The gradient norm is to be minimized by Bartel's method [8]. This is a Non-Linear Least Squares gradient minimization routine. Gradient minimization will locate one of three possible points:

(a) A minimum in the energy surface. The gradient norm will go to zero, and the lowest five or six eigenvalues resulting from a FORCE calculation will be approximately zero.

(b) A transition state. The gradient norm will vanish, as in (a), but in this case the system is characterized by one, and only one, negative force constant.

(c) A local minimum in the gradient norm space. In this (normally unwanted) case the gradient norm is minimized, but does not go to zero. A FORCE calculation will not give the five or six zero eigenvalues characteristic of a stationary point. While normally undesirable, this is sometimes the only way to obtain a geometry. For instance, if a system is formed which cannot be characterized as an intermediate, and at the same time is not a transition state, but nonetheless has some chemical significance, then that state can be refined using NLLSQ.