Transition State Theory

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Donald G Truhlar - One of the best experts on this subject based on the ideXlab platform.

  • variational Transition State Theory theoretical framework and recent developments
    Chemical Society Reviews, 2017
    Co-Authors: Junwei Lucas Bao, Donald G Truhlar
    Abstract:

    This article reviews the fundamentals of variational Transition State Theory (VTST), its recent theoretical development, and some modern applications. The theoretical methods reviewed here include multidimensional quantum mechanical tunneling, multistructural VTST (MS-VTST), multi-path VTST (MP-VTST), both reaction-path VTST (RP-VTST) and variable reaction coordinate VTST (VRC-VTST), system-specific quantum Rice–Ramsperger–Kassel Theory (SS-QRRK) for predicting pressure-dependent rate constants, and VTST in the solid phase, liquid phase, and enzymes. We also provide some perspectives regarding the general applicability of VTST.

  • Transition State Theory for enzyme kinetics
    Archives of Biochemistry and Biophysics, 2015
    Co-Authors: Donald G Truhlar
    Abstract:

    This article is an essay that discusses the concepts underlying the application of modern Transition State Theory to reactions in enzymes. Issues covered include the potential of mean force, the quantization of vibrations, the free energy of activation, and transmission coefficients to account for nonequilibrium effect, recrossing, and tunneling.

  • multi path variational Transition State Theory for chemical reaction rates of complex polyatomic species ethanol oh reactions
    Faraday Discussions, 2012
    Co-Authors: Jingjing Zheng, Donald G Truhlar
    Abstract:

    Complex molecules often have many structures (conformations) of the reactants and the Transition States, and these structures may be connected by coupled-mode torsions and pseudorotations; some but not all structures may have hydrogen bonds in the Transition State or reagents. A quantitative Theory of the reaction rates of complex molecules must take account of these structures, their coupled-mode nature, their qualitatively different character, and the possibility of merging reaction paths at high temperature. We have recently developed a coupled-mode Theory called multi-structural variational Transition State Theory (MS-VTST) and an extension, called multi-path variational Transition State Theory (MP-VTST), that includes a treatment of the differences in the multi-dimensional tunneling paths and their contributions to the reaction rate. The MP-VTST method was presented for unimolecular reactions in the original paper and has now been extended to bimolecular reactions. The MS-VTST and MP-VTST formulations of variational Transition State Theory include multi-faceted configuration-space dividing surfaces to define the variational Transition State. They occupy an intermediate position between single-conformation variational Transition State Theory (VTST), which has been used successfully for small molecules, and ensemble-averaged variational Transition State Theory (EA-VTST), which has been used successfully for enzyme kinetics. The theories are illustrated and compared here by application to three thermal rate constants for reactions of ethanol with hydroxyl radical—reactions with 4, 6, and 14 saddle points.

  • variational Transition State Theory with multidimensional tunneling
    Reviews in Computational Chemistry, 2007
    Co-Authors: Antonio Fernandezramos, Bruce C Garrett, Benjamin A Ellingson, Donald G Truhlar
    Abstract:

    This review describes the application of variational Transition State Theory (VTST) to the calculation of chemical reaction rates. In 1985 two of us, together with Alan D. Isaacson, wrote a book chapter on this subject entitled “Generalized Transition State Theory” for the multi-volume series entitled Theory of Chemical Reaction Dynamics.1 Since that time, variational Transition State Theory has undergone important improvements due mainly to the ability of this Theory to adapt to more challenging problems. For instance, the 1985 chapter mainly describes the application of VTST to bimolecular reactions involving 3–6 atoms, which were the State-of-the-art at that moment. The study of those reactions by VTST dynamics depended on the construction of an analytical potential energy surface (PES). Nowadays, thanks to the development of more efficient algorithms and more powerful computers, the situation is completely different, and most rate calculations are based on “on the fly” electronic structure calculations, which together with hybrid approaches, like combined quantum mechanical molecular mechanical methods (QM/MM), allow researchers to apply VTST to systems with hundreds or even tens of thousands of atoms. Three other major advances since 1985 are that Transition State dividing surfaces can now be defined much more realistically, more accurate methodsmore » have been developed to include multidimensional quantum mechanical tunneling into VTST, and the Theory has also been extended to reactions in condensed phases.« less

