HOLONOMIC CONSTRAINT CONTRIBUTIONS TO FREE-ENERGY DIFFERENCES FROM THERMODYNAMIC INTEGRATION MOLECULAR-DYNAMICS SIMULATIONS

A method is presented for the evaluation of holonomic constraint contributions to free energy differences obtained from molecular dynamics simulations. The method is used with the thermodynamic integration technique in which analytical derivatives of the Hamiltonian are evaluated. The free energy contributions are shown to be easily derived from the constraint forces that can be evaluated from the SHAKE coordinate corrections. The problem of poor statistical accuracy associated with the creation or annihilation of atoms can be treated using a sprouting/desprouting technique, in which it is essential to be able to evaluate constraint contributions to free energy differences. This is illustrated for the mutation of ethanol to ethane in aqueous solution and in vacuo. For this system, experimental free energies of hydration are compared with the calculated values using different sprouting/desprouting protocols.