Direct calculation of the reactive transition matrix by ℒ² quantum mechanical variational methods with complex boundary conditions

We present a new formalism of the generalized Newton variational principle for the calculation of quantum mechanical state-to-state reaction probabilities. The reformulation involves solving directly for the transition matrix rather than the reactance matrix so that calculations may be carried out for individual columns of the transition matrix without obtaining solutions for all possible initial channels. We compare the convergence of calculations with real and complex boundary conditions for H + H₂→H₂ + H, O + H₂→OH + H, and O + HD→OH + D and OD + H.