Effect of trajectory length and resolution on the Residence Time

Question

I have tried to calculate Residence time using the residence time auto-correlation function defined as
$$R(t) = \frac{\langle h(0)h(t)\rangle}{\langle h(0)h(0)\rangle}$$
In the calculation, I have used the definition of intermittent hydrogen bond where function $h(t)$ is 1 if molecules stays in defined cutoff region and zero otherwise.

After doing the calculation, I observed

1. Relaxation of the function $R(t)$ varies with the resolution of the trajectory taken for the calculation.

2. The length of the trajectory for same resolution (say $\pu{0.1ps}$) also has its effects on the relaxation of function $R(t)$.

I am trying to understand what phenomenon actually contributes in the different relaxation time of function $R(t)$ with varying resolution of the trajectory as well as the length of the trajectory for the same resolution.

Answer 1

The autocorrelation function (HBond or any other property) gives you the time that takes the system to forget that state. If the length of your analysis window in trajectory is less than the autocorrelation time, you will see that the results are dependent on the analysis window, because the system has not yet forgotten the previous state. The general rule of thumb in calculating autocorrelation time is to start with the window spanning atleast half of your trajectory and continue reducing it till your results remain constant.