Walking on potential energy surfaces

By combining a local quadratic approximation to the potential energy surface with the concept of a trust radius within which this quadratic approximation is accurate, and a scaling of one active coordinate, we have developed an automated surface walking algorithm. This algorithm allows one to walk from geometries characteristic of equilibrium molecular structures, uphill along stream beds, through transition-state geometries, and onward to product-molecule equilibrium geometries. The method has been applied to model and ab initio test cases with encouraging results. The success of using the algorithm in connection with approximate Hessian matrices formed via so-called update techniques, which require only local force information, is especially encouraging in light of the high cost of ab initio analytical evaluation of the Hessian.