Progress of basis optimization techniques in variational calculation of quantum reactive scattering

This paper describes several efficient basis optimization methods that we have developed in the application of S-matrix Kohn variational method to quantum reactive scattering. Specifically, we employ a minimum-K body-fixed representation combined with the use of quasiadiabatic basis functions for the expansion of the full reactive scattering wave function. This new basis function approach significantly reduces the size of the "larger" matrix of the final linear algebraic equation in the calculation of reaction cross sections. The accuracy of the calculation can be easily controlled by systematically increasing or decreasing the values of two parameters K_max and α, and convergence to the full basis set results can be reached. Numerical test calculations are carried out for the 3D H + H₂ reaction for the total angular momentum J = 10 and for the 3D F + H₂ reaction for J = 0, 1, and 2. These calculations demonstrate that our basis optimization approach is very efficient for computing reaction cross sections. Since variational scattering calculations are ultimately limited by the size of the basis set, our method is a stride forward in the applications of variational approach to quantum reactive scattering.