N.19 Am­bi­gu­i­ties in elec­tron affin­ity

The In­ter­na­tional Union of Pure and Ap­plied Chem­istry (IU­PAC) Gold Book de­fines elec­tron affin­ity as “En­ergy re­quired to de­tach an elec­tron from the singly charged neg­a­tive ion [...] The equiv­a­lent more com­mon de­f­i­n­i­tion is the en­ergy re­leased ($E_{\rm {initial}}-E_{\rm {final}}$) when an ad­di­tional elec­tron is at­tached to a neu­tral atom or mol­e­cule.” This is also the de­f­i­n­i­tion given by Wikipedia. Chemguide says “The first elec­tron affin­ity is the en­ergy re­leased when 1 mole of gaseous atoms each ac­quire an elec­tron to form 1 mole of gaseous 1- ions.” Hy­per­Physics says “The elec­tron affin­ity is a mea­sure of the en­ergy change when an elec­tron is added to a neu­tral atom to form a neg­a­tive ion.” En­cy­clo­pe­dia Brit­tan­ica says “in chem­istry, the amount of en­ergy lib­er­ated when an elec­tron is added to a neu­tral atom to form a neg­a­tively charged ion.” Chemed.chem.pur­due.edu says “The elec­tron affin­ity of an el­e­ment is the en­ergy given off when a neu­tral atom in the gas phase gains an ex­tra elec­tron to form a neg­a­tively charged ion.”

An­other de­f­i­n­i­tion that can be found: “Elec­tron affin­ity is the en­ergy re­leased when an elec­tron is added to the va­lence shell of a gas-phase atom.” Note the ad­di­tional re­quire­ment here that the elec­tron be added to the va­lence shell of the atom. It may make a dif­fer­ence.

First note that it is not self-ev­i­dent that a sta­ble neg­a­tive ion ex­ists. Atoms, even in­ert no­ble gasses, can be weakly bound to­gether by Van der Waals/Lon­don forces. You might think that sim­i­larly, a dis­tant elec­tron could be weakly bound to an atom or mol­e­cule through the di­pole strength it in­duces in the atom or mol­e­cule. The atom’s or mol­e­cule’s elec­tron cloud would move a bit away from the dis­tant elec­tron, al­low­ing the nu­cleus to ex­ert a larger at­trac­tive force on the dis­tant elec­tron than the re­pul­sive force by the elec­tron cloud. Re­mem­ber that ac­cord­ing to the vari­a­tional prin­ci­ple, the en­ergy of the atom or mol­e­cule does not change due to small changes in wave func­tion, while the di­pole strength does. So the elec­tron would be weakly bound.

It sounds log­i­cal, but there is a catch. A the­o­ret­i­cal elec­tron at rest at in­fin­ity would have an in­fi­nitely large wave func­tion blob. If it moves slightly to­wards the at­trac­tive side of the di­pole, it would be­come some­what lo­cal­ized. The as­so­ci­ated ki­netic en­ergy that the un­cer­tainty prin­ci­ple re­quires, while small at large dis­tances, still dwarfs the at­trac­tive force by the in­duced di­pole which is still smaller at large dis­tances. So the elec­tron would not be bound. Note that if the atom or mol­e­cule it­self al­ready has an in­her­ent di­pole strength, then if you ball­park the ki­netic en­ergy, you find that for small di­pole strength, the ki­netic en­ergy dom­i­nates and the elec­tron will not be bound, while for larger di­pole strength, the elec­tron will move in to­wards the elec­tron cloud with in­creas­ing bind­ing en­ergy, pre­sum­ably un­til it hits the elec­tron cloud.

In the case that there is no sta­ble neg­a­tive ion, the ques­tion is, what to make of the de­f­i­n­i­tions of elec­tron affin­ity above. If there is a re­quire­ment that the ad­di­tional elec­tron be placed in the va­lence shell, there would be en­ergy needed to do so for an un­sta­ble ion. Then the elec­tron affin­ity would be neg­a­tive. If there is how­ever no re­quire­ment to place the elec­tron in the va­lence shell, you could make the neg­a­tive value of the elec­tron affin­ity ar­bi­trar­ily small by plac­ing the elec­tron in a suf­fi­ciently highly-ex­cited state. Then there would be no mean­ing­ful value of the elec­tron affin­ity, ex­cept maybe zero.

Var­i­ous re­puted sources dif­fer greatly about what to make of the elec­tron affini­ties if there is no sta­ble neg­a­tive ion. The CRC Hand­book of Chem­istry and Physics lists no­ble gasses, met­als with filled s shells, and ni­tro­gen all as not sta­ble rather than giv­ing a neg­a­tive elec­tron affin­ity for them. That seems to agree with the IU­PAC de­f­i­n­i­tion above, which does not re­quire a va­lence shell po­si­tion. How­ever, the Hand­book does give a small neg­a­tive value for yt­ter­bium. A 2001 pro­fes­sional re­view pa­per on elec­tron affin­ity men­tioned that it would not dis­cuss atoms with neg­a­tive elec­tron affini­ties, seem­ingly im­ply­ing that they do ex­ist.

Quite a lot of web sources list spe­cific neg­a­tive elec­tron affin­ity val­ues for atoms and mol­e­cules. For ex­am­ple, both Wikipedia and Hy­per­Physics give spe­cific neg­a­tive elec­tron affin­ity val­ues for ben­zene. Though one web source based on Wikipedia (!) claims the op­po­site.

Also note that ref­er­ences, like Wikipedia and Hy­per­Physics, dif­fer over how the sign of elec­tron affin­ity should be de­fined, mak­ing things even more con­fus­ing. Wikipedia how­ever agrees with the IU­PAC Gold Book on this point: if a sta­ble ion ex­ist, there is a pos­i­tive affin­ity. Which makes sense; if you want to spec­ify a neg­a­tive value for a sta­ble ion, you should not give it the name affin­ity.

Wikipedia (July 2007) also claims: “All el­e­ments have a pos­i­tive elec­tron affin­ity, but older texts mis­tak­enly re­port that some el­e­ments such as in­ert gases have neg­a­tive [elec­tron affin­ity], mean­ing they would re­pel elec­trons. This is not rec­og­nized by mod­ern chemists.” How­ever, this state­ment is very hard to be­lieve in view of all the au­thor­i­ta­tive sources, like the CRC Hand­book above, that ex­plic­itly claim that var­i­ous el­e­ments do not form sta­ble ions, and of­ten give ex­plicit neg­a­tive val­ues for the elec­tron affin­ity of var­i­ous el­e­ments. If the 2007 Hand­book would af­ter all these years still mis­state the affin­ity of many el­e­ments, would not by now a lot of peo­ple have de­manded their money back? It may be noted that Wikipedia lists Yt­ter­bium as blank, and the var­i­ous el­e­ments listed as not sta­ble by the CRC hand­book as stars, in other words, Wikipedia it­self does not even list the pos­i­tive val­ues it claims.