  • Reviews in Computational Chemistry - Variational Transition State Theory with Multidimensional Tunneling
    Reviews in Computational Chemistry, 2007
    Co-Authors: Antonio Fernández-ramos, Benjamin A Ellingson, Bruce C Garrett, Donald G Truhlar
    Abstract:

    This review describes the application of variational Transition State Theory (VTST) to the calculation of chemical reaction rates. In 1985 two of us, together with Alan D. Isaacson, wrote a book chapter on this subject entitled “Generalized Transition State Theory” for the multi-volume series entitled Theory of Chemical Reaction Dynamics.1 Since that time, variational Transition State Theory has undergone important improvements due mainly to the ability of this Theory to adapt to more challenging problems. For instance, the 1985 chapter mainly describes the application of VTST to bimolecular reactions involving 3–6 atoms, which were the State-of-the-art at that moment. The study of those reactions by VTST dynamics depended on the construction of an analytical potential energy surface (PES). Nowadays, thanks to the development of more efficient algorithms and more powerful computers, the situation is completely different, and most rate calculations are based on “on the fly” electronic structure calculations, which together with hybrid approaches, like combined quantum mechanical molecular mechanical methods (QM/MM), allow researchers to apply VTST to systems with hundreds or even tens of thousands of atoms. Three other major advances since 1985 are that Transition State dividing surfaces can now be defined much more realistically, more accurate methodsmore » have been developed to include multidimensional quantum mechanical tunneling into VTST, and the Theory has also been extended to reactions in condensed phases.« less

Eli Pollak - One of the best experts on this subject based on the ideXlab platform.

  • Stochastic Transition State Theory
    Journal of Physical Chemistry Letters, 2018
    Co-Authors: Eli Pollak
    Abstract:

    Kramers’s original paper on the diffusion model of chemical reactions was based on the consideration that only the barrier region determines the outcome of transmission over a barrier. Subsequently it became understood that Kramers’s approach was identical to variational Transition State Theory (VTST) and as such used only thermodynamic information. Here, using Kramers’s philosophy in conjunction with perturbation Theory and the realization that the dynamics which is rate-determining usually occurs in the vicinity of the Transition State leads to a novel stochastic rate Theory in which the momentum change induced by the medium is the stochastic variable. A first successful application of the Theory is to the old and challenging problem of motion over a cusped barrier. This has implications for the study of Transition path time distributions as well as the Theory of tunneling via nonadiabatic coupling.

  • Quantum Transition State Theory for dissipative systems
    Chemical Physics, 2001
    Co-Authors: Jie-lou Liao, Eli Pollak
    Abstract:

    Abstract Two formulations of quantum Transition State Theory (QTST) for dissipative systems, based on the symmetrized and Kubo form of the thermal flux operator are presented. Numerical results for a symmetric double well potential are compared with the numerically exact results of Topaler and Makri [J. Chem. Phys. 101 (1994) 7500] and with centroid Transition State Theory. The two forms give similar answers and are similar in accuracy to the centroid Theory. QTST however, is found to always bounds the numerically exact result from above. QTST can be further improved, using a variational Theory or by using the mixed quantum classical version of the Theory.

  • Quantum Transition State Theory for the Collinear H + H2 Reaction
    Journal of Physical Chemistry A, 2000
    Co-Authors: Jie-lou Liao And, Eli Pollak
    Abstract:

    The recently formulated quantum Transition State Theory (QTST) in which the quantum projection operator is approximated by its parabolic barrier limit and the symmetrized thermal flux is evaluated numerically exactly, is applied to the collinear hydrogen exchange reaction. The results are found to bound the exact results from above for temperatures ranging from T = 200 K to T = 1000 K. The QTST rate is almost exact at high temperature and is a factor of 3.7 greater than the exact rate at T = 200 K, where there is extensive tunneling. Contour plots of the quantum Transition State Theory reactive flux reveal that the Theory accounts well for the “corner cutting” observed in the collinear hydrogen exchange reaction at low temperatures. These results demonstrate that one may estimate quantum rates of bimolecular reactions, using only thermodynamic information.

