Abstract
Chemical rates, the temporal evolution of the populations of species of interest, are of fundamental importance in science. Understanding how such rates are determined by the microscopic forces involved is, in turn, a basic focus of the present discussion.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
- Potential Energy Surface
- Transition State Theory
- Chemical Rate
- Time Correlation Function
- Inherent Structure
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
M. Polanyi and E. Wigner, “The interference of characteristic vibrations as the cause of energy fluctuations and chemical change”, Z. Phys. Chem., 139 (Abt. A), 439, 1928.
H. Eyring, “Activated complex in chemical reaction”, J. Chem. Phys., 3, 107, 1935.
H.A. Kramers, “Brownian motion in a field of force and the diffusion model of chemical reactions”, Physica (The Hague), 7, 284, 1940.
N.B. Slater, Theory of Unimolecular Reactions, Cornell University Press, Ithaca, 1959.
P.J. Robinson and K.A. Holbrook, Unimolecular Reactions, Wiley-Interscience, 1972.
D.G. Truhlar and B.C. Garrett, “Variational transition state theory”, Ann. Rev. Phys. Chem., 35, 159, 1984.
D. Chandler, Introduction to Modern Statistical Mechanics, Oxford, New York, 1987.
P. Hänggi, P. Talkner, and M. Borkovec, “Reaction-rate theory: fifty years after Kramers”, Rev. Mod. Phys., 62, 251, 1990.
M. Garcia-Viloca, J. Gao, M. Karplus, and D.G. Truhlar, “How enzymes work: analysis by modern rate theory and computer simulations”, Science, 303, 186, 2004.
F.H. Stillinger and T.A. Weber, “Dynamics of structural transitions in liquids”, Phys. Rev. A, 28, 2408, 1983.
F.H. Stillinger and T.A. Weber, “Packing structures and transitions in liquids and solids”, Science, 225, 983, 1984.
F.H. Stillinger, “Exponential multiplicity of inherent structures”, Phys. Rev. E, 59, 48, 1999.
O.M. Becker and M. Karplus, “The topology of multidimensional potential energy surfaces: theory and application to peptide structure and kinetics”, J. Chem. Phys., 106, 1495, 1997.
D.J. Wales and J.P.K. Doye, “Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms”, J. Phys. Chem. A, 101, 5111, 1997.
L. Onsager, “Reciprocal relations in irreversible processes, II”, Phys. Rev., 38, 2265, 1931.
M.H. Kalos and P.A. Whitlock, Monte Carlo Methods, Wiley-Interscience, New York, 1986.
M.P. Nightingale and C.J. Umrigar, Quantum Monte Carlo Methods in Physics and Chemistry, Kluwer, Dordrecht, 1998.
J.P. Valleau and G.M. Torrie, “A guide to Monte Carlo for statistical mechanics: 2. byways”, In: B.J. Berne (ed.), Statistical Mechanics: Equilibrium Techniques, Plenum, New York, 1969, 1977.
C.H. Bennett, “Exact defect calculations in model substances”, In: A.S. Nowick and JJ. Burton (eds.), Diffusion in Solids: Recent Developments, Academic Press, New York, pp. 73, 1975.
A.F. Voter, “A Monte Carlo method for determining free-energy differences and transition state theory rate constants”, J. Chem. Phys., 82, 1890, 1985.
D.D. Frantz, D.L. Freeman, and J.D. Doll, “Reducing quasi-ergodic behavior in Monte Carlo simulations by J-walking: applications to atomic clusters”, J. Chem. Phys., 93, 2769, 1990.
J.P. Neirotti, F. Calvo, D.L. Freeman, and J.D. Doll, “Phase changes in 38 atom Lennard-Jones clusters: I: a parallel tempering study in the canonical ensemble”, J. Chem. Phys., 112, 10340, 2000.
C.J. Geyer and E.A. Thompson, “Anealing Markov chain Monte Carlo with applications to ancestral inference”, J. Am. Stat. Assoc., 90, 909, 1995.
J.E. Adams and J.D. Doll, “Dynamical aspects of precursor state kinetics”, Surf. Sci., 111, 492, 1981.
J.D. Doll and A.F. Voter, “Recent developments in the theory of surface diffusion”, Ann. Revi. Phys. Chem., 38, 413, 1987.
A.F. Voter, J.D. Doll, and J.M. Cohen, “Using multistate dynamical corrections to compute classically exact diffusion constants at arbitrary temperature”, J. Chem. Phys., 90, 2045, 1989.
G. Henkelman and H. Jónsson, “Long time scale kinetic Monte Carlo simulations without lattice approximation and predefined event table”, J. Chem. Phys., 115, 9657, 2001.
A.F. Voter, F. Montalenti, and T.C. Germann, “Extending the time scale in atomistic simulation of materials”, Ann. Rev. Mater. Res., 32, 321, 2002.
V.S. Pande, I. Baker, J. Chapman, S.P. Elmer, S. Khaliq, S.M. Larson, YM. Rhee, M.R. Shirts, C.D. Snow, E.J. Sorin, and B. Zagrovic, “Atomistic protein folding simulations on the submillisecond time scale using worldwide distributed computing”, Biopolymers, 68, 91, 2003.
C.J. Cerjan and W.H. Miller, “On finding transition states”, J. Chem. Phys., 75, 2800, 1981.
C.J. Tsai and K.D. Jordan, “Use of an eigenmode method to locate the stationary points on the potential energy surfaces of selected argon and water clusters”, J. Phys. Chem., 97, 11227, 1993.
J. Nichols, H. Taylor, P. Schmidt, and J. Simons, “Walking on potential energy surfaces”, J. Chem. Phys., 92, 340, 1990.
D.J. Wales, “Rearrangements of 55-atom Lennard-Jones and (C60)_55 clusters”, J. Chem. Phys., 101, 3750, 1994.
G. Henkelman and H. Jónsson, “A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives”, J. Chem. Phys., 111, 7010, 1999.
L.R. Pratt, “A statistical method for identifying transition states in high dimensional problems”, J. Chem. Phys., 85, 5045–5048, 1986.
P.G. Bolhuis, D. Chandler, C. Dellago, and P.L. Geissler, “Transition path sampling: throwing ropes over rough mountain passes, in the dark”, Ann. Rev. Phys. Chem., 53, 291, 2002.
B.G. Mirkin, Mathematical Classification and Clustering, Kluwer, Dordrecht, 1996.
D. Sabo, D.L Freeman, and J.D. Doll, “Stationary tempering and the complex quadrature problem”, J. Chem. Phys., 116, 3509, 2002.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer
About this chapter
Cite this chapter
Doll, J.D. (2005). A Modern Perspective on Transition State Theory. In: Yip, S. (eds) Handbook of Materials Modeling. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-3286-8_78
Download citation
DOI: https://doi.org/10.1007/978-1-4020-3286-8_78
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3287-5
Online ISBN: 978-1-4020-3286-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)