A comparison of electronegativity series

Journal of Electron Spectroscopy and Related Phenomena, 46 (1988) 173-177 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

A COMPARISON

E. SACHER

OF ELECTRONEGATIVITY

173

SERIES

and J.F. CURRIE

Groupe des Couches Minces and Dbpartement de G&tie Physique, I&ColePolytechnique, Succursale ‘A”, Mont&al, Que’. H3C 3A7 (Canada)

C.P. 6079,

(First received 1 July 1987; in final form 8 September 1988)

ABSTRACT Several electronegativity series are calculated and compared with those previously calculated by others. Except for the Pauling electronegativities, there is general agreement among the various series. The differences between these and the Pauling values, particularly among the transition series, are shown to be due to problems with the thermodynamic approach on which the latter are based.

INTRODUCTION

Both the chemical and physical properties of a bond between two atoms are a function of the electron density distribution along that bond. The ability of an atom to influence that electron density distribution is called the electronegativity, defined originally by Pauling [l] as the power of an atom in a molecule to attract electrons to itself. Using the valence bond picture of the partial ionic character of covalent bonds, Pauling was able to formulate a thermodynamic approach which permitted the determination of single atom electronegativity values. The applicability of these electronegativity values was found to be severely limited for the following reasons: (1) the large number of computations on various atom-atom combinations, which led to a limited number of electronegativity values, made it evident that hybridization effects were averaged; (2) for several elements, the order disagreed with that determined experimentally; (3) as with all the other electronegativity series, the fact that the electron density distribution between two atoms is also influenced by the other atoms to which they are bound makes electronegativity values strictly applicable only to the elements. Subsequently, other views led to other electronegativity series, some even attempting to account for hybridization. Mulliken, for example, based his approach on a simple molecular orbital picture of ion production from a neutral pair to define [2] electronegativity as the sum of an atom’s ionization potential and electron affinity obtained in the correct valence state [3,4]. The Mulliken approach was subsequently extended by Iczkowski and Margrave [5]

n368-2n48mvm.~w

cl? 1988 Elsevier Science

Publishers

B.V.

174

as a power series of ionization potentials; while their approach lends little to the determination of electronegativity values, the accompanying text is incisive in its analysis of the general problem. Gordy and Orville-Thomas [6] used several different approaches to define electronegativities, among them the potential of a nuclear charge, partially screened by the orbiting electrons, on an electron at the covalent radius. Subsequently, Allred and Rochow [7, 81 expanded on this by defining electronegativity as the force rather than the potential; the force is obtained by multiplying the potential by e/r, where e is the electronic charge and r is the covalent radius. When both series are normalized to the Pauling values, they are virtually identical (although different from the Pauling values, as will be discussed later). Sanderson [C&11] calculated his electronegativity values as the average electron density of an atom relative to that of a hypothetical isoelectronic inert atom; the former value is easily calculable and the latter is obtainable on extrapolation. When these values are normalized to those of Pauling, they, too, are virtually identical to those of Gordy and Orville-Thomas [6] and Allred and Rochow [7, 81. This is, indeed, surprising for, as first noted by Iczkowski and Margrave [5], their different definitions necessitate their having different units. ELECTRONEGATIVITY

CORRELATIONS

The electronegativity scales already mentioned, as well as those to be discussed, are all found in Table 1. This table considers a representative 36 elements, chosen to give a realistic sampling of all groups (except the rare gases), and all electronic arrangements within groups. Readily available compilations were used to obtain ionization potentials (IPs) [12] and electron affinities (EAs) [13], although the former are also available as outer orbital binding energies [14]. As noted earlier, Mulliken [2] suggested that the electronegativity scale be based on the sum of IP and EA values. First, we found that both IP and EA correlate with electronegativity, as represented by the Allred-Rochow [7, 81 values. One obtains IP of: 0.879eV

