July, 1030
THEHYDROGEN BOND:ASSOCIATION IN CARBOXYLIC ACIDS
[CONTRIBUTION FROM THE PHYSICAL CHEMICAL
LABORATORY O F THE
1135
UNIVERSITY OF WISCONSIN]
The Nature of the Hydrogen Bond. I. Association in Carboxylic Acids BY R. H. GILLETTEAND ALBERTSHERMAN movement may be a necessary condition for assoIt has long been known that many organic com- ciation in general, but it is not sufficient. Phenol pounds, especially those containing hydroxyl and benzoic acid are generally regarded as assogroups, are associated a t ordinary temperatures, ciated, yet over a considerable range of concentraboth in the gaseous state and in solution in non- tion (benzene solution) these substances show no polar solvents1 The equilibrium was investi- change in their molar polarizations. Moore and Winmill’ were probably the first to gated by AuwersI2 who was able to distinguish two classes of associating substances, those in postulate a hydrogen bond, i. e., two atoms or which the molecular weight increases in propor- groups held together by a hydrogen atom or nution to the concentration and those in which the cleus between them. Pfeiffer* used the idea to molecular weight approaches a limiting value cor- explain the weakness of o-hydroxyanthraquinone responding to dimer formation. Examples of the and Hugginse used the concept as a theory in reformer class are alcohols, phenols and amides; of gard to certain organic compounds. Latimer and the latter class the carboxylic acids constitute the Rodebushlo were the first to recognize the hydrobest example. Much later work using many gen bond as a general phenomenon. different methods has yielded discordant results Pauling” has considered a hydrogen bond to be but has largely verified the above conclusions. polar in nature while Sidgwick12 as a result of his The present work is concerned with assuming a theory of the coordinate covalent link, postulated structure for the dimeric carboxylic acid, and cal- that organic acids would associate since an inner culating its energy with respect to unassociated coordination would lead to a four-membered ring, molecules. It is mainly for these substances that which is unstable, whereas two molecules could experimental values for the heat of the association join together, forming a stable configuration, reaction are available. For formic acid Coolidge3” with carboxyl groups facing one another, the hyobtained the value 14,125 cal., and Fenton and droxyl hydrogens acting as acceptors for the forGarnerab found 13,790 cal. for acetic acids. The mation of coordinate links. This view is, howfact that consistent values for the heat of associa- ever, untenable, as Sidgwick himself has since tion over a considerable range of temperature and stated, l 3 since hydrogen cannot -be divalent unless pressure were obtained lends considerable cre- some of the electrons are promoted to the 2s dence to the view that these acids are associated state, which is unstable. This argument for the only t o dimers, as does also the work of Smyth instability of divalent hydrogen assumes that the and Rogersj4 who showed that associated mole- atomic quantum numbers for hydrogen essencules of acetic acid and butyric acid have an elec- tially retain their significance in the molecule. tric moment of zero in benzene solution. Sidgwick now regards the hydrogen as first atSeveral mechanisms have been postulated to tached to one atom and then to the other, this explain this association, the simplest being that electronic resonance on a time average amountthe interaction between two juxtaposed dipoles is ing to making hydropen divalent, i. e., the resoresponsible for the reaction. This, however, is nance phenomena of wave mechanics. Bell and unimportant in this case, and in general this in- Arnold14 come to the same conclusion for dimer teraction is insufficient to deal with polar mole- formation in the case of trichloroacetic acid molecules, as has been pointed out by Hildebrand.6 cules. Williams6 remarks that the presence of a dipole (7) Moore and Winmill, J . Chem. SOL.,101, 1875 (1912).
