Electronegativity and the Bond Triangle

Research: Science and Education

www.JCE.DivCHED.org • Vol. 82 No. 2 February 2005 • Journal of Chemical Education 325

The bond-type triangle is being used increasingly in un-dergraduate textbooks to illustrate the central importance ofelectronegativity and its influence on bond type (1a, 2). Ithas long been recognized that chemical bonds can be dividedinto three fundamental types: ionic, covalent, and metallic.van Arkel’s (3) depiction of the three bond types as the verti-ces of a triangle, with compounds or elements of intermedi-ate nature being located along the edges, was the first toattract widespread attention (Figure 1A).1 Ketalaar (4) fur-ther developed the bond triangle by placing compoundswithin it as well as on the edges (Figure 1B).

Recent work has focused on the rationalization of thebond triangle by using functions of electronegativity as thebasis for determining the positions of substances within it.Jensen (5), Allen et al. (6), and Sproul (7) all recognized theessential role of electronegativity and electronegativity dif-ference in determining the properties of substances. All ofthem concluded that the position of any binary compoundin the bond triangle could be specified by two coordinates:electronegativity difference (∆χ) and average electronegativ-ity (χav) (Figure 2). These authors noted that plotting a graphof ∆χ versus χav produces a triangular array with ionic com-pounds (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 Allensuggested that the bond triangle as defined above can be di-vided into covalent, ionic, and metallic regions with straightlines as boundaries.

In the triangles devised by each of these authors (Figure2), the vertices are occupied by Cs (metallic), F2 (covalent),and CsF (ionic); the elements lie along the metallic–cova-lent axis (∆χ = 0), while cesium compounds and fluoridesare found along the metallic–ionic and covalent–ionic edges,respectively. As observed by Jensen (5), the compounds ofany element other than Cs or F lie on two diagonal lines,parallel to the metallic–ionic and covalent–ionic edges, whichmeet at the position occupied by the element itself. The leftline (with negative slope) includes compounds of the elementwith elements less electronegative than itself, while the rightline (with positive slope) includes the compounds of the ele-ment with more electronegative elements. All compoundsformed by a given pair of elements occupy the same posi-tion.

Sproul (7b) did the most extensive work on quantifica-tion of the bond triangle, plotting values of ∆χ versus χav for311 binary compounds and observing excellent correlationbetween position on the graph and bond type as specified byWells (8). He excluded compounds whose bond type was saidby Wells to be “ambiguous or questionable”, such as “semi-metallic” compounds. Sproul examined 15 different elec-tronegativity scales and found that the best agreementbetween position and bond type was obtained when Allen’sspectroscopic electronegativity (9)—later called configurationenergy (10)—was used,2 only 9 of the 311 compounds be-ing “misplaced” from their specified regions. He found that,for his selected compounds, the triangle could be divided intocovalent, ionic, and metallic regions by straight lines, paral-lel to the metallic–ionic and covalent–ionic edges of the tri-angle (Figure 2 bottom). These boundaries were defined bythe equations (with χ values converted to Pauling units):

av 0 5 1 60∆. .= +χ χCCovalent Ionic:−

Metal Nonmetal: av = − +− χ χ0 5 2 28. .∆

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

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

A

B

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326 Journal of Chemical Education • Vol. 82 No. 2 February 2005 • www.JCE.DivCHED.org

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






Comments and Limitations

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

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

2. All elements with electronegativity equal to or less thanthat of Al would form only ionic compounds with el-ements more electronegative than P; the amphotericmetals Al, Be, Cd, and Zn form covalent (or interme-diate) compounds with many nonmetals.

3. No element that has an electronegativity less than thatof H would display anionic character in any com-pound, even with cesium; compounds of P and themetalloids Te and Po with the group 1 and group 2metals are believed to have considerable ionic charac-ter, though the tellurides and polonides are not wellcharacterized.

