Figure 2.

(a) Two diffusing molecules can collide and will be reflected if they do not react; (b) Corresponding probability density function (pdf) for the distance of j relative to i as described by the Fokker–Planck equation; (c) Reaction probability depending on the initial distance; (d)–(f) Fokker–Planck equation and boundary conditions. The pdf for the distance r between two diffusing molecules as described by (d) starting from W(0) = δ(x_i − x_j) is shown in (b). In this description, particles react if they diffuse “into” the reaction partner, which is accounted for by the flux across the collision surface and depends on the microscopic rate constant κ. Therefore the boundary condition (e) is partially reflecting. For κ = 0 (e) becomes completely reflective, describing two inert particles. Note the “blister” in (b) which deforms the normal distribution at the boundary caused by the reflection. Due to incomplete reflection, the total probability ∫ WdV < 1. The loss corresponds to the reaction probability. Hence the reaction probability (c) for a given initial distance is found as $P_{FP}^{reaction}=1-{\int }_{r^{*}}^{\infty }WdV$ [75,109,114].