40.2.7 Numerical Hessian (NUMHESS)

NUMHESS,options

or

NUMHESS,hstep,options

If this directive is present a numerical Hessian is computed using finite differences. If analytical gradients are available, one can use forward gradient differences (needs one gradient calculation for each coordinate) or central differences (more accurate, needs two gradient calculations for each coordinate). For transition state optimizations it is usually sufficient to use forward differences. If analytical gradients are not available for the optimized method, the energy is differentiated twice. In this case only central differences are possible.

The following options can be given:

HSTEP=hstep

hstep=-1: Don't calculate numerical hessian (default for minimization);
hstep=0 Calculate numerical hessian only once at the start of the optimization (default for transition state searches).
hstep=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).

FORWARD

Use forward differences (default).

CENTRAL

Use the more accurate central differences.

RSTEP=rstep

Step length for distances (in bohr). The default is 0.01.

ASTEP=astep

Step length for angles (in degree). The default is 0.5 or 1 for angles below and above 90 degree, respectively.

DSTEP=dstep

Step length for symmetrical displacements (in bohr). The default is 0.01.

VARIABLE=varname

Use given variable for numerical calculation of the Hessian. Note that this disables the use of gradients, and Hessian evaluation can be very expensive.

PROCEDURE=procname

Procedure to be used for computing Hessian. This procedure must be define a complete energy calculation (orbital optimization and correlation treatment). A different method can be used than for the optimized energy. For instance, an MP2 hessian can be used for CCSD(T) optimizations, or a CASPT2 hessian for MRCI optimizations. By default, the same procedure is used for the hessian as for the optimized energy.

DISPLACE=type

type can be one of the following: 2cm

SYMM

Use symmetric displacement coordinates (default). This is the only recommended option.

CART

Use $3N$ cartesian displacements (not recommended). This requires many more energy calculations than necessary and does not preserve the molecular symmetry.

UNIQUE

Use symmetry-unique cartesian displacements (not recommended)

Note that the displacement type for gradient and hessian must be the same.

CALC=icalc

icalc=0: Recalculate the complete Hessian matrix numerically after each hstep optimization steps (default).
icalc=1: Recalculate selected Hessian matrix elements if the relative deviation of this element before and after update (see UPDATE, section 40.2.9) 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: 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=thresh

Threshold for partial or dynamical update of hessian, see above