ApriI, 1959
EFFECT OF ADJACENT BONDSON BONDDISTANCES IN HYDROCARBONS
effect completely analogous to that observed in the case of rhenium and, like the latter, independent of pH. However, in contrast to rhenium, a small and nearly constant amount of technetium also appeared ahead of the main peak in every elution (e.g., Figs. 5,6,7). The appearance of this activity could not be correlated with any of the experi-
565
mental variables. Acknowledgment.-We wish to thank Miss Carolyn A. Lovejoy for performing several of the experiments. One of us (E.A.) is also indebted to E. I. du Pont de Nemours and Company for the award of a pre-doctoral fellowship during the early stages of this investigation.
THE EFFECT OF ADJACENT BONDS ON BOND DISTANCES IN HYDROCARBONS BY H. J. BERNSTEIN Division of Pure Chemistry, National Research Council, Ottawa, Canada Received September 6,1068
The CC and CH bond distances in non-aromatic molecules are correlated with the r-bond orders of adjacent bonds, and CC bond distances in condensed aromatic molecules with the bond order evaluated by weighting KekulE:structures equally. The agreement between observed and calculated distances is within about f0.01 A.
From the accumulating structural data derived from X-ray and electron diffraction, and rotationvibration and microwave spectroscopy, it is apparent that the CC single bond distance in hydrocarbons is not constant but varies from 1.54 A. in diamond to 1.38k. for the central bond in biacetylene (see upper field of Table I). Further, the CH bond distance is longest in saturated hydrocarbons and shortest when adjacent to 9 triple bond as in alkynes, with the distance in the vinyl group being intermediate. The other CC distances of interest are those in aromatic and condensed ring compounds. It is the purpose of this note to show that CC and CH distances in hydrocarbons can be systematized on the basis of two simple notions-one for all hydrocarbons other than the condensed aromatics, and the other for the aromatics. In the case of the non-aromatic hydrocarbons as may be seen from Table I, the shortening of a CC bond adjacent to a multiple bond is additive and seems to depend only on the n-bond order of the adjacent bond. The effect of the neighbor bonds on CC single bond lengths has already been pointed out by Herzberg and St0icheff.I If PI and p z are the ?r-bond orders of the carbon bonds adjacent to the C-C “single” bond under consideration, the CC “single” distances for the situations given in Table I may be represented to about f 0.01 A. by the equation2
Walsh3 proposed that increasing the s character of a carbon hybrid orbital as one proceeds from sp3 to sp hybridization accounts for a stronger and shorter bond. Analogous to equation 1 one could write then Rcc
1.542
- 0.04216 - m - a]
(2)
where spmand spn are the states of hybridization of the orbitals of the C atoms forming the CC bond under consideration. According to the above notion then, non-aromatic CC single bond distances do not take any value between 1.38 and 1.54 A. but are grouped very closely around the “magic” distances 1.38,1.42,1.46,1.50and 1.54A. \ / For double bonds of the type C=C the ?r-bond / \ orders of the adjacent bonds are zero, so that a linear relation of the above type would predict all CC double bonds of this kind to have the same length, namely, 1.34A. As far as one can ascertain from the l i t e r a t ~ r eno , ~ experimental determination of CC double bond lengths of this type in a variety of molecules has given a length significantly different? from 1.34 A. There are two other kinds of double bonds, one kind as in allene, and the other, the cent,ral bond in butatriene. The observed distancess can be represented by the equation
+
Rc-c = 1.34
- 0.03(p, + pg)
(3)
where pl p z = 1 for allene, and 2 for the central bond of butatriene. On the basis of this notion, there is only one bond Here, it is assumed that all single bonds whether CC or CH have zero bond order and do not affect length to be expected for the CC triple bond since the CC distance, and also that the effect of non(3) A. D. Walsh, Disc. Faradag SOC.,9, IS (1947). adjacent bonds is negligible. Since we write a (4) Molecular orbital (MO) anlculations yield a bond order of 0.894 for the double bond in butadiene.’ From the conventional Kekul6 structure for the benzene ring its effect on bond order/bond distance plot6 a significant lengthening of the CC an adjacent bond is considered to be the same as double bond would be expected. However, a more recent self-conthat of a double bond. It is apparent that the sistent molecular orbital (SCMO) treatment of butadiene’ gives a agreement between the observed values and those value of 0.96 for the bond order of the double bonds which would predict a vary small change in the CC double bond length. estimated from equation 1is satisfactory. Rcc = 1.542
- O.O42(pi f p 2 )
(1)
(1) G.Herzberg and B. P.Stoicheff, Nature, 176,79(1955). (2) The shortening of a CC bond by 0.04 A. per unit of bond order in its adjacent bonds also has been recognized by McHugh. I am grateful to Prof. V. Schoniaker for sending me the Ph.D. thesis of J. P. McHogh, Calif. Inst. of Technology, 1957.
