The Existence of Chemical Interactions between the Hemes in

oxygen saturation curve of ferrohemoglobin.It was emphasized there that the chemical interactions between the four hemes, which give rise to a total f...
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THE EXISTENCE OF CHEMICAL INTERACTIOKS BETWEEN THE HEMES I N FERRIHEMOGLOBIK (METHEMOGLOBIS) AlVD THE ROLE OF INTERACTIONS I N THE INTERPRETATION OF FERRO-FERRIHEMOGLOBIN ELECTRODE POTESTIAL MEASUREMENTS' CHARLES D. CORYELL'

Gates and Crellin Laboratories of Chemistry, California Institute of Technology, Pasadena, California Received December 16, lQ38 INTRODUCTION

I n the preceding paper (6) a general application was made of the theory of chemical interactions proposed b y Pauling (15) to explain the sigmoid oxygen saturation curve of ferrohemoglobin. It was emphasized there that the chemical interactions between the four hemes, which give rise to a total free energy effect of 6000 cal. per mole, might be detected in different physicochemical studies of hemoglobin systems. Magnetochemical studies (17, 7 ) have revealed the close analogies existing between the structures of ferrohemoglobin and ferrihemoglobin (methemoglobin) and of some of their compounds. I t is the purpose of this investigation to examine all available information about equilibria in ferrihemoglobin systems in order to show that chemical interactions occur also under certain conditions between the hemes of ferrihemoglobin, and t o establish the magnitude of their effects in certain equilibria, including the electronic equilibrium with ferrohemoglobin which establishes the electrode potential. These results are of significance t o the physical chemistry of ferrihemoglobin and to the structural chemistry of hemoglobin compounds in general. T H E BOND T Y P E O F FERRIHEMOGLOBIN COMPOUNDS

The character of the bonds to the iron atom in ferrihemoglobin and in a number of its compounds has been determined in these Laboratories (7). The bonds in ferrihemoglobin were found t o be essentially ionic in nature, and the difference between the observed magnetic moment per heme, Contribution KO.666 from the Gates and Crellin Laboratories of Chemistry of the California Institute of Technology. Present address: Department of Chemistry, University of California a t Lo8 Angeles, LOBAngeles, California. 841

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CHARLES D. CORYELL

5.80, and the theoretical moment, 5.92,awas regarded as possibly due to a small amount of magnetic interaction between the ferriheme groups. The addition of diamagnetic alkali fluorides increases the Aw values (forces in milligrams observed in the Gouy apparatus) for ferrihemoglobin solutions through the formation of the more paramagnetic ferrihemoglobin fluoride, for which a magnetic moment per heme of 5.92 was measured, just equal to the theoretical value for the ferric ion. The existence of mother form of ferrihemoglobin, ionic in character but with a moment somewhat lower than 5.80, is suggested by the measurements of the magnetic susceptibility of ferrihemoglobin solutions a t p H values less than 6.5. The cyanide and hydrosulfide compounds of ferrihemoglobin, with moments of 2.50 and 2.26, respectively, are essentially covalent' in the character of the six iron bonds (with one odd electron for each ferric atom), and the azide compound was founds also to be covalent in character. It is considered that ferrihemoglobin hydroxide, with a moment of 4.47, has one 3d orbital of the iron atom involved in covalent bond formation, probably with partial covalent character of all iron bonds. Magnetic titrations of ferrihemoglobin with standard cyanide solution (7) showed linear decrease in susceptibility on adding cyanide at p H values of 6.7 and 10.8. These experiments prove the absence of any strong magnetic interaction in the system of the type discussed for hypothesis I for ferrohemoglobin systems in the paper by Coryell, Pauling, and Dodson (6), but the experiments would not detect small effects due t o weak magnetic interactions between the hemes. THE MATHEMATICAL TREATMENT OF HEMOGLOBIN EQUILIBRIUM DATA

It has been shown (15, 6) that the theory of the existence of chemical interactions in hemoglobin and the assumption of square heme configuration lead to the following equation, connecting the fraction saturation, y) of ferrohemoglobin (assumed not to have heme interactions) with the concentration, c, of a substance forming a compound with heme interac3 The magnetic moment of iron group elements is due principally to the spin moments of unpaired electronsin the 3d group. There may be a contribution from the orbital motion of the electrons, which would raise the moment somewhat for elements in the second half of the group. For ferric and manganous ions this contribution will be zero, since the normal state is 's~/*; magnetic measurements on inorganic compounds are in agreement with this prediction. There may be a further effect, unpredictable in magnitude and direction, due t o magnetic interaction of two or more paramagnetic atoms close together in the molecule. 4 The concepts of ionic and convalent bonds and bonds intermediate in type, as well as a discussion of the magnetic criterion for bond type, are clearly presented in The Nature of the Chemical Bond (16). 5 Unpublished experiments made with Dr. Fred Stitt in these Laboratories.

