Efficient and precise solvation free energies via alchemical adiabatic molecular dynamics

A new molecular dynamics method for calculating free energies associated with transformations of the thermodynamic state or chemical composition of a system (also known as alchemical transformations) is presented. The new method extends the adiabatic dynamics approach recently introduced by Rosso et al. [J. Chem. Phys. 116, 4389 (2002)] and is based on the use of an additional degree of freedom, λ, that is used as a switching parameter between the potential energy functions that characterize the two states. In the new method, the coupling parameter λ. is introduced as a fictitious dynamical variable in the Hamiltonian, and a system of switching functions is employed that leads to a barrier in the λ. free energy profile between the relevant thermodynamic end points. The presence of such a barrier, therefore, enhances sampling in the end point (λ=0 and λ = 1) regions which are most important for computing relevant free energy differences. In order to ensure efficient barrier crossing, a high temperature T_λ is assigned to λ and a fictitious mass m_λ is introduced as a means of creating an adiabatic separation between λ and the rest of the system. Under these conditions, it is shown that the λ free energy profile can be directly computed from the adiabatic probability distribution function of λ without any postprocessing or unbiasing of the output data. The new method is illustrated on two model problems and in the calculation of the solvation free energy of amino acid side-chain analogs in TIP3P water. Comparisons to previous work using thermodynamic integration and free energy perturbation show that the new λ adiabatic free energy dynamics method results in very precise free energy calculations using significantly shorter trajectories.