This equation seems trivially similar to equation 6, but there is a key difference: the autocorrelation function in equation 6 needs to be obtained from a canonical ensemble whereas here it only needs to be obtained from a microcanonical ensemble. This difference is beneficial because for a given system, the phase space of a microcanonical ensemble with a fixed energy E is notably smaller than that of a canonical ensemble with a fixed temperature T , especially for gas phase systems with limited degrees of freedoms. As such, the sampling need for a microcanonical ensemble simulation is much smaller.