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843

tions stabilizing the molecule by RT In a: cal. per mole of adjacent heme pairs : + l ) K Z c Z 3a2K3c3 a4K4c4 K~ + (1) Y=m c + (4a + 2)K2cZ 4a2K3c3 a4K4c4

+

+

+

+

The value of K , the equilibrium constant for addition of the substance t o an isolated heme, depends on acidity and temperature. Half-saturation is attained when the product Kc is equal to I/a. I t can be shown furthw that the equation similar to equation 1, derived with the assumption that interactions occur only between adjacent ferrohemes and not between oxyhemes, is identical with equation 1 except for a change in the value of the constant K , whose absolute value has not been determined experimentally. A saturation curve which can be represented by equation 1, with a: # 1, indicates therefore the occurrence of interactions in one or the other, or both, of the pure components of the system. It will be desirable to refer to the interaction constant, a, as the efective interaction comtant, without for the present designating which of the components has the stabilization free energy. (Indeed, the overall interaction effect may represent a difference of interactions in the pure components from those in the intermediates. It is proposed to discuss this problem a t a later time when a greater number of accurate studies have accumulated.) The application of equation 1 to chemical equilibria has so far been the most fruitful method of detecting the presence of and measuring the magnitude of chemical interaction in hemoglobin systems. It has been customary to represent the sigmoid saturation curves obtained in the study of hemoglobin equilibria by means of an empirical equation proposed by Hill (11): K'c" y

=

m

in which y and c are as defined above and n and K' are empirical constants. We shall use the name sigmoid coefiient for n in this equation when applied to experimental studies of hemoglobin equilibria. The value of the sigmoid coefficient is equal to the slope of the line obtained by plotting the logarithm of the ratio of combined to uncombined hemoglobin against the logarithm of the concentration of the combining substance. If equation l of this paper is analyzed in this manner with the value of 12 for a, as calculated by Pauling (15) from the horse ferrohemoglobin-oxygen equilibrium measurements of Ferry and Green (9), the value of the sigmoid coefficient is found to be 2.62 for the range of saturation between 10 per cent and 90 per cent, the range most readily accessible for experimental study. Below and above this range it falls to values which approach

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CHARLES D. CORYELL

unity.6 Values of the sigmoid coefficient prevailing in the middle range of saturation have been determined from a logarithmic plot for a number

RT Cn m

FIQ.1. Sigmoid coefficient n as a function of effective heme-heme interaction energy R T In a.

of values of a of equation 1, and they have been plotted against RT In a in figure 1.' With the help of this curve, values of n reported in the The experiments of Ferry and Green (9) give evidence of the smaller slope for very low and very high saturation values, as predicted by equation 1. Although equation 2 does not accurately represent the hemoglobin equilibrium, the sigmoid coefficient n may be defined rigorously by the following equation

n=(-)

a log R

a l o g c +,

=(()aa

log R log~c

(3)

where R represents the ratio of concentration of hemoglobin complex t o that of hemoglobin, y/(l - y), a function of the variable Kc ana the parameter a readily derivable from equation 1. Equation 3 may be modified to give the relation

The term aR/aKc is obtained by simple differentiation of the equation for R, and the restrictions of the partial differentiation are fulfilled by setting Kc equal to l / a . Collection of terms leads to the following analytic relation between n a n d a: n=

4d a '

+ 28a' + 28a4 + 4a

+ 12d -I-3W+ 1% + 1

6)

The value of n calculated from equation 5 using the value of 12 for a is 2.88, which represents the slope of the tangent to the logarithmic curve a t the point a t which log R is zero. The value 2.62 derived synthetically, using the same a,is the average value applicable over the range of saturation generally studied in equilibrium measurements. The curve in figure 1 connecting n and a was derived from calculations for the range between 10 and 90 per cent saturation and is therefore to be preferred for empirical use over the curve lying slightly higher that may be calculated from equation 5.

