The reaction X+Cl2→XCl+Cl (X=Mu,H,D). I. A new inversion procedure for obtaining energy surfaces from experimental detailed and total rate coefficient data

Abstract

A new inversion method has been developed which uses detailed vibrotational and total rate coefficient data in order to obtain the potential energy surface for a chemical reaction. The method is applied to the reaction X+Cl2→XCl+Cl (X=Mu,H,D). The philosophy of the method is to separate the dynamical effects due to the collinear and the noncollinear parts of the potential surface, which are then treated independently, and to reduce a large amount of experimental data to a few informative quantities. These are then related to a small number of potential surface parameters. This compaction of data is carried out in an iterative scheme starting from a potential surface assumed to be sufficiently similar to the correct one. In the present case, the collinear part of the potential surface is constrained to be of the extended LEPS variety with correct asymptotic properties and two adjustable Sato parameters. Information theoretic techniques are used to obtain the fraction of reactive reagents and then the vibrotational product distribution for ground state reagents P(J′,v′ ‖ v=0) in a thermal reactant distribution. Next, these three dimensional P(J′,v′ ‖ v=0) are projected onto the corresponding collinear vibrational distribution PC(v′ ‖ v=0). This distribution is then further reduced to its most informative moment 〈fv′〉C to 𝒜⊥, the attractivity of the potential surface. An estimate of the barrier height Eb of X+Cl2 is made from the isotopic ratios of thermal rate coefficients, which are assumed to be dominated by collinear potential surface properties. We thus compact the original experimental data into two parameters 𝒜⊥ and Eb which determine the Sato parameters characterizing the collinear part of the potential surface. With Eb=1.5 kcal mol−1, the collinear part of the extended LEPS surface which best reproduces 〈fv′〉C for the H+Cl2 and D+Cl2 reactions has Sato parameters of S(XCl)=0.067 and S(Cl2)=−0.113. We have not explicitly derived the noncollinear part of the potential surface due to the present unavailability of simple parametrized models for the angular behavior.