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Title: Variational Transition State Theory

Abstract

This is the final report on a project involving the development and applications of variational transition state theory. This project involved the development of variational transition state theory for gas-phase reactions, including optimized multidimensional tunneling contributions and the application of this theory to gas-phase reactions with a special emphasis on developing reaction rate theory in directions that are important for applications to combustion. The development of variational transition state theory with optimized multidimensional tunneling as a useful computational tool for combustion kinetics involved eight objectives.

Authors:
ORCiD logo [1]
  1. Univ. of Minnesota, Minneapolis, MN (United States)
Publication Date:
Research Org.:
Univ. of Minnesota, Minneapolis, MN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1324939
Report Number(s):
DOE-UMN-ER13579
DOE Contract Number:
FG02-86ER13579
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
02 PETROLEUM; 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; chemical reaction kinetics

Citation Formats

Truhlar, Donald G. Variational Transition State Theory. United States: N. p., 2016. Web. doi:10.2172/1324939.
Truhlar, Donald G. Variational Transition State Theory. United States. doi:10.2172/1324939.
Truhlar, Donald G. 2016. "Variational Transition State Theory". United States. doi:10.2172/1324939. https://www.osti.gov/servlets/purl/1324939.
@article{osti_1324939,
title = {Variational Transition State Theory},
author = {Truhlar, Donald G.},
abstractNote = {This is the final report on a project involving the development and applications of variational transition state theory. This project involved the development of variational transition state theory for gas-phase reactions, including optimized multidimensional tunneling contributions and the application of this theory to gas-phase reactions with a special emphasis on developing reaction rate theory in directions that are important for applications to combustion. The development of variational transition state theory with optimized multidimensional tunneling as a useful computational tool for combustion kinetics involved eight objectives.},
doi = {10.2172/1324939},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2016,
month = 9
}

Technical Report:

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  • Rate constants for the important combustion O(3P state) + H/sub 2/ yield OH + H are calculated using variational transition state theory (VTST) with adiabatic and least-action ground-state transmission coefficients (VTST/G). Five different potential energy surfaces were considered and rates were computed for temperatures from 200 to 1400 K. First, collinear VTST/G calculations were compared with accurate quantum-mechanical ones to assess the accuracy of the dynamical and energetic approximations, which include the no-recrossing assumption of generalized transition state theory, semiclassical methods for tunneling calculations, and a Morse approximation for quantizing the generalized-transition state theory, stretching vibrations. For all five surfaces,more » which show widely different behavior, the calculations with the least-action ground-state transmission coefficients agree with the accurate quantal results within a factor of 2.9 in all cases. Next the three-dimensional VTST/G calculations were compared with experiment in an attempt to assess the validity of the potential energy surfaces. From this work, only one of the five surfaces could be definitively eliminated. The three-dimensional reaction was found to be dominated by tunneling at room temperature and nearby for all five surfaces. For the calculations on the most accurate ab initio potential energy surface, 60% of the ground-state reaction proceeds by tunneling even at 400 K.« less
  • Variational transition state theory is used to calculate rate constants and kinetic isotope effects for the reactions F + H2 yields HF + H(with rate constant k sub 1), F + D2 yields DF + D(k sub 2), and two other isotopic analogs as functions of temperature. The calculations are performed using a recently proposed partly empirical, partly ab initio potential energy surface, called surface No. 5, and also using a new surface, called surface No. 5A, introduced here to test the effect of a higher classical saddle point on the reaction rates, kinetic isotope effects, and reaction thresholds. Themore » various theoretical results are compared to the available experiments to test the validity of these potential energy surfaces. For those rate constants and kinetic isotope effects for which there is more than one experimental value at a given temperature the theoretical results for the reactions on the surface No. 5 agree wtih the experiment about as well as the individual experiments agree with each other.« less
  • Rate constants and kinetic isotope effects for the title reactions were calculated using accurate quantum-dynamical methods, and used to test the accuracy of corresponding rate constants from conventional and variational transition-state theory. The quantum-dynamical rate constants are estimated to be within 35% of the exact rate constants for the potential energy surfaces chosen for this comparison. For all the reactions considered, the conventional and variational transition-state theory rate constants with unit transmission coefficient are found to be very close to each other (better than 7%), but in poor agreement with the accurate quantum results (off by factors of 6-22 atmore » 300K). This indicates that although variational effects are small, tunneling makes a very important contribution to the rate constants, and it is found that the tunneling contribution is described quantitatively for all the reactions considered using the least-action ground state (LAG) transmission coefficient. The combination of improved canonical variational theory (ICVT) and LAG yields rate constants that have an average error (considering all the reactions and temperatures studied) of only 15% compared to the accurate quantal rate constants, and in only one case (D + H/sub 2/ at 200K) does the ICVT/LAG rate constant differ by more than 35% from the accurate value. The comparison of ICVT/LAG kinetic isotope effects is found to be similarly good, with worst comparisons occurring for intramolecular (X+HD) isotope ratios.« less
  • During the past two years we have extended the variational transition-state theory in several ways. Especially notable is that we have developed several new methods for calculating tunneling probabilities, including two general techniques applicable to systems with small and large reaction-path curvature. We have tested these methods successfully against accurate quantal calculations, and we have applied them to real systems in three dimensions. We have also developed general algorithms for variational transition state theory calculations on polyatomic systems and we have applied these to the combustion reaction OH + H/sub 2/ ..-->.. H/sub 2/O + H. We have developed andmore » successfully applied a statistical-diabatic theory for state-selected rates. We made a totally ab initio prediction of an absolute chemical reaction rate, for the reaction Mu + H/sub 2/ ..-->.. MuH + H, using an accurate potential energy surface and ethods that we had demonstrated to be reliable by tests against accurate quantal collinear results. This prediction has now been confirmed by unpublished experiments; I believe that this is the first reliable ab initio prediction of a chemical rection rate prior to its measurement. In the rest of this technical progress report we give further details of these and other studies we have carried out in the last two years under this contract.« less
  • Projects aimed at testing, extending, or applying the variational transition state theory of reaction rates are summarized. (GHT)