4. Any compound formed between two elements less elec-tronegative than H would be metallic; some of theseelements are metalloids, and form semiconductors thatare not “well-defined” and do not display metallic con-ductivity. The “III–V” compounds are the best knownof these.

It must be noted that the distinction among bond types,especially for polymeric substances, is quite arbitrary and itis seldom possible to categorize compounds definitively asbeing 100% ionic, covalent, or metallic. This was recognizedby 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) “sharpboundaries separating substances containing metallic, cova-lent, and ionic bonds”. In fact, most compounds exhibit amixture of two types of bonding and display some charac-teristics of both—or even of all three—types, as exemplifiedby the “III–V” semiconductors and some Zintl phases. Thusthe categorization of compounds as ionic, covalent, or me-tallic is a considerable oversimplification, and nearly all com-pounds are really intermediate in character. It would be moreaccurate to say that the elements and many compounds canbe categorized as predominantly ionic, covalent, or metallic,but most of them have some characteristics of at least twobond types.

Jensen (11) also points out that the van Arkel–Ketalaartriangle is a bond triangle and the accurate specification ofcompounds and elements would require another dimensionsuch as is found in Grimm’s tetrahedron (12), with van derWaals forces as the fourth vertex and substances with inter-mediate degrees of polymerization occupying levels above thearray of three-dimensional polymers represented by the van

Arkel–Ketalaar triangle. The error of attempting to correlatea property of bulk matter with the charge distribution in anisolated molecule is further emphasized by the fact that somecompounds, although predominantly covalent molecular sub-stances in the gas phase, consist of polyatomic cations andanions in condensed phases. Well-known examples are N2O5and PCl5.

Despite these limitations, the position of a binary com-pound in the bond triangle still gives a good indication ofthe type of bonding that occurs in it and the bond trianglegives some very useful insights (Figure 3). First is the realiza-tion that bond type depends on both ∆χ and χav, which isconfirmed by the positive slope of the ionic–covalent bound-

Ele

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PU

Average Electronegativity / PU

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CM

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2

1

00 1 2 3 4 5

I

CMD

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1

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Average Electronegativity / PU0 1 2 3 4 5

I

CMDC/I

M

Ele

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tivity

Diff

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ce /

PU 5

4

3

2

1

0

Weighted Average Electronegativity / PU0 1 2 3 4 5

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

A

B

C






ary and the negative slope of the metal–nonmetal boundaryin Sproul’s and Allen’s representations (Figure 3B). Sproul (7d)points out that, if ionic character were associated only with alarge ∆χ, there would be a horizontal line at some critical ∆χvalue such as the frequently cited 1.7 Pauling units (13), sepa-rating ionic species from others.3 Furthermore, if metallic char-acter were associated only with a small χav, there would be avertical line at some critical χav value—perhaps between thoseof Pb, the most electronegative metal, and Si, the least elec-tronegative nonmetal—separating metals from nonmetals.

Although the above authors have demonstrated that bondtype depends on both ∆χ and χav, none of them has offeredan explanation for the manner in which ionic–covalent ormetallic–nonmetallic character varies with both parameters.We now address these matters. We will also show that thereare gaps between the regions occupied by predominantly ionicand predominantly covalent substances, and between metalsand nonmetals, which are occupied by substances generallyregarded 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 withvery similar ∆χ values, ionic character decreases as χav in-creases. This variation results from the fact that partial charge,rather than ∆χ alone, is the critical parameter in determin-ing ionicity. Although the unequal distribution of charge hasits origin in ∆χ, the magnitude of the partial charge is alsodependent on χav. We will show that partial charge is in factclosely related to the ratio ∆χ:χav.

