Simulated annealing on coupled free energy surfaces: Relative solvation energies of small molecules

A method previously presented for sampling coupled potential energy surfaces and selecting that with the most favorable free energy is extended to perform a similar selection on the sum or difference of free energies between two states. Whereas the original method is useful for selecting a molecule based on its absolute stability, the new method allows selection based on its ability to drive a thermodynamic equilibrium, such as binding. Operationally the original method locates the minimum in Delta G(lambda) [lambda couples two chemical compounds], whereas the modified version performs the same task on Delta Delta G(lambda), which is significantly more useful for molecular design strategies. The new algorithm has been tested on the solvation free energy difference between methanol and ethane, for which the Delta Delta G was calculated to be 6.08 kcal/mol with a barrier of 1.08 or 3.55 kcal/mol (depending on problem formulation). Simulated annealing was able to rapidly and routinely locate the most favorable minimum. A significantly more challenging artificial problem was also constructed with a calculated Delta Delta G of -3.07 kcal/mol and a barrier height of 7.64 kcal/mol; methods described herein were also able to locate routinely the correct minimum in Delta Delta G(lambda) for this problem.