Electronegativity Equalization with Pauling Units Steven G. Bratsch The University of Texas, Austin, TX 78712
A significant development in the eleetronegativity concept has been provided by Sanderson's formulation of the Principle of Electronegativity Equalization (1,Za): "When two or more elements initially different in electronegativity combine chemically, they become adjusted to the same, intermediate electronegativity within the compound." This principle, which has gained wide acceptance in recent years (3-7), abandons the idea of "fixed" electronegativity (8,9) and redefines the values in electronegativity tables as quantities characteristic of the isolated atom before a bond is formed (3.7). The physical and chemical properties of kbs&nces are lareelv determined bv the partial charges on the constituent atoms ( l 0 , I I ), and the evaluation of tKese partial charges is an important electronegativity application. In the framework of Sanderson's principle, i t is generally believed that the partial charge acquired by an atom through chemical comhination is proportional to the difference between the final, equalized electronegativity and the initial, pre-bonded electronegativity (2b,3-7,12). In order to compute the partial charge one must know the equalized electronegativity value and the proportionality factor. I t is essential in the development of any partial charge method that charge conseruation be maintained: In a polyatomic species of integral charge q , the weighted sum of all partial charges must he equal to q In this equation, u represents the number of atoms of a particular element in the species formula (e.g., for B F ~ - Q= 1and YF = 4) and 6 represents the partial charges on these atoms. Appllcatlon wlth Pauling Unlts ( 9 a ) In describing the partial charge method developed fur the Mulliken scale (13). . .. Huheev 141has mentioned that most elements approximately double their (Mulliken) electronega+1 whereas their tivities as the partial charee . a~nroaches .. electroneystivities essentially d~sapptar(approach zero) as the nartial charee avvroaches - 1. The Mulliken and l'aulinr scaies are rougKly &oportional (8, 14, 151, so Huheey's ob'servation may be expressed in Pauling units as
Here, X,, is the electronegativity as equalized through Sandemon's principle, X A is the initial, pre-bonded electronegativitv ofa particular atom A, and & A is the partial charre un A. charge ckservation (eqn.1) leads to a general expre&on for X,, N+9 X. = -
(3)
where N = 2(u) = the total number of atoms in the species formula. 588
Journal of Chemical Education
Two examples serve to illustrate the usage of eqns. (2) and (3) (Pauling electronegativities from 16). Example 1. Hydrogen Sulfide, HzS.
Example 2. Fluorosilicote Ion, SiFs2-
In example 2, the sum 6si + SF = -1.99 rather than -2.00 merely because of rounding error. Some partial charges calculated through eqns. (2) and (3) are given in the accompanying table, using Pauling electronegativities as redetermined by Allred (16). For comparison, the table also lists partial charges derived by Sanderson's method (26) (using Sanderson electronegativities (Zc)),by the Jaffe-Huheey method (3,4) (using Mulliken electronegativities (15,171) and by the Evans-Huheey method (18). The latter method uses Mulliken electronegativities hut employs an energy minimization technique which attempts to account for the loss in orbital overlap and the increase in the Madelung potential accompanying a transfer of charge between atoms. Discussion Pauling has qualitatively defined electronegativity as "the power of an atom in a molecule to attract electrons to itself' (96); however, in the present work Pauling electronegativities are treated as pre-bonded, isolated-atom quantities. This conflict may simply reflect a misconception in the Pauling definition (Zd, 3,7, l l a , 12) and need not cast doubt upon the interritv .. . of the Pauline values themselves. A definition of electronegativity more compatible with Sandenon's priuciple lulthwrh still uualitative~is .'the tendencv to become nerutively charged'; (llb). If an atom acquires negative charge through chemical combination its tendency to become negatively charged decreases, as does the electronegativity. The converse is true if an atom acquires positive charge (2e). Partial charge methods applicable to Pauling units have generally been developed within the context of "fixed" electronegativity, expressing charge distribution in terms of fractional ionic character (I) of individual bonds, ex., (9c, 19,
