Numerical method of quantum capture probability determination for molecular collisions at ultralow temperatures

The numerical method suggested by Truhlar and Kuppermann (J. Am. Chem. Soc., 1971, vol. 93, p. 1840) to determine tunneling probabilities is adapted for quantum capture calculations in barrierless molecular processes by means of absorbing boundary conditions imposed in the range of strong interactions. It is shown that the phase uncertainty of the singular scattering problem, which arises during the extrapolation of the long-range interaction potential to short distances, is revealed as the oscillatory dependence of the transmission coefficient on the point at which the boundary conditions were imposed. The mean transmission coefficient computation makes it possible to decrease the uncertainty of the results. The method is evaluated to calculate the KRb + KRb reaction rates and K₂ + K vibrational relaxation at ultralow temperatures using model dispersion and adiabatic channel potentials derived from ab initio calculations. The results are in good agreement with the data of analytic models based on the solution of the singular scattering problem close to Bethe-Wigner energy threshold and, within the capture approximation accuracy, with the data of a rigorous quantum scattering theory.