Introduction
(1) W. E.S . Turner, “Molecular Association,” Longmans, Green & Co., N.Y., 1915,p. 33. (2) Auwers, Z . physik. Chem., 12,889 (1893); 23, 449 (1897). (3) (a) Coolidge, THISJOURNAL, 50, 2188 (1928); (b) Fenton and Garner, J . Chem. Soc., 894 (1930). (4) Smyth and Rogers, THISJOURNAL, 52, 1824 (1930). ( 5 ) Hildebrand, Science, 88, 21 (1938). (6) Williams, Pfoc. N o t . A c a d . Sci., 14,932 (1928).
(8) Pfeiffer, Ann., 898, 137 (1913). (9) Huggins, Undergraduate Thesis, Univ. of California, 1919. 42,1419 (1920). (10) Latimer and Rodebush, THISJOURNAL, (11) Pauling, Proc. N u t . Acad. Sci., 13,359 (1928). (12) Sidgwick, “The Electronic Theory of Valence,” Oxford University Press, 1929; Chcm. Soc. Ann. Rep., 30, 115 (1934). (13) Sidgwick, ibid., 31,34 (1936). (14) Bell and Arnold, J . Chem. Soc., 1432 (1935).
R. H. GILLETTE AND ALBERTSHERMAN
1136
W. D. Kumlerl'la discusses the hydrogen bond in relation to dielectric constants and boiling points of organic liquids.
* 2.67AU. Y
9 n
Vol. 58
dependent bond wave functions for 8 electroiir, a convenient set being the so-called cannniral set18 given below. The energy of the complex is calculated as a function of the distance between carboxyl groups, i. e., between atoms b and d. For every distance ybd two cases were considered. In one case the hydrogen atoms are placed midway between the oxygen atoms, as shown in Fig. 1. In the other case the hydrogen atoms are a t the normal 0-H distance (0.97 A.) from diagonally opposite oxygen atoms. It is of course immaterial where the hydrogen atoms are located as far as the 14 bond wave functions in Fig. 2 are concerned.
H Fig. 1.-The model obtained from electron diffraction experiments ftx associated dimeric formic acid. The two carboxyl groups form an eight-membered plane ring.
In view of the above facts it is of interest to calculate the energy of the carboxylic acid complex with the aid of wave mechanics in order to throw some light upon the nature of the hydrogen bond, i. e., to determine whether it is polar, homopolar or both. We shall restrict our considerations for the present to formic acid, partly because i t is the simplest acid and partly because accurate experimental data for the substance are available. In order to calculate the energy of the dimer we must assume some particular spacial configuration. The one chosen was that suggested by Latimer and Rodebushlo and verified experimentally by Pauling and Brockway15by electron diffraction measurements. This structure places all the atoms in a plane with carboxyl groups opposite one another, as shown in Fig. 1. Zahnl8 has suggested an alternative model as a result of electric moment investigations, and based on the results of electron diffraction measurements by Hengstenberg and B d . " However, Pauling and Brockway state the model postulated by the latter authors is not in agreement with their electron diffraction pattern and hence can be definitely excluded.
Procedure All the electrons are considered uniquely paired except those in the ring and the problem is treated in the ordinary way as one of 8 electrons with spin degeneracy. There are in general 14 linearly in(14s) W. D.Kumler, THISJOURNAL, 07, 600 (1935). (15) Pauling and Brockway, Proc. Not. Acad. Sci., SO, 336 (1934). (16) Zahn, Phys. Reo., 87,1516 (1931); 36,1047 (1930). (17) Hengstenberg and B d , Anal. SOC. rspafi. ffs. quim., SO, 341 (1932).
Fig. 2-Fourteen linearly independent bond wave functions for eight electrons in the ring of dimeric acetic acid.
