Recent developments in the application of the quantum mechanics to problems of molecular structure1 have indicated that the properties of a bond between two atoms often are determined mainly by one single-electron orbital wave function for each atom, and are not strongly affected by the other atoms in the molecule; for when the wave function for a molecule containing single covalent bonds is set up with the use of single-electron orbital wave functions, it is found that each bond function tends to overlap to the maximum extent the other function involved in one bond, and to avoid overlapping all others, so that the resonance integrals other than those characteristics of the bonds are small. The empirical evidence of interatomic distances supports this view; it has been possible to formulate a set of covalent radii for use in purely covalent molecules (in which each atom forms covalent bonds to a number determined by its position in the periodic system) which accounts satisfactory for observed distance in molecules to which a single Lewis electronic structure can be assigned.2 It has also been found that changing the covalence of an atom, and hence the nature of the bond function, produces a change in the radius.3
Independence of the bonds in a molecule would require that the total energy of formation of the molecule from separate atoms be expressible as the sum of constant energy terms characteristic of the various bonds. This is found to be nearly true for molecules to which a single Lewis electronic structure can be assigned, the deviations from constancy of bond energy rarely exceeding 2 or 3%. Data on the heats of formation and heats of combustion of gaseous molecules may accordingly be used to evaluate the energies of various bonds. This procedure is adopted in the following pages. It is then shown that the energies of bonds, when discussed with the aid of the postulate of the additivity of the energies of normal covalent bonds, throw much light on their nature, in particular on the amount of ionic character possessed by them, and permit the localization of 1 Linus Pauling, THIS JOURNAL, 53, 1367, 3225
(1931) ; 54, 988 (1932) ; J. C. Slater, Phys. Rev., 37, 481
(1931) ; 38, 1109 (1931) ; F. Hund, Z. Physik, 73, 1, 565
(1932). 3571 atoms on an "electronegativity map," with the aid of which their properties may be conveniently discussed. It is also found that bond energies provide evidence in regard to a number of questions relating to the structure of simple molecules, such as O4, O3, P4, etc. Extreme Ionic Bonds and Normal Covalent Bonds. -- Before discussing the nature of actual bonds it is desirable to specify the sense in which the terms ionic and covalent will be used. Early discussions of molecules such as the hydrogen halides treated them as consisting of ions which deformed each other to some extent. Now the wave functions corresponding to the normal and all excited states of F¯, for example, form a complete orthogonal set, so that any electronic structure of the HF molecule, even a normal covalent structure, could be accurately represented by a wave function built up from the wave functions for F¯, the contributions of excited states being considered to result from the deforming action of the proton. If, then, we are to distinguish at all between ionic bonds and bonds of other types, some arbitrary decision as to the extent to which excited ionic states are to be considered in constructing wave functions must be made. A number of phenomena formerly explained qualitatively as due to mutual polarization and deformation of ions have been quantitatively accounted for in other ways, and it has become evident that deformation of ions does not have the importance in determining the properties of molecules that it was formerly ascribed. Consequently, I prefer, in an approximate treatment, to consider only states in which electrons occupy the most stable orbits in atoms or ions, and so to select for the wave function represented an extreme ionic molecule a function formed from those for normal undeformed ions. A bond between two identical atoms, as H : H, C : Cl, C : C, etc,. may be considered to be a normal covalent bond, involving a pair of electrons and two single-electron orbital wave functions, one for each atom. The wave function representing it may not be closely approximated by a function of the Heitler-London type, y(1)j(2) [minus] j(1)y(2), but may involve ionic terms j(1)j(2) and y(1)y(2), corresponding to A+A¯ and A¯A+, these two occurring, of course, with the same coefficient. The contribution of these terms to the normal state of the hydrogen molecule has been discussed by Slater.4 In the wave function representing the bond between unlike atoms A and B the terms corresponding to A+B¯ and A¯B+ will occur with the same coefficient, equal to that for A : A or B : B, if the two atoms have the same degree of electronegativity. Such a function may be called a normal covalent bond wave function, and the bond a normal covalent bond. If one atom is more electronegative than the other, the wave function can be formed by adding to the normal covalent bond wave function an additional ionic term. 4 J. C. Slater, Phys. Rev., 35, 509 (1930). 3572 The Additivity of the Energies of Normal Covalent Bonds. The Hydrogen Halides and the Halogen Halides. -- It is found that there exists a convincing body of empirical evidence in support of the postulate5 that the energies of normal covalent bonds are additive; that is A : B = 1/2 {A : A + B : B} Where the symbol A : B means the energy of the normal covalent bond between A and B, etc. The energy of a normal covalent bond between A and B would be given by the integral [integral sign] y*Hydt, with y the normalized normal covalent wave function. Inasmuch as the energy integral for any wave function for a system must be equal to or greater than the energy of the lowest state of the system, the energy of the actual bond between A and B must be at least as great as that for a normal covalent bond.
