Critical points

Critical points of the charge density are usually the first items you will want to compute, since the whole theory of atoms in molecules is based on their properties. Of course, critical points of other density functions can also be computed (see Control View).

At critical points all components of the gradient of the density function vanish. Apart from the gradient, the Hessian matrix of second derivatives is also available at each point (it is computed directly from the wave function or numerically).
Hence Newton's method can be employed to calculate the zeros of the gradient. Newton's method turned out to be superior to all other methods like conjugate gradient or quasi-Newton-methods. But it is heavily dependent on the choice of starting values.

AIM2000 helps you in several ways to choose starting values for a successful iteration:

For all types of starting point choices, the program will present a record of the iterations and their success. Successfully computed critical points will be entered into the right hand side list together with their inertia.
The Options-button brings you to a dialog where you can manipulate the used Newton iteration process.

Delete selected critical points removes the highlighted critical points from the list.
OK, done closes the dialog.