Gaussian 03 Online Manual
Last update: 2 October 2006


This calculation type keyword requests a single calculation of the forces on the nuclei (i.e., the gradient of the energy). The dipole moment is also computed (as a proper analytic derivative of the energy for MP2, CC, QCI and CI) [202,447].

Compute the forces by numerically differentiating the energy once. It is the default for all methods for which analytic gradients are unavailable. Note that this procedure exhibits some numerical instability, so care must be taken that an optimal step size is specified for each case.

Restarts numerical evaluation of the forces.

Sets the step size used in numerical differentiation to 0.0001*N. The units are Angstroms by default unless Units=Bohr has been specified. The default step size is 0.01 Å. StepSize is valid only in conjunction with EnOnly.

Analytic gradients are available for all SCF wavefunctions, all DFT methods, CIS, MP2, MP3, MP4(SDQ), CID, CISD, CCD, CCSD, QCISD, CASSCF, SAC-CI and all semi-empirical methods. For other methods, the forces are determined by numerical differentiation.

The forces on the nuclei appears in the output as follows (this sample is from a calculation on water):

Center     Atomic                    Forces (Hartrees/Bohr) 
Number     Number               X               Y                 Z 
1           8           -.049849321      .000000000     -.028780519 
2           1            .046711997      .000000000     -.023346514 
3           1            .003137324      .000000000      .052127033 
      MAX      .052127033      RMS       .031211490 
      Internal Coordinate Forces (Hartree/Bohr or radian) 
Cent Atom N1     Length/X     N2     Alpha/Y       N3       Beta/Z   J 
1  O 
2  H     1    -.023347(   1) 
3  H     1    -.023347(   2) 2   -.088273(    3) 
       MAX       .088272874      RMS      .054412682

The forces are determined in the standard orientation, but are restored to the original (Z-matrix) set of axes before printing (as noted in the output). This is followed by the corresponding derivatives with respect to the internal coordinates (lengths and angles used in the Z-matrix) when internal coordinates are in use. The forces are followed in each case by their maximum and root-mean-square values.