Improved importance sampling distribution for rate constant calculation

An efficient method to compute the thermal rate constant for rare events within the correlation function C(t) approach is presented. This method, which is based on a modification of the sampling function used to evaluate the dynamical correlation function C(t), can be applied to high-dimensional systems having a rough energy landscape without previous knowledge on the transition states location. In this work, the sampling of a Boltzmann-like distribution for the linear momenta with a lower inverse temperature (beta(*)=1/kT(*)) than the correct one (beta=1/kT) is proposed as a way to increase the number of reactive trajectories. The mismatch between the beta(*) and beta distributions is then corrected by a reweighting procedure which allows one to obtain the exact correlation function C(t). The efficiency of this scheme in computing the rate of a particle jumping across the barrier of a simple 2D double well potential is improved by a factor 4-25 depending on the relative value of the original beta and modified beta(*) temperatures. When merged with the "puddle potential" method [S. A. Corcelli, J. A. Rohman, and J. C. Tully, J. Chem. Phys., 118, 1085 (2003)], the new importance sampling function improves the efficiency of the correlation function approach by a factor 16-800 with respect to the unbiased sampling. To test the method in a more challenging case, the previous model system was extended by adding six harmonically restrained particles, each one interacting with the diffusing particle. This model introduces both the possibility of energy exchange and a rougher energy landscape. The new sampling function alone is found to produce an improvement in efficiency of, at least, an order of magnitude when compared with the unbiased case; when merged with the puddle potential method, a 400-fold saving in computer time is found.