For diatomic singly bonded molecules of general formulaAB, Wilmshurst (14) suggested that the partial charge on A(qA) is given by,

AB A

B A

q =−

+

χ χ

χ χ (1a)

where χA and χB are the electronegativities of elements A andB. Thus

Aav

q =χ

χ

∆

2(1b)

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

where AA

A

A Bq =−

=χ χ

χχ

χ χ2,

χχ χA B+ (2a)

thus:

χ

χ

χ χ

χ χ χ

χ χ

AA

A B

A B A

B A

= − =+

−

=−

χ χA B+

q 12 1

1

==∆χ

χ2 av

(2b)

Identical expressions are obtained using the methods ofBratsch (16) and von Szentpaly (17), if one makes the ap-proximation that the charge coefficient (16) or atomic hard-ness (17) of an atom is equal to its electronegativity.

In Allen’s modified Lewis–Langmuir method (18), fordiatomic molecules with single bonds:

= − −A Group No.No. ofUnpairedElectrons

q 22χ

χ χA

A B+(3a)

Thus, if neither atom has a formal charge:

12

2

χ

χ χ

χ χ

χ χ

χ

χAA

A B

B A

A B av= −

+=

−

+=q

∆(3b)

According to all of these equations, the partial chargesof bonded atoms (hence ionic character of a bond) increasesas the ratio ∆χ:χav increases, and all compounds whose at-oms have the same partial charges will have the same ∆χ:χavratio. Thus in a bond triangle with axes ∆χ and χav, all com-pounds with the same degree of ionic character will lie on astraight line, passing through the origin (∆χ = χav = 0) whenextrapolated, with slope equal to 2q (Figure 3C). One suchline will have a slope equal to the critical q value above whichcompounds are predominantly ionic, and will correspond tothe “ionic–covalent” boundary.

In fact, for diatomic molecules with multiple bonds thepartial charge is equal to the ∆χ:2χav ratio multiplied by thebond 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 twicethe partial charge per bond and gives a good indication ofthe extent of ionic character in the bond.

Metals versus Nonmetals: Band Gap

The critical parameter in determining metallic behavioris band gap (Eg), since conductivity is proportional toexp(�Eg�kT). Thus substances with very small band gaps aremetallic conductors, while those with large band gaps are in-sulators. For the elements, it has been established (19) that

noretcarahCcinoIfoecnednepeD.1elbaT χχχχχ va

ecnatsbuS ∆χ UP/ χ va UP/ ∆χ:χ vatnanimoderP

epyTdnoB

lCiL 69.1 98.1 730.1 cinoI

FH 98.1 52.3 285.0 tnelavoC

IiL 54.1 46.1 488.0 cinoI

NlA 54.1 43.2 026.0 etaidemretnI

FrB 05.1 44.3 634.0 tnelavoC

iBiL 01.1 64.1 357.0 cillateM

eSgM 31.1 68.1 806.0 cinoI

OC 70.1 80.3 743.0 tnelavoC

NO :et χ fermorf)stinugniluaP(seulav .91






χ alone can be used to determine metallic character, as thewidth of an energy band is inversely proportional to the en-ergy of the level from which it arises. All metals have χ val-ues less than 1.92 (Si), while all nonmetals have χ valuesgreater than 2.21 (As); the metalloids occupy the narrowrange of χ between these values.

For compounds, the extent of metallic character dependson both ∆χ and χav. Sets of compounds with very similaraverage electronegativities display increasing band gaps andthus decreasing metallic character as electronegativity differ-ence increases, as seen in Table 2. This was noted by Allenand Capitani (20) and is consistent with equations, devisedby various authors, that define the band gap.

Phillips and van Vechten (21) suggested that, for binarycompounds with a total of eight valence electrons per ABunit, the band gap in crystalline substances is composed ofionic (Ei) and covalent (Ec) contributions according to:

gE 22 2 2= +E Ec i (4)

Adams (22) redefined these terms in his equation,

2 2 2= +E E Cg h (5)

where C, the charge transfer energy, is proportional to ∆χ,and Eh, the homopolar energy gap, (like Ec in eq 4) is de-fined as the energy difference between the center of the va-lence band and that of the conduction band. Eh is a measureof the effectiveness of interaction between atoms, and thusshould depend on the same factors as χ and χav.

