45.2 Numerical gradients

`FORCE,NUMERICAL`,*options*

Numerical gradients are computed automatically if no analytical gradients are available
for the last energy calculation. By default, no further input are needed, and the
gradient will be computed for the last energy calculation. The following options
can be given on the `FORCE` command or on subsequent directives (see subsequent sections):

`STARTCMD`=*command*- The input between
*command*and the current`FORCE`command defines the energy calculation for which the gradient is computed. This input section is executed for each displacement. `PROC`=*procname*- specifies a procedure to be executed for each displacement. This must define a complete energy calculation and must not contain gradient or Hessian calculations.
`VARIABLE`=*varname*- Compute the gradient of the value of variable
*varname*. This implies numerical gradients. The variable must be set in the corresponding energy calculation. `COORD=ZMAT|CART|3N`- coordinates with respect to which the gradient is evaluated. See section 45.2.1 for more information.
`DISPLACE=ZMAT|SYM|UNIQUE|CART`-

Displacement coordinates to be used for numerical gradient. The default is`ZMAT`if the geometry is given as a zmatrix which depends on variables, and`SYM`(symmetrical displacement coordinates) otherwise. See section 45.2.1 for more information. `SYMMETRY=AUTO|NOSYM`- Symmetry to be used in wavefunction calculations of numerical gradients.
This option is only relevant if
`DISPLACE=UNIQUE|CART`. If`AUTO`is given, the maximum possible symmetry is used for each displacement. This implies that the energy is independent of the symmetry used. Note that this often not the case in MRCI or CASPT2 calculations. The option can also not be used in local correlation calculations. `AUTO`- (logical). Same as
`SYMMETRY=AUTO` `ZMAT`- (logical). Same as
`COORD=ZMAT` `OPT3N`- (logical). Same as
`COORD=3N` `RSTEP`=*rstep*- Step length for distances in numerical gradient calculations (in bohr). The default is 0.01.
`DSTEP`=*dstep*- Step length for symmetrical displacements (in bohr). The default is 0.01.
`ASTEP`=*astep*- Step length for angles in numerical gradient calculations (in degree). The default is 1.
`CENTRAL`- (logical). Use 2-point central formula; needs energy calculations for degrees of freedom.
`FORWARD`- (logical). Use forward gradients (needs only energy calculations, but less accurate)
`FOURPOINT`- (logical). Use 4-point formula for accurate numerical gradient; needs energy calculations.
`NUMERICAL`- (logical). Force the use of numerical gradients, even if gradients are available.
`VARSAV`- (logical). Save gradient in variables
`GRADX`,`GRADY`,`GRADZ`.

Example

hf ccsd(t) forces,numerical

The program will then automatically repeat `HF` and `CCSD(T)` at as many
geometries as needed for evaluating the gradient.
This is equivalent to

hf ccsd(t) forces,numerical,startcmd=hf

or, using a procedure

forces,numerical,proc=runccsdt ... runccsdt={ hf ccsd(t)}

- 45.2.1 Choice of coordinates (
`COORD`) - 45.2.2 Numerical derivatives of a variable
- 45.2.3 Step-sizes for numerical gradients
- 45.2.4 Active and inactive coordinates

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molpro@molpro.net 2018-08-17