Comparison of Quantum Dynamics and Quantum Transition State Theory Estimates of the H + CH₄ Reaction Rate

Abstract

Thermal rate constants are calculated for the H + CH 4 f CH 3 + H 2 reaction employing the potential energy surface of Espinosa-García (Espinosa-García, J. J. Chem. Phys. 2002, 116, 10664). Two theoretical approaches are used. First, we employ the multiconfigurational time-dependent Hartree method combined with flux correlation functions. In this way rate constants in the range 225-400 K are obtained and compared with previous results using the same theoretical method but the potential energy surface of Wu et al. (Wu, T.; Werner, H.-J.; Manthe, U. Science 2004, 306, 2227). It is found that the Espinosa-García surface results in larger rate constants. Second, a harmonic quantum transition state theory (HQTST) implementation of instanton theory is used to obtain rate constants in a temperature interval from 20 K up to the crossover temperature at 296 K. The HQTST estimates are larger than MCTDH ones by a factor of about three in the common temperature range. Comparison is also made with various tunneling corrections to transition state theory and quantum instanton theory.

Derivation of a true (t → 0+) quantum transition-state theory. I. Uniqueness and equivalence to ring-polymer molecular dynamics transition-state-theory

“…III B]. Equation 21 shows why C fs (t) tends smoothly to zero as t → 0 + : it is because C fs (t) is equivalent to the shorttime classical flux of a two dimensional system in which the flux and side dividing surfaces are different functions of the coordinates q; more formally, these surfaces are different functions of (imaginary-time) path-integral space.…”

“…* Corresponding author: sca10@cam.ac.uk most famous instance of this being the Wigner-Eyring formula. 13 A more systematic approach is to use semiclassical theories [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] (some of which we discuss below), or the quantum instanton approach. 29,30 However, there is one approach 20,[31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] that is especially relevant to this article, which is to note that classical TST takes the form of a free-energy combined with a flux factor, and then to exploit the fact that it is relatively easy to compute a quantum free energy, using 'ring-polymer' pathintegration.…”

Simulation of surface processes

“…The harmonic approximation has, however, been found to work remarkably well, even in simulations of, for example, H 2 desorption (Fig. 4) and molecular reactions (52). An algorithm for evaluating tunneling rates in large complex systems using atomic forces directly from DFT or ab initio calculations (without the need to parameterize a potential energy surface) has been developed (53).…”

Efficient algorithms for semiclassical instanton calculations based on discretized path integrals

“…gle kink path, the action is expressed using the discretized imaginary time axis [18][19][20][21][39][40][41][42][43][44][45] as well as using the continuous time axis. [15][16][17][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] In the present paper, we focus a method using the discretized imaginary time approach developed by Richardson and Althorpe, because their method is constructed on the basis of the standard path integral molecular simulation technology, which facilitates the reuse of existing computational libraries on the path integrals.…”