Variational transition state theory tests

Allison TC, Trahlar DG (1998) Testing the accuracy of practical semiclassical methods variational transition state theory with optimized multidimensional tunnelling. In Thompson DL (ed) Modern Methods for Multidimensional Dynamics Computations in Chemistry. World Scientific, Singapore, p 618... 

Tests of Variational Transition State Theory (Including Tunneling)... 

Table 6.2 Tests of Variational Transition State Theory by Comparing with Exact Quantum Calculations (Extracted from Allison, T. C. and Truhlar, D. G. Testing the accuracy of practical semiclassical methods variational transition state theory with optimized multidimensional tunneling, in Thompson, D. L., Ed. Modem methods for multidimensional dynamics computations in chemistry, World Scientific, Singapore 1998. pp 618-712. This reference quotes results on many more reactions and BO surfaces over broad temperature ranges.)The numbers in the table are ratios of the results of the approximate calculation to the quantum calculation, all at 300 K...

Table 6.3 Tests of variational transition state theory by comparing with exact quantum calculations isotope effects at 300 K. The numbers in the table are ratios of rate constants for the two selected reactions...

Garrett, B. C., Abusalbi, N., Kouri, D. J., Truhlar, D. G. (1983) Test of variational transition state theory and the least-action approximation for multidimensional tunneling probabilities against accurate quanta rate constants for a collinear reaction involving tunneling in an excited state, J. Chem. Phys. 83, 2252-2258. 

B. C. Garrett, D. G. Truhlar, R. S. Grev, A. W. Magnuson, and J. N. L. Connor, Variational transition state theory, vibrationally adiabatic transmission coefficients, and the unified statistical model tested against accurate quantal rate constants for collinear F + H2, H + F2, and isotopic analogs, 7. Chem. Phys. 73 1721 (1980). 

B. C. Garrett and D. G. Truhlar, Critical tests of variational transition state theory and semiclassical tunneling methods for hydrogen and deuterium atom transfer reactions and use of the semiclassical calculations to interpret the overbarrier and tunneling dynamics, 7. Phys. Chem. 95 10374 (1991). 

D. K. Bondi, J. N. L. Connor, B. C. Garrett, and D. G. Truhlar, Test of variational transition state theory with a large-curvature tunneling approximation against accurate quantal reaction probabilities and rate coefficients for three collinear reactions with large reaction-path curvature Cl + HC1, Cl + DC1, and Cl + MuCl, 7. Chem. Phys. 78 5981 (1983). 

Another use for standard models is as a target. It is important to determine at what point the model breaks down and whether that point is significant in realistic chemical dynamics. Some of the more important developments in the tests of Grote-Hynes theory have been in the application of variational transition state theory (VTST) to models of solution reaction dynamics. The origin of the use of VTST in solution dynamics is in the observation that the GLE can be equivalently formulated in Hamiltonian terms by a reaction coordinate coupled to a bath of harmonic oscillators. It has been shown by van der... 

Unfortunately, accurate quantum dynamics calculations are beyond the state of the art for systems with 5 or more atoms. But the atom-diatom calculations can be used to test the accuracy of more practical theories. For example, a 1986 calculation [5] based on variational transition state theory (VTST) with semiclassical tunneling (ST) contributions agrees with the accurate quantum dynamical results within 10-20% over the whole 300-1500 K range of T. This is particularly encouraging for two reasons (i) VTST/ST calculations provide an easily understood and classically visualizable picture of dynamical bottlenecks and tunneling paths [6] (ii) VTST/ST calculations are practical for much larger systems [7]. 

Pu JZ, Corchado JC, Truhlar DG (2001) Test of variational transition state theory with multidimensional tunneling contributions against tm accurate fuU-dimensional rate constant calculation fora six-atom system. J Chem Phys 115 6266-6267... 

Accurate quantum mechanical calculations on the D -f H2 reaction allow one to test the quantitative predictive ability of variational transition state theory with multidimensional tunneling contributions. Such VTST calculations agree with accurate quantum dynamics with an average eiTor of only... 

If the populations of the transition state s vibrational-rotational levels are assumed to be those of transition state theory, the trajectories may be used to test the fundamental assumption of transition state theory. Both micro-canonical and canonical variational transition state theory are based on the assumption that trajectories cross the transition state (TS) only once in forming product(s) or reactant(s). The correction k to the transition-state theory rate constant is determined by initializing trajectories at the TS and sampling their coordinates and momenta from the appropriate statistical distributions.The value for k is the number of trajectories that form product(s) divided by the number of crossings of the TS in the reactant(s) product(s) direction. Transition state theory (TST) assumes this ratio is unity. 

Computations in Chemistry, D. L. Thompson, Ed., World Scientific, Singapore, 1998, pp. 618-712. Testing the Accuracy of Practical Semiclassical Methods Variational Transition State Theory With Optimized Multidimensional Tunneling. 

Test of Variational Transition State Theory and the Least-Action Approximation for Multidimensional Tunneling Probabilities Against Accurate Quantal Rate Constants for a Collinear Reaction Involving Tunneling into an Excited State. 

Variational Transition State Theory With Least-Action Tunneling Calculations for the Kinetic Isotope Effects in the Atomic Chlorine + Molecular Hydrogen Reaction Tests of Extended-LEPS, Information-Theoretic, and Diatomics-in-Molecules Potential Energy Surfaces. 

Test of Variational Transition State Theory with a Large-Curvature Tunneling Approximation Against Accurate Quantal Reaction ProbabiUties and Rate Coefficients for Three Collinear Reactions with Large Reaction-Path Curvature Atomic Chlorine -I- Hydrogen Chloride, Atomic Chlorine + Deuterium Chloride, and Atomic Chlorine + MuCl. 

Following Fey nman s original work, several authors pmsued extensions of the effective potential idea to construct variational approximations for the quantum partition function (see, e g., Refs. 7,8). The importance of the path centroid variable in quantum activated rate processes was also explored and revealed, which gave rise to path integral quantum transition state theory and even more general approaches. The Centroid Molecular Dynamics (CMD) method for quantum dynamics simulation was also formulated. In the CMD method, the position centroid evolves classically on the efiective centroid potential. Various analysis and numerical tests for realistic systems have shown that CMD captures the main quantum effects for several processes in condensed matter such as transport phenomena. 

A number of new results obtained with the "direct" ab initio methods include phonon frequencies, anharmonicities, predictions of displacement patterns, soft-mode phase transitions, effective charges, dielectric constant, local field variations, elements of inverse dielectric matrix, etc. they were all obtained from the same fundamental equations. The Density Functional method opens a way to unified description of ground state properties of solids static, dynamic and dielectric ones. Though all the partial results above are interesting by themselves, they are even more important by providing further tests of and support for the validity of the Density Functional theory. 

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