Transition State

A transition state (TS) search is very much like a minimization: the purpose is to find a stationary point on the energy surface, primarily by monitoring the energy gradients, which should vanish. The difference between a transition state and a (local) minimum is that at the transition state the Hessian has a negative eigenvalue.

Because of the similarities between a minimization and a TS search most subkeys in geometry are applicable in both cases, see the Geometry Optimization section. However, practice shows that transition states are much harder to compute than a minimum. For a large part this is due to the much stronger anharmonicities that usually occur near the ts, which threaten to invalidate the quasi-Newton methods to find the stationary point. For this reason it is good advice to be more cautious in the optimization strategy when approaching a Transition State and for some subkeys the default settings are indeed different from those for a simple optimization. In addition, certain additional aspects have to be addressed.

GEOMETRY
 TransitionState {Mode=Mode} {NegHess=NegHess}
end

NegHess

The number of negative eigenvalues that the Hessian should have at the saddle point. In the current release it is a rather meaningless key, which should retain its default value (1).

Mode

Controls the first step from the starting geometry towards the saddle point: it specifies in which direction the energy is to be maximized while the optimization coordinates will otherwise be varied so as to minimize the energy. A positive value means that the eigenvector #mode of the (initial) Hessian will be taken for the maximization direction. This means: put all Hessian eigenvalues in ascending order, ignoring those that correspond to impossible movements (rigid rotations and translations, symmetry breaking) and then take the eigenvector of #mode in the remaining list. A negative value for mode instructs the program to take the eigenvector that makes the largest change of the abs(mode)-th atomic coordinate (counting only the coordinates that are allowed to be changed independently, in order as they occur in the input list of coordinates under atoms).

Default: mode=1. Generally the program performs best with this default: it will simply concentrates on the mode with the lowest eigenvalue, which should of course finally be the path over the transition state (negative eigenvalue!).

After the first geometry step, the subsequent steps will attempt to maximize along the eigenvector that resembles most (by overlap) the previous maximization direction until the Hessian is found to have a negative eigenvalue. At that point the program switches to that mode. As soon as the program has focused on the eigenvector with the lowest eigenvalue (mode=1) the overlap criterion to select the search direction is internally discarded and subsequently only the lowest eigenvector is taken. An input value mode=0 effectuates this immediately: the direction with the lowest eigenvalue will be the maximization direction for all iterations.

As mentioned before, the other subkeys have the same functionality as for minimizations, but different defaults or options may apply:

HessianUpdate

Different (fewer) options apply now:
(i) Powell: Powell
(ii) BFGS: Broyden-Fletcher-Goldfarb-Shanno
(iii) DFP: Davidon-Fletcher-Powell
(iv) BOFILL : Bofill, Eq. (13) and (14) of Ref. [139]
default: Powell

MaxRadStep

Default: 0.2 angstrom for Z-matrix optimization, 0.1 angstrom for Cartesian optimization.

MaxAngleStep

Default: 5 degrees.

Note: in Transition State searches precision is often much more critical than in minimizations. One should set the Numerical Integration precision at a fair value (4.5 at least). The default (i.e. automatic) value is 5.0 in a Transition State search.