INTERACTIONS I N FERRIHEMOGLOBIN EQUILIBRIA

845

literature for application of Hill's equation may be interpreted directly in terms of heme-heme interaction energy or effective heme-heme interaction constant. For infinite interaction energy the value of the sigmoid coefficient is 4 ; for zero interaction energy, the values of nand CY are unity and equations 1 and 2 reduce to that for the rectangular hyperbola. We are now in a position to examine the results of certain equilibrium studies reported in the literature. There will first be treated equilibria of ferrihemoglobin with ions involving formation of the covalent hydrosulfide, azide, and cyanide complexes, then the equilibrium involving formation of the ionic fluoride complex, and finally that involving the partially covalent hydroxide complex. Following this there will be given a discussion of the part played by interactions in an interpretation of the electrode potential studies of hemoglobin. I

IONIC-COVALENT FERRIHEMOGLOBIN EQUILIBRIA

Keilin (12) established the fact that hydrogen sulfide reacts with ferrihemoglobin a t a pH of approximately 6 to give a reversible complex and determined by a spectrophotometric method a dissociation constant for the complex, assuming independence of the hemes. The values given for the constant show, however, a systematic increase with decrease in hydrogen sulfide concentration at constant pH. I have treated his data anew,* including the results of his Tables I and I11 as well as those of Table 11, from which he determined the simple dissociation constant (1.3 X in terms of total uncombined sulfide). The results of this treatment are HbSH presented in figure 2, in which log -_ is given as ordinate with the Hb+ logarithm of the total uncombined sulfide concentration, log (ZHZS), as abscissa. The points plotted in figure 2 certainly cannot be represented adequately by a line with slope unity, corresponding to the absence of interaction effects. A straight line with slope 1.84 has been fitted to the points; this sigmoid coefficient 1.84 corresponds, as seen from figure 1, to the effective heme-heme interaction energy of 840 cal. per mole or to the interaction constant 4.1. At pH 6.0 two-thirds of the total sulfide not combined with hemoglobin is in the form of hydrogen sulfide, and one-third is in the form of hydrosulfide ion, which can combine with hemoglobin ( K , of hydrogen sulfide taken as 3.31 X lo-' (8)). From figure 2 it is seen that the concentration of total sulfide a t which half of the ferrihemoglobin is in complex form is 1.6 X or the concentration of hydrosulfide ion is calculated to be

* Possible effects of the reduction of ferrihemoglobin by hydrogen sulfide (7) have been neglected, as the rate is probably too slow to be observed under the conditions prevailing in these experiments.

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CHARLES D. CORYELL

5.3 X on the assumption that Keilin’s solutions were buffered a t pH 6.0: Equation 1 accordingly represents the hydrosulfide equilibrium data if CY is set a t 4.1 and K is set at 4.6 X lo4. Keilin (13) carried out a less extensive series of experiments, similar to the above, on ferrihemoglobin-azide mixtures, but he did not calculate equilibrium constants from the data. Horse hemoglobin was used, and the pH of t,he equilibrium experiments was not recorded, although it presumably was approximately 6. Since hydrazoic acid has a dissociation constant of 1.9 x it can be treated as practically completely ionized a t pH 6. The data are presented in figure 3, where the abscissas represent

10-

05-

9

0-

s -05

-

u

- I-%.

-50

-45

LOG (1H2S)

-40

LOG (.? N;)

FIG.2 FIG. 3 FIG.2. Equilibrium between ferrihemoglobin, hydrogen sulfide, and ferrihemoglobin hydrosulfide. Data of Keilin: @, Table I; 0, Table 11; 8 , Table 111. FIG. 3. Equilibrium between ferrihemoglobin, azide ion, and ferrihemoglobin azide.

the logarithm of the total concentration of azide not combined with hemoglobin. A straight line of slope 1.76 has been fitted to the points as a reasonable representation, corresponding (figure 1) to a heme-heme interaction energy of 780 cal. per mole or an effective interaction constant of 3.7. The azide concentration a t half-saturation is 1.3 X leading to the value 2.1 X lo4 for K in equation 1. For these two reactions values of the effective interaction energy are, respectively, 840 and 780 cal. per mole of adjacent heme pairs. These figures are based on the assumption of square heme configuration, but the values per molecule (3360 and 3120 cal.) are essentially independent of the structural configuration assumed (15). Considering the relatively large

