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Vol. 74 No. 7 July 1997 • Journal of Chemical Education 813
Research: Science & Educat ion
A Three-Dimensional Energy Surface for the Conformational
Inversion of Cyclohexane
Nicholas Leventis,* Samir B. Hanna, and Chariklia
Sotiriou-Leventis
Department of Chemistry, University of Missouri-Rolla, Rolla, MO
65409
Cyclohexane has been the archetype for teaching con-formational
analysis of six-membered rings (1–7 ). In thiscommun ication
we sh ar e our a pproa ch of using a th ree-di-mensional potential
energy diagram to help students visu-alize, understand, a nd
remember tha t conformational inver-sion of cyclohexane, in w hich
all equa torial subst ituents be-come a xial a nd vice versa, does
not n ecessarily involve theboat conformation and the low
activation energy f lexingmotion called pseudorota tion.
The most st a ble conforma tion of cyclohexan e, the cha
ir,interconverts through a metastable conformation cal led“ twis t
”1 (Fig. 1), w hich lies 5.5 kcal/mol high er in en th a
lpythan the cha i r (8 ). This t ra nsla tes t o one molecule
of cyclo-hexa ne in t he tw ist conformat ion for every 10,000
molecules
in the chair conformation at 25 °C (9 ).2 Experimental
de-tection of the twist conformation has been accomplishedwit h
low-temperat ure infra red spectroscopy (10 ). The
tra n-sition sta te for th e chair-to-tw ist conversion is ca lled
“half-twis t ” ;3 it lies 10.8 kcal/mol higher in ent ha lpy
th an th echair (2, 3 ).
Meanw hile, the boat conformat ion of cyclohexane liesa bout 1–2
kcal/mol of enth alpy above the tw ist conforma -t ion and i s
regarded as a t r ans i t ion s ta te in the in ter-conversion of
twist conformations (Fig. 2) (1–3 ). The boatconformat ion is
desta bilized relat ive to the tw ist by eclips-ing interactions
along the C-2–C-3 and C-5–C-6 bonds, andby flagpole interactions
between th e substituents a t C -1 andC-4. The higher energy of th
e tw ist a nd boat conformat ionsrelative to the chair not
withstanding, all carbons in bothtwist and boat conformations are
tetrahedral with normalbond angles and bond lengths, so that these
conformationscan be locked in space by a judicious structural
design. Inthis realm, both t wista ne and norbornan e are w
ell-knowncompounds (1 ).
Twistane Norbornane
In standard organic chemistry texts one encounterstwo main
versions of energy diagrams that descr ibe the
inter conversion of the va rious conformers of cyclohexane w
ereviewed a bove (Figs. 3a a nd 3b) (2, 3 ). The energy dia
gra mof Figure 3a shows that chair conformations
interconvertthrough pseudorotat ion; th is ma y be confusing by
giving thefalse impression that the boat conformation is always
in-volved in the conformational inversion of cyclohexane.
Con-versely, the energy diagra m of Figure 3b shows th at
chairsinterconvert through only one tw ist conforma tion. However,a
new question now concerns the location of the boat con-forma tion
on the energy surfa ce, becau se it is clear th a t w ecannot
include the boat conformation in the plane of Fig-ure 3b and remain
consistent with the frequently c i ted
sta tement tha t “chair forms can interconvert w ithout pass-ing
through the boat ” (2 ). An energy diagram that locatesthe
chair, twist, and boat conformations of cyclohexane ona single
surface w hile correctly showing t he int erconversiondynamics is
the three-dimensional energy diagram of Fig-ure 4.*Corresponding
author.
Figure 1. Conformational inversion of cyclohexane. Balls are
used
not to differentiate, but to trace, substituents during
conformational
inversion.
6 5
4
32
1
6 5
4
32
1
6 5
4
32
1
1
6 5
3
4
2
Half -twist
(transition state)
Twist Chair
(transition state)
Half -twistChair
5
4
3
2
1
6
Figure 2. Interconversion of two twist conformations via a
boat
(pseudorotation).
