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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) [Raghavachari81, Wiberg92].


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.


Can be used with large MM force calculations to avoid the O(N3) work involved in computing the putative geometry optimization step.

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

The forces on the nuclei appear 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.

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