N. C. Baird
University of Western Ontario London, Ontario, Canada
Dewar Resonance Energy
1he concept of resonance energy is extremely useful in predicting and in rationalizing the physiochemical properties of conjugated organic molecules. Although there is general agreement as to the verbal definition of this important quantitythat the resonance energy of a molecule equals its actual bonding energy less that "expected" for its most stable valence-bond structure composed of single and double bonds1-no general agreement exists regarding how the bond energies for the reference structure are to be evaluated. On the one hand, theoretical chemists usually prefer to use "pure double" and "pure single" bonds between q2-hybridized carbon atoms (i.e., bonds with pi character of exactly 1.0 and exactly 0.0, respectively) as references, and thus equate resonance energy with the delocalization energy predicted by molecular orbital theory. I n contrast, thermochemists normally do not use the abstract concept of a "purely single" C(sp2)-C(sp2) bond, but instead use the energy associated with a C(sp3)-C(sp2) or a C(sp3)-C(q3) bond as the single-bond reference. Although both types of defiuitions have their own particular uses, it is difficult, if not impossible, to "translate" a theoretical delocalization resonance energy into thermochemical terms, and vice-versa. The second basic objection to conventional definitions of resonance energy involves the difficulty in relating resonance energy of an unsaturated compound to its aromaticity. For example, estimates of the thermochemical resonance and delocalization energies for fulvene range from about to about of that for benzene-should this imply that fulvene should be one-third to two-thirds as aromatic as benzene? On the basis of bond energies calculated by his molecular orbital theory, Dewar has proposed a definition of resonance energy which should prove of major importance in organic chemistry, since it provides a clear and quantitative measure of the aromaticity of conjugated molecules (1). Although Dewar's method was developed in a theoretical context, the same approach can be applied to experimental thermochemistry (8). I n the present paper, some of the general properties of the Dewar Resonance Energy (DRE) definition are developed. In particular, the DRE value for a compound is shown to be independent of the numerical values used for bond energies, and the use of DRE in judging the aromaticity of organic molecules is illustrated. 'We have excluded from consideration here compounds eontaining triple bonds and involving sp-hybridized carbon. We exclude from consideration compounds (such as phenol) having hydrogen a t o m bonded to oxygen.
Dewar, Definition of Resonance Energy
The principal advantage of Dewar's definition of resonance energy (DRE) lies in the clear distinction made between aromatic, nonaromatic, and antiaromatic conjugated molecules; the DRE is positive for an aromatic compound, negative for an antiaromatic compound, and zero (within 1 or 2 kcal/mole) for a nonaromatic compound. This distinction is achieved by the use of "double" and "single" bond energies appropriate to nonaromatic systems (rather than those for nonconjugated systems) in the reference structure. Dewar noted that, according to moleculrtr orbital calculations for acyclic polyenes (systems which, by definition, can exhibit neither aromatic nor antiaromatic characteristics) both the effective energy EC=Cof the carboncarbon "double" bonds and the effective energy EG-cof the carbon-carbon "single" bonds are constants in such molecules (1). In other words, the values of EC=~ and ECO which reproduce the total carboncarbon bonding energy of butadiene are the same as those which reproduce the