Electronegativity and the Bond Triangle

Research: Science and Education

W

Electronegativity and the Bond Triangle Terry L. Meek* and Leah D. Garner Department of Biological and Chemical Sciences, University of the West Indies, Cave Hill, Barbados; *[email protected]

The bond-type triangle is being used increasingly in undergraduate textbooks to illustrate the central importance of electronegativity and its influence on bond type (1a, 2). It has long been recognized that chemical bonds can be divided into three fundamental types: ionic, covalent, and metallic. van Arkel’s (3) depiction of the three bond types as the vertices of a triangle, with compounds or elements of intermediate nature being located along the edges, was the first to attract widespread attention (Figure 1A).1 Ketalaar (4) further developed the bond triangle by placing compounds within it as well as on the edges (Figure 1B).

A

B

Figure 1. Early bond triangles: (A) van Arkel, ref 3, and (B) Ketalaar, ref 4.

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Recent work has focused on the rationalization of the bond triangle by using functions of electronegativity as the basis for determining the positions of substances within it. Jensen (5), Allen et al. (6), and Sproul (7) all recognized the essential role of electronegativity and electronegativity difference in determining the properties of substances. All of them concluded that the position of any binary compound in the bond triangle could be specified by two coordinates: electronegativity difference (∆χ) and average electronegativity (χav) (Figure 2). These authors noted that plotting a graph of ∆χ versus χav produces a triangular array with ionic compounds (high ∆χ, moderate χav) near the top, metals (low ∆χ, low χav) near the lower left, and covalent substances (low ∆χ, high χav) near the lower right. Both Sproul and Allen suggested that the bond triangle as defined above can be divided into covalent, ionic, and metallic regions with straight lines as boundaries. In the triangles devised by each of these authors (Figure 2), the vertices are occupied by Cs (metallic), F2 (covalent), and CsF (ionic); the elements lie along the metallic–covalent axis (∆χ = 0), while cesium compounds and fluorides are found along the metallic–ionic and covalent–ionic edges, respectively. As observed by Jensen (5), the compounds of any element other than Cs or F lie on two diagonal lines, parallel to the metallic–ionic and covalent–ionic edges, which meet at the position occupied by the element itself. The left line (with negative slope) includes compounds of the element with elements less electronegative than itself, while the right line (with positive slope) includes the compounds of the element with more electronegative elements. All compounds formed by a given pair of elements occupy the same position. Sproul (7b) did the most extensive work on quantification of the bond triangle, plotting values of ∆χ versus χav for 311 binary compounds and observing excellent correlation between position on the graph and bond type as specified by Wells (8). He excluded compounds whose bond type was said by Wells to be “ambiguous or questionable”, such as “semimetallic” compounds. Sproul examined 15 different electronegativity scales and found that the best agreement between position and bond type was obtained when Allen’s spectroscopic electronegativity (9)—later called configuration energy (10)—was used,2 only 9 of the 311 compounds being “misplaced” from their specified regions. He found that, for his selected compounds, the triangle could be divided into covalent, ionic, and metallic regions by straight lines, parallel to the metallic–ionic and covalent–ionic edges of the triangle (Figure 2 bottom). These boundaries were defined by the equations (with χ values converted to Pauling units):

Covalent − Ionic:

χ av = 0.5 ∆ χ + 1.60

Metal − Nonmetal:

χ av = −0.5 ∆ χ + 2.28

Vol. 82 No. 2 February 2005

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Journal of Chemical Education

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Figure 2. Quantified bond triangles: (top) Jensen, ref 5 (center) Allen et al., ref 6 (bottom) Sproul, ref 7b

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A

These boundaries are not entirely satisfactory, probably because some of the compounds used were inappropriate (see below) and Wells’s specifications of bond type are inaccurate in some cases and ambiguous in others. The covalent–ionic borderline is just below the line that includes all compounds of aluminum (χ = 9.53 eV = 1.61 PU) with elements of higher electronegativity, while the metal–nonmetal (metal– insulator) line lies between those that include compounds of phosphorus (χ = 13.3 eV = 2.25 PU) and of hydrogen (χ = 13.6 eV = 2.30 PU) with metals and metalloids. Accordingly, B

3. No element that has an electronegativity less than that of H would display anionic character in any compound, even with cesium; compounds of P and the metalloids Te and Po with the group 1 and group 2 metals are believed to have considerable ionic character, though the tellurides and polonides are not well characterized.