INTERACTIONS I N FERRIHEMOGLOBIN EQUILIBRIA

847

experimental uncertainty (of the order of magnitude of 10 per cent) in the determination of these two effective interaction energies, it might be concluded that the interaction constants are really identical to within experimental error for these two ionic-covalent equilibria. The possibility that the corresponding ionic-covalent equilibria of ferrohemoglobin with oxygen and with carbon monoxide have identical interaction constants has already been discussed (6). Final conclusions about the identity of effective interaction constants for different reactions must await the execution of more accurate investigations. The equilibrium between ferrihemoglobin and hydrocyanic acid was studied magnetometrically by Coryell, Stitt, and Pauling (7) a t pH 4.77. The results, presented in figure 3 of their paper, are represented by a theoretical curve calculated for equilibrium with independent hemes. The author has reexamined their original data, and has found that the measurements are not sufficiently accurate to prove the presence or the absence of interaction effects, or to eliminate the possibility of an interaction constant as large as 4. EQUILIBRIA WITH PREDOMINANT IONIC CHARACTER I N BOTH COMPONENTS

Ferrihemoglobin readily forms ferrihemoglobin fluoride, and in both compounds the iron atom is held by essentially ionic forces. No analogous system has yet been found with ferrohemoglobin, so it is interesting to determine whether the effect of interactions is observable in these equilibrium data. Lipmann (14) has made a spectrophotometric study of the equilibrium, using swine ferrihemoglobin a t pH 6.9. His data are analyzed for the sigmoid coefficient in figure 4. The greatest significance is to be attached to the experiments made with comparable concentrations of the two compounds, in the middle range of the plot, and through these points has been drawn a line with slope unity, which crosses the zero ordinate a t an abscissa corresponding to the simple dissociation constant of 0.0138 given by Lipmann. It is concluded from these experiments that the effective interaction constant for the equilibrium is 1.00; the corresponding value of K for equation 1 is 72.5, the reciprocal of the dissociation constant. As discussed in the second section of this paper, it is believed that iron atoms in ferrihemoglobin hydroxide are held by bonds which are only partly covalent, and therefore partially ionic, in nature. Extensive experiments on the ferrihemoglobin-ferrihemoglobin hydroxide equilibrium have been made spectrophotometrically by Austin and Drabkin (1) and magnetometrically by Coryell, Stitt, and Pauling (7). The data of both sets of workers have been published, with curves showing the equilibrium as a function of pH, assuming the absence of interaction effects. There are presented in figure 5 data of the latter set of workers analyzed for the

848

CHARLES D. CORYELL

sigmoid coefficient, using all of the data in the pH range 7.3 to 9.1 from their Table I (7). A straight line of slope unity has been fitted to the points; the data of Austin and Drabkin would give the same slope with equal certainty. We conclude, therefore, that the effective interaction constant is 1.00 for this equilibrium. The value of K for equation 1 is 7.1 X lo6 for this series of measurements. There are two possible explanations of the observation of effective interaction constants of unity in ionic hemoglobin equilibria. It is possible, first, that no interactions exist between the hemes of either component, or, second, that the effect of ferriheme-ferriheme fluoride interactions, for

LOG F *

PH

FIG.4

FIQ.5

FIG.4. Equilibrium between ferrihemoglobin, fluoride ion, and ferrihemoglobin fluoride.

FIG.5. Equilibrium between ferrihemoglobin and ferrihemoglobin hydroxide

a8

a

function of pH.

example, cancels exactly the effect of ferriheme-ferriheme and ferriheme fluoride-ferriheme fluoride interactions. Evidence to be brought forward in the next section gives indication of the existence of interactions in ionic hemoglobin compounds and therefore supports the second possibility, but more quantitative information about the absolute magnitudes of the interaction effects has not yet been obtained. THE FERRO-FERRIHEMOGLOBIN

ELECTRODE POTENTIAL

I t was shown by Conant (2) that the oxidation of ferrohemoglobin to ferrihemoglobin involves one equivalent per heme group. The electrode reaction for the ferro-ferrihemoglobin half-cell, symbolically written,

849

INTERACTIONS I N FERRIHEMOGLOBIN EQUILIBRIA

Hb'