energy of, for example, octatetraene. Note that this invariance of the effective bond energies does not imply that there is no conjugation across single bonds in polyenes, but does imply that the conjugation has the same energetic consequences (per bond) in all nonaromatic .systems. Dewar's theoretical calculations also indicate that the same constancy applies to carbon-oxygen and carbon11itn)grnhond energies in nc.yelic compounds ( l c ) . Although I)e\wr developed his definitio~~ ~ , fresononrc energy within the context of a particular molecular orbital theory, we have found that it is possible to generalize his method so that the DRE of a compound can be evaluated either from calculations or from the experimental thermochemistry of the compound. Of particular significance is the finding that the DRE of a molecule is dependent only upon its beat of formation (AH,) and is independent of the particular values assumed or deduced for the "nonaromatic" C=C, CzC, C=O, etc., linkages. In order to develop a general definition for DRE, consider any completely unsaturated organic compound C,H,O,O, where p denotes the number of carbonyltype oxygen atoms, q denotes the number of ethertype oxygen atoms, and all m hydrogen atoms are bonded to the system of n unsaturated carbon atoms.2 For a compound of this type, one can easily deduce that the Number of Number of Number of Number of Number of
C-H bonds present C=O bonds present C=C bonds present C-0 bonds present C2'-C bonds present
= = = = =
m p (n - p)/2 29 n - p - m/2
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Table 1. AHJ'S (at 25°C) for Reference Compounds
If the compound is exactly nonaromatic, its total bonding energy Eo is given as the appropriate summation of effective hond energies
We now choose to evaluate the bond energy terms in the following manner 1) Eta is derived from the total bonding energy E o , ~ ,of ethylene
a
b
Ec-o = Ec~E, - 4Ecn
(2)
2) Ec-o is derived from the bonding energy Em,o of formaldehyde Ec-o = Eca,o
- 2Ecx
(3)
c derived from the bonding energy of the one polyene 3) E c ~ is (trans-hutadiene) for which both accurate experimental and theoretical data is available E c x = Ec,a.
- 2Ec-o
- 6Ecn
(4)
By use of the definition of EcTc above, Eczc can he written in terms of Eo~H, as
EWO= Ec,n8 - ~Ecs,
+ ZEcn
(.5)
4) Finally, Eo-6 is evaluated from the bonding energy of divinylether Ec-6 = l/dEc,~oo- 2Ec-o
- 6Ecn)
(6)
which, upon substitution for Ec-c, heeomes Ec-a = '/~Ec.H.o
- ~Ec,E.+ 2Em)
(7)
If the final expressions for the bond energies are substitutedinto eqn. (1), thentheenergy of the reference structure is
Note in particular that the total "nonaromatic" bonding energy E o of the compound is independent of the value of Em, and depends only upon the total bonding energy of the four reference molecules. Thus any combination of bond energies which is consistent with the thermochemistry of the reference compounds must yield the same total E n value for any molecule! The DRE value for any compound can he deduced easily if a theoretical value for its total bonding energy, E, is available DRE = E
- E"
(9)
If experimental thermochemistry is to be used, the DREvalue can he more easily evaluated using heats of formation (AH,) rather than total bonding energies, since one can easily show that
+
DRE = pAH1(CHlO) qAH,(CtHeO) '/&m - 3n - P)AHJII(CSH~ '/&2n - 2q - m)AH,(C,Hd - AH,(C.H,O$,) (10)
+
+
Given the experimental AH;s of the reference compounds (Table I), then by substitution3
or upon rearrangement DRE = 7.435n
- 0.605m - 32.175~- 29.38q A H I ( C ~ H ~ O ~ %(12) )
It should be appreciated that, in deriving effective 510
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See reference ( 9 ) unless otherwise indicated Referenca (3).
