Before revision:  We also present a general framework to optimize the parameters of the alchemical perturbation potentials based on avoiding first order pseudo phase transitions along the alchemical path.
After revision:  We also present a general framework to optimize the parameters of the alchemical perturbation potentials of this kind. The optimization procedure is based on the \lambda-function formalism and the maximum-likelihood parameter estimation procedure we developed earlier to avoid the occurrence of multi-modal distributions of the coupling energy along the alchemical path.