For the second case we give q3 and $4 the same coefficient in the wave function for the system, and similarly for $6 and $6 and $I,$8, $9 and The functions $11, $12, $la and are neglected. They are what Pauling and Whelandl9 have called second excited structures, and it is evident that they will contribute little to the energy of the system and may be neglected in an approximate calculation. Thus, we define $1
= $1, 62
$2,
$S
=
$8
+ $4t44 =9s + + + + $6,
$6
=
$7
$8
+9
$10
The matrix components between the 4's were computed by first calculating the components in terms of the $'s, by either Pauling'sl* or Eyring and Kimball's method,M and then using the definition of the 4's. In this case ab = ah = de = ef; ac = eg; ad = af = be = eh; ag = ce; bc = f g ; bd = fh; bf = dh; bg = df; cd = gh; dg = ch and bh = df. (IS) Pauling, J . Chem. Phys., 1,280 (1933). (19) Pauling and Wheland, ibid., 1 , 3 6 2 (1933). (20) Eyring and Kimball, rbid., 1, 636 (1933).
1137
THEHYDROGEN BOND: ASSOCIATION IN CARBOXYLIC ACIDS
July, 1936
Results
The components in terms of the 4's are given below.
+ +
For every distanae between oxygen atoms b and
+
H11 = Q (ab - ac - ag - bc - bd - bf - bx - bh - dg) +2(cd - ad) - ~ / Z ( Q C cg) Hzi = Q (ab - uc - ag - bd - bf - cd - bg - bh - dg) 2(bc - a d ) ' / ~ ( u c ag) 4 h b - ag - bh) - 21/2(ac bc bd bf dg) 2(bg cd) - 11/4(ac cg) - 5ad Hss = Zl/,Q 3(ab a d ) 6(cd bc - bg - dg) - 4l/2cg ~ ' / Z U C- 10'/z(ac ag) - 12(bd bh) - 9bf H44 = 7l/2Q H56 21/2Q 4(ab - nc - bh) - 2l/z(ag bd bf bg cd) 2(bc dg) - 11/4(ae cg) - 5ad H I 2 = l/*Q llZ(ab ad - ac - bd - ag - bh - bf) 1/4(bc cd bg dg - ae - cg) H 1 3= Q 21/&~b - ag - bh) 2(cd - a d ) - (ac bc bd bf dg) 1/2(bg - ae - cg) HI4 = l l / z Q 21/((ab ag - bf - bh) 3/4(ad bc - cg - bg) 3cd - 1 l/l(ae dg) - '5/4(ac bd) 1114(ab ac - bd bf - bh - ag) l/((bc bg - ad - ac) cd dg cg H I 5 = 1/2Q Hz3 = 1/2Q 11l4(ab ac - bd bf - bh - ag) 1/4(cd dg - ad - ae) bc bg - cg H24 = l1/2Q 21/4(ab - ac - bf - bh) 3/4(ad cd - dg - cg) - 16/4(bd ag) 3bc - l'/z(ae bg) H25 = Q 2l/z(ab - bh - ac) 2(bc - a d ) l/z(dg - ae - cg) - ag - bd - bf - bg - cd H34 = 21/,Q 4l/&b - bd - ag - bh) ll/n(ad bc bg) 6(bf ac) 3cd - 21/4(ae cg) H35 = 11/4Q 2(ab - ac ag - bh - bf) ad bc cd bg dg - ae 21/2cg - 3'/2bd H45 = 21/4Q 41/&b - ac - bd - bh) 11/2(ad cd dg) 6(bf ag) 3bc 21/4(ae cg)
+ + + + + + + + + + + + +
+
+ +
-
-
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - + + - + + + + + + + - + +
Here Q is the Coulombic energy of the system, ab the exchange energy between electrons a and
+
+
+ +
+
+
+
+
+
+ + -
+ +
c or It andf the configuration where the hydrogen atoms are placed a t the normal distance from
The Coulombic and exI change energies were evaluated from the various Morse potential energy curves in 0 question, and an approximate formula was used for correcting the Morse values for di- qd rected valence. It was as- -10 sumed that Ktab= KtabCOS'C~ holds for a bond formed from one s and one p electron, -20 where Kab is the exchange energy of a bond determined from a Morse curve, a the 1.8 2.0 2.2 2.4 2.6 2.8 3.0 m. angle through which the bond Fig. 3.