Algorithm for normal mode analysis with general internal coordinates

A technique for performing normal vibrational analysis for biological macromolecules using general internal coordinates is proposed. The technique is based on the conventional algorithm for calculating the second derivatives of potential and kinetic energies using intramolecular dihedral angles, intermolecular translation, and rotation as variables [Braun, W. et al., J Phys Soc Jpn 1984, 53, 3269]. We extend the algorithm to include more general internal coordinates, bond stretching, angle bending, and so forth, without assuming two-body interactions. The essential point is the separation of the variables for potential functions and vibrational analysis. With our technique, we can arbitrarily choose any combination of internal coordinates as variables, free from the functional form of potential energy. We can analyze complex systems such as a multiple molecular system including solvents or a transition state of chemical reactions. In addition, mixed use of the potentials of molecular mechanics and quantum chemistry is possible.