.. _NLLSQ:

``NLLSQ``
=========

The gradient norm is to be minimized by Bartel's
method [`8 <references.html#nllsq>`__]. 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.