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I'm a physics professor who often teaches students who have taken a lot of chemistry (read: pre-meds). In physics, the dipole moment of a charge configuration is defined as pointing from concentrations of negative charge towards concentrations of positive charge. This is embodied in the formula we use for the dipole moment of a charge configuration, $$ \vec{p} = \sum_i q_i \vec{r}_i. $$ It's not too hard to see that this yields a vector that points from negative charges to positive charges. For example, if I have a charge of $-e$ at the origin ($\vec{r} = 0$) and a charge of $+e$ a distance $d$ away, this formula yields a vector that points from the negative charge to the positive charge, with magnitude $ed$.

However, the first time I taught this material in a class with a large number of chemistry students, they were very confused; they had always learned that the dipole vector of a polar molecule points from positive charge towards negative charge, i.e., in the opposite direction of the convention from physics. For example, by the physics convention, the dipole moment of the water molecule points away from the point of the "V" formed by the bonds, while under the chemistry convention, the dipole moment points in the direction of the point of the "V".

How did this convention arise? Is there an advantage to defining the dipole vectors this way in chemistry calculations? Or is it one of those scientific conventions that someone wrote down one point, and got ingrained in textbooks ever since? (Is it all Benjamin Franklin's fault?)

One of the answers to this question notes the difference between the conventions, but doesn't really explain why the first chemist to write down a dipole vector wrote it down that way. I would love to know how this convention arose historically!

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    $\begingroup$ This answer by Jan Jensen in the "question" to which you linked indicates that it is a historical problem. IUPAC is now defining electric dipole from negative to positive also. ( goldbook.iupac.org/E01929.html ) $\endgroup$ – MaxW Feb 2 '16 at 19:33
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    $\begingroup$ All in all the conventions are giving me a headache. Doesn't an electric field go from positive to negative? $\endgroup$ – MaxW Feb 2 '16 at 19:49
  • $\begingroup$ I studied Chemistry and I only know your convention, namely that dipoles point from negative to positive charges. $\endgroup$ – LLang Feb 2 '16 at 20:29
  • $\begingroup$ Keep using the physicist's convention, I belive that students should be confronted with these problems and get used to it! ; ) $\endgroup$ – user23061 Feb 9 '16 at 20:00
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    $\begingroup$ @user1420303 - The vector style notation you are using is from the US being first published in the textbook 'vector analysis' in 1901. In 1905 it was translated into German. Even Einstein said he would have written his papers differently prior to 1905 had he known about the book. In 1912, when the concept of the dipole moment was developed, the vector notation was still new. New and ugly often go together in science, try looking up a picture of the first transistor. $\endgroup$ – Agriculturist Mar 5 '16 at 5:29
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Some sources point out the direction of the dipole moment is convention dependent. Since both conventions are mathematically correct it seems important when solving a problem to identify the convention. Both conventions seem to be derived from the bones of dead theories.

The physics convention does seem to have Franklin's work identifying negative "resinous electricity" and positive "vitreous electricity" as one step in the progression to the modern theory. In modern theory a positive to negative electric field will orient a dipole such that the field is in the same direction as a negative to positive dipole.

On the chemistry side, Peter Debye (who the unit for a dipole moment is named) developed the concept of the dipole moment in 1912 to explain anomalous dispersion. This dispersion was explained as being caused by a negative charge collecting on one side of a molecule leading to a dipole moment. This moment's magnitude explained anomalous dispersion, so direction did not seem to receive much attention. Molecules during this time where described using the Thompson, or "plum pudding," model. In this model molecules were described as positively charged spheres. (These spheres had no nucleus because the nucleus concept was in its infancy during this time period.) These spheres formed the basis of mathematical models used to describe the behavior of materials with a dipole moments. The dipole moment in this sense went from the center of a molecule to the point of highest electron density. With the center of the sphere as a pivot point, the rotation of molecules in an electric field could be explained. In this sense the positive to negative convention may be an artifact of the early spherical molecular models first used to describe dipole moments.

