Improved free-energy interpolation scheme for obtaining gas-phase reaction rates from ring-polymer molecular dynamics

Quantum reaction rates for bimolecular gas-phase reactions can be computed efficiently and to a realistic degree of approximation by applying ring-polymer molecular dynamics within a free-energy interpolation scheme [R. Collepardo-Guevara, Y.V. Suleimanov, and D. E. Manolopoulos, J. Chem. Phys. 130, 174713 (2009)]. Here, we present modifications to this scheme which simplify the implementation of the method, and have the advantage of yielding directly the free-energy as a function of the interpolation coordinate. We also take the opportunity to verify the benchmark results obtained for the H + H-2 and Cl + HCl reactions by Collepardo-Guevara et al., obtaining excellent agreement for H + H-2 and reasonable agreement for Cl + HCl.