Unified statistical model for ’’complex’’ and ’’direct’’ reaction mechanisms: A test on the collinear H+H2 exchange reaction

Abstract

Articles you may be interested inCanonical unified statistical model. Classical mechanical theory and applications to collinear reactions 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 Miller's unified statistical theory for bimolecular chemical reactions is tested on the collinear H + H2 exchange reaction. treated classically. The reaction probability calculated from unified statistical theory is more accurate than that calculated from ordinary transition state theory or from variational transition state theory; in particular, unified statistical theory predicts the high-energy falloff of the reaction probability, which transition state theory does not. A derivation of unified statistical theory is presented that emphasizes the dynamical and statistical assumptions that are the foundation of the theory. We show how these assumptions unambiguously define the "collision complex" in unified statistical theory, and we test these assumptions in detail on the H+H2 reaction. Finally, a lower bound on the reaction probability is derived; this bound complements the upper bound provided by transition state theory and is significantly more accurate. for the H+H2 reaction, than either transition state theory or unified statistical theory.

Chemical reactions induced by oscillating external fields in weak thermal environments

“…[10][11][12][13] In systems with higher dimensionality, the generalization of this PO is a normally hyperbolic invariant manifold (NHIM). [14][15][16][17][18][19][20][21][22] The NHIM bounds the TS, being one less in dimension.…”

Reactivity boundaries for chemical reactions associated with higher-index and multiple saddles

“…Pechukas et al revealed the role of a periodic orbit dividing surface in two-dimensional collinear atom-diatom reaction systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. The importance of a periodic orbit around the interaction region was first recognized by Pechukas [1].…”

“…Especially reactivity boundaries of atom-diatom reactions were extensively studied by Wright et al [18][19][20][21][22][23] and Pechukas et al [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Wigner introduced the asymptotic reactant and product regions to calculate the reaction rate in his transition state theory [34].…”

“…Some phase-space points in the reactant region may go into the product region after time propagation, whereas other phase-space points stay in the reactant region without undergoing the reaction. Between these reactive initial conditions and nonreactive ones lies a boundary which we simply call here the reactivity boundary, which has previously been described as "boundary trajectories" [1][2][3][4][5][6][7][8][9][10][11][12][13][14] asymptotic to a periodic orbit dividing surface (pods) [7][8][9][10][11][12][13][14], a "boundary" of [1][2][3][4][5][6][7][8][9][10][11][12][13][14] reactivity bands [15][16][17][18][19][20][21][22][23][24][25], a "tube" [26], ...…”

Variational principle for the determination of unstable periodic orbits and instanton trajectories at saddle points

“…[24][25][26][27] Unstable POs are of importance in the field of classical reaction dynamics in classical systems where they form recrossingfree dividing surfaces. 2,3, 11,[28][29][30] They are important for understanding tunneling dynamics through a barrier in quantum mechanical reactions wherein the PO on the inverted potential, −V , is the instanton trajectory providing the leading contribution to the path integral. 31 In common between all of these cases, is the invariance of POs as they provide a scaffold from which to obtain other geometric structures, and thus remain objects of current interest such as in, e.g., Refs.…”