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Electronegativity and Bond Type. 3. Origins of Bond Type Gordon Sproul Department of Chemistry, University of South Carolina at Beaufort, Beaufort, South Carolina 29902 Received: July 13, 1994@
Using the bond character of numerous solid binary compounds, graphs of two functions of electronegativity can provide information on the atomic contributions to bonding. While a plot of the difference and average electronegativity, Ax vs i,shows the historical isosceles triangle, other plots provide additional insight into bonding. The graph of lower and higher electronegativity, xlo vs xk, indicates that it is the individual electronegativity values of bonded atoms that uniquely determine bond type. When Ax is plotted against xlor the data forms a right triangle aligned with the axes, implying that these functions best correlate with bond type.
Among the various attributes of chemical compounds, bond type is perhaps the most characteristic. For heteroatomically bonded binary compounds, three types of bonding are recognized: metallic, covalent, and ionic. The relationships among bond types of binary compounds has historically been represented by means of qualitative tripolar graphs,lW4with the three apexes identified as the metallic, covalent, and ionic poles. More recently it has been recognized that a quantitative plotting of functions of electronegativity can be Such twodimensional graphs provide suggestive insights into the nature of bonding. Numerous definitions of electronegativity have been proposed,8 most of which show good correlation with various observable quantities. This plethora of definitions has led to confusion because of a lack of experimental measurements that could differentiate among the alternatives. A recent publication has compared several scales, including some most commonly referenced and some that use various defining algorithm^.^ In it, a data set consisting of 311 solid binary compounds with well-defined bonding character was developed to serve as a descriptive chemical basis for evaluating the scales. By plotting the difference between electronegativities of bonded atoms, Ax, against the average electronegativities,i,isosceles triangles were produced (for example, see Figure 1). This provided a unique means of independently rating the scales. These plots clearly show that bonding among binary compounds can be divided into three distinctly demarcated regions; this supplied evidence for the tripartite hypothesis, by means of which 15 different electronegativity scales were e ~ a l u a t e d . ~ (The tripartite hypothesis proposes that bond types of metallic, covalent, and ionic compounds will be clearly segregated into three regions for graphs of two independent functions of electronegativity.) While nearly all of these scales gave good predictive merit, the scales of Allenlo and of Nagle" produced the best results. For this reason, and the fact that Allen's scale has been shown to have good correlation with various other chemical properties,'* Allen's scale of electronegativity will be utilized in this paper. The quantitative graph Ax vs i produces a triangle (Figure 1) similar to the qualitative ones of van Arkel' and of Ketelaar,* reproducing the tripolar nature of those triangles. Quantified graphs exhibit a tripartite segregation when lines of best separation of bond type are drawn. Also, these lines of demarcation lie parallel to the boundaries of the triangle. The nature of these dividing lines will be considered here. @
Abstract published in Advance ACS Abstracts, November 1, 1994.
0022-3654/94/2098-13221$04.50/0
It is obvious that, in order to maintain the full information contained in two variables (such as the electronegativities of two bonded atoms), two independent functions of those variables are necessary. - Selection of the two functions of electronegativity Ax and has been somewhat arbitrary and corresponds with historical precedent. As already indicated, a plot of Ax vs i reproduces historically described triangles. The function Ax was used by Pauling13 in correlation with dipole moment to provide a means of establishing the ionic character between bonded atoms. While this relationship has since been shown to be inadeq~ate,'~ it has nevertheless provided a qualitative measure of ionic character. For the other variable, various types of mean of electronegativities have been p r o p o ~ e dbut ,~ the one most commonly used is the geometric mean. A graph of Ax vs the geometric mean of the electronegativities, xgeo, was plotted (Figure 2) and evaluated against the tripartite hypothesis. It was found that, for this particular data set of electronegativities, Ax vs i gives a better agreement fraction of 0.97 than Ax vs xgeowhich gives an agreement fraction of only 0.94. (The agreementfraction is the ratio of the number of compounds falling within the expected bond-type region to the number of compounds considered.) While the difference appears small, it is significant since nearly twice as many compounds are misplaced from their expected bonding regions when the geometric mean is used rather than the arithmetic mean. The function will be used here because of its inherent simplicity and because it provides the better correlation with osberved bonding properties. Other combinations of functions of electronegativity could be considered; another will now be shown to provide interesting insights into the origins of chemical bonding. The simplest functions of electronegativities of bonded atoms are, of course, the unfunctionalized electronegativity arguments themselves. By plotting the lower value of electronegativity, xl0, against the higher value of electronegativity,xk, a right triangle is produced (Figure 3). While this graph contains the same information as that in the isosceles triangles of Ax vs i,the information is presented differently. This particular graphical presentation shows that the origin of lines demarcating the three bonding regions arises from the individual electronegativity values of the component atoms and does not appear to be due to some combination of these values. More particularly, it indicates that metallic bonding always occurs if xk is less than a certain value (in the case of the electronegativity scale CE of Allen, xk(Al) = 13.47 eV); ionic or covalent bonding will occur if xb is greater than this same value; and ionic bonding is separated from
