# Effect of trajectory length and resolution on the Residence Time

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.

• Did the provided answer sufficiently clarify the concept you were looking for? If yes, kindly mark the answer as accepted. Mar 24 at 3:06