Variational transition-state theory (original) (raw)
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Computer Physics Communications, 1987
We present a computer program for calculating rate constants of gas.phase chemical reactions involving one or two reactants with a total of three to ten atoms. The program accepts information about the potential energy surface in the form of either an analytic potential energy function or a sequence of geometries, energies, gradients and second (or higher) derivative matrices at points along the reaction path. In the former case the program itself calculates the reaction path and the sequence of derivative matrices. From this information the program calculates the rate constant for quantized internal degrees of freedom and classical reaction-path motion by variational transition state theory (VTST). The probabilities for tunneling and nonclassical reflection are estimated by semiclassical methods and incorporated by a transmission coefficient, which for thermal reactions is based on the ground state. There are several options for including the effects of anharmonicity in the independent-normal-mode approximation, and the reaction-path curvature may be included in the tunneling calculation by the small-curvature approximation. The article also presents test calculations illustrating the use of new reaction-path interpolation and extrapolation procedures which should be useful in conjunction with VTST calculations based on ab initio gradients and Hessian calculations.
The Journal of Chemical Physics, 1991
We present a new systematic set of algorithms for interpolated variational transition-state theory by mapping (IVTST-M). In this method, which is designed to allow efficient direct dynamics calculations, rate constants for chemical reactions are evaluated by variational transition-state theory with multidimensional tunneling approximations based on reaction-path data. The data (energies, energy gradients, and Hessians) are computed at a small number of points along a reaction path and fitted to splines under tension as functions of a mapped independent variable that is a nonlinear function of the reaction coordinate. The theory is illustrated and tested by several examples, and standard choices are employed for all parameters and functional forms to provide a realistic test of how the method might perform when applied as an automatic scheme without fine-tuning each reaction. For eight test cases, we obtain reasonable accuracy (as compared to calculations with the same potential surface with the reaction path followed as far as necessary for convergence) with Hessians at only six nonstationary points.
7.3. Transition State Theory and Chemical Reaction Dynamics in Solution
2000
Most chemical and chemical technological processes, including most synthetic and all biochemical reactions, take place in the liquid phase. The solvent often plays a central role in determining the kinetics and outcome of liquid-phase chemical reactions, and the present chapter describes theoretical and computational methods that may be used to understand such effects in terms of continuum solvation models. How does the solvent influence a chemical reaction rate? There are three ways. 1,2 The first is by affecting the attainment of equilibrium in the phase space (space of coordinates and momenta of all the atoms) or quantum state space of reactants. The second is by affecting the probability that reactants with a given distribution in phase space or quantum state space will reach the dynamical bottleneck of a chemical reaction, which is the variational transition state. The third is by affecting the probability that a system, having reached the dynamical bottleneck, will proceed to products. We will consider these three factors next. Reactant equilibrium. In a fixed-temperature gas, molecular collisions populate the various states of the reactants. In the absence of chemical reaction, the populations of these states would come into thermal equilibrium, as governed by Boltzmann statistics (or, in a quantal system, by Fermi-Dirac and Bose-Einstein statistics). However, when reactions occur, the most reactive states (usually the highest-energy ones) may react rapidly. In this case a steady-state distribution is set up in which the rate of population of these states by molecular collisions (and possibly back reaction) is balanced by their depletion by reactions. The resulting nonequilibrium distribution can be quite different from the equilibrium one, especially for unimolecular reactions in low-pressure gases. 3,4 It is often assumed that such nonequilibrium effects are always
Journal of Molecular Structure: THEOCHEM, 2004
A computational approach to calculating potential energy surfaces for reactive systems is presented and tested. This hybrid approach is based on integrated methods where calculations for a small model system are performed by using analytical potential energy surfaces, and for the real system by using molecular orbital or molecular mechanics methods. The method is tested on a hydrogen abstraction reaction by using the variational transition-state theory with multidimensional tunneling corrections. The agreement between the calculated and experimental information depends on the quality of the method chosen for the real system. When the real system is treated by accurate quantum mechanics methods, the rate constants are in excellent agreement with the experimental measurements over a wide temperature range. When the real system is treated by molecular mechanics methods, the results are still good, which is very encouraging since molecular mechanics itself is not at all capable of describing this reactive system. Since no experimental information or additional fits are required to apply this method, it can be used to improve the accuracy of molecular orbital methods or to extend the molecular mechanics method to treat any reactive system with the single constraint of the availability of an analytical potential energy surface that describes the model system.
