Estimation of minimum energy pathways and transition states using velocities in internal coordinates.

Many algorithms for finding chemical reaction pathways require an initial estimate of the minimum energy path. Linear synchronous transit generates this estimate by interpolating a set of internal coordinates and using least-squares minimization to find the closest Cartesian atomic positions. However, this method is prone to discontinuities, and like other estimation methods, it is usually seeded from an even simpler path, such as one generated by Cartesian interpolation. As an alternative, we project a velocity vector from internal coordinates into the space of Cartesian coordinates, which we treat as an embedded manifold. Numerically integrating this velocity results in a continuous estimate for the minimum energy path without the need for seeding. We demonstrate this method by calculating the pathways for the rotation of a methyl group in ethane and for HONO elimination from dimethylnitromine. Linear synchronous transit fails to produce a continuous pathway for HONO elimination, and simple interpolation of Cartesian coordinates overshoots the peak energy of our path by more than 560 kcal/mol.