energies for C L C and C-0 bonds, i t is implicitly assumed that the C=C bonds in trans-butadiene and in divinylether have the same energy as in ethylene itself. Although molecular orbital calculations indicate that this assumption is correct (to within 0.5 kcal/mole a t least), it would be pleasing to eqerimentally verify the constancy of effective bond energies. Unfortunately, very little in the way of accurate thermochemistry is available for conjugated acyclic organic compounds, systems for which the theory yields the following unambiguous prediction for the heat of formation (since DRE = 0 by definition) AH,
=
7.435n - 0.605m
- 32.17513 - 29.389
(13)
An accurate AH, has recently become available for glyoxal, O=CH-CH=O, and the predicted AH, of -50.7 kcal/mole agrees exactly with the experimental AH, of -50.7 kcal/mole (3). For trans,trans1,3,5-hexatriene the theory predicts a AH, of 39.8 which agrees well with the preliminary experimental e s t i m a t e . V h u s the experimental data available does support Dewar's contention that effective bond energies are constant in acyclic compounds. I n summary, we have shown in this section that Dewar's definition can be generalized beyond the scope of a particular SCF molecular orbital theory to all such theories and to empirical thermochemistry, and that the DRE of a compound depends only upon its (calculated or experimental) AH,, since the effect of any "error" in the effective bond energies assumed always cancels out. In this context, it is interesting to note that Hess and Schaad have shown that even the simple Hiiclcel molecular orbital method predicts additivity of C=C and CILC hond energies in acyclic polyenes (5). These energies can be used in conjunction with HMO calculations to yield accurate predictions of aromaticity, nonaromaticity, and antiaromaticity for cyclic systems, in contrast to the many well-known failures of this theory when interpreted from the "delocalization energy" viewpoint. Aromaticity of Conjugated Molecules
I n this section, the aromatic character of a variety of conjugated systems is discussed by reference to the Dewar resonance energy of each. The latter quantity a All energies and enthdpies quoted in this paper are in unite of kcal/mole; to avoid repetition these units will normally be dropped henceforth. ' The heat of hydrogenation of trans-hexatriene in acetic acid solution is 79.4 kcd/mole ( 4 ) Assuming this value is unchanged in the gas phase and using the A H I for n-hexane of -39.92 (S), the value of AH, of hexatriene is f39.5 kcal/mole.
is computed for each compound from its AHl (see Appendix) using eqn. (12). Since experimental AHis are lacking for many molecules of interest, and since many of the experimental AH/s include not only conjugation effects but also energetic changes due to both torsional and steric strain, we shall rely mainly upon "strain-free" AHis calculated by pi electron molecular orbital theories. As representative of the modern SCF-LCAO-MO methods which predict accurate ground state properties, we have chosen to use one scheme in which overlap is neglected (Denfar-deLlano (1)) and one in which it is included explicitly (the NNDO theory (6)). In most cases, the agreement between the two methods is excellent. Experimental DRE values for benzene and six of its simple derivatives are given in Table 2. I n each Table 2.
Experimental DRFs for Benzene Derivatives
Compound
Total DRE*
No. of +Units
DRE per Q Un~t
molecule. For example, the DRE of phenanthrene (IV) is 6-8 kcal/mole greater than that of anthracene (V) due to branching in the former; presumably a corresponding difference in stability should also occur for naphthacene (VI) and 1,2-benzanthracene (VII). Although this differenceis predicted by both theoretical methods, the experimental DRE's differ by only 1 kcal/mole, a discrepancy which Dewar attributes to uncertainty in the experimental AH1 of VI ( l a ) . Clar has advanced the hypothesis that in compounds such as triphenylene (X) and perylene (XI), in which all the double bonds can be written outside the central ring, such rings do not contribute to the aromaticity of the compound (7). This view is substantiated by the DRE's for X and for X I which are almost identical with three times that for benzene and twice that for naphthalene, respectively. The five-membered ring in dibenzofuran is another example of a "hole," since the experimental DRE for the compound (corrected for torsional strain) is 41 kcal/mole, i.e., twice that for benzene. Table 3.
DRFs for Benzenoid Hydrocarbons
Calculated from the experimental AH, acmrdin to eqn. (12). Steric strain mrrection of 2 kcaljmole a d d 2 per pair of hindered hydrogen atom.