It must be noted that the distinction among bond types, especially for polymeric substances, is quite arbitrary and it is seldom possible to categorize compounds definitively as being 100% ionic, covalent, or metallic. This was recognized by Allen (6), who introduced a small triangular “metalloid” region of substances with low ∆χ and moderate χav. Jensen (11) observed that there are not (or should not be) “sharp boundaries separating substances containing metallic, covalent, and ionic bonds”. In fact, most compounds exhibit a mixture of two types of bonding and display some characteristics of both—or even of all three—types, as exemplified by the “III–V” semiconductors and some Zintl phases. Thus the categorization of compounds as ionic, covalent, or metallic is a considerable oversimplification, and nearly all compounds are really intermediate in character. It would be more accurate to say that the elements and many compounds can be categorized as predominantly ionic, covalent, or metallic, but most of them have some characteristics of at least two bond types. Jensen (11) also points out that the van Arkel–Ketalaar triangle is a bond triangle and the accurate specification of compounds and elements would require another dimension such as is found in Grimm’s tetrahedron (12), with van der Waals forces as the fourth vertex and substances with intermediate degrees of polymerization occupying levels above the array of three-dimensional polymers represented by the van www.JCE.DivCHED.org

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4

I

3

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1

M

C

0 1

2

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Average Electronegativity / PU

2. All elements with electronegativity equal to or less than that of Al would form only ionic compounds with elements more electronegative than P; the amphoteric metals Al, Be, Cd, and Zn form covalent (or intermediate) compounds with many nonmetals.

4. Any compound formed between two elements less electronegative than H would be metallic; some of these elements are metalloids, and form semiconductors that are not “well-defined” and do not display metallic conductivity. The “III–V” compounds are the best known of these.

5

0

Electronegativity Difference / PU

1. No element with electronegativity greater than that of Al would exhibit cationic character in any compound, even with fluorine; Hg, Ga, In, Tl, Sn, and Pb are cationic in some compounds.

5

4

3

I 2

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MD M

C

0 0

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Comments and Limitations



5

4

3

I

2

C/I

1

M

C

MD

0 0

1

2

3

4

5

Weighted Average Electronegativity / PU

Figure 3. Evolution of quantified bond triangles: (A) dependence on one variable, (B) boundaries according to Sproul and Allen, and (C) this work.

Arkel–Ketalaar triangle. The error of attempting to correlate a property of bulk matter with the charge distribution in an isolated molecule is further emphasized by the fact that some compounds, although predominantly covalent molecular substances in the gas phase, consist of polyatomic cations and anions in condensed phases. Well-known examples are N2O5 and PCl5. Despite these limitations, the position of a binary compound in the bond triangle still gives a good indication of the type of bonding that occurs in it and the bond triangle gives some very useful insights (Figure 3). First is the realization that bond type depends on both ∆χ and χav, which is confirmed by the positive slope of the ionic–covalent bound-


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ary and the negative slope of the metal–nonmetal boundary in Sproul’s and Allen’s representations (Figure 3B). Sproul (7d) points out that, if ionic character were associated only with a large ∆χ, there would be a horizontal line at some critical ∆χ value such as the frequently cited 1.7 Pauling units (13), separating ionic species from others.3 Furthermore, if metallic character were associated only with a small χav, there would be a vertical line at some critical χav value—perhaps between those of Pb, the most electronegative metal, and Si, the least electronegative nonmetal—separating metals from nonmetals. Although the above authors have demonstrated that bond type depends on both ∆χ and χav, none of them has offered an explanation for the manner in which ionic–covalent or metallic–nonmetallic character varies with both parameters. We now address these matters. We will also show that there are gaps between the regions occupied by predominantly ionic and predominantly covalent substances, and between metals and nonmetals, which are occupied by substances generally regarded as being of “intermediate” nature. Ionic versus Covalent Bonding: Partial Charge The dependence of ionic character on χav as well as on ∆χ is shown in Table 1; for each group of compounds with very similar ∆χ values, ionic character decreases as χav increases. This variation results from the fact that partial charge, rather than ∆χ alone, is the critical parameter in determining ionicity. Although the unequal distribution of charge has its origin in ∆χ, the magnitude of the partial charge is also dependent on χav. We will show that partial charge is in fact closely related to the ratio ∆χ: χav. For diatomic singly bonded molecules of general formula AB, Wilmshurst (14) suggested that the partial charge on A (qA) is given by, qA =

