39.2 Numerical gradients

It is possible to compute gradients by finite differences using

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 39.2.1 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 39.2.1 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 $2M$ energy calculations for $M$ degrees of freedom.

FORWARD

(logical). Use forward gradients (needs only $M+1$ energy calculations, but less accurate)

FOURPOINT

(logical). Use 4-point formula for accurate numerical gradient; needs $4M$ 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)}