(5) C. A. Coulson, “Valence,” Clarendon Press, Oxford, 1952. p. 254. (6) G. Wheland, “Resonance in Organia Chemistry,’’ John Wiley and Sons,h a . , New York, N. Y.,1955. (7) 5. A. Pople, Trans. FaradaV SOC.,49, 1375 (1953). (8) E. P. Ftoicheff, Can. J . Phys., 33, 811 (1955); SD, 837 (1967).
566
H. J. BERNSTEIN
Vol. 63
TABLE I C-C BONDDISTANCES PI
-C-E-
1
1 C - L
/
\
\cL -c /
-c-
\ -c-c=c /
c \= c - c D
-
-c\ d =o / \
/
o==c-c=o \ / c=c-c=o \
L I M ~ Robad’
Molecule
PI
Pa
ZP
0
0
0
1.54
1.54
Alkanes, diamond
0
1
1
1.50
1.5Oe
Propene, isobutene
0
1
1
1.50
1.50
p-Xylene
0
2
2
1.46
1.47
Methylacetylene
1
1
2
1. 46d
1.48
Bipheny1
1
1
2
1.46
1.44
trans-Stilbene l,lO-diphenyl-l,3,5,7,9-dec:~pentane
2
1
3
1.42
1.40
Tolane
1
1
2
1.46
1.47
1,3-Butadiene
2 2
1 2
3 4
1.42 1.38
1.42 1 . 376b
Pirylene Biacetylene
0
1
1
1.50
1 .5OCse
Acetaldehyde
1
1
2
1.46
1.47
Glyoxal
1
1
2
1.46
1.46
Acrolein
1
1
2
1.46
1.48
Nicotinic acid
N=C-C=N 2 2 4 1.38 1.37 Cyanogen a All dnternuclear distances unless otherwise indicated are from reference 4 and are usually quoted with an accuracy of f0.02 A. J. H. Calloman and B. P. Stoicheff, Can. J . Phys., 35, 373 (1957). R. W. Kilb, C. C. Lin and E. B. Wilson, Jr., J. Chem. Phys 26, 1695 (1957). This distance may be greater than 1.46 8. if the two phenyl rings are not coplanar. V. Schomaker, p&ate communication, 1957.
its adjacent bonds have zero bond order. This expectationg is borne out by the experimental results. It might be possible to extend these notions t o molecules other than hydrocarbons. In the first instance, one might consider the effect of atoms other than C and H on CC bond lengths. I n some cases (see the h e r field of Table I) the CC distances are not too dependent on the nature of the other atom. In oxalic acid, however, the carboxyl groups do not have the same effect as in glyoxal, the central CC bonds being 1.54 A. This suggests that electrons are withdrawn from the CC bond into the carboxyl groups in keeping with the short C=O and CO distances observed.6 A discussion of CN and CO bonds is less satisfactory than for the CC bonds due primarily to mesomeric effects and the lack of equally reliable experimental data. l1 The aromatic distances such as in benzene and log6
(9) Again MO theory gives a bond order of 1.92 for the triple bond in diacetylene.10 It is probable that a SCMO treatment for the molecule would result in a higher bond order corresponding to vary little lengthening. (10) B. Pullman and A. Pullman, “Les Theories Electroniques de la Chimie Organiquo,” Masson et Cie, 1952, p. 371. (11) C. H. Townes end A. H. Sohawlow, “Microwave Spectroscopy,” RIcGraw-Hill Book Co., New York, N. Y., 1955.
graphite, and the different CC distances in naphthalene for example may be systematized on the basis of the following simple notion. A bond order is calculated considering only Kekuld structures (all weighted equally), and neglecting all formally bonded s t r u c t u r e ~ . ~ J ~This - ~ ~is essentially the Pauling bond order ( P ) . We assume also that the CC distance under consideration may be given by an equation of the type
+
Rcc = P(doub1e bond distance) (1 - P)(single bond distance) (4)
Mesomerism between the two Kekuld structures for benzene yields a bond order of l / 2 . I n (i) bond a is the same as the central CC bond in butadiene and in (ii) it is a double bond. This
D (I,
a
0 (ii)
indicates that the value for the single bond dis(12) L. Pauling. L. 0. Brockway and J. Y. Beach, J . Am. Chem. SOC..17,2705 (1935).