For s-valent diatomic molecules, Pettifor (23) gives theequation,

2 2 24= + ( )w h EAB ∆ (6)

where wAB is the separation between bonding and antibond-ing states, h is the bond integral and is related to the averageatomic potential, and E, the free atomic energy level, is ap-proximately equal to χ. Each of these equations is of the formE 2 = a2 + b2, where a is related to the average energy of theatoms or to the effectiveness of their interaction (hence toχav) and b is related to an energy difference (hence to ∆χ).This suggests that substances with the same band gap will lieon a line with the same values of (c1∆χ2 + c2χav

2). Such aline would be a curve —a segment of a circle if ∆χ and χav

contribute equally to band gap, or of an ellipse if they donot. Thus the metal–nonmetal boundary would be the curvefor which the E value corresponds to the largest band gapthat allows metallic conduction (Figure 3C).

It must be realized that ∆χ and χav are derived fromproperties of isolated atoms whereas band gap is a propertyof an aggregated solid, so a rigorous relationship betweenband gap and these parameters is unlikely. Still, qualitativeagreement has been observed—Jensen (5) reported a “quick-and-dirty” test with a crude probe-buzzer-battery device thatshowed a curved boundary, in a graph of ∆χ vs χav, betweensubstances that showed detectable conductivity and sub-stances that did not.

Polyatomic Molecules: Weighted Average χχχχχ

One anomaly that arises in this representation of bondtype is that all of the compounds formed by a given pair ofelements occupy the same position on the graph. In fact, bondtype can vary with the valence of the central atom. For ex-ample, tin(IV) halides are predominantly covalent, as are thefew stable ones of lead(IV), with all but the fluorides nor-mally existing as monomeric molecules. However, lead(II) ha-lides are ionic and those of tin(II) have substantial ioniccharacter.

For polyatomic molecules, the relationship among par-tial 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 thepartial charge on each terminal atom decreases as the valenceof the central atom increases. This suggests that the simpleχav may not be the appropriate parameter to use. We pro-pose a weighted average electronegativity, defined for AmBnas:

=+m n

wavAχχ χχB

m n+(7)

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

χ χχ χA B

m n

m n=

+( )+

∆ ∆

wavχ (8)

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

χ

χ χA

A

qn

n

=−

+

∆2 1

BB(9)

—but nevertheless ∆χ:(χav)w serves to discriminate betweencompounds of the same two elements with different stoichi-ometries. From eq 8, such compounds will have the same∆χ but different (χav)w values. (Using the fluorides of lead asexamples, the (χav)w values for PbF4 and PbF2 are 3.73 and3.41 Pauling units.) Each compound thus occupies a uniqueposition in the triangle. Because of the positive slope of thecovalent–ionic boundary, this can result in two such com-pounds being in different bonding regions.

htiwretcarahCcillateMfonoitairaV.2elbaT ∆χχχχχ

ecnatsbuS χ va UP/ a ∆χ UP/ a dnaBVe/paG ecnatcudnoC

eG 99.1 0 7.0 b rotcudnocimeS

sAaG 89.1 64.0 5.1 b rotcudnocimeS

eSnZ 10.2 38.0 8.2 b rotalusnI

nS 28.1 0 00. 0 8. bb lateM

bSnI 28.1 33.0 2.0 c rotcudnocimeS

eTdC 48.1 46.0 5.1 c rotcudnocimeS

eSgM 58.1 31.1 ? 8. b rotalusnI

rBiL 08.1 88.1 ? 8. b rotalusnIa fermorf)stinugniluaP(seulaV .91 b feR .b1 c feR .03






Boundaries: Well-Defined Compounds and Elements

The selection of compounds for establishing boundariesbetween predominant bond types should be restricted to bi-nary compounds that have been isolated and purified, haveknown structures, and contain only heteronuclear bonds. Thislast criterion excludes many types of compounds, for example:

(a) Compounds with discrete dinuclear ions, which couldbe described as both ionic (since they contain ions)and covalent (since some of the ions are polyatomic).