χB − χ A

(1a)

χB + χ A

where χA and χB are the electronegativities of elements A and B. Thus qA =

∆χ 2 χ av

(1b)

At least four other more recently derived equations for evaluating partial charge can be shown to be equivalent to eq 1b. Smith (15) used an electronegativity equilibration approach to show that, in the singly bonded molecule AB, the partial charge on A is given by,

qA =

χ − χA χA

2 χ A χB

, where χ =

χ A + χB

(2a)

Table 1. Dependence of Ionic Character on χav Substance

∆χ/PU

χav/PU

∆χ:χav

Predominant Bond Type

LiCl

1.96

1.89

1.037

Ionic

HF

1.89

3.25

0.582

Covalent

LiI

1.45

1.64

0.884

Ionic

AlN

1.45

2.34

0.620

Intermediate

BrF

1.50

3.44

0.436

Covalent

LiBi

1.10

1.46

0.753

Metallic

MgSe

1.13

1.86

0.608

Ionic

CO

1.07

3.08

0.347

Covalent

NOte: χ values (Pauling units) from ref 19.

Identical expressions are obtained using the methods of Bratsch (16) and von Szentpaly (17), if one makes the approximation that the charge coefficient (16) or atomic hardness (17) of an atom is equal to its electronegativity. In Allen’s modified Lewis–Langmuir method (18), for diatomic molecules with single bonds: No. of χA qA = Group No. − Unpaired − 2 χA + χB Electrons

(3a)

Thus, if neither atom has a formal charge:

2 χA

qA = 1 −

χ A + χB

=

χB − χ A χ A + χB

=

∆χ 2 χ av

(3b)

According to all of these equations, the partial charges of bonded atoms (hence ionic character of a bond) increases as the ratio ∆χ: χav increases, and all compounds whose atoms have the same partial charges will have the same ∆χ: χav ratio. Thus in a bond triangle with axes ∆χ and χav, all compounds with the same degree of ionic character will lie on a straight line, passing through the origin (∆χ = χav = 0) when extrapolated, with slope equal to 2q (Figure 3C). One such line will have a slope equal to the critical q value above which compounds are predominantly ionic, and will correspond to the “ionic–covalent” boundary. In fact, for diatomic molecules with multiple bonds the partial charge is equal to the ∆χ:2χav ratio multiplied by the bond order; this is recognized by Wilmshurst (14) and Allen (18) in their articles, but the equalization-based methods (15, 16) do not take bond order into account and von Szentpaly (17) considers only singly bonded molecules. Still, the ratio ∆χ: χav in molecules with multiple bonds is equal to twice the partial charge per bond and gives a good indication of the extent of ionic character in the bond.

thus: qA =

χ −1 = χA =

328

2 χ A χB χ A + χB χB − χ A χA + χ B

Metals versus Nonmetals: Band Gap

1 χA =


−1

∆χ 2 χ av

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(2b)

The critical parameter in determining metallic behavior is band gap (E g), since conductivity is proportional to exp(᎑Eg兾kT). Thus substances with very small band gaps are metallic conductors, while those with large band gaps are insulators. For the elements, it has been established (19) that


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contribute equally to band gap, or of an ellipse if they do not. Thus the metal–nonmetal boundary would be the curve for which the E value corresponds to the largest band gap that allows metallic conduction (Figure 3C). It must be realized that ∆χ and χav are derived from properties of isolated atoms whereas band gap is a property of an aggregated solid, so a rigorous relationship between band gap and these parameters is unlikely. Still, qualitative agreement has been observed—Jensen (5) reported a “quickand-dirty” test with a crude probe-buzzer-battery device that showed a curved boundary, in a graph of ∆χ vs χav, between substances that showed detectable conductivity and substances that did not.