Cornparl~nsot Partial Charms Mullikend
Species
Atom
This Wak'
Sandersonb
vsL
Jaffe-
Evans-
Huheey'
Huheeyg
NaF
KC1 CaCI* SrBr*
BFai CH, CHso-
CF, Sill
NH3 NFs
N(CHdf H30+
He0
OHHIS H F
ncl
the years he has developed an elaborate system of bond energy calculation ( 2 , l l , 24-26). Sanderson's successful treatment of bond energy suggests an "absolute" significance to his partial charges (2f). However, Evans and Huheey (18)have indicated oossible theoretical deficiencies in Sandersou's work, examples being Sanderson's method of selection of an "ionic blendine coefficient" and his assumotion of a linear relationship between covalent energy and partial charge. The oartial charges of Evans and Huheev are often ouite different &om ~anderson'svalues (see table);but they are nevertheless useful in calculating lmnd energies. This apparent paradox is the result of the different chemical bonding models used and indicates that the question of "absolute" partial charges remains unanswered. Partial charges calculated through eqns. (2) and (3) are not claimed to he better than previous estimates. The intent of this oauer has merelv been to offer a simole ada~tationof sanderion's ~ r i n c i ~of i e~lectrone~ativit; ~ ~ u a i i z a t i oton Pauling units. The Pauling scale is the most familiar electronegativity scale and is often the only one seen (or at least remembered) by beginning chemistry students. This new partial charge method should find immediate use in the qualitative understanding of chemical behavior. However, it will probably take considerable time and effort to develop quantitative ao~licationsof esns. ( 2 ) and (3) (note that Sanderson's bond enkrgy method did not come about overnight). In addition, there are situations where electronegativity equalization does not occur: 1) When the structure of an ionic substance prevents danor-aceeptor interaction between adjacent counter-ions, for example in IN(CH4f .. llB(CH4-I ,, . .. , and oerhaos in s i m ~ l eammonium and ;h&honiwn salts, hydrated salts, etc. It meille hest to vreu such cmnpwnds ar cumplurely ionic. 21 When the maximum possible charge transfer ior a pnrciculor atom uccurs before rlcctroneyativity equali7.ation can be achieved. An example r+cesiumfluunhratc ( C ~ B F Itor I , which eqns. 12) and 13, predict 6,:, = ~ 1 . 7(an 5 rmwsiilrle value). In such caseseach ion (e.g, Csf, B F ~ - )must be treaied individually
.
.
.
.
Acknowledgment
IF
BrCl
a
Paullng elecwneqativnieo from t1@;Partial charges calculated via eqns. (2) and
I am grateful to the Robert A. Welch Foundation (Grant Number Foal), and especially to Joseph J. Lagowski, for their s u.~.n o rof t this research. Literature Clted
A"".
(31 Hinze, J., Whitehead, M. A,, and Jsffe, H. H., J. Amor. Chom. Soe.,85,148(19631. I41 Huheey, J. E., J. Phys. Cham., 69,3284 (19651. (51 Pam, R. G.,Donnelly, R. A,, Levy, M., and Palke, W. E., J. Chem. Phys.. 68. 3801 114711) ,. .-,. I61 Politzer,P.,snd Wcinstein,H., J Chem. Phys.,71,4218t1979). (7) Reed, J.L.,J. Phys Chem.,85. 148(19811. I81 Pritehard,H.O.,snd Skinner, H.A.,Chem. Rau.,55.745 (19551. (9) Pauling, L.;'The Nature of the Chemical Bond." 3rd ed., Cornell University Press, Ithaea,NY, 1960, Is1 pp.8b95, (bl p.88, lcl p. 98. (LO) Ssnderson. R. T., 'Chemical Periodicity."Reinhold, New York, 1960. (111 Sanderson. R T., "lnuwnieChemistry: Reinhold, NewYork, 1967, (a) p. 81,(blp.
-
Equation (6) (Wilmshurst's equation (20)) is interesting because eqns. (2) and (3) reduce to it in the special case of a uni-univalent molecule (HC1, NaF, etc.). Sanderson has correlated his partial charges with a wide variety of chemical phenomena (IO,11,21-231, and through
(12) Ponec, R., Theoret. Chim. Acla ( B e d ) ,59,629 (1990). (131 Mullikan. R. S.,J Chem. Phys.. 2.782 (1934). (I41 Skinner,H.A.,and Pritehard.H.0,TlDw FamdoySoc..49,125411953). I151 Hinze, J., and Jaffe,H. H.. J. Amr. Chem. Sm., 84.540 (19621. (161 Allrpd,A.L.,J. Inorg Nuci Cham., l7.215 (19611. (171 Hinze, J.,anJ Jaffe,H.H.. J . Phya..Chem.,67,1501(19631. (18) Evans,R. S.. and Huheey, J. E.. J Inorg. Nucl Chem.. 32.777 (19701. (191 Hannay, N. B.,andSmyth,C.P.,J Amer Chem. Soe.,68,171I19461. (201 Wilmshurst, J. K., J. Chem Phys.30.561 l1959l. EDUC.,29,539(19521. (211 Sanderson, R.T.,J.CHEM. (22) Ssnderson.R. T.,J. CHEM EDUC.,31.2 119541. (231 Sander8on.R.T..J.CHBM. EDUC.,31,238 (19541. (241 Sanders0n.R. T.,Inor#.Chsm.3.925 119641. (25) Sanderson. R. T., J. Inore. Nucl Chem., 28.1553 11966). (26) Sanderson,R. T.. J. CHEW E~~c.,44,516 (19671.
Volume 61 Number 7 July 1984
589
