A New Approach for Estimating the Free Energy Differences among Multiple Thermodynamic States in Statistical...

Area of Science:

• Computational chemistry
• Statistical mechanics
• Thermodynamics

Background:

• Calculating free energy differences (FEDs) is crucial in molecular simulations.
• Current methods like Bennett acceptance ratio (BAR), multistate generalization (MBAR), and weighted histogram analysis method (WHAM) rely on iterative solutions of nonlinear equations.
• These iterative solutions can be slow to converge, hindering efficient computation.

Purpose of the Study:

• To introduce a new, efficient approach for computing free energy differences (FEDs) between multiple thermodynamic states.
• To provide an alternative to existing iterative methods that are known for slow convergence.
• To leverage accurate energy probability densities from equilibrium simulations.

Main Methods:

• The proposed method directly utilizes energy probability densities obtained from equilibrium simulations.
• It involves solving linear equations, contrasting with the nonlinear iterative approaches of BAR, MBAR, and WHAM.
• The method's equations for MBAR FEDs are equivalent to the "binless WHAM" approach.

Main Results:

• The new method computes FEDs by solving linear equations, avoiding slow iterative processes.
• For two-state systems, the statistical error of this linear equation approach analytically matches that of BAR under typical conditions.
• High accuracy in FED calculation is achieved by directly using energy probability densities.

Conclusions:

• The developed method offers a computationally efficient and accurate way to determine free energy differences.
• It provides a viable alternative to existing methods, particularly for systems requiring computation of FEDs between multiple thermodynamic states.
• The direct use of energy probability densities and linear equation solving simplifies and accelerates the calculation of FEDs.