21
:x3
case the bonds exocyclic to the phenyl rings (+) are localized in the classical structures; that is, these bonds do not change their character (from single to double or double to single) in any of the equivalent, uncharged valence-bond diagrams. For example, the link between the two phenyls in stilbene is always "single-doublesingle"
42
.?ill
55
4s
With the exception of benzaldehyde, the DRE per phenyl ring is identical with that of 21 kcal/mole for benzene itself. Thus Dewar's postulate-that exocyclic bonds of this type do not contribute to the total DRE of the compound-is confirmed. In other words, the extent of conjugation across the single bonds in such systems (e.g., stilbene) is identical to the conjugation across single bonds in conjugated acyclic systems (e.g., butadiene). An estimate of the magnitude of this "normal conjugation" is given in the following section. Both experimental and theoretical values for the DRE in a series of aromatic benzenoid hydrocarbons are given in Table 3. Note that the DRE is not additive in the number of benzene rings (e.g., that for naphthalene (11) is only 50y0, not 100yo, greater than that of benzene (I)) or in the number of double bonds, and does depend upon the relative orientation of the six-membered rings. In general, the greater the extent of "branching" the larger the DRE of the
(ill
6.5
6.5
GS
(is
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Knowledge of the fact that the presence of localized bonds in side chains does not alter the DRE allows the values quoted in Table 3 to be employed in predicting the site of addition reactions in benzenoid aromatics. Consider the changes in Dewar resonance energy which occur when an ortho addition is made in phenanthrene ADRE-5
In contrast, the second "4n" hydrocarbon, cyclooctatetraene, is essentially nonaromatic and has alternating bond lengths close to those in polyenes. Larger 4n annulenes are all predicted to alternate in bond lengths, but possess small, positive DRE values. Within the 4n 2 series, only benzene is predicted to be most stable when all bond lengths are equal; both MO theories predict that a slight degree of bond alternation is preferred in the most stable planar cyclodecapentaene. Note that the total DRE for ClaHlois less than that for benzene; in the higher annulenes, the DRE values become approximately equal in the 4n and 4n 2 series. Since, among the annnlenes, significant antiaromatic character is predicted only for cyclobutadiene, i t is of some interest to explore the DRE in some derivatives of this hydrocarbon (Table 5). For example, the
+
+
DRE
-
ADRE-16
49
DRE =33 (i.e, naphthalenevalue)
Thus ortho addition to the 9,10 bond in phenanthrene requires 11 kcal/mole less energy than addition in a terminal ring; the 9,10 addition is some 5 kcal/mole less favorable than for bonds in polyenes. Differences in the energetics of addition across para positions (e.g., using 0 2 ) can also he discussed using DRE values, as illustrated by the following examples
The theoretical predictions concerning aromaticity and antiaromaticity in 4n and 4n 2 pi electron annulenes are conveniently discussed using Dewar resonance energy values (Table 4). Both molecular orbital theories predict that cyclobutadiene is antiaromatic to the extent of 17-18 kcal/mole, with single bond distances longer than those for acyclic polyenes.
+
Table 4.
Compound
DRFs for Annulenes D R E VnluDewarNNDO deLlnna Theory
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Table 5.
DRFs for Cyclobutadiene and Derivatives D
Cornlxwnl
R E Values-DewarNN1)O drLlnno Thmrv
DRE of benzcyclobutadiene is +10 kcal/mole and that of dipheuylene, +35 kcal/mole. Thus the destabilizing influence of a four-membered ring is -17, -11, and -7 kcal/mole, respectively, when 0, 1, and 2 benzene rings are joined to it. Finally, the DRE of butalene is -4 kcal/mole, which is midway between that expected for two four-membered rings containing a total of 3 double bonds (-26 kcal/mole) and that for benzene (+21 kcal/mole). A significant degree of antiaromaticity is predicted by the NNDO theory, but not by the Dewar-deLlano method,in two systems containingthree-membered rings (Table 6): methylenecyclopropene (NNDO DRE = -7) and methylenedicyclopropene (NNDO DRE = -2lkcal/mole). The source of the discrepancy is associated with the neglect of overlap integrals in the Dewar-deLlano theory; a detailed discussion of this point is beyond the scope of the present paper. The DRE's predicted for other hydrocarbons containing an odd-membered ring and an exocyclic double bond (fulvene and heptafulvene) are small; the values for the systems in which two such rings are linked via the exocyclic double bond are approximately double those for the "parents." The lack of aromatic character for such systems is probably surprising to those who have been impressed by the large "delocalization energies" predicted for fulvene, etc., by the simple Hiickel method. In fact it is not the Hiickel theory itself which is "wrong" here, but rather the manner in which such calculations are usually interpreted. Thus, in considering the aromaticity of a system, one should not consider simply the magnitude of the delocalization energy (DE), but rather one
