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

Thermodynamic integration (TI) is one of the most commonly used free-energy calculation methods. The derivative of the Hamiltonian with respect to lambda, ⟨∂H/∂λ⟩, is determined at multiple λ-points. Because a numerical integration step is necessary, high curvature regions require simulations at densely spaced λ-points. Here, the principle of extended TI is introduced, where ⟨∂H/∂λ⟩ values are predicted at nonsimulated λ-points. On the basis of three model systems, it is shown that extended TI requires significantly fewer λ-points than regular TI to obtain similar accuracy.