Electronegativity and Bond Type I. Tripartate Separation Gordon D. sproull University of South Carolina at Beaufort, Beaufort, SC 29902 The Evolvlng Concept of Electronegativity The Definitions
The concept of electronegatinty has been widely accepted and enhanced since it was f r s t described by Pauling (1, 2) as an invariant thermodynamic property of bonded atoms. Mulliken (3) soon provided an alternative d e f ~ t i o nrelating it to ionization potential and electron affinity. Using spectral data, several workers further developed the concept as a variable property dependent on environment ( 4 8 ) ;it has been redefmed in terms of the energy of an atom in its various valence states. Because bonding and its energetics are at the core of chemistry,it is no surprise that these and other definitions of electronegativity have received extensive scrutiny. A Unifying Concept in Bonding
As a unifying concept of bonding, electronegativity has been widely applied. It is surprising, therefore, that this concept receives such limited treatment in most general chemistry texts. A typical text may provide a table of conventional invariant electronegativities ~ ( cIt) may also indicate that the difference in the electronegativity values between bonded atoms (Ax(c))is an indication of bond polarity or ionic character. Such differences in electronegativity were indeed the essence of Pauling's initial analysis that indicated enhanced hond strength arising from a n ionic component i n heteroatomic covalent bonds. The function AyJc) alone, however. fails to differentiate covalent from ionic bondine (9).~ d d i t i o n aalthough ~~, the relationship of electronegL tivitv to covalent and ionic bondine character mav be addressed in texts, the relationshipto metallic bo;;ding is universally ignored. Alternative Descriptions of Bonding
Several researchers have recognized the limitations in using electronegativities to describe bond formation, and alternative descriptions of bonding have been developed. For example, Pearson (10-12) has promoted a description of bonding known as the hard-soft acid-base principle (HSAB): Hard acids prefer to bind to hard bases, and soft acids prefer to bind to soR bases.
Drago (13)developed the empirical E and C (electrostatic and covalent) donor-acceptor model of acid-base interactions. Sanderson (14-16) has uniquely defined electronegativity in terms of relative electron density. Sanderson's Electronegativity Equalization
Sanderson (17-20) also recognized a powerful relationship describing electronegativity values for bonded atoms. 'These resuns were presented in pan at the Annual Meetmg of Soutn Carolina Academy of Sc~ence,held Apr 1 10. 1992 at Coastal
According to his principle of electronegativity equalization, when atoms combine, the electronegativity of the bonded atoms will be an average of the electronegativities of the component atoms. Electrons are transferred to the more electronegative atom in a bond, thereby increasing the charge density and electron-electron repulsion on that atom and decreasing its electronegativity. Bonded atoms reach a point of electronegativity equalization when their charge-dependent electronegativities become equal. This relationship describes the contribution to bond-energy lowering in heteroatomic species that occurs when atoms of different electronegativities comhine. Since receiving theoretical rationalization (21-23) using density functional methods, this principle has become widely discussed hut unheralded in general chemistry texts. Theoretical Background Electronegativity as a Potential
The energy E of an electron in an atom fits a quadratic equation (51.. The electronegativity can be consLdered as the change in the energy of that atom as the charge on the atom changes, with &its of energy per charge (24). This electric potential can be given in units of volts. Because the d e f ~ n quadratic g equation for energy is a function of charge, it is possible to redefine electronegativity in terms of partial charge 6. In doing so, Huheey (25,26) indicates that the electronegativity can be represented as
where a and b are constants that depend on both the element and the specific orbital hybridization. The a parameter is identified as the inherent electronegativity originally described by Mulliken, and the b parameter (actually %b)has been identified as the atomic hardness (271, the central parameter inpearson's HSAB description of bonding. The b factor is the change of electmnegativity with respect to partial charge.
An A n a l f l i ~ lDescription of Electronegativity Equalization
According to the principle of electronegativity equalization for a hond between atoms 1and 2, electronegativities of the atoms become equal when bonding oceurs, and Because 6, = 4~ for an interaction between two bonded atoms, the partial charge on atom 1can he derived from eq 1.
