Reaction paths and free energy profiles for conformational transitions: An internal coordinate approach

A new approach is proposed for the determination of transition states and reaction paths for conformational transitions. The method makes use of adiabatic energy surfaces in the space of "essential" degrees of freedom of the molecule. The reduced dimensionality of this space, compared to the full Cartesian space, offers improved computational efficiency and should allow determination of exact reaction paths in systems much larger than those currently amenable to study in Cartesian space. A procedure to obtain reaction paths and free energy profiles in solution is also proposed. The free energy profile along the path in solution is calculated utilizing a free energy perturbation method with constrains and perturbations in internal coordinate space. Applications to a conformational transition of the alanine dipeptide and the folding transition of a model reverse turn in water are presented. For the reverse turn, the sequential flip of dihedral angles reported by Czerminsky and Elber on a similar peptide [J. Chem. Phys. 92, 5580 (1990)] is also observed in the present calculations. The free energy of the extended form of the reverse turn in water is found to be lower than that for the folded conformation by about 3 Kcal/mol, in qualitative accord with previous umbrella sampling calculations.