Statistical mechanics of isomerization dynamics in liquids and the transition state approximation (original) (raw)
Research Article| March 15 1978
School of Chemical Sciences, University of Illinois, Urbana, Illinois 61801
Department of Chemistry, Columbia University, New York, New York 10027
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J. Chem. Phys. 68, 2959–2970 (1978)
In this article, time correlation function methods are used to discuss classical isomerization reactions of small nonrigid molecules in liquid solvents. Molecular expressions are derived for a macroscopic phenomenological rate constant. The form of several of these equations depend upon what ensemble is used when performing averages over initial conditions. All of these formulas, however, reduce to one final physical expression whose value is manifestly independent of ensemble. The validity of the physical expression hinges on a separation of time scales and the plateau value problem. The approximations needed to obtain transition state theory are described and the errors involved are estimated. The coupling of the reaction coordinate to the liquid medium provides the dissipation necessary for the existence of a plateau value for the rate constant, but it also leads to failures of Wigner’s fundamental assumption for transition state theory. We predict that for many isomerization reactions, the transmission coefficient will differ significantly from unity and that the difference will be a strong function of the thermodynamic state of the liquid solvent.
REFERENCES
D.
Chandler
and
L. R.
Pratt
,
J. Chem. Phys.
65
,
2925
(
1976
).
L. R.
Pratt
and
D.
Chandler
,
J. Chem. Phys.
66
,
147
(
1977
).
P. J. Flory, Statistical Mechanics of Chain Molecules (Interscience, New York, 1969).
L. R. Pratt, Ph.D. thesis, (University of Illinois, 1977).
E.
Wigner
,
Trans. Faraday Soc.
34
,
29
(
1938
).
W. H.
Miller
,
Acc. Chem. Res.
9
,
306
(
1976
).
P. Pechukas in Dynamics of Molecular Collisions; Part B, edited by W. H. Miller (Plenum, New York, 1976).
T.
Yamamoto
,
J. Chem. Phys.
33
,
281
(
1960
).
R.
Zwanzig
,
Ann. Rev. Phys. Chem.
16
,
67
(
1965
).
H. D.
Kutz
,
I.
Oppenheim
, and
A.
Ben‐Reuven
,
J. Chem. Phys.
61
,
3313
(
1974
).
F. H. Stillinger, Advances in Theoretical Chemistry, 3, edited by H. Eyring and D. Henderson, (in press).
J. L.
Lebowitz
and
J. K.
Percus
,
Phys. Rev.
122
,
1675
(
1961
).
M. S.
Green
,
Phys. Rev.
119
,
829
(
1960
).
B. J. Berne and R. Pecora, Dynamic Light Scattering (Interscience, New York, 1976); Sec. 11.6 and 11.B.
D. Forster, Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions (Benjamin, Reading, Ma. 1975) Sec. 5.4.
R.
Zwanzig
,
J. Chem. Phys.
40
,
2527
(
1964
).
P. C. Martin, in Statistical Mechanics of Equilibrium and Non‐Equilibrium, edited by J. Meixner (North‐Holland, Amsterdam, 1965).
D. Forster, Ref. 15, Chap. 2.
T. L. Hill, Introduction to Statistical Thermodynamics (Addison‐Wesley, Reading, Ma, 1960) Sec. 10.3.
R. Zwanzig, in Lectures in Theoretical Physics, Vol. 3 (Interscience, New York, 1961).
H.
Mori
,
Prog. Theor. Phys. (Kyoto)
34
,
423
(
1965
).
D. Forster, Ref. 15 Chap. 5;
B. J. Berne and R. Pecora, Ref. 14 Chap. 11.
B. J.
Berne
,
J. P.
Boon
, and
S. A.
Rice
,
J. Chem. Phys.
45
,
1086
(
1966
).
K. J. Laidler, Chemical Kinetics (McGraw‐Hill, New York, 1965), Chap. 3.
H. A.
Kramers
,
Physika
7
,
284
(
1940
).
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© 1978 American Institute of Physics.
1978
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