Identification of the transition state is an important step in the study of reaction kinetics and mechanisms. However, for non-rigid chemical systems where multiple viable reaction pathways may exist, enumeration of all possible transition states quickly becomes computationally expensive, if at all feasible. As an alternative approach, we recently proposed a methodology where the volumetric properties of a flexible reaction system are used to locate its transition state ensemble through a comparison of its theoretically determined volume profile and experimental activation volumes derived from high pressure kinetic data. In this work, we apply this method to internal rotation of the benzene ring in 1,12-dimethoxy-[12]-paracyclophane. For this system, the transition state ensemble was found to be the state with the lowest volume, where the benzene ring and the flexible methylene tether are coplanar. This result was verified by comparison with a Gibbs free energy profile obtained via umbrella sampling.

1.
S.
Glasstone
,
K. J.
Laidler
, and
H.
Eyring
,
The Theory of Rate Processes: The Kinetics of Chemical Reactions, Viscosity, Diffusion and Electrochemical Phenomena
(
McGraw-Hill
,
New York
,
1941
).
2.
D. G.
Truhlar
and
B. C.
Garrett
,
Acc. Chem. Res.
13
,
440
(
1980
);.
D. G.
Truhlar
and
B. C.
Garrett
,
Annu. Rev. Phys. Chem.
35
,
159
(
1984
).
4.
J. D.
Bryngelson
,
J. N.
Onuchic
,
N. D.
Socci
, and
P. G.
Wolynes
,
Proteins
21
,
167
(
1995
).
5.
See, for example:
W. J.
Hehre
,
L.
Radom
,
P. R.
von Schleyer
, and
J.
Pople
,
Ab Initio Molecular Orbital Theory
(
Wiley
,
New York
,
1986
);
S. S.
Shaik
,
H. B.
Schlegel
, and
S.
Wolfe
,
Theoretical Aspects of Physical Organic Chemistry: The SN2 Mechanism
(
Wiley
,
New York
,
1992
);
Transition State: A Theoretical Approach
, edited by
T.
Fueno
(
Gordon and Breach Science Publishers
,
1999
);
F.
Jensen
,
Introduction to Computational Chemistry
, 2nd ed. (
John Wiley & Sons
,
Chichester, England, Hoboken, NJ
,
2007
);
E.
Lewars
,
Computational Chemistry: Introduction to the Theory and Applications of Molecular and Quantum Mechanics
(
Springer
,
Dordrecht, London
,
2011
).
6.
See, for example:
S.
Wolfe
,
A. V.
Buckley
, and
N.
Weinberg
,
Can. J. Chem.
79
,
1284
(
2001
);.
Y.-H.
Hsieh
,
N.
Weinberg
,
K.
Yang
,
C.-K.
Kim
,
Z.
Shi
, and
S.
Wolfe
,
ibid.
83
,
769
(
2005
);.
Q.
Meng
,
C.
Zhang
, and
M.-B.
Huang
,
ibid.
87
,
1610
(
2009
);.
Z.
Shi
,
Y.-H.
Hsieh
,
N.
Weinberg
, and
S.
Wolfe
,
ibid.
87
,
544
(
2009
);.
R.
Gómez-Bombarelli
,
E.
Calle
, and
J.
Casado
,
J. Org. Chem.
78
,
6868
(
2013
);.
[PubMed]
E.
Tílvez
,
G. I.
Cárdenas-Jirón
,
M. I.
Menéndez
, and
R.
López
,
Inorg. Chem.
54
,
1223
(
2015
).
[PubMed]
7.
Y.
Yuan
,
M. J. L.
Mills
,
P. L. A.
Popelier
, and
F.
Jensen
,
J. Phys. Chem. A
118
,
7876
(
2014
);
[PubMed]
See also
C. P.
Chun
,
A. A.
Connor
, and
G. A.
Chass
,
J. Mol. Struct.: THEOCHEM
729
,
177
(
2005
);.
M.
Wierzejewska
and
A.
Olbert-Majkut
,
Chem. Phys. Lett.
476
,
287
(
2009
);.
R. E.
Atwood
and
J. J.
Urban
,
J. Phys. Chem. A
116
,
1396
(
2012
);.
[PubMed]
C.
