Efficient alchemical intermediate states in free energy calculations using λ-enveloping distribution sampling

Alchemical free energy calculations generally require intermediate states along a coupling parameter λ to establish sufficient phase space overlap for obtaining converged results. Such intermediate states can also be engineered to lower the energy barriers and, consequently, reduce the required sampling time. The recently introduced λ-enveloping distribution sampling (λ-EDS) scheme combines the properties of the minimum variance pathway and the EDS methods to improve sampling and allow for larger steps along the alchemical pathway compared to conventional approaches. This scheme also eliminates the need for soft-core potentials and retains the behavior of conventional λ-intermediate states as a limiting case. In this study, an automated procedure is developed to select the parameters of λ-EDS for optimal performance. The underlying theory is illustrated based on simulations of simple test systems (bond length changes in harmonic oscillators, mutations of dihedral angles, and charge creation in water), as well as on the calculation of the absolute hydration free energies of 12 small organic molecules.