Stress-stress fluctuation formula for elastic constants in the NPT ensemble.

Several fluctuation formulas are available for calculating elastic constants from equilibrium correlation functions in computer simulations, but the ones available for simulations at constant pressure exhibit slow convergence properties and cannot be used for the determination of local elastic constants. To overcome these drawbacks, we derive a stress-stress fluctuation formula in the NPT ensemble based on known expressions in the NVT ensemble. We validate the formula in the NPT ensemble by calculating elastic constants for the simple nearest-neighbor Lennard-Jones crystal and by comparing the results with those obtained in the NVT ensemble. For both local and bulk elastic constants we find an excellent agreement between the simulated data in the two ensembles. To demonstrate the usefulness of the formula, we apply it to determine the elastic constants of a simulated lipid bilayer.