(b) Molecular compounds, including clusters, which con-tain both homonuclear and heteronuclear covalentbonds.

(c) Zintl compounds, which display some degree of me-tallic interaction as well as containing simple cationsand extended polyatomic networks of covalentlybonded atoms, each with a formal negative charge (1c).

(d) The group 1 compounds M3E of the group 15 ele-ments As, Sb, and Bi, whose structures feature homo-nuclear intermetallic bonding as well as heteronuclearinteractions (26a). The group 2 compounds M3E2 ofthese elements also display some metallic properties.

(e) The suboxides of rubidium and caesium, which con-tain cationic clusters of identical atoms, such as M9

4+

and M116+, associated through metallic interactions

(1c).

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

wood and Earnshaw (26) as being predominantly of one type.A plot of ∆χ vs (χav)w (Figure 4) was constructed for thesecompounds; the 37 “well-defined” elements of these groups—omitting the metalloids—were also included, to help es-tablish the covalent–metallic boundary. All of these speciesare listed in the Supplemental Material.W The electronega-tivity values used were those of Allen et al. (19), expressed inPauling units. For polyatomic molecules the weighted aver-age electronegativity defined by eq 7 was used rather thanthe simple average.

In this graph a triangular array of points is still obtained,but there are some significant differences from the trianglesdevised by other workers:

1. The compounds of a given element no longer lie on asingle line (Cs and F) or a pair of converging lines (allother elements). Instead a number of lines, converg-ing at the position of the element, are obtained; forexample, all monofluorides lie on one line, alldifluorides on another line, and so forth.

2. Some of these lines (polyfluorides, caesium compoundsof multiply-charged anions, etc.) extend outside theboundaries of the Cs–CsF–F2 triangle. This necessi-tates a relocation of the vertices, to produce a trianglethat includes all compounds. The metallic and cova-lent vertices can be defined as the points with (∆χ =0, (χav)w= 0) and (∆χ = 0, (χav)w = 5); the ionic vertexwould then be at (∆χ = 5, (χav)w = 2.5). This enlargedtriangle includes all well-defined compounds of themain-group elements. Figure 4 shows that there is gooddiscrimination among predominant bond types.

Figure 4. Bond triangle for well-defined substances: circles = mainly ionic, squares = mainlycovalent, and triangles = mainly metallic.

Weighted Average Electronegativity / PU

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negativ

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iffere

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/ P

U

5.0

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

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






Covalent–Ionic Boundary

Compounds specified as covalent and those specified asionic are well separated by a straight line with the equation∆χ = 0.62(χav)w, as shown in Figure 4. This suggests that bi-nary compounds with partial atomic charges greater than±0.31 (per bond) are predominantly ionic, while those withqA values less than 0.31 are predominantly covalent. This find-ing contrasts with Pauling’s implication (13) that 50% ioniccharacter marks the dividing line.

There is a small triangular region adjacent to the “cova-lent–ionic” and “covalent–metalloid” boundaries—the thirdside being the dashed line in Figure 4—which contains veryfew compounds specified as ionic or covalent. We will ob-serve later that most of the compounds generally regarded asbeing intermediate between ionic and covalent occupy thisregion. A few compounds do not appear in their expectedregions of the triangle; most of these can be categorized asfollows:

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 de-scribed above.) It is possible that the misplacement ofthese “subvalent” compounds arises from the defini-tion of χ as the average one-electron energy (εl) of allof the valence electrons of an atom (7); for an atomwith the configuration snpm:

χε ε

=+

+

n m

n ms p

(10)

The predominately ionic character of these compoundssuggests that the metal atoms have electronegativitiesconsiderably lower than those obtained from eq 10.This would be consistent with the s electrons of themetal taking little (if any) part in bonding, so that in-cluding εs gives erroneously high χ values for these el-ements, hence low ∆χ and high (χav)w values for theircompounds with nonmetals. This would be especiallypertinent for compounds of Tl(I), Pb(II), and Bi(III),whose 6s orbitals are considerably stabilized by rela-tivistic effects (27). (Apparently all subvalent ioniccompounds are misplaced, except SnO, PbO, PbF2,and TlF). Only two other compounds specified asionic—MgI2 and MgSe—are in the “covalent” section.

