Recross

Recross is a term used in chemical kinetics and reaction-rate theory to describe trajectories that cross the transition-state dividing surface from the reactant side to the product side but subsequently cross back to the reactants. In conventional transition state theory (TST), it is assumed that crossing the dividing surface once guarantees progression to products, with no recrossings. However, in many systems, especially with multidimensional potential energy surfaces, thermal fluctuations and coupling to bath modes cause trajectories to recross, reducing the net flux to products.

The effect is typically quantified by the transmission coefficient, κ, which modulates the TST rate constant: k = κ k_TST, with 0 ≤ κ ≤ 1. A κ less than 1 indicates recrossing and other dynamical effects that prevent some trajectories from reaching products. To address recrossing, variational transition state theory seeks a dividing surface that minimizes recrossings, thereby maximizing κ. In practice, researchers use a combination of variational approaches and dynamical simulations to estimate and correct for recrossing, employing trajectory-based methods and refinements of the dividing surface as needed.

Recrossing is a central concept in chemical dynamics and has implications for predicting reaction rates from first principles. It highlights the limitations of a single, static transition state picture and motivates the use of dynamical corrections in complex, multidimensional systems. See also transition state theory, variational transition state theory, and transmission coefficient.