1
2
3
4
56
4
3
2
1
6 5
1
2 3
4
56
Twist Boat
(transition state)Twist
flagpole interaction
HH HH
Figure 3. Two commonly used energy diagrams for the
conforma-
tional inversion of cyclohexane. The reaction coordinate
represents
the progression of one conformation of cyclohexane to
another
and is related to several torsional angles.
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814 Journal of Chemical Education • Vol. 74 No. 7 July 1997
Research: Science & Educat ion
Along reaction coordinate 1 of Figure 4, chair confor-ma t i o
ns 1–6 in terconver t to cha i r conformat ions 1′–6′through
the corresponding twist conformations. Structures1–6 are
identical (therefore energetically equivalent), andthey differ only
in the rotational position from which welook at the entire
molecule; in fact structures 1–6 can beobtained by a simple
stepwise rotation of the entire mol-ecule by 60° at a time,
and of course the same is true fors t ruc tures 1′–6′. Clear ly ,
there i s no ac t iva t ion bar r ieramong structures 1 t o
6 (or 1′ t o 6′) along reaction coordi-na te 2, wh ich
represents t he conversion of one tw ist confor-ma tion to an other
twist conforma tion through the boa t con-
formation. However , the twist conformations that corre-spond to
the pa i r s 1–1′ t o 6–6′, e ve n tho ug h the y a r
eisoenergetic, th ey a re not equiva lent because in order t o
ob-ta in th e one from the other, bonds m ust be rota ted (see
Fig.2), and the energetically unfavorable steric interactions ofthe
boat conformat ions a long rea ction coordinat e 2 must beovercome.
The different boa t t ra nsit ion stat es, shown in Fig-ure 4 along
t he interconversion of th e tw ist conforma tions,correspond
precisely t o the su ccessive conforma tions of onefull cycle of
pseudorotation, as can be verified easily withthe use of a
model.
According to Figure 4, a chair conformation, for ex-ample 1, can
move along reaction coordinat e 1 via the ha lf-twist to the twist
conformation, from where it has two op-tions: either t o cont inue
along rea ction coordina te 1 througha second half-twist
conformation to the inverted chair 1′without passing through any
boat, or to move along reac-tion coordinate 2 through one or more
boat conformat ionsto another twist conformation before it moves
again alongreaction coordinate 1 to any of the inverted chairs
2′–6′,which are only notationally different from 1′. In summa
ry,the energy diagram of Figure 4 shows simultaneously
t ha t(i) cha ir conformations can interconvert with out pa
ssingthr ough an y boat conforma tion, an d (ii) boat conforma
tions
Figure 4. A three-dimensional
energy diagram for the con-
formational inversion of cyclo-
hexane. The diagram shows
the relative energy and posi-
tion along the reaction coor-dinates of the various twist
and boat conformations dur-
ing one full cycle of pseudo-
rotation, and emphasizes that
chair forms can interconvert
without passing through any
boat.
are simply transition states in the interconversion of
twistconformations.
Our classroom experience with teaching conforma-tional analysis
of cyclohexane at both the undergraduateand gradua te levels using
Figure 4 is tha t st udents’ abil i tyto grasp the subtle points of
the subject has improved sig-nificantly.
Notes
1. The names “twist-boat” (3 ) and “skew-boat” (8 )
are alsoused for the twist conformation (1, 2, 9 ).
2. This value is calculated using the equation
∆G ° =RT ln K
and assuming that ∆G ° ≈ ∆H °. However, if
entropic corrections areapplied through ∆G ° =
∆H ° – T ∆S ° with ∆H ° = 5.5
kcal/mol and
∆S ° = R ln 2 (because there are two
conformers in the chair/twistequilibrium), it is calculated that at
room temperature there areactually fewer than 5 molecules in the
twist conformation per100,000 molecules in the chair
conformation.
3. The name “half-chair” (3 ) is also used for the
half-twist con-
formation (2 ).
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New York, 1990; Pa rt A, pp 130–132.
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