Wang
,
Z.
Lin
, and
R.
Zhang
,
Comput. Theor. Chem.
1008
,
96
(
2013
);.
S.
Xu
,
D.
Zhao
,
L.
Gong
,
C.
Liu
, and
Z.-Z.
Yang
,
Chem. Phys. Lett.
618
,
147
(
2015
);.
J.
Kaminský
and
F.
Jensen
,
J. Chem. Theor. Comput.
12
,
694
(
2016
).
8.
H.
Wiebe
and
N.
Weinberg
,
J. Chem. Phys.
140
,
124105
(
2014
).
9.
M. J.
Evans
and
M.
Polanyi
,
Trans. Faraday Soc.
31
,
875
(
1935
);.
A. E.
Stearn
and
H.
Eyring
,
Chem. Rev.
29
,
509
(
1941
);.
S. D.
Hamann
,
Physico-Chemical Effects of Pressure
(
Academic Press
,
New York
,
1957
);
M. G.
Gonikberg
,
Chemical Equilibria and Reaction Rates at High Pressures
(
National Science Foundation
,
Washington
,
1963
);
N. S.
Isaacs
,
Liquid Phase High Pressure Chemistry
(
Wiley
,
New York
,
1981
).
10.
W. J.
Le Noble
,
Rev. Phys. Chem. Jpn.
50
,
207
(
1980
);.
W. J.
Le Noble
and
H.
Kelm
,
Angew. Chem., Int. Ed.
19
,
841
(
1980
);.
R.
van Eldik
and
H.
Kelm
,
Rev. Phys. Chem. Jpn.
50
,
185
(
1980
);.
G.
Stochel
and
R.
van Eldik
,
Coord. Chem. Rev.
187
,
329
(
1999
);.
R.
van Eldik
and
C. D.
Hubbard
,
Afr. J. Chem.
53
,
139
(
2000
);
R.
van Eldik
and
C. D.
Hubbard
,
Adv. Phys. Org. Chem.
41
,
1
(
2006
);.
C. D.
Hubbard
and
R.
van Eldik
,
J. Coord. Chem.
60
,
1
(
2007
);.
C.
Hubbard
and
R.
van Eldik
,
Inorg. Chim. Acta
363
,
2357
(
2010
).
11.
S.
Pronk
,
S.
Pall
,
R.
Schulz
,
P.
Larsson
,
P.
Bjelkmar
,
R.
Apostolov
,
M. R.
Shirts
,
J. C.
Smith
,
P. M.
Kasson
,
D.
van der Spoel
,
B.
Hess
, and
E.
Lindahl
,
Bioinformatics
29
,
845
(
2013
).
12.
H. J. C.
Berendsen
,
J. P. M.
Postma
,
W. F.
van Gunsteren
,
A.
DiNola
, and
J. R.
Haak
,
J. Chem. Phys.
81
,
3684
(
1984
).
13.
A. R.
Leach
,
Molecular Modelling: Principles and Applications
(
Pearson Education Ltd
,
Essex, England
,
2001
).
14.
W. L.
Jorgensen
and
J.
Tirado-Rives
,
J. Am. Chem. Soc.
110
,
1657
(
1988
);.
[PubMed]
W. L.
Jorgensen
,
D. S.
Maxwell
, and
J.
Tirado-Rives
,
J. Am. Chem. Soc.
118
,
11225
(
1996
).
15.
B.
Hess
,
J. Chem. Phys.
116
,
209
(
2002
).
16.
S.
Kumar
,
J. M.
Rosenberg
,
D.
Bouzida
, and
R. H.
Swendsen
,
J. Comput. Chem.
13
,
1011
(
1992
).
17.
M. J.
Frisch
,
G. W.
Trucks
,
H. B.
Schlegel
,
G. E.
Scuseria
,
M. A.
Robb
,
J. R.
Cheeseman
,
G.
Scalmani
,
V.
Barone
,
B.
Mennucci
,
G. A.
Petersson
,
H.
Nakatsuji
,
M.
Caricato
,
X.
Li
,
H. P.
Hratchian
,
A. F.
Izmaylov
,
J.
Bloino
,
G.
Zheng
,
J. L.
Sonnenberg
,
M.