3573
2O = O2 + 5.09 v.e. Some doubt has been thrown on the value 9.1 v.e. for the dissociation energy of N2 by the recent experiments of Tate and Lozier,8 whose interpretation 7 Values of thermal quantities used throughout this
paper are from "International Critical Tables," Landolt-Börnstein, or Kharasch's
compilation of heats of combustion, Bur. Standards J. Research, 2,
359 (1929) except where otherwise indicated. 3574 of their results has in turn, however, been criticized by Arnot.9 The value 6.61 v.e. for the heat of sublimation of graphite to normal carbon atoms is very uncertain, and the assumed value of 1.00 v.e. for the excitation energy to the 2s2p3 5S state is also uncertain. It is not essential for the discussion of deviations from additivity that these energy quantities be known; but it is convenient to deal with definite values for bond energies, even though they are relative to an arbitrarily chosen starting point, so that the values given have been used in this paper. When accurate values of these quantities become known, the bond energies can be easily corrected accordingly. Compounds of Oxygen and Nitrogen. -- From the heat of formation of water from atoms 2H + O = H2O(g) + 9.493 v.e. the H : O bond is found to have the energy 4.747 v. e. The equation10 H2O2(l) = H2O(l) + (1/2) O2 + 1.02 v. e. Combined with the heat of vaporization of H2O2, 0.50 v. e., lead to 2H + 2O = H2O2(g) + 10.99 v. e. Making use of the postulate of the constancy of bond energies, we subtract 4.75 v. e. for each H : O bond to obtain 1.49 v. e. for the O : O bond. The 1S state of the oxygen molecule, 1.62 v. e. above the normal state, probably corresponds to a double bond between the two atoms. This gives 3.47 v. e. for O::O. From the heat of formation of ammonia, 0.475 v. e. , we obtain N + 3H = NH3 + 11.685 v. e. And the value 3.895 v. e. for the N : H bond. The heats of formation of OF2 (-0.40 v.e.), NF3 (1.13v.e.), Cl2O (-0.79 v.e.) and NCl3 (-2.38 v.e.), lead to the values 2.48 v.e. for O : F, 3.29 v.e. for N : F, 2.12 v.e. for Cl : O and 1.95 v.e. for N : Cl. Compounds of Carbon. -- Heats of combustion of diamond and the aliphatic hydrocarbons show, as was pointed out by Fajans,11 that the postulate of the constancy of bond energies is not accurate, for assuming that the H : C bond energy is the same in the higher members of the series as in methane, a value for the C : C bond energy is obtained which is 0.2 v.e. lower than that from diamond. It is difficult to decide how to treat this discrepancy. I have arbitrarily chosen to ignore diamond. The values H : C = 4.34 v. e. and C : C = 3.60 v. e. then give good agreement with experiment for the aliphatic hydrocarbons, as is seen by comparing the heats of formation (Eobs.) of gaseous molecules from atoms as calculated from heats of combustion with the sum of the bond energies (Ecalcd.). 9 F. L. Arnot, Nature, 129, 617
(1932). 3575
Similar calculations for saturated cyclic hydrocarbons show that a three-membered ring is unstable to the extent of over 1 v. e., larger rings showing little strain. The table compares observed heats of combustion with those calculated from bond energies.12
Heats of combustion of gaseous hydrocarbons containing double bonds lead to the average value 6.46 v.e. for C :: C.
Heats of combustion for hydrocarbons containing triple bonds are uncertain. Thomsen's values lead to C ::: C = 8.68 v. e.
