For SCALE=0 the `step length' is taken to be the total step length in the multidimensional space of Cartesian coordinates. For SCALE=1 we scale according to the largest displacement in Cartesian coordinates. For SCALE=2 we scale according to the largest displacement in the Hessian eigenvector basis. For SCALE=3 we scale according to the total step size called for by the steepest descent routine. The default for all other search types is now SCALE=10 for which a different trust ratio is calculated for each eigendirection and used to adjust the maximum allowed step for each eigenvector. This is described in more detail below. It has not been published yet.
SCALE=10 employs a trust radius whose default value is 4.0. This value can be changed using the keyword TRAD. Appropriate values for the maximum initial step size and the trust radius for different systems may need to be found by experimentation. After the first step the program compares the predicted value of the Hessian eigenvalue for a given eigendirection, as calculated by finite difference of the present and previous component of the gradient in this direction, with the actual eigenvalue. The trust ratio for a particular eigendirection is the modulus of this predicted value minus the actual value, divided by the actual value. If the trust ratio is less than the trust radius then the maximum step allowed in this direction is increased by a factor of 1.1 (up to a maximum of 0.5); if it is more than the trust radius the maximum allowed step in this direction is divided by 1.1 (down to a minimum allowed value of 0.005). The maximum allowed step for each direction is initialized at the value read from the odata file.
This approach assumes that all the eigenvectors are in correspondence for the present and previous geometries when they are arranged according to the eigenvalues in ascending or descending order. When large steps are being taken some eigendirections are likely to cross over, and it might be better to use an overlap criterion for all the present and previous eigenvectors. However, this has not proved to be necessary to date.
Scaling of the above sort does not apply in conjugate gradient minimizations, although the trust radius approach described above for SCALE=10 is used for the eigenvector-following step in hybrid transition state searches.