No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
Accelerating quantum instanton calculations of the kinetic isotope effects
33.M. Ceotto and W. H. Miller, private communication (2004).
34.R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, 1965).
51. Note that the 1% error for ΔH translates into a 2% error for ΔH2 and that 1% relative error for Qr and Cdd ratios translate into 0.01 absolute error for ∂lnQr/∂λ and ∂lnCdd/∂λ. As for , as will be shown later, when we calculate the KIE ⋅H + H2/ ⋅ D + D2 at T = 200 K with a properly optimized DS, is integrated over an interval of the length 0.59 a.u., implying that the target error should be 0.01/0.59 (a.u.)−1.
52. Since thermodynamic estimators were used in Ref. 19, reducing the discretization error directly using very large P was not feasible—increasing P not only decreased discretization error, but also increased the statistical error. Introducing virial estimators for each relevant quantity allows avoiding this issue because it permits improving convergence with respect to P without encountering problems with statistical error.
60.E. Wigner, Z. Phys. Chem. Abt. B 19, 203 (1932).
64.J. Kerr and J. Parsonage, Evaluated Kinetic Data on Gas Phase Hydrogen Transfer Reactions of Methyl Radicals (Butterworths, 1976).
65.D. G. Truhlar, D. Hong Lu, S. C. Tucker, X. G. Zhao, A. Gonzalez-Lafont, T. N. Truong, D. Maurice, Y.-P. Liu, and G. C. Lynch, “Variational transition-state theory with multidimensional, semiclassical, ground-state transmission coefficients,” in Isotope Effects in Gas-Phase Chemistry, edited by J. A. Kaye (American Chemical Society, Washington, DC, 1992), Chap. 2, pp. 16–36.
Article metrics loading...
Path integral implementation of the quantum instanton approximation currently belongs among the most accurate methods for computing quantum rate constants and kinetic isotope effects, but its use has been limited due to the rather high computational cost. Here, we demonstrate that the efficiency of quantum instanton calculations of the kinetic isotope effects can be increased by orders of magnitude by combining two approaches: The convergence to the quantum limit is accelerated by employing high-order path integral factorizations of the Boltzmann operator, while the statistical convergence is improved by implementing virial estimators for relevant quantities. After deriving several new virial estimators for the high-order factorization and evaluating the resulting increase in efficiency, using ⋅Hα + HβHγ → HαHβ + ⋅ Hγ reaction as an example, we apply the proposed method to obtain several kinetic isotope effects on CH4 + ⋅ H ⇌ ⋅ CH3 + H2 forward and backward reactions.
Full text loading...
Most read this month