34.2.18 Numerical Hessian (NUMHES)

NUMHES,mstep,type,icalc,thresh;

This option allows you to calculate numerical second derivatives of the energy by finite differences. If you use analytical gradients, these are differentiated once whereby it is possible to use forward differences (needs one additional gradient calculation for each coordinate) or central differences (more accurate, needs two additional gradient calculations for each coordinate). For transition state optimizations it is usually sufficient to use forward differences. If you use numerical gradients the energy is differentiated twice. In this case only central differences are possible. mstep defines the number of optimization steps after which the numerical hessian is recalculated:

mstep=-1

Don't calculate numerical hessian (default for minimization).

mstep=0

Calculate numerical hessian only once at the start of the optimization (default for transition state searches).

mstep=n

Calculate numerical hessian after each n optimization steps. This is useful for difficult transition state optimizations (e.g. if the eigenvalue structure of the hessian changes during the optimization).

type defines the finite differences to be used:

type=0

Use forward differences (default).

type=1

Use the more accurate central differences.

icalc defines in which way the Hessian matrix shall be recalculated:

icalc=0

Static regeneration: Recalculate complete Hessian matrix numerically after each mstep optimization steps (default).

icalc=1

Partial regeneration: Recalculate selected Hessian matrix elements if the relative deviation of this element before and after update (see UPDATE, section 30.2.12) is larger than thresh. If thresh is not specified, a default value of $thresh=0.05$ (i.e. a maximum deviation of $5 \%$) is used.

icalc=2

Dynamic regeneration: Recalculate complete Hessian matrix if the RMS deviation of the Hessian matrix before and after update is larger than $thresh$. If thresh is not specified a default value of $thresh=0.5$ $a.u.$ is used.

Note that the static regeneration of the complete Hessian matrix after mstep iterations is not disabled if the partial (icalc=1) or dynamical (icalc=2) regeneration is used; i.e. if you want to use only the partial or dynamical regeneration, you should set mstep to zero.

If cartesian coordinates are used, the molecular symmetry can be used to shorten the number of gradient and/or energy calculations (see COORD keyword section 30.2.16).