Level-shifted mode-following

The input needed for doing a level-shifted mode following is very similar to the input for following a gradient extremal, and the keyword that is needed in order to invoke this kind of calculation is .MODFOL. As for gradient extremals, we need to specify which mode we follow. However, a mode following does not use mass-weighted molecular coordinates as default, and isotopic composition of the molecule is therefore not needed. Note, however, that mass-weighted coordinates can be requested through the keyword .MASSES as described in the input section for the *WALK module. A typical input following the third mode will thus look like:

**DALTON INPUT
.WALK
*WALK
.MODFOL
.INDEX
 1
.MODE
 3
**WAVE FUNCTIONS
.HF
**END OF DALTON INPUT

The level-shifted mode-following uses an algorithm similar to the one used in the ordinary geometry optimization of a molecule, but whereas one in minimizations chooses a step so that the level shift parameter is less than the lowest eigenvalue of the molecular Hessian, this level shift parameter is chosen to be in-between the eigenvalues $\lambda_{t-1}$ and $\lambda_{t}$ if we are following mode number $t$. This approach was pioneered by Cerjan and Miller [36], and is also described in Ref. [26]. As for the gradient extremal approach, higher-order transition states can be requested through the use of the keyword .INDEX.

Note that it may often be necessary to start the mode-following calculation by stepping out of the stationary point along the mode of interest using the keyword .EIGEN in the .WALK module. We refer to the reference manual for a further description of this option.

The index of the critical point--that is, the number of negative Hessian eigenvalues--sought, need to be specified (by the keyword .INDEX), as the calculation would otherwise continue until a critical point with index zero (corresponding to a minimum), is found.