(13) L. Pauling and L. 0. Brockway, i b i d . , 69, 1223 (1937). (14) C. K. Ingold, “Structure and Mechanism in Organio Chemistry,” Cornel1 University Press, Ithaca, N. Y.
April, 1959
EFFECT OF ADJACENT BONDS ON BONDDISTANCES IN HYDROCARBONS
tance to be used16 in equation 4 should be 1.46 8. (corresponding to P = 0), and that for the double bond distance, 1.34 A. (corresponding to P = 1). The equation for aromatic CC distances is then Rcc = 1.34P + 1.46(1 - P ) (5) which produces the observed distance of 1.40 A. for benzene. A further test of this relation is obtained for graphite. The bond order evaluated from the Kekul6 structures is l/3, which upon substitution in equation 5 gives a value of 1.42 A. for the bond distance, in excellent agreement with the experimentally determined value.6 In the Kekul6 structures for naphthalene the bond orders obtained by weighting structures equally are a = 1/3, b = 1/3, c = 2/3 and d = 1/3. The observed CC distances for naphthalene are compared with the calculated ones in Table 11. The values calculated from equation 5 have a root mean square (r.m.s.) deviation intermediate to that calculated by MO and SCMO methods. A similar comparison for anthracene shows that there is about the same agreement between the results calculated by either equation 5 or the SCMO method and the observed data.lT The MO estimates are not in as good agreement, however. It is instructive to compare the relation between Pauling bond orders and those obtained by M'O and SCMO methods. I n Fig. 1 this bond order correlation is shown. For ethylene, benzene and graphite the SCMO and MO bond orders are the same, but they are quite different for the central CC bond of butadiene. One might expect therefore to be able to estimate about the same values for CC distances by either equation 5 or a SCMO bond order plot.18 A significant difference would be expected for SCMO bond orders below 0.28 since equation 5 predicts the largest possible CC distance in condensed aromatic hydrocarbons to be 1.46 A. whereas a SCMO bond order/bond distance plot indicates a value of 1.4768. A reasonably reliable quantitative relation can be developed for aromatic CN bonds as well. From the CN distance of 1.34 A. observed in pyridinel9 and symmetrical triazine20 (corresponding to a bond order of l/2), and the value of 1.28 A. usually adopted for the CN double bond distance, the (15) This differs from previous Considerations of this type in which the single bond distance was taken to be that found in ethane, viz,, 1.54 A. (18) There is a small curvature in a SCMO bond order/bond distance plot whereas the P u8. R plot is linear. The departure from linearity of the former plot, however, does not affect significantly tbe conclusion drawn. (19) B. Riik, W. Hansen and J. Rastrup-Andersen, J . Chcm. Phge., 89, 2013 (1954). (20) J. E. Lancsster and B. P. Stoicheff, Can. J . Phgs., 84, 1016 (1856).
567
ETHYLENE
ORDER
P BUTADIENE
0.2
0.4
0.8
1.0
0.8
M O BOND ORDER p
4
Fig. 1.-The relation between Pauling bond order and those given by molecular orbital theory: 0,SCMO bond order for butadiene.
TABLE I1 CALCULATED AND OBSERVED BONDDISTANCER FOR NAPHTHALENE Pauling bond P C a l c d . Bond order Obsd.%c Eq. 5 MOb
SCMOC
1.40 1.410 1.42 1.42 1.41 1.42 1.425 1.42 b 1.36 c 1.361 1.38 1.38 1.40 1.42 d 1.421 1.42 r.m.8. dev. 0.011 0.017 0.006 Ref. 17, D.W. Cruickshank, Ada Cryst., 9,915 (1956). "ef. 16, H.0. Pritchard and F. H. Sumner, Proc. Roy. SOC.(London), A226, 128 (1954). SCMO calculations given in ref. 16. a
1/3 1/3 2/3 1/3
equation for aromatic CN bonds analogous to equation 5 for aromatic CC bonds may be written as RCN = 1.28P + 1.40(1 - P ) (6) CH Bonds.-From the above considerations, the CH distance may have three values only, in the \ \ situations -c-H, =c-H or =-H, / and =C-H. The experimental distances' can be represented by the equation RCH = 1.10 - 0.02~ (7) where p is the u-bond order of the bond adjacent to the CH bond, or by RCH = 1.10 - 0.02(3 - m )
(8)
where spm is the state of hybridization of the C atom. It is probable that equations analogous to (7) and (8) also may be written for C-halogen bonds. Acknowledgment.-Helpful and illuminating discussions with Drs. B. Bak, D. W. J. Cruickshank, J. A. Pople and B. P. Stoicheff are gratefully acknowledged.