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Electronegativity and Bond Type
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13224 J. Phys. Chem., Vol. 98, No. 50, 1994
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covalent bonding by a line of demarcation manifested by a particular value of xlo &lo(Al) = 9.46 eV). The values for xlo and for several scales of electronegativity have been previously published and are the same as the x-intercept of the analytical lines r e p ~ r t e d . ~ Alternative selections of variables can provide additional conceptual clarification. By plotting Ax vs xlo, a different right triangle is obtained (Figure 4). This graph, like the previous ones, shows that metallic bonding character is maintained as xlo increases, until xlo reaches a particular value, at which point a discontinuity of bond type occurs. This graph also shows the discontinuity as Ax increases, again changing from metallic character at its minimum values. These graphs indicate, then, that there are two independent functions operating that determine bond type. This is similar to Sanderson's description of bonding,15 in which he recognized any increase in ionic bonding as necessitating a corresponding decrease in covalent bonding. Metallic delocalization of electrons diminishes and localization increases either ionically or covalently away from the metallic vertex, and an increase of ionic or covalent bonding occurs with the decrease of the other. This graph of Ax vs xlo, because it indicates bond-type data aligning with the Cartesian axes, indicates these two (or closely related) variables provide direct variation of bonding data with these functions. There are six simple electronegativity variables (both the lower and higher electronegativity arguments as well as the four simple mathematical functions of these): xlo,XE (the two arguments), (the additive mean), Ax (the difference function), xgeo(the multiplicative geometric mean), and x&b (a ratio function). Of the 15 possible pairs of these, only the combination Ax and xlo exhibits direct variation of bond type as a function of Therefore, Ax and xlo are the two independent variables that may be the most useful when evaluating physically measurable contributions to bonding.
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Conclusion These observations, based on plots of well-characterizedbond types using various combinations of functions of electronega-
tivity, provide empirical direction for reevaluating the relationships between electronegativity and bonding. While a quantitative graph of Ax vs provides a useful tripartite separation of bonding types, two other combinations of functions of electronegativityare shown to clarify the infomation it contains. A graph of xlo vs xk indicates that the electronegativity values of the bonded atoms uniquely distinguish bond type in binary compounds. Plots of Ax vs XI,, show that these two variables are the ones that may be the most useful when describing the relationship of electronegativity to the three bond types.
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Acknowledgment. I am grateful for encouragement and helpful comments given by Prof. Ben Gimarc at the University of South Carolina and Prof. Lee Allen at Princeton University. University of South Carolina's Research and Productive Scholarships Fund provided financial support. References and Notes (1) Van Arkel, A. E. Molecules and Crystals; Interscience: London, 1949; p 205. (2) Ketelaar, J. A. A. Chemical Constitution--An Introduction to the Theory of the Chemical Bond; Elsevier Pub. Co.: New York, 1953; p 21. (3) Jolly, W. L. The Principles of Inorganic Chemistry; McGraw-Hill Book Co.: New York, 1976. (4) Moeller, T.; Bailer, J. C., Jr.; Kleinberg, J.; Guss, C. 0.; Castellion, M. E.; Metz, C. Chemistry with Inorganic Analysis; Academic Press: New York, 1980; p 259. (5) Allen, L. C. J . A m . Chem. SOC. 1992, 114, 1510-1511. (6) Sproul, G. D. J . Chem. Ed. 1993, 70, 531-534. (7) Allen, L. C.; Capitani, J. F.; Kolks, G. A.; Sproul, G. D. J . Molec. Struct. 1993, 300, 647-655. (8) Mullay, J. In Srructure and Bonding, Vol. 66; Sen, K. D., Jorgensen, C. K., Eds.; Springer-Verlag: New York, 1987; pp 1-25. (9) Sproul, G. D. J . Phys. Chem. 1994, 98, 6699-6703. (10) Allen, L. C. J. Molec. Struct. (Theochem.) 1992, 261, 313-330. (11) Nagle, J. K. J. Am. Chem. Soc. 1990, 112, 4741-4747. (12) Allen, L. C. J. Am. Chem. Soc., in press. (13) Pauling, L. The Nature of the Chemical Bond, 3rd ed.; Comell Univ. Press: Ithica, NY, 1960; pp 97-101. (14) Barrow, G. M. Physical Chemistry, 3rd ed.; McGraw-Hill: New York, 1973; pp 403-406. (15) Sanderson, R. T. Simple Inorganic Substances; R. E. Krieger Pub. Co.: Malabar, FL, 1989; pp 24-25, 129-134.