Substituting into eq 1,we can see this implies that XI, the equalized electronegativity for atom 1,is given by Volume 70 Number 7 July 1993
531
However, this is just the equalized electronegativity for each of the two bonded atoms, which may be represented (28) by
Because the oarameter b is identified with hardness. fractional harddess for atom i in a bond between two atoms i and j can be similarly defined as
Thus, eq 4 can be rewritten a s -
x = alh2 +azh,
(6)
This provides a n analytical description of Sanderson's principle of electronegaiivity equalization. Equation 6 indicates that the contribution to? from each bonded atom i will be a weighted average equal to each atom's inherent electronegativity, modified by the fractional hardness of the atom j to which it bonds. For bonded atoms, the harder the atomj is, the less the electronegativity of i is diminished and the greater is its contribution to The implication is that if atom j is hard with respect to atom i. then the contribution of atom i to the eaualized electronegativity will be large. Conversely, if atom;. is soft, then electrons will flow toward atom i and reduce its contribution to the equalized electronegativity This weighted mean function 7 provides one value characteristic of the bond between Gdatoms.
z.
The Difference Function
If? is defied as the arithmetic mean of electronegativities before bonding, then eq 1indicates that because 6 = 0, we get
Then a second function that is characteristic of a bond between atoms 1 and 2 can be defined a s the difference between the average electronegativities before and after bonding has occurred. This difference function is ~f=ji"-f
(8)
Acomparison of the values of a and b shows that they are related approximately linearly (25. 27). This means that inherent eiectronegativity is roughly proportional to hardness. Thus, values of will be generallv smaller than vala n d A z should usually have positive values. ues of Eauation 8 therefore describes the tendencv of bonded atoms to acquire a n electronegativity that isdiminished from the average inherent electmnegativity of unbonded atoms due to withdrawal ofelectrons toward the more electrouegative atom and away from the more ~olarizable atom. For example, if atom 1has both higher inherent electronegativity and hardness than atom 2, then more electron density will flow toward atom 1. This diminishes the contribution of atom 1to the equalized electronegativity. Be-
r,
*
2Conceptuallysimilar triangular diagrams with compounds of pure metallic, covalent, and ionic character located at the three vertices and with substances of varying degrees of bonding character shown at proportional distances along the triangles' sides can be found in Van Arkel, A. E. Molecules and Crystals; Interscience, 1949;p 205; 1st Dutch ed., 1941;Ketelaar, J. A. A. Chemical Constitution; Elsevier: Amsterdam, 1953;p 21 (1st Dutch ed., 1947).
532
Journal of Chemical Education
cause atom 2 has a lower inherent electronegativity, the result of bonding between heteroatomic atoms is the loww i n g of the equalized electronegativity compared with that of the arithmetic mean of inherent electronegativities. Both the difference function A x and the sum function ji by themselves convert two electronegativity values into single values. This decreases the useful information by one-half. If a two-dimensional comparison were made using both the difference and the sum functions, the information inherent in tabulated values of electronegativities would be maintained. Relating the Nature of Bonding to Electronegativity To compare the nature of chemical bonding with various electronegativity functions for diverse compounds, a set of 297 binary compounds of described bond type (molecular, ionic, or metallic) were selected from Well's (30) compendium:
essentially all binary s and p block compounds zinc and copper family compounds that have well-definedbonding character several homoatomic compounds Mulliken electronegativities, as revised by Bratsch (29, 311, provided the two-parameter data set for these compounds. Hybridization was selected for each atom based on VSEPR, except for metals, for which the hybridization most typical of the invariant (Pauling) value was used. The Tripartite Separation
z
The functions Aji and were calculated for these binary compounds, and a plot of the A? data vs. ji was made. (See Fig. 1.) This plot indicates a tripartite separation of compounds into three regions of differing interatomic bonding natures. Covalent substances are found in regions of low A f and high ji. Metallic substances are found in regions of low Af and low ji. Ionic ~ubatancesare found in region8 of intermediate f with A- ranging from low to high values.8 These three regions are clearly separated with essentially no overlap along their mutual boundaries. Exceptions Only ten compounds fall slightly outside of regions appropriate for their bonding . . - natures. These ten exceotions are: the ionic compounds TICI, TBr, and TIBr, which fall within the mvalent region the mvalent compounds ALP,AIAs, InP, and Inks, which fall within the ionic region the covalent compound AIB2, which falls within the metallic region the metals AuSn and Au3Sn, which fall within the covalent region For all, except the thallium halides, the plotted displacement is small and less than 0.4 V from the expected bondtype region.
The Defining Boundaries The boundaries that define the three types of bonding regions can be described analytically by straight lines. Metallic, covalent, and ionic bonding regions all meet along the T axis a t about 6.4 V. ~ lbinary i compounds fall within the boundaries demarcated by the following equations:.