It is interesting to note that the unsaturation of a double bond amounts to 0.74 v. e., this being the energy liberated by a reaction leading to the formation of two carbon-carbon single bonds in place of a double bond. For a triple bond the unsaturation is 2.1 v. e. Five primary alcohols give an average of 3.56 v. e. for C : O, with a maximum deviation of 0.10 v. e., and six ethers give 3.55 v. e., with a maximum deviation of 0.07 v. e. Secondary and tertiary alcohols seem to be 0.3-0.5 v. e. more stable than corresponds to this C : O value. In view of the agreement between ethers and primary alcohols, we select C : O = 3.55 v. e. Primary, secondary and tertiary amines give the following values for C : N, Thomsen's values of heats of combustion being used. 12 The heat of combustion of ethylene oxide, C2H4O, combines with C : O = 3.55 v. e., shows the three-membered ring involving oxygen to be unstable to the extent of 0.67 v. e. 3576
Neglecting the possibility that the bond energy in primary amines be slightly less than in secondary and tertiary amines, we take the average value 2.88 v. e. for C : N. Cyanogen, acetonitrile and hydrogen cyanide (using Thomsen's value for heats of combustion of the first two) lead to 8.86, 8.98 and 8.74 v. e., respectively, for C ::: N. The average of these, 8.86 v. e., is very nearly the mean of C ::: C = 8.68 v. e. and N ::: N = 9.10 v. e. (in N2). Heats of combustion of fluorine-substituted hydrocarbons give C : F = 5.40 v. e. as the average of eight values, maximum deviation 0.35 v. e. Twelve chlorine compounds give an average of 3.41 v. e. for C : Cl. The same value is obtained from the heat of formation of CCl4. Three bromine compounds (heats of combustion from Thomsen) give C : Br = 2.83 v. e., and two iodine compounds, CH3I and C2H5I (Thomsen), give C : I = 2.2 v. e. The last two values are uncertain. Other data, obtained by Berthelot and by Roth and Macheleldt and quoted by Swietoslawski,13 give the value 2.45 v. e. for C : I. Bond Energies and the Relative Electronegativity of Atoms. -- In Table II there are collected the energies of single bonds obtained in the preceding sections. One additional value, obtained by a method to be described later, is also included: 1.44 v. e., for N : N. Under each bond energy is given the value for a normal covalent bond, calculated from additivity, and below that the difference D. It is seen that D is a positive in twenty of the twenty-one cases. The exception, C : I, may be due to experimental error, and be not real. Regularities observed in the D-values suggest that it is possible to make a rough assignment of the atoms to positions along a scale representing degree of electronegativity, with the assumption that D is a function of the linear separation of the loci of the two atoms on the scale, in the way that genes are mapped in a chromosome from crossover data. It is to be observed that the values of D1/2 are approximately additive (these values are givenD). For example, the sum of D1/2 for H : A and A : F is 2.05, 2.06, 1.91, and 2.06 for A = C, N, O, and Cl, respectively. We accordingly write
with D measured in volt-electrons, and construct the scale shown in Figs. 3 and 4 on this basis. The reliability of the method is indicated by Fig. 3, in which four distinct procedures are illustrated. The coördinates of the elements on this scale are given in Table III. 13W. Swietoslawski, "Thermochemie," Akademische Verlagsgesellschaft m. b. H., Leipzig, 1928 3577
These coördinates, introduced in Equation 1, lead to values of D which agree with those of Table II with an average error of 0.09 v.e., excluding H : F. The calculated D for H : F is 4.00 v.e., 1.23 v.e. higher than observed; this indicates that Equation 1 is inaccurate when xA [minus] xB becomes as large as 2. 3578 The electronegativity map may be used with considerable confidence in predicting bond energies, especially for atoms which lie near each other on the map. It will be observed that the difference in bond energy of H : A and