Table 2. Variation of Metallic Character with ∆χ χ Substance

χav/PUa

Band Gap/eV

∆χ/PUa

Conductance

Ge

1.99

0

0.7b

Semiconductor

GaAs

1.98

0.46

1.5b

Semiconductor

0.83

b

Insulator

bb

Metal

ZnSe

2.01

2.8

Sn

1.82

0.00

0.8

InSb

1.82

0.33

0.2c c

Semiconductor

CdTe

1.84

0.64

1.5

MgSe

1.85

1.13

?.8b

Insulator

LiBr

1.80

1.88

?.8b

Insulator

a

Values (Pauling units) from ref 19.

b

Semiconductor

Ref 1b.

c

Ref 30.

Polyatomic Molecules: Weighted Average χ

χ alone can be used to determine metallic character, as the width of an energy band is inversely proportional to the energy of the level from which it arises. All metals have χ values less than 1.92 (Si), while all nonmetals have χ values greater than 2.21 (As); the metalloids occupy the narrow range of χ between these values. For compounds, the extent of metallic character depends on both ∆χ and χav. Sets of compounds with very similar average electronegativities display increasing band gaps and thus decreasing metallic character as electronegativity difference increases, as seen in Table 2. This was noted by Allen and Capitani (20) and is consistent with equations, devised by various authors, that define the band gap. Phillips and van Vechten (21) suggested that, for binary compounds with a total of eight valence electrons per AB unit, the band gap in crystalline substances is composed of ionic (Ei) and covalent (Ec) contributions according to:

E g2 = E c 2 + E i 2

One anomaly that arises in this representation of bond type is that all of the compounds formed by a given pair of elements occupy the same position on the graph. In fact, bond type can vary with the valence of the central atom. For example, tin(IV) halides are predominantly covalent, as are the few stable ones of lead(IV), with all but the fluorides normally existing as monomeric molecules. However, lead(II) halides are ionic and those of tin(II) have substantial ionic character. For polyatomic molecules, the relationship among partial charge, ∆χ, and χav is more complex than for diatomics. For compounds formed between the same two elements, natural population analysis calculations (24) show that the partial charge on each terminal atom decreases as the valence of the central atom increases. This suggests that the simple χav may not be the appropriate parameter to use. We propose a weighted average electronegativity, defined for AmBn as:

(4)

χ av

Adams (22) redefined these terms in his equation, E g2 = E h2 + C 2

(5)

where C, the charge transfer energy, is proportional to ∆χ, and Eh, the homopolar energy gap, (like Ec in eq 4) is defined as the energy difference between the center of the valence band and that of the conduction band. Eh is a measure of the effectiveness of interaction between atoms, and thus should depend on the same factors as χ and χav. For s-valent diatomic molecules, Pettifor (23) gives the equation, wAB

2

= 4h

2

+ ( ∆E )

2

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=

m χA + n χB m + n

(7)

It follows that, using this definition of (χav)w: ∆χ χ av

= w

( m + n ) ∆χ m χ A + n χB

(8)

The ratio ∆χ:(χav)w is not rigorously related to atomic charge—we have shown elsewhere (25) that, for molecules AnB, the charge on A is given by qA =

(6)

where wAB is the separation between bonding and antibonding states, h is the bond integral and is related to the average atomic potential, and E, the free atomic energy level, is approximately equal to χ. Each of these equations is of the form E 2 = a 2 + b 2, where a is related to the average energy of the atoms or to the effectiveness of their interaction (hence to χav) and b is related to an energy difference (hence to ∆χ). This suggests that substances with the same band gap will lie on a line with the same values of (c1∆χ2 + c2χav2). Such a line would be a curve —a segment of a circle if ∆χ and χav

w

∆χ 2n − 1 χ A + χB n

(9)

—but nevertheless ∆χ:(χav)w serves to discriminate between compounds of the same two elements with different stoichiometries. From eq 8, such compounds will have the same ∆χ but different (χav)w values. (Using the fluorides of lead as examples, the (χav)w values for PbF4 and PbF2 are 3.73 and 3.41 Pauling units.) Each compound thus occupies a unique position in the triangle. Because of the positive slope of the covalent–ionic boundary, this can result in two such compounds being in different bonding regions.


