Thermodynamic Integration Versus Expanded Ensemble and Replica-Exchange Monte Carlo Simulation

2 Thermodynamic Integration Versus Expanded Ensemble and Replica-Exchange Monte Carlo Simulation 

The free energy change along the transformation path in the two-dimensional parameter space spanned by and XN can be calculated via thermodynamic integration. Let XiN XN X N denote such a path, then the free 

Within each interval, we use an expanded ensemble technique to explore the sampling points and configurations between neighboring intervals are swapped via replica-exchange Monte Carlo moves [118]. The partition fimction, takes the form  

The Monte Carlo simulation comprises three distinct moves (i) Canonical Monte Carlo moves update the molecular conformations in the Mr repUca. In this specific application, we employ a Smart Monte Carlo algorithm [119] that utilizes strong bonded forces to propose a trial displacement [43, 87]. The amplitude of the trial displacement has been optimized in order to maximize the mean-square displacement of molecules [91], and the single-chain dynamics closely resembles the Rouse-dynamics of unentangled macromolecules [120]. (ii) Since each replica is an 

In order to sample all states of the expanded ensembles with uniform probability, the weighting factors, T)(kjN), should closely resemble the free energy 

---