Extended Thermodynamic Integration: Efficient Prediction of Lambda Derivatives at Nonsimulated Points

Area of Science:

• Computational Chemistry
• Statistical Mechanics
• Physical Chemistry

Background:

• Thermodynamic integration (TI) is a standard method for calculating free energy differences.
• TI requires computing the derivative of the Hamiltonian with respect to a coupling parameter (λ) at multiple λ-points.
• High curvature regions in the free energy landscape necessitate densely spaced λ-points, increasing computational cost.

Purpose of the Study:

• To introduce and validate the principle of extended thermodynamic integration (TI).
• To demonstrate that extended TI can predict Hamiltonian derivatives at nonsimulated λ-points.
• To assess the efficiency of extended TI compared to conventional TI in terms of the number of required λ-points.

Main Methods:

• The study introduces the extended thermodynamic integration (TI) method.
• The core principle involves predicting ⟨∂H/∂λ⟩ values at unsampled λ-points.
• The method was tested on three distinct model systems.

Main Results:

• Extended TI successfully predicts ⟨∂H/∂λ⟩ values at nonsimulated λ-points.
• The extended TI method requires significantly fewer λ-points than regular TI.
• Similar accuracy was achieved with substantially reduced sampling for the tested model systems.

Conclusions:

• Extended TI offers a more computationally efficient approach to free energy calculations.
• This method can reduce the number of simulations required, particularly in regions of high curvature.
• Extended TI presents a promising advancement for free energy calculations in computational chemistry.