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Boundaries: Well-Defined Compounds and Elements The selection of compounds for establishing boundaries between predominant bond types should be restricted to binary compounds that have been isolated and purified, have known structures, and contain only heteronuclear bonds. This last criterion excludes many types of compounds, for example: (a) Compounds with discrete dinuclear ions, which could be described as both ionic (since they contain ions) and covalent (since some of the ions are polyatomic). (b) Molecular compounds, including clusters, which contain both homonuclear and heteronuclear covalent bonds.

wood and Earnshaw (26) as being predominantly of one type. A plot of ∆χ vs (χav)w (Figure 4) was constructed for these compounds; the 37 “well-defined” elements of these groups —omitting the metalloids—were also included, to help establish the covalent–metallic boundary. All of these species are listed in the Supplemental Material.W The electronegativity values used were those of Allen et al. (19), expressed in Pauling units. For polyatomic molecules the weighted average electronegativity defined by eq 7 was used rather than the simple average. In this graph a triangular array of points is still obtained, but there are some significant differences from the triangles devised by other workers: 1. The compounds of a given element no longer lie on a single line (Cs and F) or a pair of converging lines (all other elements). Instead a number of lines, converging at the position of the element, are obtained; for example, all monofluorides lie on one line, all difluorides on another line, and so forth.

(c) Zintl compounds, which display some degree of metallic interaction as well as containing simple cations and extended polyatomic networks of covalently bonded atoms, each with a formal negative charge (1c). (d) The group 1 compounds M3E of the group 15 elements As, Sb, and Bi, whose structures feature homonuclear intermetallic bonding as well as heteronuclear interactions (26a). The group 2 compounds M3E2 of these elements also display some metallic properties.

2. Some of these lines (polyfluorides, caesium compounds of multiply-charged anions, etc.) extend outside the boundaries of the Cs–CsF–F2 triangle. This necessitates a relocation of the vertices, to produce a triangle that includes all compounds. The metallic and covalent vertices can be defined as the points with (∆χ = 0, (χav)w= 0) and (∆χ = 0, (χav)w = 5); the ionic vertex would then be at (∆χ = 5, (χav)w = 2.5). This enlarged triangle includes all well-defined compounds of the main-group elements. Figure 4 shows that there is good discrimination among predominant bond types.

(e) The suboxides of rubidium and caesium, which contain cationic clusters of identical atoms, such as M94+ and M116+, associated through metallic interactions (1c).

The above criteria were applied to 321 binary compounds, formed by the elements of groups 1, 2, and 12–18 in periods 1–6,4 in which the bonds are described by Green-

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2.5

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0.5

0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Weighted Average Electronegativity / PU Figure 4. Bond triangle for well-defined substances: circles = mainly ionic, squares = mainly covalent, and triangles = mainly metallic.

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Covalent–Ionic Boundary Compounds specified as covalent and those specified as ionic are well separated by a straight line with the equation ∆χ = 0.62(χav)w, as shown in Figure 4. This suggests that binary compounds with partial atomic charges greater than ±0.31 (per bond) are predominantly ionic, while those with qA values less than 0.31 are predominantly covalent. This finding contrasts with Pauling’s implication (13) that 50% ionic character marks the dividing line. There is a small triangular region adjacent to the “covalent–ionic” and “covalent–metalloid” boundaries—the third side being the dashed line in Figure 4—which contains very few compounds specified as ionic or covalent. We will observe later that most of the compounds generally regarded as being intermediate between ionic and covalent occupy this region. A few compounds do not appear in their expected regions of the triangle; most of these can be categorized as follows: 1. The 14 compounds InCl, InBr, InI, GaCl, GaBr, GaI, TlCl, TlBr, TlI, PbCl2, PbBr2, PbI2, BiF3, and Bi2O3, specified as ionic, are in or very near to the “covalent” region. (Five are in the small triangular region described above.) It is possible that the misplacement of these “subvalent” compounds arises from the definition of χ as the average one-electron energy (εl) of all of the valence electrons of an atom (7); for an atom with the configuration snpm:

χ =

n ε s + m εp

(10)

n + m

The predominately ionic character of these compounds suggests that the metal atoms have electronegativities considerably lower than those obtained from eq 10. This would be consistent with the s electrons of the metal taking little (if any) part in bonding, so that including εs gives erroneously high χ values for these elements, hence low ∆χ and high (χav)w values for their compounds with nonmetals. This would be especially pertinent for compounds of Tl(I), Pb(II), and Bi(III), whose 6s orbitals are considerably stabilized by relativistic effects (27). (Apparently all subvalent ionic compounds are misplaced, except SnO, PbO, PbF2, and TlF). Only two other compounds specified as ionic—MgI2 and MgSe—are in the “covalent” section. 2. The only compounds specified as covalent that appear in the “ionic” region are the polymeric species HgO, PbF4, SnF4, SnF2, and GeF2. This is another instance of the qualitative nature of the agreement between predominant bond type and location in the bond triangle. As noted above, the ratio ∆χ:(χav)w is not directly proportional to partial charge,5 even in polyatomic molecules.

Metal–Nonmetal Boundary It is very difficult to establish the border between metals and nonmetals, since very few stoichiometric binary com-

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2.5

2.0

1.5

1.0

0.5

0.0 0.5

1.0

1.5

2.0

2.5

3.0

Weighted Average Electronegativity / PU Figure 5. Portion of bond triangle showing intermediate substances: circles = covalent–metallic, squares = covalent–ionic, and triangles = ionic–metallic.

pounds are known to be metallic. There is a substantial gap in Figure 4 between compounds specified as metals and those specified as nonmetals. The borders of these two regions in the triangle appear to be defined by curved lines, which could well mark the boundaries of a metalloid or semiconductor region. However, linear boundaries cannot be ruled out at this stage The alloys LiBi and NaBi are very close to the intermediate, metalloid region in spite of having “typical alloy structures” (26a). They would be in the middle of the “metallic” region if the electronegativity of Bi were assessed only from the energy of its 6p orbitals, 0.599 Rydberg = 1.38 PU (19). “Intermediate” Substances The boundaries between bonding regions can be defined more closely with the aid of another graph of ∆χ versus (χav)w values, plotted in Figure 5 for 62 substances (8 elements and 54 compounds) that are usually described as “intermediate”. These are also listed in the Supplemental Material.W They are further categorized as follows:

Covalent–Ionic (23 Compounds) Eighteen of these compounds are within the small triangular area described above, separated from the “covalent” region by the dashed line in Figures 4 and 5. Of the other five, AlN is on the “covalent–ionic” boundary, two (Cd3N2 and Zn3N2) are in the “ionic” region although quite close to the “covalent–ionic” boundary, and two (SnS and PbS) are in the “covalent” region but very close to the triangular area containing most of the intermediate compounds. ZnSe, BeSe, CdSe, and Be2C are very close to the metalloid region; Shriver and Atkins (28) describe Be2C (and Al4C3) as “borderline between saline and metalloid”, and an ab initio calculation (29) suggests that Be2C is largely ionic. CdSe is a semiconductor with a band gap of 1.7 eV (30).


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Covalent–Metallic (34 Substances) The eight metalloid elements and 17 of the 26 “covalent–metallic” compounds are in the metalloid region defined above. AlSb and InSb are just inside the “metallic” region, and GaSb is on the border between metals and metalloids. The location of the semiconducting sulfides and selenides of As, Sb, and Bi well inside of the “covalent” region seems very anomalous.

cally by optimizing the sorting of a set of elements and binary compounds that have been qualitatively characterized as being predominantly ionic, predominantly covalent, or predominantly metallic in their bonding. Such a sorting procedure is at best only semiquantitative, since we have no independent quantitative measure of predominant bond character. 4. Compounds of intermediate bond type also occupy specific sections of the triangle.

Ionic–Metallic (5 Compounds) These are also in the metalloid region. The somewhat saltlike (26b) intermetallic compound CsAu, containing a transition metal with electronegativity 1.92 PU (31), would be on the metal–nonmetal boundary. Thus the diagram for intermediate substances indicates that:

(a) Most metalloids and semiconductors occupy an area bounded by two curves, one separating them from metals and the other separating them from insulators. (b) Most compounds generally regarded as intermediate between ionic and covalent occupy a small, nearly triangular region adjacent to the covalent–ionic and covalent–metallic boundaries.