Hada
,
M.
Ehara
,
K.
Toyota
,
R.
Fukuda
,
J.
Hasegawa
,
M.
Ishida
,
T.
Nakajima
,
Y.
Honda
,
O.
Kitao
,
H.
Nakai
,
T.
Vreven
,
J. A.
Montgomery
, Jr.
,
J. E.
Peralta
,
F.
Ogliaro
,
M.
Bearpark
,
J. J.
Heyd
,
E.
Brothers
,
K. N.
Kudin
,
V. N.
Staroverov
,
R.
Kobayashi
,
J.
Normand
,
K.
Raghavachari
,
A.
Rendell
,
J. C.
Burant
,
S. S.
Iyengar
,
J.
Tomasi
,
M.
Cossi
,
N.
Rega
,
J. M.
Millam
,
M.
Klene
,
J. E.
Knox
,
J. B.
Cross
,
V.
Bakken
,
C.
Adamo
,
J.
Jaramillo
,
R.
Gomperts
,
R. E.
Stratmann
,
O.
Yazyev
,
A. J.
Austin
,
R.
Cammi
,
C.
Pomelli
,
J. W.
Ochterski
,
R. L.
Martin
,
K.
Morokuma
,
V. G.
Zakrzewski
,
G. A.
Voth
,
P.
Salvador
,
J. J.
Dannenberg
,
S.
Dapprich
,
A. D.
Daniels
,
Ö.
Farkas
,
J. B.
Foresman
,
J. V.
Ortiz
,
J.
Cioslowski
, and
D. J.
Fox
, gaussian 09, Revision E.01,
Gaussian, Inc.
,
Wallingford, CT
,
2009
.
18.
W.
Humphrey
,
A.
Dalke
, and
K.
Schulten
,
J. Mol. Graphics
14
,
33
(
1996
).
19.
H.
Yamada
,
S.
Yonehara
,
S.
Tanaka
,
F.
Muro
,
A.
Watanabe
, and
K.
Nishikawa
,
J. Am. Chem. Soc.
123
,
279
(
2001
).
20.

See Table 2 in Ref. 19.

21.
For reviews, see
C. A. N.
Viana
and
J. C. R.
Reis
,
Pure Appl. Chem.
68
,
1541
(
1996
);.
J.
Spooner
and
N.
Weinberg
,
Can. J. Chem.
95
,
149
(
2017
).
22.
B. S.
El’yanov
and
E. M.
Gonikberg
,
J. Chem. Soc., Faraday Trans. 1
75
,
172
(
1979
);.
B. S.
El’yanov
and
E. M.
Vasylvitskaya
,
Rev. Phys. Chem. Jpn.
50
,
169
(
1980
).
23.
(a)
E.
Deglint
,
H.
Martens
,
E.
Edwards
,
N.
Boon
,
P.
Dance
, and
N.
Weinberg
,
Phys. Chem. Chem. Phys.
13
,
438
(
2011
);
[PubMed]
(b)
H.
Wiebe
,
J.
Spooner
,
N.
Boon
,
E.
Deglint
,
E.
Edwards
,
P.
Dance
, and
N.
Weinberg
,
J. Phys. Chem. C
116
,
2240
(
2012
);
(c)
J.
Spooner
,
H.
Wiebe
,
N.
Boon
,
E.
Deglint
,
E.
Edwards
,
B.
Yanciw
,
B.
Patton
,
L.
Thiele
,
P.
Dance
, and
N.
Weinberg
,
Phys. Chem. Chem. Phys.
14
,
2264
(
2012
).
[PubMed]
24.
W. J.
Le Noble
,
Prog. Org. Chem.
5
,
207
(
1967
);
T.
Asano
and
W. J.
Le Noble
,
Chem. Rev.
78
,
407
(
1978
);.
R.
van Eldik
,
T.
Asano
, and
W. J.
Le Noble
,
Chem. Rev.
89
,
549
(
1989
);.
A.
Drljaca
,
C. D.
Hubbard
,
R.
van Eldik
,
T.
Asano
,
M. V.
Basilevsky
, and
W. J.
Le Noble
,
Chem. Rev.
98
,
2167
(
1998
).
[PubMed]
You do not currently have access to this content.