_\mathrm{e}\frac{-4.398|e^2|10^{24}}{37636}$$

$$F_\mathrm{Mg}=k_\mathrm{e}\frac{-3.308|e^2|}{(\pu{145E-12})^2}=k_\mathrm{e}\frac{-3.308|e^2|10^{24}}{21025}$$

From the output magnitudes, the higher electronegativity of magnesium than calcium is justified. Numerically speaking, the distance of separation (i.e. atomic radius) as a (squared) denominator term influences the final electrostatic force of attraction much more than effective nuclear charge does. This actually also applies to the electric potential energy term derived from the Coulomb Force. Using atomic radius as a more significant indicator of an atom's electronegativity would account for the general decrease in electronegativity down a group, as well as its increase across a period (left to right), even though effective nuclear charge acting on an atom's valence electrons technically increases in both cases (since the addition of protons with increasing atomic number will always outweigh any shielding done by the addition of a similar number of electrons to the surrounding shells).

Note: The example here uses Zeff values assuming the corresponding valence subshells are not filled, so the actual electric force acting on a mobile electron may be further influenced by interelectronic repulsion with the valence subshell electrons, as well as how many valence subshell electrons there are in the first place. The point is just to raise a method of visualising the electronegativity trend.

Initially, I was also confused as to why a higher Zeff could, in fact, yield larger atomic radii down periodic groups; a simple explanation would be that the increase in the number of electron energy levels (in the form of principal shells) would inherently cause a corresponding rise in atomic radii. This doesn't apply across a period because the number of principal shells doesn't change then; the number of subshells can, change, which is why the trend in atomic radii across a period is also not perfectly "neat".

P.S. Apologies for the 7 year late reply, thought I'd elaborate further on the points brought up by Jan and better illustrate them with some calculations.

The effective nuclear charge can be thought of the charge of the nucleus minus the charge of the core electrons. For an element such as fluorine, the nuclear charge is $+9$ and the core electrons have a charge of $-2$ so the effective nuclear charge is $+7$. Similarly for carbon it would be $+6 - 2 = + 4$.

Now let’s assume a $\ce{C-F}$ bond. There are two electrons in this bond, each charged $-1$. On the left, from the carbon atom, they ‘see’ a charge of $+4$; on their right, from the fluorine atom, they ‘see’ s charge of $+7$.

Electrostatic interactions are greater at shorter distance and at greater charge separation, so the interaction (i.e. force) the bonding electrons experience from fluorine’s side is almost double that from carbon’s side. (The carbon and fluorine atoms can be considered to be roughly of the same size.) It should now be clear why the electrons are drawn to the fluorine.

Electronegativity is just a name humans gave the observed effect of ‘this atom can pull electrons towards it better than others’. It takes a look at the result of the above process and rationalises it. The effective nuclear charge approach is the underlying physical force.

Note: This explanation is extremely simplified, does not take any quantum effects or the like into consideration and should thus only be used at introductory levels.

Electronegativity can be thought of how much an atom "wants" electrons.

An atom that wants electrons is one that has a high positive charge, or effective nuclear charge. Effective nuclear charge is the pull the nucleus has on outer electrons (taking into account the repulsion of electrons in the atom.)

The higher the effective nuclear charge, the more the nucleus wants electrons, which is why atoms high in one is high in the other and vice versa.

I think Lewars textbook gives a good outline as to what electronegativity is. The thing with electronegativity is that that it is vague. Anyhow, here is what Lewars says:

From this viewpoint electronegativity of a species is the drop in energy when an infinitessimal amount (infinitessimal so that it reamins the same species) of electronic charge enters it. It is a measure of how hospitable an atom or ion, or a group or an atom in a molecule, is to the ingress of electronic charge, which fits in with our intuitive concept of electronegativity.

You could put it this way: the nucleus attracts the electron more if it has a high effective nuclear charge. Remember that nuclear charge is positive, and that electrons are negative https://en.wikipedia.org/wiki/Electric_potential_energy. Thus an electronegative atom/ion/etc "gains more energy" when it pulls an electron towards it. And the reason it "gains more energy" is because it has high effective nuclear charge.

• What's "Lewars textbook"? Commented Oct 3, 2015 at 8:53
• "An Introduction to Computational Chemistry" Errol G. Lewars Commented Oct 4, 2015 at 1:17