  • A test of quantum Transition State Theory for a system with two degrees of freedom
    Journal of Chemical Physics, 1999
    Co-Authors: Jie-lou Liao, Eli Pollak
    Abstract:

    A recently formulated quantum Transition State Theory is applied to scattering over an Eckart barrier coupled bilinearly to a harmonic mode. Results are compared with the numerically exact and the centroid density method computations of McRae et al. [J. Chem. Phys. 97, 7392 (1992)]. We find that quantum Transition State Theory is of comparable accuracy to the centroid approximation for all parameter ranges studied.

  • A new quantum Transition State Theory
    Journal of Chemical Physics, 1998
    Co-Authors: Eli Pollak, Jie-lou Liao
    Abstract:

    An old challenge in rate Theory is the formulation of a quantum thermodynamic Theory of rates which gives accurate estimates but does not demand any real time propagation. In this paper we attempt to answer the challenge by extending an idea suggested by Voth, Chandler and Miller [J. Phys. Chem. 93, 7009 (1989)]. A new quantum expression for the rate is derived by replacing the exact time dependent dynamics with the analytically known dynamics of a parabolic barrier and utilizing the symmetrized thermal flux operator. The new rate expression is exact for a parabolic barrier, and leads by derivation rather than by ansatz to a phase space integration of a Wigner thermal flux distribution function. The semiclassical limit is similar but not identical to Miller’s semiclassical Transition State Theory. Numerical computations on the symmetric and asymmetric one dimensional Eckart barrier give results which are equal to or greater than the exact ones, as expected from a Transition State Theory. In contrast to ot...

Flemming Yssing Hansen - One of the best experts on this subject based on the ideXlab platform.

  • Oxford Scholarship Online - Static Solvent Effects, Transition-State Theory
    Oxford Scholarship Online, 2018
    Co-Authors: Niels Engholm Henriksen, Flemming Yssing Hansen
    Abstract:

    This chapter discusses static solvent effects on the rate constant for chemical reactions in solution. It starts with a brief discussion of the thermodynamic formulation of Transition-State Theory. The static equilibrium structure of the solvent will modify the potential energy surface for the chemical reaction. This effect is analyzed within the framework of Transition-State Theory. The rate constant is expressed in terms of the potential of mean force at the activated complex. Various definitions of this potential and their relations to n-particle- and pair-distribution functions are considered. The potential of mean force may, for example, be defined such that the gradient of the potential gives the average force on an atom in the activated complex, Boltzmann averaged over all configurations of the solvent. It concludes with a discussion of a relation between the rate constants in the gas phase and in solution.

  • Oxford Scholarship Online - Bimolecular Reactions, Transition-State Theory
    Oxford Scholarship Online, 2018
    Co-Authors: Niels Engholm Henriksen, Flemming Yssing Hansen
    Abstract:

    This chapter discusses an approximate approach—Transition-State Theory—to the calculation of rate constants for bimolecular reactions. A reaction coordinate is identified from a normal-mode coordinate analysis of the activated complex, that is, the supermolecule on the saddle-point of the potential energy surface. Motion along this coordinate is treated by classical mechanics and recrossings of the saddle point from the product to the reactant side are neglected, leading to the result of conventional Transition-State Theory expressed in terms of relevant partition functions. Various alternative derivations are presented. Corrections that incorporate quantum mechanical tunnelling along the reaction coordinate are described. Tunnelling through an Eckart barrier is discussed and the approximate Wigner tunnelling correction factor is derived in the limit of a small degree of tunnelling. It concludes with applications of Transition-State Theory to, for example, the F + H2 reaction, and comparisons with results based on quasi-classical mechanics as well as exact quantum mechanics.

  • Transition-State Theory and dynamical corrections
    Physical Chemistry Chemical Physics, 2002
    Co-Authors: Niels Engholm Henriksen, Flemming Yssing Hansen
    Abstract:

    We consider conventional Transition-State Theory, and show how quantum dynamical correction factors can be incorporated in a simple fashion, as a natural extension of the fundamental formulation. Corrections due to tunneling and non-adiabatic dynamics are discussed, with emphasis on the latter. The correction factor due to non-adiabatic dynamics is considered in relation to the non-activated dissociative sticking of N2 on Fe(111). For this process, conventional Transition-State Theory gives a sticking probability which is about 10 times too large (at T=300 K). We estimate that the sticking probability is reduced by a factor of 2 due to non-adiabatic dynamics.

