Accurate quantum thermal rate constants for the three-dimensional H+H2 reaction

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Abstract
The rate constants for the three‐dimensional H+H2 reaction on the Liu–Siegbahn–Truhlar–Horowitz (LSTH) surface are calculated using Pack–Parker hyperspherical (APH) coordinates and a C2v symmetry adapted direct product discrete variable representation (DVR). The C2v symmetry decomposition and the parity decoupling on the basis are performed for the internal coordinate χ. The symmetry decomposition results in a block diagonal representation of the flux and Hamiltonian operators. The multisurface flux is introduced to represent the multichannel reactive flux. The eigenvalues and eigenvectors of the J=0 internal Hamiltonian are obtained by sequential diagonalization and truncation. The individual symmetry blocks of the flux operator are propagated by the corresponding blocks of the Hamiltonian, and the J=0 rate constant k0(T) is obtained as a sum of the rate constants calculated for each block. k0(T) is compared with the exact k0(T) obtained from thermal averaging of the J=0 reaction probabilities; the errors are within 5%–20% up to T=1500 K. The sequential diagonalization–truncation method reduces the size of the Hamiltonian greatly, but the resulting Hamiltonian matrix still describes the time evolution very accurately. For the J≠0 rate constant calculations, the truncated internal Hamiltonian eigenvector basis is used to construct reduced (JKJ) blocks of the Hamiltonian. The individual (JKJ) blocks are diagonalized neglecting Coriolis coupling and treating the off‐diagonal KJ±2 couplings by second order perturbation theory. The full wave function is parity decoupled. The rate constant is obtained as a sum over J of (2J+1)kJ(T). The time evolution of the flux for J≠0 is again very accurately described to give a well converged rate constant.