A force-calculation is to be run. The Hessian, that is the matrix in millidynes per Ångstrom) of second derivatives of the energy with respect to displacements of all pairs of atoms in x, y, and z directions, is calculated. On diagonalization this gives the force constants for the molecule. The force matrix, weighted for isotopic masses, is then used for calculating the vibrational frequencies. The system can be characterized as a ground state or a transition state by the presence of five (for a linear system) or six eigenvalues which are very small (less than about 30 reciprocal centimeters). A transition state is further characterized by one, and exactly one, negative force constant.

By default, the geometry is rotated so that the principal moments of inertia are oriented along the Cartesian axes, x, y, and z. If this is not wanted, add keyword NOREOR.


Calculating the Hessian for a large system takes a long time, and often the only reason for running a FORCE calculation is to verify that the system is a transition state.  To speed up this calculation, FORCETS is provided. The FORCETS calculation builds a Hessian for the atoms involved in the transition state, that is, all atoms with optimization flags of "1" or "2" (For the meaning of "2", see MINI).  All atoms used in building the Hessian matrix must be at the start of the geometry.  This Hessian will be used in generating vibrations for the transition state.  If the system is a genuine transition state, then there will be one imaginary vibration, indicated in the output as a "negative" vibration.  Its value will be within a few percent of the value that would be obtained if a full calculation were done. The imaginary vibration should involve the atom(s) that move during the reaction. All other vibrations should be positive, but their value is not useful, because they would involve atoms other than those in the transition state.

Before a FORCE calculation is run, the gradients are calculated to see if the geometry is at a stationary point. If it is not, then the calculation will be stopped, to allow the user to take corrective action.

Sometimes, the gradient norm at the start of a FORCE calculation will be larger than at the end of the geometry optimization which was used to generate the geometry for the force calculation. This is due to the FORCE calculation using a different method, double-sided derivatives, to calculate the gradients. In order to have the same GNORM at the end of a geometry optimization as at the start of a FORCE calculation, use PRECISE in the geometry optimization. Gradients calculated with PRECISE and with FORCE both use double-sided derivatives.

At the end of a FORCE calculation, the force constants for the coordinates supplied will be printed. If other force constants are needed, then use ISOTOPE to save the Hessian. The connectivity can then be changed, and the job restarted using RESTART. Of course, care must be taken to ensure that the atoms are in exactly the same positions in both calculations.

Before a FORCE calculation is started, a check is made to ensure that a stationary point is being used. This check involves calculating the gradient norm (GNORM) and if it is significant, the calculation will be stopped. See also LET and TRANS. In a FORCE calculation, PRECISE will eliminate quartic contamination part of the anharmonicity). This is normally not important, therefore PRECISE should not routinely be used. In a FORCE calculation, the SCF criterion is automatically made more stringent; this is the main cause of the SCF failing in a FORCE calculation.