An exact a posteriori correction for hydrogen bond population correlation functions and other reversible geminate recombinations obtained from simulations with periodic boundary conditions. Liquid water as a test case

摘要

The kinetics of breaking and re-formation of hydrogen bonds (HBs) in liquid water is a prototype of reversible geminate recombination. HB population correlation functions (HBPCFs) are a means to study the HB kinetics. The long-time limiting behavior of HBPCFs is controlled by translatoric diffusion and shows a t(-3/2) time-dependence, which can be described by analytical expressions based on the HB acceptor density and the donor-acceptor inter-diffusion coefficient. If the trajectories are not properly "unwrapped," the presence of periodic boundary conditions (PBCs) can perturb this long-time limiting behavior. Keeping the trajectories "wrapped," however, allows for a more efficient calculation of HBPCFs. We discuss the consequences of PBCs in combination with "wrapped" trajectories following from the approximations according to Luzar-Chandler and according to Starr, each deviating in a different fashion from the true long-time limiting behavior, but enveloping the unperturbed function. A simple expression is given for estimating the maximum time up to which the computed HBPCFs reliably describe the long-time limiting behavior. In addition, an exact a posteriori correction for systems with PBCs for "wrapped" trajectories is derived, which can be easily computed and which is able to fully recover the true t(-3/2) long-time behavior. For comparison, HBPCFs are computed from MD simulations of TIP4P/2005 model water for varying system sizes and temperatures of 273 and 298 K using this newly introduced correction. Implications for the computations of HB lifetimes and the effect of the system-size are discussed.