A coupled states calculation of accurate quantum rate constants for H + H2

Mitchell C. Colton, George C Schatz

Research output: Contribution to journalArticle

36 Citations (Scopus)

Abstract

In this article we present the results of converged quantum reactivescattering calculations of thermal rate constants for H + H2 using the Liu‐Siegbahn‐Truhlar‐Horowitz (LSTH) potential energy surface. These calculations are based on the coupled states (CS) approximation wherein rotational states having different body fixed angular momentum projection quantum numbers are decoupled. By comparision with accurate coupled channel results on the Porter‐Karplus No. 2 (PK2) potential surface, we estimate that the maximumerror in thermal rate constants arising from both this approximation and from other numerical approximations in the calculation is less than 25%. We also show that the sum over projection quantum numbers Ω associated with the CS calculation may be approximated quite accurately in terms of the Ω = 0 rate constants by assuming that the |Ω| > 0 rate constants differ from Ω = 0 by a shift in activation energy, which reflects the vibrationally adiabatic bending energy associated with each Ω. Comparison of the LSTH rate constants with experiment indicates average errors of 16% and 24% relative to the two modern measurementsof the rate constants for H + H2. These errors are reduced to 18% and 9% if the CS rate constants are multiplied by exp(0.0065 eV/kT). The expected error (based on recent quantum structure calculations) associated with the 0.425 eV barrier of theLSTH potential surface is 0.0065 eV. Overall, the agreement of either the LSTH or modified LSTH rate constants with experiment is within the 32% maximum disagreement between the two experimental measurements at all butthe lowest temperature that has been studied. Comparison of our CS rate constants with the results from simpler theories is considered using both the LSTH and PK2 potential surfaces. The best overall agreement is with transition state theories that use accurate dynamical methods to calculate tunnelling factors. These include reduced dimensionality quantum dynamics methods and variational transition state theory using either the Marcus‐Coltrin or least action ground‐state tunnelling paths. Comparison with the results of quasiclassical trajectory calculations indicates substantial errors at low temperatures.

Original languageEnglish
Pages (from-to)961-975
Number of pages15
JournalInternational Journal of Chemical Kinetics
Volume18
Issue number9
DOIs
Publication statusPublished - 1986

Fingerprint

Rate constants
Hot Temperature
Temperature
quantum numbers
projection
approximation
Potential energy surfaces
Angular momentum
rotational states
angular momentum
Activation energy
Experiments
potential energy
Trajectories
trajectories
activation energy
shift
estimates

ASJC Scopus subject areas

  • Biochemistry
  • Physical and Theoretical Chemistry
  • Organic Chemistry
  • Inorganic Chemistry

Cite this

A coupled states calculation of accurate quantum rate constants for H + H2 . / Colton, Mitchell C.; Schatz, George C.

In: International Journal of Chemical Kinetics, Vol. 18, No. 9, 1986, p. 961-975.

Research output: Contribution to journalArticle

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abstract = "In this article we present the results of converged quantum reactivescattering calculations of thermal rate constants for H + H2 using the Liu‐Siegbahn‐Truhlar‐Horowitz (LSTH) potential energy surface. These calculations are based on the coupled states (CS) approximation wherein rotational states having different body fixed angular momentum projection quantum numbers are decoupled. By comparision with accurate coupled channel results on the Porter‐Karplus No. 2 (PK2) potential surface, we estimate that the maximumerror in thermal rate constants arising from both this approximation and from other numerical approximations in the calculation is less than 25{\%}. We also show that the sum over projection quantum numbers Ω associated with the CS calculation may be approximated quite accurately in terms of the Ω = 0 rate constants by assuming that the |Ω| > 0 rate constants differ from Ω = 0 by a shift in activation energy, which reflects the vibrationally adiabatic bending energy associated with each Ω. Comparison of the LSTH rate constants with experiment indicates average errors of 16{\%} and 24{\%} relative to the two modern measurementsof the rate constants for H + H2. These errors are reduced to 18{\%} and 9{\%} if the CS rate constants are multiplied by exp(0.0065 eV/kT). The expected error (based on recent quantum structure calculations) associated with the 0.425 eV barrier of theLSTH potential surface is 0.0065 eV. Overall, the agreement of either the LSTH or modified LSTH rate constants with experiment is within the 32{\%} maximum disagreement between the two experimental measurements at all butthe lowest temperature that has been studied. Comparison of our CS rate constants with the results from simpler theories is considered using both the LSTH and PK2 potential surfaces. The best overall agreement is with transition state theories that use accurate dynamical methods to calculate tunnelling factors. These include reduced dimensionality quantum dynamics methods and variational transition state theory using either the Marcus‐Coltrin or least action ground‐state tunnelling paths. Comparison with the results of quasiclassical trajectory calculations indicates substantial errors at low temperatures.",
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