Accurate estimation of solvation free energy using polynomial fitting techniques

Area of Science:

• Computational Chemistry
• Physical Chemistry
• Thermodynamics

Background:

• Accurate free energy difference calculations are crucial in chemistry.
• Thermodynamic integration is a standard method, but its accuracy can be limited.
• Existing methods for fitting thermodynamic integration data have limitations.

Purpose of the Study:

• To improve the accuracy of free energy difference estimates.
• To develop and test new polynomial fitting and interpolation techniques for thermodynamic integration data.
• To apply these methods to calculate small molecule solvation free energy.

Main Methods:

• Utilizing polynomial regression, polynomial interpolation, and spline interpolation to fit thermodynamic integration data.
• Testing the accuracy of interpolation methods on systems with analytically solvable relative free energies.
• Applying regression and interpolation methods to determine solvation free energy for a small molecule.

Main Results:

• Polynomial and spline interpolation techniques were introduced and tested.
• High accuracy in solvation free energy estimation was achieved using polynomial techniques with nonequidistant λ values.
• Accurate estimates were obtained without soft-core scaling or separate simulations for Lennard-Jones and partial charges.

Conclusions:

• Polynomial fitting and interpolation techniques significantly improve the accuracy of free energy difference estimates.
• Using nonequidistant λ values further enhances accuracy without additional simulations.
• The developed methods offer a more efficient and accurate approach to free energy calculations.