To determine the lifetimes of hydrogen bonds, we used the approach suggested by van der Spoel et al.(63) In essence, the lifetime of a hydrogen bond τHB was given by inverse forward rate constant k through τHB = 1/k. The parameter k was determined as follows. The hydrogen bonds during the simulations were allowed to break and reform, allowing us to analyze lifetimes by using binary function h(t), which is 1 when a hydrogen bond is present and 0 otherwise