Fig 3. -- The construction of the electronegativity map. [N.B. Here are Figs. 3 to 5 done larger.] A : F increases rapidly in the order A = C, Cl, O. Now the value of this difference for N is only slightly greater than for Cl, showing that the locus on N on the map should lie just to the right of that for Cl, and that in
[N.B. The second line from the top has the elements listed in the following order: H, P, I, S, C, Br, Cl, N, O, F. Here are Figs. 3 to 5 done larger.] consequence D = 0.00 for N : Cl. The bond energies for N : Cl and Cl : Cl then lead to 1.44 v. e. for N : N, the value given in Table II. This value could be checked if the heat of formation of gaseous hydrazine were known. The predicted value is N2 + 2H2 = N2H4(g) [minus] 0.96 v. e. It may be mentioned that the heats of combustion of hydrazobenzene and azobenzene give 1.59 v. e. for N : N and 4.24 v. e. for N :: N, with rather large probable errors. 3579 From the equations S(g) = Srhombic + 2.80 v. e. We obtain S : Cl = 2.85 v. e. and H : S = 3.78 v. e. From 2Srh. + Cl2 = S2Cl2(g) + 0.24 v. e. we obtain, with the use of the above S : Cl value, S : S = 2.79 v. e. in S2Cl2. The equation (1/8) S8(g) = Srh. + 0.11 v. e. gives S : S = 2.78 v. e., if the S8 molecule consists of an eight-membered ring involving eight single bonds; the agreement with the S2Cl2 value provides strong support for this structure. From these energy values the map position of sulfur was obtained. The S6 molecule, supposed to contain six single bonds, is less stable than expected by 0.30 v. e., presumably because of steric effects. From the trend of map loci with position in the periodic table phosphorus may be placed very near hydrogen on the map, perhaps at about 0.10. This requires D to be very small (0.01 v. e.) for H : P. From (1/4) P4(g) + (3/2) H2(g) = PH3(g) + 0.246 v. e. we obtain P : H = 2.302 v. e. + C, in which C is one-third of the energy of dissociation of (1/4) P4(g) into P(g). This then gives, with D = 0.01 v. e., the value 0.14 v. e. + 2C for P : P. P4 presumably has a tetrahedral structure, with single bonds at 60° angles;14 the bonds are 0.14 v. e. weaker than normal P : P bonds, as compared with 0.05 v. e. for S : S bonds in S6. The equation (1/4) P4(g) + (3/2) Cl2(g) = PCl3(g) + 3.30 v. e. gives P : Cl = 2.41 v. e. + C. The extent to which Equation 1 is valid and the accuracy of the map are graphically shown in Fig. 5. The vertical lines, representing D-values, should increase in height with the square of their distance from the diagonal. It is evident that the map and Equation 1 can be used for the prediction of the energies of bonds for which no experimental data are available, the values being trustworthy to about 0.05 v. e. for map distances less than 0.50, and 0.1-0.2 v. e. for distances up to 1 or 1.5. Table IV contains predicted values, with the aid of which heats of formation of purely covalent compounds containing single bonds, such as SF2 (but not SF6), can be calculated. In some cases all data needed for testing these values are available except heats of vaporization or sublimation. Thus the heat of formation of S2Br2(l), 0.09 v. e., agrees with the bond energies if the heat of vaporization of S2Br2 be 0.44 v.e., which is a not unreasonable value (that for Br2 being 0.33 v.e.). the somewhat doubtful value 0.0 v.e. reported 14 R. Hultgren, Phys. Rev., 40, 891 (1932). 3580 for the heat of formation of S2I2(c) leads to a heat of sublimation of 0.9 v. e. (that for I2 being 0.65 v.e.). Similarly the heats of formation of PBr3(l),
Fig 5. -- In this figure ordinates and abscissas represent
loci [N.B. Here are Figs. 3 to 5 done larger.] 1.97 v. e., and PI3(c), 0.45 v. e., lead to the reasonable values 0.51 v. e. and 0.98 v. e. for the heat of vaporization of PBr3 and the heat of sublimation of PI3, respectively.