2. The only compounds specified as covalent that appearin the “ionic” region are the polymeric species HgO,PbF4, SnF4, SnF2, and GeF2. This is another instanceof the qualitative nature of the agreement between pre-dominant bond type and location in the bond triangle.As noted above, the ratio ∆χ:(χav)w is not directly pro-portional to partial charge,5 even in polyatomic mol-ecules.

Metal–Nonmetal Boundary

It is very difficult to establish the border between met-als and nonmetals, since very few stoichiometric binary com-

pounds are known to be metallic. There is a substantial gapin Figure 4 between compounds specified as metals and thosespecified as nonmetals. The borders of these two regions inthe triangle appear to be defined by curved lines, which couldwell mark the boundaries of a metalloid or semiconductorregion. However, linear boundaries cannot be ruled out atthis stage

The alloys LiBi and NaBi are very close to the interme-diate, metalloid region in spite of having “typical alloy struc-tures” (26a). They would be in the middle of the “metallic”region if the electronegativity of Bi were assessed only fromthe energy of its 6p orbitals, 0.599 Rydberg = 1.38 PU (19).

“Intermediate” Substances

The boundaries between bonding regions can be definedmore closely with the aid of another graph of ∆χ versus (χav)wvalues, plotted in Figure 5 for 62 substances (8 elements and54 compounds) that are usually described as “intermediate”.These are also listed in the Supplemental Material.W Theyare further categorized as follows:

Covalent–Ionic (23 Compounds)Eighteen of these compounds are within the small tri-

angular area described above, separated from the “covalent”region by the dashed line in Figures 4 and 5. Of the otherfive, AlN is on the “covalent–ionic” boundary, two (Cd3N2and Zn3N2) are in the “ionic” region although quite close tothe “covalent–ionic” boundary, and two (SnS and PbS) arein the “covalent” region but very close to the triangular areacontaining most of the intermediate compounds. ZnSe, BeSe,CdSe, and Be2C are very close to the metalloid region; Shriverand Atkins (28) describe Be2C (and Al4C3) as “borderlinebetween saline and metalloid”, and an ab initio calculation(29) suggests that Be2C is largely ionic. CdSe is a semicon-ductor with a band gap of 1.7 eV (30).

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

Weighted Average Electronegativity / PU

Ele

ctro

ne

ga

tivity

Diff

ere

nce

/ P

U

0.0

0.5 1.0 1.5 2.0 2.5 3.0

0.5

1.0

1.5

2.0

2.5






Covalent–Metallic (34 Substances)The eight metalloid elements and 17 of the 26 “cova-

lent–metallic” compounds are in the metalloid region definedabove. 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 ofAs, Sb, and Bi well inside of the “covalent” region seems veryanomalous.

Ionic–Metallic (5 Compounds)These are also in the metalloid region. The somewhat

saltlike (26b) intermetallic compound CsAu, containing atransition metal with electronegativity 1.92 PU (31), wouldbe on the metal–nonmetal boundary.

Thus the diagram for intermediate substances indicatesthat:

1. The metalloid–nonmetal boundary is curved. Astraight line, drawn from the metalloid–nonmetal bor-der of the elements along the edge of the region occu-pied by compounds specified as covalent and ionic,places most known semiconductors among the pre-dominantly covalent compounds; a straight line be-tween covalent compounds and semiconductors placesseveral predominantly ionic compounds—the iodides,hydrides, sulfides, and selenides of the group 1 met-als—among the semiconductors.