S. Wiggins - One of the best experts on this subject based on the ideXlab platform.

  • A Quantum Version of Wigner’s Transition State Theory
    Few-Body Systems, 2009
    Co-Authors: R. Schubert, H. Waalkens, S. Wiggins
    Abstract:

    A quantum version of a recent realization of Wigner's Transition State Theory in phase space is presented. The Theory developed builds on a quantum normal form which locally decouples the quantum dynamics near the Transition State to any desired order in (h) over bar. This leads to an explicit algorithm to compute cumulative quantum reaction rates and the associated Gamov-Siegert resonances with high accuracy. This algorithm is very efficient since, as opposed to other approaches, it requires no quantum time propagation

  • A Quantum Version of Wigner's Transition State Theory
    Few-body Systems, 2009
    Co-Authors: R. Schubert, H. Waalkens, S. Wiggins
    Abstract:

    A quantum version of a recent realization of Wigner’s Transition State Theory in phase space is presented. The Theory developed builds on a quantum normal form which locally decouples the quantum dynamics near the Transition State to any desired order in \({\hbar}\). This leads to an explicit algorithm to compute cumulative quantum reaction rates and the associated Gamov–Siegert resonances with high accuracy. This algorithm is very efficient since, as opposed to other approaches, it requires no quantum time propagation.

  • wigner s dynamical Transition State Theory in phase space classical and quantum
    arXiv: Chaotic Dynamics, 2007
    Co-Authors: R. Schubert, H. Waalkens, S. Wiggins
    Abstract:

    A quantum version of Transition State Theory based on a quantum normal form (QNF) expansion about a saddle-centre-...-centre equilibrium point is presented. A general algorithm is provided which allows one to explictly compute QNF to any desired order. This leads to an efficient procedure to compute quantum reaction rates and the associated Gamov-Siegert resonances. In the classical limit the QNF reduces to the classical normal form which leads to the recently developed phase space realisation of Wigner's Transition State Theory. It is shown that the phase space structures that govern the classical reaction d ynamicsform a skeleton for the quantum scattering and resonance wavefunctions which can also be computed from the QNF. Several examples are worked out explicitly to illustrate the efficiency of the procedure presented.

Stuart C. Althorpe - One of the best experts on this subject based on the ideXlab platform.

  • An alternative derivation of ring-polymer molecular dynamics Transition-State Theory
    Journal of Chemical Physics, 2016
    Co-Authors: Timothy J. H. Hele, Stuart C. Althorpe
    Abstract:

    In a previous article [T. J. H. Hele and S. C. Althorpe, J. Chem. Phys. 138, 084108 (2013)], we showed that the t → 0+ limit of ring-polymer molecular dynamics (RPMD) rate-Theory is also the t → 0+ limit of a new type of quantum flux-side time-correlation function, in which the dividing surfaces are invariant to imaginary-time translation; in other words, that RPMD Transition-State Theory (RMPD-TST) is a t → 0+ quantum Transition-State Theory (QTST). Recently, Jang and Voth [J. Chem. Phys. 144, 084110 (2016)] rederived this quantum t → 0+ limit and claimed that it gives instead the centroid-density approximation. Here we show that the t → 0+ limit derived by Jang and Voth is in fact RPMD-TST.

  • shallow tunnelling correction factor for use with wigner eyring Transition State Theory
    Physical Chemistry Chemical Physics, 2014
    Co-Authors: Yanchuan Zhang, Judith B Rommel, Marko T Cvitas, Stuart C. Althorpe
    Abstract:

    We obtain a shallow-tunnelling correction factor for use with Wigner–Eyring Transition-State Theory (TST). Our starting point is quantum Transition State Theory (QTST), which approximates the accurate quantum rate as the instantaneous flux through a delocalised Transition-State ensemble of ring-polymers. Expanding the ring-polymer potential to second order gives the well-known Wigner tunnelling-factor which diverges at the cross-over temperature between deep and shallow tunnelling. Here, we show how to remove this divergence by integrating numerically over the two softest ring-polymer normal modes. This results in a modified Wigner correction factor involving a one-dimensional integral evaluated along a straight line on the potential energy surface. Comparisons with accurate quantum calculations indicate that the newly derived correction factor gives realistic estimates of quantum rate coefficients in the shallow-tunnelling regime.