Kinetic Isotope Effects in Multipath VTST: Application to a Hydrogen Abstraction Reaction
The Journal of Physical Chemistry B, 2016
In this work we apply multipath canonical variational transition state theory with small-tunneling corrections (MP-CVT/SCT) to the hydrogen abstraction reaction from ethanol by atomic hydrogen in aqueous solution at room temperature. This reaction presents two transition states which can interconvert by internal rotations about single bonds and another two transition states that are non interconvertible enantiomers to the former structures. The study also includes another three reactions with isotopically substituted species for which there are experimental values of thermal rate constants
Journal of the American Chemical Society, 1994
This paper outlines a new approach for characterizing the transition state (TS) of a chemical reaction by introducing the concept of an avoided crossing state (ACS). The ACS (defined by eq 1) is a well-defined point on the reaction surface in the immediate vicinity of the TS and therefore may be used as a TS model. The key property of the ACS is that reactant and product Heitler-London configurations contribute equally to its wave function, and as a result the ACS is well-defined in electronic terms. A general methodology for locating ACSs for a range of ionic and Menschutkin S N~ reactions of CHjX (X = F, C1, Br, I) derivatives is described. The reactions that were examined span a wide range of reaction energy (over 100 kcal/mol) and possess TSs which spread the gamut from "early" through "late". Nevertheless, all these TSs were found to be located very close to an ACS. Our study indicates that for this wide range of S N~ reactions there is no simple linkage between TS charge and geometry; TS charge is largely governed by the extent of mixing of the intermediate configuration, while TS geometry is governed by reaction exothermicity. We conclude that the ACS is an excellent approximation for the TS and propose that the ACS may serve as a useful transition-state paradigm in chemical reactivity.
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 coupledmode 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 multidimensional 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.
The Journal of Physical Chemistry, 1995
We consider a new approach to reaction-path dynamics calculations in which the reaction path is calculated at a low level (LL) of theory and stationary point information from a high level (HL) of theory is used to interpolate corrections to energetic quantities, vibrational frequencies, and moments of inertia. Such a calculation is labeled W / N , where X denotes the high level and Y the low level. The theory is applied to the reaction OH + N H 3 and three isotopomeric analogs. The highest-level optimization reported for the saddle point is QCISD(T)//MP2/aug-cc-pVTZ, which yields a classical barrier height of 3.65 kcdmol. The rate constant is calculated at two levels, QCISD(T)//MP2/aug-cc-pVTZ[MP2/aug-cc-pVDZ]///MP2/6-3 1 G** and QCISD(T)//MP~/~U~-CC-~VTZ[MP~/~U~-CC-~VDZ]///PM~-SRP; the calculated rate constant for the unsubstituted reaction is approximately invariant to the low level used in the dual-level scheme and agrees
We present a new formulation of variational transition state theory (VTST) called multi-structural VTST (MS-VTST) and the use of this to calculate the rate constant for the 1,4-hydrogen shift isomerization reaction of 1-pentyl radical and that for the reverse reaction. MS-VTST uses a multifaceted dividing surface and provides a convenient way to include the contributions of many structures (typically conformers) of the reactant and the transition state in rate constant calculations. In this particular application, we also account for the torsional anharmonicity. We used the multiconfiguration Shepard interpolation method to efficiently generate a semi-global portion of the potential energy surface from a small number of high-level electronic structure calculations using the M06 density functional in order to compute the energies and Hessians of Shepard points along a reaction path. The M06-2X density functional was used to calculate the multi-structural anharmonicity effect, including all of the structures of the reactant, product and transition state. To predict the thermal rate constant, VTST calculations were performed to obtain the canonical variational rate constant over the temperature range 200-2000 K. A transmission coefficient is calculated by the multidimensional small-curvature tunneling (SCT) approximation. The final MS-CVT/SCT thermal rate constant was determined by combining a reaction rate calculation in the singlestructural harmonic oscillator approximation (including tunneling) with the multi-structural anharmonicity torsional factor. The calculated forward rate constant agrees very well with experimentally-based evaluations of the high-pressure limit for the temperature range 300-1300 K, although it is a factor of 2.5-3.0 lower than the single-structural harmonic oscillator approximation over this temperature range. We anticipate that MS-VTST will be generally useful for calculating the reaction rates of complex molecules with multiple torsions. † Electronic supplementary information (ESI) available: Information used for calculating the conformational-rotational-vibrational partition functions of 1-pentyl, 2-pentyl and the transition state by MS-RS-HO and MS-RS-T methods, the transmission coefficient of the reaction using SCT approximation, the optimized geometries of the 1-pentyl radical, the 2-pentyl radical and the transition state structures, the effect of scaling factors on the multi-structural torsional anharmonicity factors and a plot of the calculated MS-VTST rate constants with the fitting curves. See