# Does partial charge violate the law of quantization of charge?

Well, we know that charge is quantized. Quoting wikipedia below,

Charge quantization is the principle that the charge of any object is an integer multiple of the elementary charge.

And we know that there is partial charge. Quoting wikipedia below,

A partial charge is a non-integer charge value when measured in elementary charge units.

Don't the above two things (and both being from the same respectable source) contradict with each other?

If yes, then which one is correct? And if both are true, then in which conditions do they follow?

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Definitions are powerful words, you have just proved that definition of wikipedia to be wrong. That definition needs to be improved based on the exceptions as you mentioned. –  Feynman Mar 23 '14 at 13:43

Partial charges are like resonance structures: they are a convenient notation which captures the most important aspects of a phenomenon, but they are not what is "really" going on.

When we say that a molecule contains partial charges, what we mean is that the electric field surrounding a bond is polarized as if some fractional number of elementary charges had been displaced from one end to the other. The phenomenon — the polarized electric field — is real, but the mechanism that produces it does not violate charge quantization.

All of the electrons always have charge −1, and all of the protons always have charge +1. But the electrons' positions are indeterminate. (The protons' positions are also indeterminate, but on a much smaller scale which is usually neglected in this scenario.) A standard technique for calculating the electric field of the molecule is to take the nuclei as fixed and then allow the valence electrons' wave functions to range over the entire molecule. When you do this, you often discover that some bonds are polar, with electrons (formally belonging to the atoms at both ends of the bond) more likely to be found at one end than the other.

The electric field of such a bond is numerically the same as the electric field that would be produced if you could transfer a fraction of an elementary charge from one end of the bond to the other. But that is not what has happened. You can think of what is really going on in these terms: the electrons are moving rapidly back and forth along the bond, but they are slightly more often at one end of the bond, so the average charge density at one end is greater, but not by a full elementary charge. (This too is inaccurate, but is a standard way to bend quantum theory to make it more comfortable to intuition.)

(N.B. this is the same as permeakra's answer, but in less technical language.)

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But I still can't get why that should give result to partial charges. I see it better as forces which could only be exerted by partial charges, and the reason, as you said, would be the redistribution of elementary charges (or their center of masses) in space. Am I correct with this point of view? Or are you trying to say the same thing? Please comment back... –  Awal Garg Mar 23 '14 at 15:07
I'm afraid I have no idea what you mean by "I see it better as forces which could only be exerted by partial charges, and the reason, as you said, would be the redistribution of elementary charges (or their center of masses) in space." so I can't tell you if it is correct or not. –  zwol Mar 23 '14 at 15:09
I am trying to say that there is actually nothing like partial charges. It is only that the atoms participating in the bond are exerting forces on each other, which are not complete. I am trying to say that its not the charge which is partial, but the bond or its force has some partial character induced in it due to electro-negativity. –  Awal Garg Mar 23 '14 at 15:12
Ah. Yes, that is correct. The charge on each electron remains exactly −1 elementary charge unit, but the electric field around the bond is polarized, and the partial charge notation accurately describes the polarization (to first order, anyway). Partial charges are like resonance structures: they are not what is actually going on, but they capture enough of the important details to be convenient notation. –  zwol Mar 23 '14 at 15:19
Yes, that is more or less what I was trying to say. If you are just beginning to study chemistry, do not worry about the details right now. Also, please take from this that Wikipedia is not entirely to be trusted. It's usually more accurate than not, but pages often contain minor errors, and even more often were written by people who understand a topic very well, but don't know how to explain it to people who don't already understand. –  zwol Mar 23 '14 at 15:38

Both are.

Any isolated object has integral charge, as any elementary particle has integral charge. However, as we know, elementary particles are not truly located in one point.

When we talk about stationary states in physics, we can assume, that particles inhabit some volume with special density function indicating how much of the particle in question is in any given unit of volume. When we consider isolated molecule, we can assume that it is in a stationary state. This means, that electrons may be viewed as electron clouds, and different parts of said cloud may be assigned to different atoms in the molecule. In case if total amount of electron density, assigned to specific atom is non-integral, we gain a partial charge.

Whenever atomic partial charges are estimated, there is a significant arbitrariness in the process, as there is no unquestionable way to define, which parts of electron density assigned to any given atom, as there is not strict definition of atom borders (atomic radii are estimated using equilibrium positions in some circumstances, but in truth electron density is non-zero even far beyond that radii). Still, the concept is useful enough.

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I can't get what you are trying to say. Are you saying that partial charge does not actually exist but it is said to be so on an average position? –  Awal Garg Mar 23 '14 at 12:17
I'm trying to say that electrons in atom are more like clouds than dots, and such a cloud may occupy volume of two or more atoms. In that case, elementary charge of the electron is distributed between two (or more) atoms. –  permeakra Mar 23 '14 at 15:01
But I still can't get why that should give result to partial charges. I see it better as forces which could only be exerted by partial charges, and the reason, as you said, would be the redistribution of elementary charges (or their center of masses) in space. Am I correct with this point of view? –  Awal Garg Mar 23 '14 at 15:05
It doesn't have to. It may in some cases. You see, there is no reason why, if one electron have to occupy two atoms, exactly one half of it will be in both. For example, consider $HF$ molecule. It can be considered as having 2 core electron in core of $F$ atoms, 6 electron clouds in F exclusively, and 2 in both $H$ and $F$ atoms. However, 2 latter have more density in $F$ atom than in $H$ atom, say 2/3 of density in $F$ atom. this leads to partial charge of F equal +9 (charge of nuclei) - 2 (core) -6 (exclusive) -2 * 2/3 = -1/5, while hydrogen have +1 - 2 * 1/3 = +1/3. –  permeakra Mar 23 '14 at 15:17
At the beginning. Both statements are correct. However, they describes situation in two different models. Say, partial charges belongs to approach, developed in molecular mechanics (see wikipedia), that, having absolutely no physical sense, works reasonably well for prediction of molecular geometry and interaction for many biological molecules. Charge quantization, on the other hand, belongs to the field of quantum mechanics, that, making absolutely no common sense, is correct, but hard to understand. So, in general we use simpler model if we can and switch to complex one if simple one fails. –  permeakra Mar 23 '14 at 15:41

It does violate that particular statement (and not quantization of charge). You just need to understand that charge is quantized mean that there exists a unit of charge which is indivisible.

We may say that charge on an object is always integral multiple of multiple of elementary charge, but it is wrong, as you have pointed out. It is just used to say that elementary charge is indivisible.

In your case, when an electrically neutral atom bonds chemically to another neutral atom that is more electronegative, its electrons are partially drawn away. This leaves the region about that atom's nucleus with a partial positive charge, and it creates a partial negative charge on the atom to which it is bonded. It is to be noted that elementary charge (electron in your case) is not divided.

Principle of quantization of charge can be stated as: Charge on any isolated object is always integral multiple of elementary charge.

It is to be noted that electron is still elementary particle. Proton and neutrons are not elementary. Quarks are now believed to be smallest indivisible unit of charge.

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Your comment to the main question seemed more appealing to me! Shorter and better. Anyways, thanks for the great explanation... –  Awal Garg Mar 23 '14 at 15:07