It can be seen that the ionic character (6)can be included in this function. B y analom the value of the eoualized electmnegativity ji can be considered as the c o v a l k potential because the ordinate axis varies continuously: from "pure" metallic bond character at the left extreme and 2.0 V through the mixed metdlidmvalent (metalloid) character at around 6.4 V to the "pure" covalent bond character at the right extreme Because 6 = 0 for homoatomic bonds, homoatomic compounds fall along the baseline of the graph, with Csz near the far l e e and Fznear the far right.
1
3
5
7
9
1
1
1
3
1
5
Covalent Potential, 2, in Volts Figure 1. Graph of A? vs. 2 using orbital eleclronegativites for bina~y compounds. Metallic mmpounds are symwhzed by -; ionic by '; covalent by 0 . HornoatomiccompoLnas are shown by x. MetallioIonic (on the left) Covalent-Ionic (on the right) ji + 2.5AF= 15.8V
The bonding regions are separated by two sets of parallel lines; the slopes of the lines in each pair are indistinguishable. Two inequalities effectively separate binary compounds into their bond types. A compound will be mvalent when
ji - 0.50Aji > 6.4 V
' A compound will be metallic when ji + 2.5Ar < 6.4 V Otherwise, the banding forces will be ionic. Thus, the preceding two analytical functions provide a useful guide for predicting bonding character for binary compounds. The DifferenceFunction as an Ionic Potential
The function AT can be described a s the change in electronegativity due to electron redistribution when atoms bond. It can be related to both fractional hardness and partial charge.
Comparing Conventional and Mulliken Electmnegatiuities Values of conventional electmnegativities are related to Mulliken electronegativities; they are the square root of energy terms (5,31). Differences greater than 1.7 between conventional electronegativities for bonded atoms, Ax(c), have been used in general chemistry texts to describe ionic bonding, whereas differences less than 1.7 have been related to covalent character (32). While the foundation of this relationship a s a valid measure of ionic or covalent character has been discredited (261, Figure 1indicates why this relationship has had some predictive merit. All compounds are ionic if AT ji 2.3 V, but many ionic compounds also exist that fall below AT = 2.3 V. The plot also emphasizes the relationship that metallic bonding exhibits as a natural companion to ionic and covalent bonding, rather than as a n unrelated addition. Choice of the Pmper Mean Equalized electronegativity of bonded atoms is generally less than or equal to the mean unbonded electronegativity of the component atoms. This is due to electron redistribution in heteroatomic bonds that arises from unequal electrostatic forces. Therefore, AT should usually be greater than or equal to zero. Then negative values of AT serve a s a n indication of the accuracy of this generalization. Of the nearly 300 compounds studied, all values of AT were greater than -0.20 V. This indicates a small but significant deviation from this generalization. These negative values may arise from adoption of the arithmetic mean in eq 7. Choice of the proper mean for the equalized electronegativity ji has been discussed by several authors. Assuming Sanderson's principle of electronegativity equalization for bonded atoms, recommendations have been made to use the geometric mean (16,331 the harmonic mean (34,35,28) a weighted mean (36 and eq 6 ) I n comparison with the arithmetic mean, use of either the geometric or the harmonic means will overemphasize the importance of the smaller of the two contributin~electronegativities. If the quadratic mean (sometimes i d l e d the root mean square) were used, the larger of the electronegativities would become slightly emphasized. Because proper choice of the mean of electronegativities behas no theoretical background, the fore bonding arithmetic mean was selected for definine it in eo 7. Bv substituting the quadratic mean for the anthmeticmean, the maxlmum negatlve valueofAji from eq 8 would be only -0.06 V.
(r)
The greater the differences are in the inherent electronegativities (or, equivalently, the hardness terms because a is mughly proportional to b), the larger the difference will be in electrical potential between bonded and unbonded species. As an indicator of the extent of electron redistribution, the function A x can be identified as the ionic potential, with units of volts.
