Can somebody explain the Hydrogen bond Auto-correlation function in Computational Chemistry (Molecular Dynamics and Simulations) and what does Intermittent and Continuous Hydrogen bond means?
Why the graph decays over time? and it's applications?
This is with reference to the paper: Chandra, A. Effects of Ion Atmosphere on Hydrogen-Bond Dynamics in Aqueous Electrolyte Solutions. Phys. Rev. Lett. 2000, 85 (4), 768–771. DOI: 10.1103/PhysRevLett.85.768.
In eqn 1 and 2 the correlation functions are written in the form $<A B >/<A>$ , the denominator is the average of $A$ and the numerator the correlation function. This is the the integral product $U(t_d)=\int A(t) B(t-t_d)dt$ where $t_d$ is some time delay. When $A$ and $B$ are the same thing then this is the auto-correlation. It measure how similar the signal A is to B at different times. If $A$ and $B$ are random signals (such as white noise, or from a random number generator) then $U$ is 1 at zero time delay (both signals exactly superimposed) and zero at all other delays and this is because the correlation has no 'memory'; any point in a random signal is not related to any other. If $A$ and $B$ are constant then $U$ is one at all times, i.e perfect 'memory'. In your example the H bonds have a certain lifetime because are being broken due to molecular motion (as explained in the paragraph under eqns 1 & 2) and so the correlation function decays away. A plot of the correlation gives the lifetime of the H bonds.
Since porphyrin covered the general case of a correlation function, I'll try to give a little more detail on what they were specifically modelling in this paper.
The correlations functions they define in the paper are correlations of indicator variables (a value of 1 when some criteria is true, and zero otherwise). The continuous correlation function gives the probability that a given hydrogen bond at time 0 remains all the way until a time t. The intermittent correlation function gives the probability that a given hydrogen bond at time 0 is also present at time t, even if the bond breaks and reforms in the time in between.
That these functions decay over time is a consequence of how these bonds fluctuate over time. If t=0, the correlation function is at a maximum, in this case because we know the hydrogen bond is still there. Shortly after, the function is still fairly because the bond hasn't had a lot of time to separate. At very long times, it is unlikely that particular hydrogen bond has remained in place or even reformed.
