40.2.10 Numerical gradients (NUMERICAL)

NUMERICAL,options,active$_1$=step$_1$, active$_2$=step$_2$ ...;

With this directive the gradients are computed by finite differences. step$_i$ is the increment for the active geometry parameter $active_i$. For active parameters which are not specified, the default values are used. By default, the increment is 0.01 bohr for bond distances and 0.5 or 1 degree for angles less than or greater than 90 degrees, respectively. These defaults can be modified by specifying RSTEP or ASTEP. DSTEP is the length of symmetrical displacements, which are used if the optimization is performed in 3N coordinates.

For each active variable, two energy calculations are necessary in each geometry optimization step - so numerical optimizations may be expensive! In optimizations of 3N coordinates symmetrical displacement coordinates are normally used to minimize the number of energy calculations. (see section 39.2.1).

For optimization of special energies see VARIABLE section 40.2.17.

The following options can be given:

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.

CENTRAL

Use central differences for gradient (default)

FORWARD

Use forward differences (not recommended for gradient).

FOURPOINT

Use four-point formula for very accurate numerical gradients.

PROCEDURE=procname

Use given procedure for numerical calculation of the gradient. This procedure must define a complete energy calculation (orbital optimization and correlation treatment).

VARIABLE=varname

Use given variable for numerical calculation of the gradient.

DISPLACE=type

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