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.
- 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
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.
