Calculating Pathways

Having found a transition state it is possible to find the corresponding minima (and pathway) by displacing the transition state along the transition vector in both senses and starting minimizations for each point. To make a complete path the data from one of these searches must be reversed and the results for the other side of the path appended to it. Shell scripts to do this automatically for all the transition states in a given directory, and to perform miscellaneous analysis of the pathways, exist for various potentials. All pathway calculations produce one more entry in the points file than they do energies. The first energy corresponds to the first entry in the points file, but in EF runs we don't know the energy for the final set of points. The same behaviour has been set up for all the possible pathway searches so that the same scripts can be used for analysis.

For search types 0, 2, 3 and 4 OPTIM also detects convergence to stationary points with the wrong Hessian index and steps away from them. The test is triggered when the RMS force falls below 10^-5 in the prevailing units. The test is only applied at the first step and every fourth step. If a transition state search converges to (or starts from) a minimum a step is taken in the direction specified by MODE of magnitude PUSHOFF. If PUSHOFF has not been set then the displacement is one tenth of the current maximum step size allowed for the eigenmode in question. If a transition state search converges to (or starts from) a higher index saddle then the action depends upon the value of MODE. If MODE=0 then displacements are taken for all the eigenmodes with negative eigenvalues except for the one with the most negative eigenvalue. The magnitude of the displacement is determined in the same way as above. If MODE29#29 then a displacement is applied only along the specified value of MODE. For search types 0 and 3 similar action is taken. If the search converges to (or starts from) a stationary point that is not a minimum then if MODE=0 displacements are applied for all the eigenmodes with negative eigenvalues. If MODE29#29 then a displacement is only applied in the direction specified by MODE.

Pathways can be calculated by starting a minimization from a transition state. Using MODE values of 1 and -1 will give the two sides of the path. With search type 0 (or 3) the resulting pathway will only be an approximation to a true gradient line. For search type 6 (or 7) it should be closer to the true steepest descent path. Note that gradient lines are properties of the potential energy surface alone, and do not depend upon masses. Mass weighting, or calculating pathways in the fictitious space with a kinetic metric,[40] has now been implemented, but not in the conjugate gradient minimization or hybrid EF/CG routines.

Calculation of pathways within the hybrid conjugate gradient/eigenvector-following framework is discussed in §IV.