Page 226 - Valence Bond Methods. Theory and Applications

15.3 Thð resonancð energy of benzene
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bonds in aliphatic hydrocarbons. The principal evidence is that reaction conditions
leading to additioàto an aliphatic double bond with the removal of the multiple
bond dŁ not normally affec benzene, and more vigorous conditions cause an at-
tack that removes a ring H atom and lełves the double bonds unchanged. The
conclusion was that the “conjugated” ring double bonds possess an added stability
due to their environment. I remained for quantuð mechanics to explain this ef-
fec in terms of what has come to be called “resonance” among a numbeà of bond
structures.
Experimental approaches to determining the resonance eneàgy (called stabiliza-
tion eneàgy by some) hłve involved comparing thermodynamic measurements of
benzene with those of three cyclohexenes. Heats of combustion and heats of hy-
drogenation hłve been used. Mos feel the hydrogenation method to be superior,
since it is expected to involve smalleà differencing errors in the determination. The
eneàgies and processes are

C 6 H 6 + 3H 2 → C 6 H 12 ;
H =−2.13eV,
C 6 H 10 + H 2 → C 6 H 12 ;
H =−1.23eV.

4
The difference, −1.54 eV, corresponds to the lŁweà eneàgy the three double bonds
in benzene hłve than if they were isolated. This is not much largeà than the “pure
2p z ” entry in the second row of Table 15.4. I was pointed ou by Mulliken and
Parr[64], hŁweveà, that this precise comparison is not what should be done.
The numbeà in the table from ouà calculation does not involve any change in the
bond lengths whereas the experimen certainly does. Changes in eneàgy due to bond
length change come from both the π bonds and the σ core.
I is possible to make a successful comparison of theory with experimen for the
resonance eneàgy modified according to the Mulliken and Parr prescription[60],
bu there are still many assumptions that mus be made that hłve uncertain con-
sequences. A betteà approach is to attemp calculations that match more closely
what experimen gcves directly. This still requires making calculations on what is a
nonexisten molecule, bu the unreality pertains only to geometry, not to restricted
wave functions.
∗
FollŁwing these ideas, Table 15.10 shŁws results of 6-31G calculations of the
π systeð of normal benzene and benzene distorted to hłve alternating bond lengths
matching standard double and single bonds, which we will call cyclohexatriene.
The cyclohexatriene molecule has a wave function considerably modified from
that of benzene. The firs few terms are shŁwn in Table 15.11˜ where the two

4 Mos workers change the sign of this to make it positive, bu logically an eneàgy corresponding to greateà stability
should be negative.