sources:

J. W. Williams Dipole theory and the size of molecules. Trans. Faraday Soc., 1934,30, 723-728

John W. Williams The Dielectric Constants of Binary Mixtures. VIII. The Electric Moment as a Vector Quantity, J. Am. Chem. Soc., 1928, 50 (9), pp 2350–2357 DOI: 10.1021/ja01396a005 Publication Date: September 1928

L. E. Sutton Electric dipole moments and resonance in molecules, Trans. Faraday Soc., 1934,30, 789-801

https://www.quora.com/Why-does-a-dipole-have-a-direction-from-negative-to-positive-while-electric-field-lines-go-from-positive-to-negative

http://goldbook.iupac.org/E01929.html

http://www.ushistory.org/franklin/info/inventions.htm

http://www.wondersandmarvels.com/2011/12/accentuate-the-vitreous-eliminate-the-resinous.html

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    $\begingroup$ This is a much better answer than mine so it should get upvoted to ensure if anyone gets the bounty (assuming no better answers) it's you. $\endgroup$ – jheindel Feb 12 '16 at 21:57
  • $\begingroup$ The chemistry convention seems German while the physics convention seems British. I can read the original physics theory because it is in English but not German theory. The dipole theory was developed throughout the years of WWI and WWII. These wars may have contributed to the lack of unity in a single convention. $\endgroup$ – Agriculturist Feb 12 '16 at 23:39
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I don't have a very good historical explanation, but I would point out that it actually makes a good deal of sense for chemists to think in this way. That is, chemists are almost exclusively concerned with what the electrons in any system are doing.

For instance, when I ask myself about a charge separation and hence a dipole, I want to know what is separated from what. In this case, it's some electrons separated from some space they could be in. So, I intuitively think to point my arrow towards where the electrons are, not where they could be. Of course I only think that because that's the convention. I'd also point out that chemists reverse the arrows for current as well by drawing the arrow pointing with the flow of electrons rather than the flow of positive charge which goes the opposite direction.

So at least we're self consistent!

Sorry that's not more historical, but my guess is that at least part of the true historical reason is that chemists think in terms of electrons and thus point the arrows to their negatively charged friends.

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    $\begingroup$ True. Even in reaction mechanisms in organic chemistry we depict the flow of electrons by arrows pointing from higher electron density to lower electron density. $\endgroup$ – shre_sudh_97 Feb 10 '16 at 2:01
  • $\begingroup$ This is certainly true. Still as a chemist I have never saw a problem or inconsistency. One thing is depicting Lewis formula and discussing reaction mechanisms, another is to calculate orientation of a molecule in an external field. And I would stress that the vector moment of electric dipole goes from negative to positive in chemistry, too. goldbook.iupac.org/html/E/E01929.html $\endgroup$ – Alchimista Mar 2 at 14:20
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Just a guess:

For many years, until 1946, accurate values of dipole moments could only be derived from measurements of dielectric constants.

If you think of the dipole moment as weakening the electric field, it would point in the direction opposite to the electric field, and therefore from the positive to the negative end of the dipole.

(sorry, cannot comment the post due to lack of reputation)

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I asked that other question. Most useful to me was one of the comments, which pointed me to this page: http://av8n.com/physics/electric-dipole.htm#sec-mutations

While it does not have definitive answers, it at least shows that the problem was known in 2007.

For archiving purposes I'm posting a screenshot here (hope that is not in violation of any terms):

enter image description here

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    $\begingroup$ I wouldn't be surprised if the problem was known before 2007, but I certainly never knew about it until quite recently. My first contact with the problem was when I tried to make more explicit connections between physics and stuff the students had seen in other science disciplines — which is something that a lot of physics classes have been trying to do over the past 10–15 years. Perhaps that's why the problem has become better-known. $\endgroup$ – Michael Seifert Feb 4 '16 at 17:36

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