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

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

Summary

1. The dependence of bond type on the two parameters∆χ and (χav)w is examined. It is shown that, for di-atomic molecules,

(a) The extent of ionic character in a bond dependson the partial charges on the atoms, which for diatomicmolecules is proportional to the ratio ∆χ:(χav).

(b) Metallic character is governed by the gap betweenthe highest occupied molecular orbital and the lowestunoccupied molecular orbital, which is related toc1(∆χ)2 + c2(χav)2.

2. These relationships are responsible for the shapes ofthe covalent–ionic and metal–nonmetal boundaries inthe bond triangle. The former is a straight line, whilethe latter is a curve.

3. The critical values of partial charge and band gap atwhich the boundaries occur may be estimated empiri-

cally by optimizing the sorting of a set of elements andbinary compounds that have been qualitatively char-acterized as being predominantly ionic, predominantlycovalent, or predominantly metallic in their bonding.Such a sorting procedure is at best onlysemiquantitative, since we have no independent quan-titative measure of predominant bond character.

4. Compounds of intermediate bond type also occupyspecific sections of the triangle.

(a) Most metalloids and semiconductors occupy anarea bounded by two curves, one separating them frommetals and the other separating them from insulators.

(b) Most compounds generally regarded as interme-diate between ionic and covalent occupy a small, nearlytriangular region adjacent to the covalent–ionic andcovalent–metallic boundaries.

5. In spite of the limitations mentioned above, the posi-tion in the triangle of a binary compound of maingroup elements gives a reasonable indication of its pre-dominant bond type. Lecturers and textbook writersshould bear the limitations in mind and point out thatthe great majority of compounds contain bonds thatare in fact intermediate between two (or more) types,even if they are predominantly of one kind. The exist-ence of well-defined intermediate ionic–covalent andmetal–nonmetal regions of the triangle, both of whichcontain very few species having one predominant bondtype, is also notable.

6. Applicability of the bond triangle appears to be lim-ited to simple binary compounds. Even for those, theclassification of Zintl compounds and others contain-ing polyatomic ions, and of suboxides and other clus-ter compounds, presents some difficulties. Suchcompounds clearly contain at least two distinct typesof bonding, and the bond triangle in its present formcannot represent this.

7. The usefulness of the bond triangle for categorizingcompounds of the main-group elements may be ex-tended by the use of weighted average electronegativi-ties to allow distinction between compounds of thesame elements with different stoichiometries. In suchcases a higher valency for the central atom leads togreater covalent character and the compounds mayhave different bond types.

WSupplemental Material

A list of the substances specified as being one predomi-nate type or an intermediate type are available in this issueof JCE Online.

Acknowledgments

The authors are grateful to L. C. Allen of PrincetonUniversity for the insights obtained in many stimulating dis-cussions and to the reviewers for a number of helpful com-ments and suggestions.




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Notes

1. Jensen (11) has pointed out that triangles of this type canbe traced back to the work of Grimm and Fernelius in the period1928–1936.

2. In fact, most of the major electronegativity scales show ex-cellent correlation with one another and with Sproul’s data set. Al-though we will use the Allen scale in this article, any of thecommonly used ones would give similar results.

3. Pauling (13) in fact gives this ∆χ value as the one that re-sults in 50% ionic and 50% covalent character.

4. The data set was restricted to main-group elements andtheir compounds at this time; the d-block metals and their com-pounds will be examined in a subsequent article.

5. In fact the atomic charges per bond in these compoundshave all been calculated by a modified Lewis–Langmuir-type equa-tion (25) as being substantially less than the ∆χ:(χav)w ratios calcu-lated from their empirical formulas. In all cases the charge per bondis less than 0.31 in the polymer.

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Electronegativity and the Bond Triangle