Isotope dependence of thec³Π_u−b³Σ${}_{u}^{+}$ andD¹Π${}_{u}^{+}$−B′¹Σ${}_{u}^{+}$ predissociation rates of molecular hydrogen

Abstract

The state-specific predissociation rates of the c u 3 P (v,N,J) state by b u 3 S + and the D u 1 P + (v,J) state by the B¢ u 1 S + continuum of various isotopologues of molecular hydrogen have been calculated from accurate ab initio potential energy curves and electronic coupling matrix elements. Lifetimes and predissociation rates of the c u 3 P (v,N,J) and D u 1 P + (v,J) levels and accurate energies of the c u 3 P -(v,N) and D u 1 P -(v,J) levels of the isotopologues have been obtained. Significant isotope dependence of state specific predissociation rate has been found even after adjustment for Franck-Condon factors and reduced mass. The use of average electronic matrix elements of H 2 for other isotopologues underestimates the c u 3 P + −b u 3 S + predissociation rates of the HD, HT, D 2 , DT and T 2 molecules by ∼12%, ∼16%, ∼30%, ∼40%, ∼52%, respectively, and the D u 1 P + −B¢ u 1 S + rates of the HD, HT, D 2 , DT and T 2 molecules by ∼10%, ∼15%, ∼26%, ∼35% and ∼45%, respectively. When compared at similar rotation, vibration and kinetic energies, the underestimation is nearly independent of the kinetic energy. The absolute value of the average electronic coupling matrix element increases with the reduced mass while that of the vibrational overlap integral decreases with the reduced mass. This accidental substantial cancellation in the D u 1 P + −B¢ u 1 S + system is responsible for the experimental observation that the relative D u 1 P + predissociation rate of two isotopologues approximately equals the squared inverse reduced mass ratio. The origin and implications of the isotope dependence of the averaged electronic coupling matrix elements are discussed.