Alchemical free energy simulations are commonly carried out by constructing an effective Hamiltonian that linearly interpolates between the two end-state Hamiltonians with a coupling parameter λ. A variation of λ between 0 and 1 allows a smooth transition between the two end states. However, when inserting or removing atoms from the simulated system, the simulation suffers from numerical instabilities at the two end-points, known as the end-point catastrophe. The conventional soft-core potential avoids this problem by shifting and scaling Lennard-Jones interactions. As a result, the resulting Hamiltonian becomes nonlinear with respect to changes in λ. While yielding stable simulation, the non-linearity of the soft-core potential unnecessary complicates the determination of the free energy, such as, by the thermodynamic integration (TI), Bennett’s acceptance ration (BAR), and free energy perturbation (FEB) methods, and increases the number of intermediate states to be simulated to obtain the converged free energy value. Here, we present a new soft-core potential that is sufficiently repulsive to prevent the numerical instability while maintaining the overall linearity of the effective Hamiltonian with λ, which makes the analysis of the simulation results straightforward. The new potential is validated by comparing the computed solvation free energies to the corresponding values determined by the traditional separation-shifted soft-core potential. Further, along with the TI integrant estimation method, we show that the alchemical free energy calculation can be performed with fewer intermediate states with accuracy comparable to more intermediates.

New repulsive soft-core potential for accelerated alchemical free energy calculations

254th National Meeting (2017)

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