-The heat of the association reaction of two carboxyl groups as a function is distorted from its normal the distance between them. The minimum corresponds to the formation of a stable value (i. e., from the angle for of which the bond energy is a maximum), and K'ab the directed valence ex- diagonally opposite oxygen atoms turned out to change energy. The carbon wave functions were be more stable than when they were placed midconsidered to be tetrahedral and orthogonal. The way between the oxygens. Hence only the ma~ o u l o m b i cenergy Was assumed to be 14% of the trix component for the more stable configuration total bond valuesz1 was given in the preceding section, since it is the The used for constructing Morse only one of interest for our present problem.22 curves are given in Table I. The results of the calculation are shown in TABLE I Fig. 3. Bond *@(A,) o(cm.-I) D(kca1 ) AE is the heat of the association reaction 2R0-0 1.32 1304 34.3 C-H 1.12 2930 92 3 COOH -+ (2-0 1.43 1030 81.8 OH0 H-H
c-c 0-H
0.74 1.54 0.97
4375 990 3660
R-Cc
102.4
83.0 113.1
(21) This percentage is taken over from activation energy calculotiona See Van Vleck and Sherman, Rev. Mcdcra Phys.. I, 168 (193s).
\C-R,I. H O/
e., AE
Edimer
- 2Emouomar
-
-
(22) The secular equation for the more unstable configuration was taken as a cubic, defined by the wave functions @I iI -t +a, 82 +a
+ ih +
+6
fI s ,
0s
-
I 7
+ 41 t 3, 4-
*I@.
R. E. GILLETTE AND ALBERT SHERMAN
1138
Discussion I t is seen from Fig. 2 that the curve has the form to be expected and that for the reaction 2HCOOH --+(HCO0H)Z we calculate an activation energy of 4.8kcal., a minimum a t r b d = 1.94 A.,and a heat of reaction of 23.8 kcal. This is to be compared with the experimental values r = 2.67 A.,and AE a t the minimum equal to 14.1 kcal. From theoretical considerations we know that a complete wave function for a system should include terms to allow for both polar and homopolar states. I t is exceedingly difficult, however, to include polar states in the calculation in any practical way, but it was considered of interest to see to what extent homopolar states alone could account for the results in order to determine, if possible, the relative importance of each. The existence of such states as H-C+/ H-C+/
0- H + 0 -
\C +-H, H + o-/ 0-H+ 0
\O-
\o
KC-H,
H+(-j-/
etc.
Vol. 5s
agreement with experiment is obtained. Thus if directed valence be decreased by 25% and the Coulombic percentage increased from 14 to 17.5 the calculated value of AE agrees with experiment. Resonance between bond wave functions #1 and $2 may be considered to be the resonating hydrogen bond of Sidgwick, mentioned in the introduction. It is t o be noticed, however, that if the functions $1 and $2 alone were involved AE would be +5 kcal. rather than -23.8 kcal. although Thus we see that states 11.3 through not as important as 1CI1, and h, must also be considered since they contribute considerable energy to the complex. If all excited stateslg be neglected, both for the dimer and the monomers, the heat of the association reaction turns out to be approximately equal to that found by taking all states into account.24 Hence i t turns out that the ordinary chemical formulation of the reaction 2RCJo +R-C/ \OH
\O-H-C *H-o>C-R
happens to
be fortuitously correct if the bonds drawn in the complex are interpreted to represent the functions and 11.2. Various assumptions concerning the value of a in the expression K' = aK cos2 a,together with various choices of the Coulombic percentage all affect the value of AE and the activation energy 0 of the association, but many detailed calculations tive to the structure R-C/ We have \O-H' show that the position of maximum stability almade additional calculations and find the reso- Ways OCCUTS a t Ybd = 1.94 A. The fact that Ybd nance energy to be 0.8 v. e. if it arises from the two (exptl.) = 2.67 A. indicates polar states are im0 0 states R-CY and R-c\
