We have investigated the feasibility of predicting free energy differences between a manifold of molecular states from a single simulation or ensemble representing one reference state. Two formulas that are based on the so-called lambda-coupling parameter approach are analyzed and compared : (i) expansion of the free energy F(lambda) into a Taylor series around a reference state (lambda = 0), and (ii) the so-called free energy perturbation formula. The results obtained by these extrapolation methods are compared to exact (target) values calculated by thermodynamic integration for mutations in two molecular systems : a model dipolar diatomic molecule in water, and a series of para-substituted phenols in water. For moderate charge redistribution (approximate to 0.5 e), both extrapolation methods reproduce the exact free energy differences. For free energy changes due to a change of atom type or size, the Taylor expansion method fails completely, while the perturbation formula yields moderately accurate predictions. Both extrapolation methods fail when a mutation involves the creation or deletion of atoms, due to the poor sampling in the reference state simulation of the configurations that are important in the end states of interest. To overcome this sampling difficulty, a procedure based on the perturbation formula and on biasing the sampling in the reference state is proposed, in which soft-core interaction sites are incorporated into the Hamiltonian of the reference state at positions where atoms are to be created or deleted. For mutations going from p-methylphenol to the other five differently para-substituted phenols, the differences in free energy are correctly predicted using extrapolation based on a single simulation of a biased, non-physical reference state. Since a large number of mutations can be investigated using a recorded trajectory of a single simulation, the proposed method is potentially viable in practical applications such as drug design.