=

(3.663 t 0.189) ~~~~~~~~~~~~~ + 2.010

(1)

and EA f 0.753eV

=

(0.856 + 0.200) XA1lre&koch,,w - 0.127

(2)

both with statistical significances greater than 0.9995, as indicated by correlation coefficient values and standard significance tables [15]. It is, in a sense, surprising that both IP and EA separately correlate with electronegativity but, this being so, it is no great surprise that their linear combination would also do so x + 0.297

=

(0.197 + 0.016) (IP + EA) - 0.123

(3)

175 TABLE 1 Electronegativity

values

Element

Atomic

IP

EA

number

Ll2l

u31

Electronegatwties Pauling

Gordy

Allred-

Sanderson

Mulliken

[ll

[6l

Bochow

[SW

@I

Eqn. (4a)

Eqn. (4b)

[7, 81 Li

3

5.392

0.620

0.98

0.96

0.97

0.86

1.06

1.05

1.06

C

6

11.267

1.264

2.55

2.52

2.50

2.47

2.35

2.53

2.55

N

7

14.649

3.04

3.01

3.07

2.93

0

8

13.618

1.461

3.44

3.47

3.50

3.46

2.85

3.13

3.15

3.337

3.98

3.94

4.10

3.92

3.96

4.07

4.12

1.31

1.16

1.23

1.42

F

3.39

9

17.416

Mg

12

7.646

Sl

14

8.151

1.244

1.90

1.82

1.74

1.74

1.73

1.74

176

P

15

10.980

0.767

2 19

2.19

2.06

2.16

2.19

2.47

2.48

S

16

10.360

2 075

2 58

2.56

2.44

2.66

2.33

2.29

2.32

Cl

17

13.020

3.614

3 16

3.00

2.83

3.28

3.15

2.94

300

K

19

4.341

0.502

0.82

0.82

0.91

0.74

0.83

0.78

0.79

SC

21

6.561

0.653

1.36

1.30

1.20

1.09

1.30

1.34

1.35

CT

24

6.765

1.66

1.50

1.56

1.35

Fe

26

7.900

1.83

1.64

1.47

cu

29

7.726

1.275

1.90

175

1.74

1.65

1.63

Ge

32

7890

lxl2

2.01

177

2 02

2.31

1.67

1.67

1.69

Se

34

9 752

2.021

2.55

2.35

2.48

2.76

2.20

2 14

2.17

Br

35

11850

3.367

2.96

2.68

2.74

296

2.87

2 65

2.70

Sr

38

5.694

0.95

0.92

0.99

096

Y

39

6.528

1.22

1.21

1.11

0.98

MO

42

7.099

2.16

1.60

1.30

1.24

Ru

44

7.366

2.20

1.42

1.40

Ag

47

7.574

1.93

1.42

1.72

I

53

10.457

3.057

2.66

2.36

2.21

2.50

2.54

2.30

2.35

CS

55

3.894

0.472

0.79

0.78

0.86

0.69

0.74

0.66

067

La

57

5.615

1.10

1.20

1.08

0.92

1.11

1.10

1.01

094

1.13

1.27

1.20

1.14

0.96

2.36

1.60

1.40

1.13

2.u)

1.52

1.26

2.54

1.42

0.995

EU

63

5680

LU

71

5.410

W

74

7.980

OS

76

8.700

AU

79

9.223

2.308 1.036

0 518

1.62

1.41 1.70 1.65

1.13 1.35 147

1.47

1.49 1.56 1.61

1.06 1.55

171

1.72

1.72

2.15

199

2.03

2.06

1.52

152

1.54

1.90

Bi

83

7.289

2.02

180

1.67

Ba

88

5.277

0.90

0.92

0.97

1.03

AC

89

6.900

1.10

1.10

1.00

1.44

Am

95

6.000

1.30

1.30

1.22

1.21

Lr

103

1.22

again with a statistical significance greater than 0.9995. The question of the best correlation of IP and EA may be answered performing a double linear regression. This leads to x f 0.262

=

(0.255 f 0.028) IP -

(0.016 + 0.087) EA -

0.318

by

(4a)

with a statistical significance greater than 0.9995. Note that the uncertainty in EA is greater than the coefficient, indicating that this term may be dropped x f 0.262

=

(0.255 f 0.028) IP - 0.318

(4b)

A comparison of the values in Table 1 generated by eqns. (4a) and (4b) indicates that the EA term adds an average 0.02 electronegativity units.

