Efficient, direct calculation of reaction rate coefficients based on a partially rearranged rovibrational Hamiltonian. A full-dimensional case study of the H${}_2$ + D $\to$ HD + H reaction

It is shown that an efficient, direct, and fully quantum mechanical calculation of thermal reaction rate coefficients requires a new, partially rearranged form of the numerically-constructed exact kinetic energy part of the rovibrational Hamiltonian expressed in internal coordinates. Using this Hamiltonian and an accurate, full-dimensional potential energy surface characterizing the H${}_2$ + H exchange reaction, developed by Mielke, Garrett, and Peterson (J. Chem. Phys. 2002, 116, 4142), reaction rate coefficients in the temperature range of $75-800$ K have been computed for the H${}_2$ + D $\to$ HD + H reaction. The paper puts particular emphasis on the exact treatment of overall molecular rotation and on nuclear spin symmetry.