+ E- = H b

(6)

represents an equilibrium between electrons (E-), ferrihemes (Hb+) of ferrihemoglobin, and ferrohemes (Hb) of ferrohemoglobin. The concentration of electrons, a t 25"C., in terms of those in the reference half-cell is given by the following expression Eobsd. log (E-) = -~ 0.059

(7)

W e expect therefore that the electrode potential of hemoglobin, represented by equation 6, should be in accord with the general hemoglobin equilibrium equation (equation l ) . A determination of the slope of the curve representing log (Hb) as (Hb+) ~

Eobsd.

as abscissas gives the value of n of the 0.059 Nernst equation which is in agreement with the measurements. By virtue of equation 7, however, the n of the Nernst equation is identical with the sigmoid coefficient for reaction 6. We can therefore make use of reported values of n in the Nernst equation and figure 1 to obtain information about the effective interaction constant for equation 1. The representation of the half-cell reaction as a typical hemoglobin equilibrium offers an explanation for the occurrence of values for n in the Nernst equation greater than unity for an oxidation involving a change in valence of unity for the iron atoms. The ferro-ferrihemoglobin electrode potential has been studied potentiometrically by Conant and coworkers (2, 3, 4) and by Havemann and Wolff (10) and spectrophotometrically in oxidation equilibria by Conant and Scott (5). There are numerous difficulties in the measurement of the potential, and consequently measurements of the sigmoid coefficient are subject to some uncertainty. There are presented in table 1 values of the sigmoid coefficient for the oxidation reaction from all available experiments in the literature with sufficient data for the calculation to be made. All experiments except one a t pH 7.7 have been made with horse hemoglobin. Conant and Scott ( 5 ) and Conant and Pappenheimer (4) have carried out the only experiments specifically devised to determine n; some of the other calculations of n rest on comparatively few measurements with large experimental error.g The potentiometric measurements give values of the sigmoid coefficient between 1.2 and 1.7, without clear evidence for any dependence on pH. ordinates plotted against -

~

Note added in proof: Dr. John F. Taylor (private communication) has recently carried out measurements of the electrode potential in which a high degree of reproducibility was attained. He reports that R of the Nernst equation is greater than unity but seems t o depend somewhat on the fraction of hemoglobin oxidized.

850

CHARLES D. CORYELL

The transformation of ferrihemoglobin to the hydroxide is half effected a t pH 8.2 (figure 5 ) ; studies in solutions much more alkaline than this involve the reduction of ferrihemoglobin hydroxide to ferrohemoglobin. The two spectrophotometric studies ( 5 ) , in which the equilibrium waa TABLE 1 Sigmoid coeficient for the ferro-ferrihen PH

REFER ENCE

METHOD OF STUDY

6.4 E.M.F. of mixtures

Best series in paper. Three concentration ratios in duplicate 2.0 f 0 . 5 Sixteen experiments (figure 3)

Spectrophotometric. 1Naphthol-2-sulfonate indophenol. Equilibrium 6 . 9 Spectrophotometric. Ferricyanide-Hb equilibrium in presence of carbon monoxide 7 .O E.M.F. of mixtures. Fe(CN)s--- catalyst

2.0 f 0.3 Thirteen experiments (figure 4)

1.35

1 .o-2

7 .O E.M.F. of mixtures Fe (CN)s--titration curves

1.2

7.7 E.M.F.

8.4 E.M.F. of mixtures Fe(CN)s--8.5 E.M.F. titration curve 8.5 E.M.F. S,Od-- titration curve E.M.F. of mixtures

DlsCUBBlON OF DATA

1.4

6.9

9.5

n*

rlobin electrode potential

1.4 1.2

;

(3)

1.7

Data of figure 1, reinterpreted to give smaller average deviation (1.23 given by authors). Nine concentration ratios, best series in paper Reported results of other series (no data given) Interpretation of titration curve, figure 2. Three points, cow hemoglobin Data not self-consistent Data of Table 11. Nine points Data of Table 11; assumed starting point, a t -4.0 ml. Ten points Data not very consistent. Three ooncentration ratios in duplicate

__ * The value of the sigmoid coefficient n is also the experimental value of n from the application of the Nernst equation to the results.

.

. . _ . . .. . .. . . . approached from both sides, gwe much higher values, approxlmately Z.U. It seems to be definitely shown by the evidence given in table 1, however, that the sigmoid coefficient is greater than unity. Values of 1.2, 1.6, or 2.0 (covering the range of values found in table 1) correspond respectively A,.