1. The metalloid–nonmetal boundary is curved. A straight line, drawn from the metalloid–nonmetal border of the elements along the edge of the region occupied by compounds specified as covalent and ionic, places most known semiconductors among the predominantly covalent compounds; a straight line between covalent compounds and semiconductors places several predominantly ionic compounds—the iodides, hydrides, sulfides, and selenides of the group 1 metals—among the semiconductors.

5. In spite of the limitations mentioned above, the position in the triangle of a binary compound of main group elements gives a reasonable indication of its predominant bond type. Lecturers and textbook writers should bear the limitations in mind and point out that the great majority of compounds contain bonds that are in fact intermediate between two (or more) types, even if they are predominantly of one kind. The existence of well-defined intermediate ionic–covalent and metal–nonmetal regions of the triangle, both of which contain very few species having one predominant bond type, is also notable.

The curvature of the metalloid–nonmetal line suggests that the metal–metalloid boundary is probably also a curve rather than a straight line. All of the covalent– metallic and ionic–metallic substances examined lie between or very close to the region between two curves, as noted above.

6. Applicability of the bond triangle appears to be limited to simple binary compounds. Even for those, the classification of Zintl compounds and others containing polyatomic ions, and of suboxides and other cluster compounds, presents some difficulties. Such compounds clearly contain at least two distinct types of bonding, and the bond triangle in its present form cannot represent this.

2. There is an “intermediate” covalent–ionic region in the bond triangle. Most compounds of this type occupy a small triangular area adjacent to the covalent–ionic and metal–nonmetal boundaries. Of the “specified” compounds, only a few subvalent ones and BeCl2, BeBr2, MgI2, and MgSe are in this area. The latter four compounds could well be described as intermediate.

7. The usefulness of the bond triangle for categorizing compounds of the main-group elements may be extended by the use of weighted average electronegativities to allow distinction between compounds of the same elements with different stoichiometries. In such cases a higher valency for the central atom leads to greater covalent character and the compounds may have different bond types.

Summary 1. The dependence of bond type on the two parameters ∆χ and (χav)w is examined. It is shown that, for diatomic molecules, (a) The extent of ionic character in a bond depends on the partial charges on the atoms, which for diatomic molecules is proportional to the ratio ∆χ:(χav). (b) Metallic character is governed by the gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital, which is related to c1(∆χ)2 + c2(χav)2. 2. These relationships are responsible for the shapes of the covalent–ionic and metal–nonmetal boundaries in the bond triangle. The former is a straight line, while the latter is a curve. 3. The critical values of partial charge and band gap at which the boundaries occur may be estimated empiri-

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Supplemental Material

A list of the substances specified as being one predominate type or an intermediate type are available in this issue of JCE Online. Acknowledgments The authors are grateful to L. C. Allen of Princeton University for the insights obtained in many stimulating discussions and to the reviewers for a number of helpful comments and suggestions.


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Notes 1. Jensen (11) has pointed out that triangles of this type can be traced back to the work of Grimm and Fernelius in the period 1928–1936. 2. In fact, most of the major electronegativity scales show excellent correlation with one another and with Sproul’s data set. Although we will use the Allen scale in this article, any of the commonly used ones would give similar results. 3. Pauling (13) in fact gives this ∆χ value as the one that results in 50% ionic and 50% covalent character. 4. The data set was restricted to main-group elements and their compounds at this time; the d-block metals and their compounds will be examined in a subsequent article. 5. In fact the atomic charges per bond in these compounds have all been calculated by a modified Lewis–Langmuir-type equation (25) as being substantially less than the ∆χ:(χ av)w ratios calculated from their empirical formulas. In all cases the charge per bond is less than 0.31 in the polymer.

8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.