176

Fig. 1. A plot of the difference in Pauling [l] and Allred-Rochow versus atomic number, across the first transition series.

[7, 81 electronegativity

values

Except for the Pauling [l] electronegativity values, the data in Table 1 show minor variations, due to the approximations used in their definitions and the uncertainty in the original data’(EA values, for example, are notoriously uncertain, as seen in eqns. (2) and (4) and reflected in Table 1). There is little reason to choose among them, although the Allred-Rochow values [7,8] have achieved the status of acceptance. The Pauling values, however, are an exception: particularly among the transition elements, there are major differences with the other series. Figure 1 contains a plot of the difference in Pauling and Allred-Rochow values as a function of atomic number across the first transition series. The double hump, with its minima at Ca, Mn and Zn, is also characteristic of the relative ionic radii, and hydration and lattice energies of these elements [16]. The reason is thought to be the following: “the fact that electrons are entering d orbitals of different energies as we progress through a transition series has the effect of causing plots of various measures of thermodynamic stability . . . to be nonlinear.” [16]. The Pauling series, which is the only one based on thermodynamic considerations, is unique in showing this effect. Given the fact that there are other electronegativity series, which do not show this problem, and which show basic agreement among themselves, there is no further need to use the Pauling series. CONCLUSION

With the exception of the Pauling electronegativities, electronegativity series derived by several different methods are essentially identical when similarly normalized in spite of the fact that their different derivations carry different units. The Pauling values, on the other hand, differ from all these other compilations because they alone are based on thermodynamic data and are, thus, subject to orbital energy variations. ACKNOWLEDGMENTS

The authors wish to thank the Natural Sciences and Engineering Research Council of Canada and the Fonds pour la formation des chercheurs et l’aide a la recherce du Quebec for funding this work.

177 REFERENCES 1

8 9 10 11 12 13 14 15 16

L. Pauling, The Nature of the Chemical Bond, 3rd edn., Cornell University Press, Ithaca, NY, 1960, Chapt. 3. R.S. Mulliken, J. Chem. Phys., 2 (1934) 782; 3 (1935) 573, 586. W. Moffitt, Proc. Sot. London Ser., A, 202 (1950) 534,548. H.A. Skinner and H.O. Pritchard, Trans. Faraday Sot., 49 (1953) 1254. R.P. Iczkowski and J.L. Margrave, J. Am. Chem. Sot., 83 (1960) 3547. W. Gordy and W.J. Orville-Thomas, J. Chem. Phys., 24 (1956) 439. A.L. Allred and E.G. Rochow, J. Inorg. Nucl. Chem., 5 (1958) 264, 269. A.L. Allred, J. Inorg. Nucl. Chem., 17 (1961) 215. R.T. Sanderson, J. Chem. Educ., 29 (1952) 539. R.T. Sanderson, J. Am. Chem. Sot., 74 (1952) 4792. R.T. Sanderson, Inorganic Chemistry, Reinhold, New York, 1967, Chapt. 6, 24. A.J. Gordon and R.A. Ford, The Chemist’s Companion, Wiley-Interscience, New York, 1972, p. 82. J.E. Huheey, Inorganic Chemistry, 2nd edn., Harper and Row, New York, 1978, p. 46. T.A. Carlson, Photoelectron and Auger Spectroscopy, Plenum, New York, 1976, p. 337. E.S. Pearson, and H.O. Hartley, Biometrika Tables for Statisticians, Vol. I, Cambridge University Press, Cambridge, 1956, p. 138. F.A. Cotton and G. Wilkinson, Advanced Inorganic Chemistry, 4th edn., Wiley, New York, 1980, Chapt. 20.