INTERACTIONS I N FERRIHEMOGLOBIN EQUILIBRIA

851

to values of 1500, 2600, or 3800 cal. total effective interaction energy per mole, or to values of 1.9, 3.0, or 5.0 for the effective interaction constant. It is thus seen that interaction effects play an important part in the oxidation of hemoglobin. It was mentioned in connection with equation 1 that the effective interaction may be a function of various interactions between like and unlike adjacent hemes. The occurrence of interaction effects in the ferro-ferrihemoglobin-electron equil.'xium does indicate, however, that ionic compounds have stabilizing i iteractions, and that the non-observance of interactions in the ferrihemoglobin-fluoride and ferrihemoglobin-hydroxide systems is probably due to a cancellation of interaction effects, rather than to their non-existence. SUMMARY

Analyses of the equilibrium data for the reactions between ferrihemoglobin and hydrosulfide and azide ions lead to the conclusion that stabilizing heme-heme interactions occur in these systems analogous to those occurring in the ferrohemoglobin system with oxygen. A method is presented by which the empirical n of Hill's equation for hemoglobin saturation equilibria (the sigmoid coefficient) can be correlated with the corresponding value of a (the effective interaction constant) for Pauling's theoretical treatment of chemical interactions between adjacent hemes. The values of the total effective interaction energies (4RT In a ) for four equilibria have been ascertained. The experimental values in calories per mole are 3360, 3120, 0, and 0, respectively, for the equilibria with hydrosulfide, azide, fluoride, and hydroxide ions. I n the first two equilibria, complexes with covalent ferric atoms are formed; in the last two, complexes with predominantly ionic ferric atoms are formed. The ferro-ferrihemoglobin half-cell has been treated as an equilibrium between these two substances and electrons. This treatment leads to the conclusion that the n of the Nernst equation applied to these potential measurements is identical with the sigmoid coefficient, and explains the occurrence of values of n greater than unity for a one-step oxidation of iron atoms. The fact that n is in the neighborhood of 1.6 indicates that interactions occur in this system of hemoglobin compounds, both of which contain ionically bound iron, and that an interaction energy effect of approximately 2600 cal. per mole is involved. The author is grateful to Professor Linus Pauling for many helpful discussions and for valuable advice in connection with this investigation, and to Dr. Sidney Weinbaum for assistance in preparing the figures.

852

CHARLEB D. CORYELL

HEFERENCES

(1) AUSTIN,J. H., AND DRABKIN, D. L.: J. Biol. Chem. 112, 67 (1935). (2) CONANT,J. B.: J. Biol. Chem. 67, 401 (1923). (3) CONANT, J. B., AND FIESER, L. F.: J. Biol. Chem. 62,595 (1925). (4) CONANT, J. B., AND PAPPENHEIMER, A. M. : J. Biol. Chem. 98,57 (1932). (5) CONANT, J. B., AND SCOTT, N. D.: J. Biol. Chem. 79,207 (1928). (6) CORYELL,C. D.,PAULING, L., AND DODBON, R. W.,: J. Phys. Chem. 43, 825 (1939). (7) CORYELL, C. D.,STI'IT, F., AND PATJLING, L.: J. Am. Chem. SOC.69,633 (1937). (8) EPPRECHT, A. G.: Helv. Chim. Acta 21, 208 (1938). (9) FERRY, R. M.,AND GREEN,A. A.: J. Biol. Chem. 81,175 (1929). (10) HAVEMANN, R., AND WOLFF,R.: Biochem. Z. 293, 399 (1937). (11) HILL, A. V.: Biochem. J. 7, 471 (1913). (12) KEILIN,D.:Proc. Roy. SOC. (London) B113, 393 (1933). (13) KEILIN,D.:Proc. Roy. SOC.(London) B121, 165 (1936). (14) LIPMANN, F.: Biochem. Z. 106, 171 (1929). (15) PAULING, L.: Proc. Natl. Acad. Sci. U. S. 21, 186 (1935). (16) PAULING, L.: The Nature of the Chemical Bond. Cornel1 University Press, Itheca, New York (1939). 17) PAULING,L., AND CORYELL, C. D.: Proc. Natl. Acad. Sci. U. S. 22, 210 (1936).