Literature Cited 1. Alcock, N. W. Bonding and Structure; Ellis Horwood: London, 1990; (a) pp 18–22, (b) pp 290–291, (c) pp 309–313. 2. (a) Norman, N. C. Periodicity and the p-Block Elements; Oxford University Press: Oxford, 1993; pp 55–56. (b) Mackay, K. M.; Mackay, R. A.; Henderson, W. Introduction to Modern Inorganic Chemistry, 5th ed.; Stanley Thornes: New York, 1996; p 84. (c) van der Put, P. J. The Inorganic Chemistry of Materials; Plenum: New York, 1998; p 12. (d) Wulfsberg, G. Inorganic Chemistry; University Science Books: Sausalito, CA, 2000; pp 775–778. 3. van Arkel, A. E. Molecules and Crystals; Interscience: London, 1949; p 205. 4. Ketalaar, J. A. A. Chemical Constitution—An Introduction to the Theory of the Chemical Bond; Elsevier: New York, 1953; p 21. 5. Jensen, W. B. J. Chem. Educ. 1995, 72, 395–398. 6. Allen, L. C.; Capitani, J. F.; Kolks, G. A.; Sproul, G. D. J. Mol. Struct. 1993, 300, 647–655. 7. (a) Sproul, G. D. J. Chem. Educ. 1993, 70, 531–534. (b) Sproul, G. D. J. Phys. Chem. 1994, 98, 6699–6703. (c) Sproul,

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22. 23. 24. 25. 26. 27. 28. 29. 30. 31.

G. D. J. Phys. Chem. 1994, 98, 13221–13224. (d) Sproul, G. D. J. Chem. Educ. 2001, 78, 387–390. Wells, A. F. Structural Inorganic Chemistry, 5th ed., Clarendon Press: Oxford, 1984. Allen, L. C. J. Am. Chem. Soc. 1989, 111, 9003–9014. Allen, L. C. J. Am. Chem. Soc. 1992, 114, 1510–1511 and other articles. Jensen, W. B. J. Chem. Educ. 1998, 75, 817–828. (a) Dehlinger, U. Z. Metallkunde 1934, 26, 227. (b) Laing, M. A. Educ. Chem. 1993, 30, 160–163. Pauling, L. The Nature of the Chemical Bond, 3rd ed.; Cornell University Press: Ithaca, NY, 1960; p 100. Wilmshurst, J. K. J. Chem. Phys. 1959, 30, 561–565. Smith, D. W. J. Chem. Educ. 1990, 67, 559–562. Bratsch, S. G. J. Chem. Educ. 1988, 65, 223–226. von Szentpaly, L. J. Mol. Struct. 1991, 223, 71–81. Allen, L. C. J. Am. Chem. Soc. 1989, 111, 9115–9116. Mann, J. B.; Meek, T. L.; Allen, L. C. J. Am. Chem. Soc. 2000, 122, 2780–2783. Allen, L. C.; Capitani, J. F. J. Am. Chem. Soc. 1994, 116, 8810. Phillips, J. C.; van Vechten, J. A. Phys. Rev. Lett. 1969, 22, 705. Adams, D. M. Inorganic Solids; Wiley: New York, 1974; p110. Pettifor, D. G. Bonding and Structure of Molecules and Solids; Oxford University Press: Oxford, 1995; p 54. Reed, A. E.; Weinstock, R. B.; Weinhold, F. J. Chem. Phys. 1985, 83, 735–746. Garner, L. D.; Meek, T. L.; Patrick, B. G. J. Mol. Struct. (THEOCHEM) 2003, 620, 43–47. Greenwood, N. N.; Earnshaw, A. Chemistry of the Elements, 2nd ed.; Butterworth: Oxford, 1997; (a) p 555, (b) p 1177. (a) Pitzer, K. S. Acc. Chem. Res. 1979, 12, 271–276. (b) Pykko, P.; Desclaux, J.-P. Acc. Chem. Res. 1979, 12, 276–281. Shriver, D. F.; Atkins, P. W. Inorganic Chemistry, 3rd ed.; Oxford University Press: Oxford, 1999; p 362. Fowler, P. W.; Tole, P. J. Chem. Soc, Chem. Commun. 1989, 1652–1654. Goryunova, N. A. Chemistry of Diamondlike Semiconductors; ChapmanHall: London, 1965; pp 116, 122. Mann, J. B.; Meek, T. L.; Knight, E. G.; Capitani, J. F.; Allen, L. C. J. Am. Chem. Soc. 2000, 122, 5132–5137.


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Electronegativity and the Bond Triangle

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