Table 6. DRE's for Compounds with Odd-Membered Rings
energies, these quantities are of some inherent interest and are required if rotational barriers and resonance in free radicals are to be discussed. I n this section, one of the possible routes by which such bond energies can be evaluated is explored; once again, the approach used is thermochemical rather than quantum mechanical. In the evaluation of C=C, C Z C , and C(sp2)-H bond energies, the two most important pieces of experimental data are the AH;s of ethylene (12.45) and of trans-butadiene (+26.11), since from these values and the AH;s of free carbon atoms ($170.89) and free hydrogen atoms (+52.10), the total bonding energies (heats of atomization) of the compounds are calculated to be 537.7 and 970.1, respectively. Thus we can write
+
E(C=C) 4E(C-H) = 537.7 2E(C=C) E ( C z C ) GE(C--H) = 970.1
+
should compare it to the total DE predicted by the same method for three conjugated double bonds plus three conjugated single bonds in an acyclic polyene. If the reference compounds used are ethylene and butadiene, then the effective C=C pi bond energy is 2.0008 and that for CLC is 0.4728. Thus the total DE for fulvene of 1.478 is only 0.058 larger than that for the reference structure, and hence even the simple Hiickel method predicts (correctly) that fulvene should be a nonaromatic hydrocarbon. Finally, it is interesting that both the theoretical and the experimental AH,% (corrected for ring strain) of azulene predict a DRE value of 7 1; this value is much lower than that for naphthalene and is approximately equal to that for cyclodecapentaene, in agreement with Dewar's arguments (1).
*
Bond Energies
Although individual values for the energies of carbon-carbon, carbon-oxygen, and carbon-hydrogen bonds need not be known to compute Dewar resonance
+
Unfortunately one cannot use the AH, for a third polyene and obtain a unique solution for the three bond energy terms, since the three simultaneous equations are not linearly independent. From the two expressions above, however, individual values of E(C=C) and E(CLC) can be derived as a function of E(C-H); these relationships are illustrated in the figure. It is interesting to note that any value of E ( C H ) and the corresponding values for the carboncarbon energies is consistent with the ground state thermochemistry of all closed-shell, conjugated hydrocarbons! If unique bond energy terms are to be derived, it is necessary to resort to using either thermochemical data for the methyl free radical (vide injra) or experimental barriers to rotation about C=C and CLC bonds. If the latter course is adopted, a fourth bond energy term must be introduced-that corresponding to the energy of a single bond between two sp2-hybridized carbons, the ligands of which are twisted perpendicular to each other. Two rotation barriers are known which relate the energy, E(C-C), of such a bond to other carbon-carbon bond terms. First, the energy difference between the planar ground state of ethylene and the conformation twisted by 90" is known6to be 61 4. Thus E(C=C) - E(C-C)
=
61
+4
Second, the barrier to rotation about the central bond in trans-butadiene is known to be -5 (Q), which yields the equation E ( C z C ) - E(C-C)
=5
The combination of these barriers with the thermochemistry of ethylene and trans-butadiene results in four simultaneous, linearly-independent equations involving four unknowns, and yields the following unique set of bond energies E(C=C) E(CLC) E(C-C) E(CH)
,
110 90 Interrelation of
,
95 100 E(C-H)
C=C. C-C, m d C-H
146.4 90.4 = 85.4 = 97.8 = =
470 105
bond energies.
The value of 61 kcal/mole is the werage of the enthdpy of activation of 65 for isomerization about the ethylenic double bond (8a) and the 0-0 transition energy of 57 from the planar ground state to the twisted triplet (8b).
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