Ricardo F.mlra Eorlham College Richmond, Indiana 47374
I
Electronegativities of Metallic Phases
Physicists of the late ninetwnth centnry could s t u d i t h r properties of matter without hothering to know the composition of the mnterinls they uwre I i c u s i n g . Chen~i.;t-i,on the ot her hnncl, spent most of their time tnckliug pure snhstnnccs with relntively smnll molrculrs whosr structnrcs yield to the mrtl~od*of orgnnic structurnl thmry. The properties of actual mntrrinls, strongly dependent on the forces involved in the chemirnl hond nnd on detnilnl structurnl pnrnmeters, were neglwtecl. As n result, ndvnnces in metnllurgy nncl othrr nrrns of activity such ns the ruhher, ccr:~mics,and glnss industries werr lnrgely empiricnl. With the nclvcnt of qunntum mechnnics, this differencr i n out look n n r m s n l conri(lernhly, to the henrlit of Imth sciences. IIo\vevrr, pnrtinlly hrcnuse the propertic; of nggrrp;ntcr nre so iliffrrr~~t from those of their conntiturnt units, we arc \vitnrssing n ncw division of lnhor. l'hr study of mnttrr and ruergy nntl how they intrrnct with one nnother c o ~ ~ s t i t n t rnow s the johrl clomnin of physics nnd rhrmistry, hut :it thesnme time n mnterinIs scirncr is emerging, prmluct of the dichotomy of mnttrr vrrsus mnterinls, so hrnutifully cliscussed hy Stnnlry Smith in n rwcnt lecturr (1). To counter this trndrncy, i t might not he out of plncc to identify u-elldrfinnl pnrnmrters of solid stntc theory with concepts originally introclucecl todml with thcpropertiesof vmnll molrrulrs. T h r unified viewpoint is not only nesthrticelly s:~tisfying,hut it may bring ne\v npproaehes to the study of solid phnses. Such n conrrpt is electronrgntivity, oridnnlly defined 8 4 "the power of nn ntom in 11 molecule to nttrnct electrons to itself" (2). Its importnncr ns n research tool for smnll molecules is recnliug, hut it could he useful in situntiona intrnctnhle to rigorous enlculntions such as those confronting the mntrrials scientists. Let L(n) h r the energy of nn ntomic spin-orbitnl with oecrrpntion numher 11. Electronrgntivity can he defined (3-5) ns the nrgntivr of t h r potentinl (including the kinetic energy psnldo-potentinl) acting on n hnlffilled spin-orbitnl
Thin is n very general definition and a t the same time it is restricted to situntions where the concept of electrcnegntivity is menniwful, mmcly, to v n h c e state atomic orhitnls i n molrcules nnd crystnls. F m Atoms
~ h e e n c r g yof an ntomic orbital is thesum of the oneelectmll term and the twvo-electmll terms. Using the 1Ioffitt-Pnrisernpproximntion for the latter (6,7) E(n)
-
-In
+ ' / , n (n - 1) (I - A )
(2)
For n hnlf-filled orbital, corresponding to n neutral ntom with n non-zero vnlence state, thr interelectronic repulsion drops out and we have E(1)= -I. The negntive of the lmtentinl is simply the ionization pnlrnlial. Thus the concept of electronegntivity is redundanl for isolnted ntoms. Molecules
Strictly speaking, molecules nre not made of ntoms.
I n the 1,CAO-110 methods, however, the Coulomh intrgrnls (IlA*3QbA) may he pnrtitioned into ntomic nnd interntomie terms. The use of erln. (2) for the ntomic rnerp;v terms in molecules corresponds to nssumr complvte lrft-right correlation of the electronic motion ( 8 , 8 ) . 0 1 1 thr other hnnd, if electronic corrrlntion is entirely urglrctnl, the ntomic orhitnl energy is given hy (10, 11) E(n) -In '/, n' ( I - A ) (3)
-
+
For molecules, I nnd A nre the vnlence-stnte energy trrms and frnctionnl occupation numhers nre nllo~vrrl. thnt is, 71 vnrics continuou?;lyin the intervnl 0 n 2. The mnin point is thnt hoth q n s . (2) nnd (3) give ( - I $ ' ( ) / ) = I A ) I t is secn thnt for ntoms in molecules we ohtnin 1111lliken'n tlrfinition of electronrgntivity (12) with vnlues roughly proportionnl to l'nuling's thrrmochemicnl ones (13).
<
.
work
EdeVI
fu~trtion (PYI
potentinl, definrd ns p = (aE(n)/an)s, is equnl t o -I/, (I A ) whrn T -c 0. The rnme eonclur;ion is ensily n r r i v ~ nt l if one rmllectn thnt in the free-electron n p proximnt ion t h r clrctrnn-electron repulsion is zero. \Ye cnn writc ( I - A ) = 0, nnd I = A = E,. Hence
+
The tnhlc sho!vs the unlum of the Fcrmi energics of mnle mctnls nn(I the rlrctror~egntivitiesof the gnsmus a t o m in the indicated vnlence states (6, 13, 1 4 , 18). Trnnsition met:~lswere lot inclucled I~ccnurcof t h r 1111certainties on the npproprinte vnlrncc states nnd on the n u n ~ l ) rof r conclucting rlrctrons. Escrpt for, II., .AX,> \V,,,T~,,ZA", >I. :\,, T k 0 , . CM*.
+
t l ~ c b
200 / Journal of Chemical Education
0!4,!5,,
(191 \YXX.XXN,It,, Z. , A ' n : u ~ ~ o ~ w7,k. ~ ,774 , 11S521. 120) SLAT^.". J . r . , A V D Kos~m.(;.I,.,f'hv*. I i m . , M , 14118 (1951). (21) S t ' c ~ v rJ. . I,.. J . I ' h y ~ , C h r m . . < n l i d ~ . 2 1 , IICI(I!1RI). (22) I w ~ ~ w o N. r . 8.. ~ r K o l ' r r w . It. N.. S a i d Phw.. J E T P . 48. I N
