Modern integral equation techniques for quantum reactive scattering theory

Rigorous calculations of cross sections and rate constants for elementary gas phase chemical reactions are performed for comparison with experiment, to ensure that our picture of the chemical reaction is complete. We focus on the H/D + H{dollar}sb2 to{dollar} H{dollar}sb2{dollar}/DH + H reaction, and use the time independent integral equation technique in quantum reactive scattering theory.; We examine the sensitivity of H + H{dollar}sb2{dollar} state resolved integral cross sections {dollar}sigmasb{lcub}vspprime jspprime,vj{rcub}(E){dollar} for the transitions (v = 0, j = 0) to ({dollar}vspprime = 1,jspprime{dollar} = 1,3), to the difference between the Liu-Siegbahn-Truhlar-Horowitz (LSTH) and double many body expansion (DMBE) ab initio potential energy surfaces (PES). This sensitivity analysis is performed to determine the origin of a large discrepancy between experimental cross sections with sharply peaked energy dependence and theoretical ones with smooth energy dependence. We find that the LSTH and DMBE PESs give virtually identical cross sections, which lends credence to the theoretical energy dependence.; To facilitate quantum calculations on more complex reactive systems, we develop a new method to compute the energy Green's function with absorbing boundary conditions (ABC), for use in calculating the cumulative reaction probability. The method is an iterative technique to compute the inverse of a non-Hermitian matrix which is based on Fourier transforming time dependent dynamics, and which requires very little core memory. The Hamiltonian is evaluated in a sinc-function based discrete variable representation (DVR) which we argue may often be superior to the fast Fourier transform method for reactive scattering. We apply the resulting power series Green's function to the benchmark collinear H + H{dollar}sb2{dollar} system over the energy range 3.37 to 1.27 eV. The convergence of the power series is stable at all energies, and is accelerated by the use of a stronger absorbing potential.; The practicality of computing the ABC-DVR Green's function in a polynomial of the Hamiltonian is discussed. We find no feasible expansion which has a fixed and small memory requirement, and is guaranteed to converge. We have found, however, that exploiting the time dependent picture of the ABC-DVR Green's function leads to a stable and efficient algorithm. The new method, which uses Newton interpolation polynomials to compute the time dependent wavefunction, gives a vastly improved version of the power series Green's function. We show that this approach is capable of obtaining converged reaction probabilities with very straightforward accuracy control.; We use the ABC-DVR-Newton method to compute cross sections and rate constants for the initial state selected D + H{dollar}sb2(v = 1,j) to{dollar} DH + H reaction. We obtain converged cross sections using no more than 4 Mbytes of core memory, and in as little CPU time as 10 minutes on a small workstation. With these cross sections, we calculate exact thermal rate constants for comparison with experiment. For the first time, quantitative agreement with experiment is obtained for the rotationally averaged rate constant {dollar}ksb{lcub}v=1{rcub}(T = 310 K) = 1.9 times 10sp{lcub}-13{rcub}{dollar} cm{dollar}sp3{dollar} sec{dollar}sp{lcub}-1{rcub}{dollar} molecule{dollar}sp{lcub}-1{rcub}{dollar}. The J-shifting approximation using accurate J = 0 reaction probabilities is tested against the exact results. It reliably predicts {dollar}ksb{lcub}v=1{rcub}(T){dollar} for temperatures up to 700 K, but individual (v = 1, j)-selected rate constants are in error by as much as 41%.