Comparison with Conventional Electronegativity When the difference between conventional, single-valued electmnegativity values for bohded atoms Ax(c) is plotVolume 70 Number 7 July 1993
533
ted versus the mean electronegativity ~ ( c )data , points generally fall within regions of similar bond type. However, such a plot produces considerable overlap of regions, particularly between metallic and ionic compounds. The well-defined graphical separation shown in Figure 1using variable (Mulliken) electronegativity values indicates the success of using both Mulliken a and b parameters in determining the nature of interatomic bonding. Ionic character, as defined by the concept of bond eledmneeativitv. is the fractional charee redistribution necesequal electmnega&ities in bonded atoms. sary to Redistribution arises from differences in inherent electmnegativities as well as the charge-dependant hardness of the bonded atoms, as shown in eq 6. Thus, two-parameter variable electmnegativities are successful in separating different bond types in binary wmpounds. A Bond or Global Property
This treatment has assumed eledmnegativity equalization between pairs of bonded atoms in binary compounds: thus, it has analyzed orbital eledronegativities. However, there has been disagreement regarding whether eledmnegativity is Covalent Potential, 2, in Volts
a n orbital pmperty affecting each interatomic bond separately,or an atomic or global property (21,37)affecting all banded atoms within a compound Nalewajski (281implies compatibility of these altemative descriptions. Amaphical analysis similar to that made for orbital klectmne~ativitieshas been made using a global treatment, with relationships described by Reed (37).The global equalized electronegativity (xmOl,)is
The difference function ( A b s , ) is the difference between the mean unbonded inherent electmnegativity -
xunt...dd
vs x~~~~ usmg g obal electmnegat vmes Flgure 2 Graph of AX,, for blnary CornpoJnds Metall c compoLnos are syrnbollzea by T , lonlc by '. mvalent by 0 Hornoatornc wrnpo~ndsare shown by x 6. Hinze. J.;Jsffe, H. H. J . A m Cham Sac. 186e.34, 540. 7. Hinze, J.;Jaffe, H. H. J P h w Chpm. 1963,67,1501. 8. Hinze, J.; Whitehead, M. A.; JaEe, H. H. J . h . Cham. Soe. 1388.85. 148. 9. Holtzelsw, H. F,Jr:Robinson. W R.;Odom, J. D. General Chemlslrylvtth fiwAnolysis. 9th ed.:D.C.Heath Leldngton,MS. 1991;p186. 10. Pearson, R. 0.J.Am. Cham. S a 1983.85.3533, 11. Pearaon.R. 0. J.Chem. Edvc. IS.% 45.541. 12. pearson; R. G.J . Ckm. Educ. 1968:45: 643 13. Drseo. R. S.J . Cham Edvc 1974.51.300.
17. Sanderson, R. T &knee 1851,114,670. 18. Sanderson. R. T J. Chem Educ 1952,29.549.
=a
and the global eledmnegativity. 4xma~ee = xunbounded - xmolee
(12)
When AX,I, is plotted versus x,I, the results shown in Figure 2 are similar to those of Figure 1. The tripartite regions are of somewhat different shape, but they have similar, excellent separation between compounds of different bond types. Literature Cited 1. Pauhng,L.;Yost,D.M.Pme.N=t &rul.Sci. 19%2,18,414. 2. P a d i g , L.J cham Edue. 1388,65,375. 3. Mu1Pken.R. S. J. Chem.Php. 1934,2,782. 4. Pritehard, H. 0.;Sumnsr,F H . P ? a R w Sac. (London)186B,A215,136. J. L. J h . Ckm. Soe 1981,W,3547. 5. 1ezkowski.R.P:Ma?gr~~rv~~r,
534
Journal of Chemical Education
k. See. IS^, 85,148 25. Huhew J. E.J.Phvs. Cham. 1965.693284, 26. ~ u h e e J. i E. chemist&: ~ & i ~ofstnretvm k ~ ond Reoetiuih: 3rd d.; HarperandRow: NewYmk. 1983:pp 152-160. 27. P w G . R.;Peamn.R.O.J . h . Chem. Soe 1983,105,7512. 28. Na1euaJski.R.F.J.Am. Ckm. Sac 1885.83.2831. 29. Bratseh, 5. G.J.Chem. Edvc 1988.65.223, 30. Wells, A. F S f fturn1 lnowwcic Chpmisfry, 4th 4.;Clarendon: Oxford, 1975. 31. Bratach, S. G. J C h e m Educ 1983.65.34, 32. For example, Masterton, W. L.: Slowinski. E. J.; StanitsE, C. L.Chemiml&ncipks, 5th ed.; Saundere: Philadelphia, 1981:p 223. 33. P m , R O;Bartolatd. L. J. J.Am. Chpm. Sm. 1882,1M,3801. 34. Bratach, S. G. J. Chem.Educ. 1934,61,548. 35. Bratach, 5. G. J ChemEduc 1965.62. 101. 36. Smikh,D. W J C k m E d u e 1990.87.559. 37. Reed, J. L.J . h . C k m . Sac. 1981.85,146. 14. H ~ ~j.;zWhitehead. ~ , M. A,;J ~ EH.~ , J.
cLm.