3581 Assuming that the energy of formation of crystalline silicon (with the diamond structure) is the energy of the Si : Si bonds, the heats of formation 15.70 and 6.20 v.e. of gaseous SiF4 and SiCl4 lead to values of 1.98 and 1.24 for D1/2 for Si : F and Si : Cl, respectively. These substantiate the map position of about -0.15 obtained by extrapolating the series Cl, S, P. This and many other map positions which could be similarly obtained are not included in Fig 4. and Table III, however, because of the somewhat greater uncertainty attached to them. With this map position, the heat of formation of SiH4 should be about 0.08 v.e., or less if the metallic character of crystalline silicon makes some contribution to its energy. The value 0.5 v.e. given in "International Critical Tables" is without doubt too large; Landolt- Börnstein [negative] 0.29 v.e. Arsenic, antimony, selenium, and tellurium no doubt lie close to hydrogen on the map, so that single bond energies can be obtained for them from the heats of formation of hydrides, as in the case of phosphorus, by assuming D to be very small. Crystals of selenium and tellurium contain long spiral strings, in which each atom is presumably held to two others by covalent bonds, and those of arsenic and antimony contain layers, in which each atom is presumably similarly attached to three others. With DM : H very small, the heat of reaction of such a string or layer with hydrogen should be nearly zero, so that the observed negative heats of reaction for the crystals give just the energy necessary to separate the strings or layers in the crystals. This energy is per atom, 1.08 v.e. for selenium, 1.52 v.e. for tellurium, 1.92 v.e. for arsenic, and 1.5 v.e. for antimony, the last value being probably too low because of error in the reported heat of formation of the hydride. The observed value of the heat of formation of O4 from atoms ,
10.19 v.e., is so much greater than the energy of four O : O bonds, 5.96 v.e. that the structure The metallic elements may also be roughly located on the map, though the significance and usefulness of their map positions is not so great as for the non- metals. 3582 The property of electronegativity discussed in this paper and defined by Equation 1 is not analogous to the election affinity of atoms, but is closely related to the intuitive conception of electronegativity possessed by the chemist. The relation to the periodic system is the expected one. Flourine and oxygen are by far the most electronegative atoms, with flourine much more electronegative than oxygen. The series C, N, O F is almost uniform. Flourine is much more electronegative than the other halogens, and deserves to be classed by itself as a super halogen. OF2 should be called oxygen fluoride, and Cl2O chlorine oxide, the more electronegative element being written last. In nitrogen trichloride, NCl3, nitrogen and chlorine are neither positive nor negative, the bonds being normal covalent bonds, and the molecule the best example of a normal covalent molecule that we have, other than the symmetrical molecules. Nitrogen trichloride would decompose into gaseous elementary molecules with no heat effect if elementary nitrogen contained N:N bonds. Since the triple bond in N2 is 4.78 v.e. more stable than three N:N bonds, half this energy quantity, 2.39 v.e. is emitted during the decomposition of NCl3. The contribution of ionic terms, giving ( = 1.17 v.e., overcomes this for NF3 and leads to a positive heat of formation. Summary
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THE
NATURE OF THE CHEMICAL BOND. IV. THE ENERGY OF SINGLE BONDS
AND THE RELATIVE ELECTRONEGATIVITY OF ATOMS
for this molecule
must be rejected. The corresponding values for ozone are 6.15 v.e. and 4.47
v.e., causing the structure 
to be rejected also. Ozone probably
has a structure like that of SO2, as suggested by Lewis. The very
small heat of formation of O4 from 2O2 and the ease with
which dissociation occurs (even crystalline oxygen showing some paramagnetism)
indicate that O4 consists of two 3SO2 molecules held together loosely by van der
Waals forces, the exchange terms being larger for two triplets molecules
combining to a singlet than they are for singlet molecules.
After
the discussion and definition of extreme ionic bonds and normal
covalent bonds, values of the energy of twenty- one single
bonds are obtained from experimental values of heats of formation
and combustion of gaseous molecules, with the use of assumption
that the energy formation from separated atoms of a molecule
to which a single Lewis electronic structure can be assigned
is the sum of constant terms representing the various bonds.
The postulate of the additivity of the energies of normal
covalent bonds is then formulated, and it is found that deviations
from additivity, D, are positive
for all bonds (with one doubtful exception), and increase
as the ionic character of the bond increases. An assignment
of atoms to positions on a map representing relative degree
of electronegativity is then made with the use of the D-
values, according to the equation DA : B = (xA
[minus] xB)2, where xA and
xB represent the coördinates of atoms A and B on
the map. Values of the energy of twenty bonds for which experimental
data are not available are predicted by means of this equation,
and a number of questions regarding the structure of molecules
are discussed.
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