The first example is for an eigenvector-following transition state search with maximum step size and trust radius different from the default values. The eigenvector corresponding to the second-lowest non-zero eigenvalue is followed uphill at the first step, with subsequent uphill directions being determined by the overlap condition. The convergence criteria are an unscaled maximum step size of 0.005 and an RMS gradient tolerance of 0.000001.
| SEARCH | 2 |
| MODE | 2 |
| MAXSTEP | 0.1 |
| TRAD | 2.0 |
| STEPS | 100 |
| CONVERGE | 0.005 0.000001 |
| POINTS | |
| etc. |
The next dataset is the same as above except that we perform an eigenvector-following minimisation and set an initial displacement from the assumed transition state of 0.05 units.
| SEARCH | 0 |
| PUSHOFF | 0.05 |
| MAXSTEP | 0.1 |
| TRAD | 2.0 |
| STEPS | 100 |
| CONVERGE | 0.005 0.000001 |
| POINTS | |
| etc. |
Next is an LBFGS energy minimisation with a maximum of 100 steps and convergence conditions of 0.00001 for the RMS gradient. There follows a check of the Hessian index using iteration to calculate eigenvalues to an accuracy of 0.01 with 200 and 50 iterations maximum for the smallest and largest eigenvalues, respectively. A Hessian will be calculated in order to perform the check. NOIT could be used, in which case the lowest ten Hessian eigenvalues will be calculated. If NOHESS is specfified then the smallest non-zero Hessian eigenvalue will be calculated variationally.
| STEPS | 100 |
| BFGSMIN | 0.00001 |
| CHECKINDEX | 200 0.01 50 |
| POINTS | |
| etc. |
Next is a transition state search using the hybrid EF/BFGS method. The maximum EF step and trust radius are 0.1 and 2.0, respectively, and the maximum step in the LBFGS tangent space minimisation is 0.2. The maximum number of combined EF/BFGS steps is 100. The maximum number of iterations allowed is 200 for the smallest and 50 for the largest eigenvalue. A maximum of 20 BFGS steps is permitted in the orthogonal subspace after each eigenvector-following step until the eigenvalue appears to have converged, when the maximum jumps to 100 steps. The convergence criterion for the Hessian eigenvalues is that the percentage change between steps is less than 0.01. The convergence criterion for each BFGS subspace minimisation 0.0001 for the RMS gradient. Setting PUSHOFF to 0.1 enables us to start from a converged minimum with a large step. Convergence is achieved when the maximum unscaled eigenvector-following step falls below 0.01, the total RMS force falls below 0.0001, and the previous subspace minimisation has converged. The smallest eigenvalue and the corresponding eigenvector are saved in file vector.dump. The Hessian index is checked using iteration to calculate the eigenvalues with the same parameters as the BFGSTS keyword. Note: if the RMS tolerance specified by BFGSCONV is larger than that specfied by CONVERGE the algorithm cannot converge.
| MAXSTEP | 0.1 |
| MAXMAX | 0.1 |
| MAXBFGS | 0.2 |
| PUSHOFF | 0.1 |
| TRAD | 2.0 |
| STEPS | 100 |
| BFGSTS | 200 20 100 0.01 50 |
| BFGSCONV | 0.0001 |
| CONVERGE | 0.01 0.0001 |
| DUMPVECTOR | |
| CHECKINDEX | |
| POINTS | |
| etc. |
The following odata file is the same as above, except that no Hessian is available. A maximum of 30 steps is permitted in the BFGS Rayleigh-Ritz minimisation, which is designed to produce the lowest eigenvalue, and the convergence condition on this eigenvalue is that the RMS force in the variational BFGS minimisation falls below 0.1. Otherwise the parameters have the same meanings as above. The maximum step size in the Rayleigh-Ritz minimisation is set to 0.2 by the MAXBFGS keyword.
| MAXSTEP | 0.1 |
| MAXMAX | 0.1 |
| MAXBFGS | 0.2 0.2 0.2 |
| PUSHOFF | 0.1 |
| TRAD | 2.0 |
| STEPS | 100 |
| NOHESS | |
| BFGSTS | 30 20 100 0.1 |
| BFGSCONV | 0.0001 |
| CONVERGE | 0.01 0.0001 |
| DUMPVECTOR | |
| CHECKINDEX | |
| POINTS | |
| etc. |
Next we calculate the part of the reaction pathway resulting from a displacement of 0.05 antiparallel to the transition vector saved in file vector.dump. The calculation reverts to a pure LBFGS minimisation after the first step.
| MAXSTEP | 0.1 |
| MAXBFGS | 0.1 |
| TRAD | 2.0 |
| STEPS | 100 |
| PUSHOFF | 0.05 |
| MODE | -1 |
| READVEC | |
| BFGSSTEP | |
| BFGSCONV | 0.0001 |
| CONVERGE | 0.01 0.001 |
| POINTS | |
| etc. |
The next example shows how to calculate a complete pathway from the transition state geometry specified in odata reading the eigenvector from file vector.dump. NOIT or NOHESS could also be specified in conjunction with BFGSTS. Alternatively, READVECTOR would cause the required eigenvector to be read from file vector.dump; in this case either BFGSSTEP or BFGSTS must also be present in odata. The maximum LBFGS step is set to 0.05; this setting helps to make the path smoother and generally gives a closer approximation to the true steepest-descent path. The LBFGS convergence criterion is that the RMS force falls below 0.000001. BFGSMIN could be replaced by RKMIN or BSMIN to obtain more accurate steepest-descent paths.
| PATH | |
| MAXBFGS | 0.05 |
| STEPS | 500 |
| BFGSTS | 500 10 10 0.01 500 |
| PUSHOFF | 0.04 |
| BFGSMIN | 0.000001 |
| DUMPPATH | |
| POINTS | |
| etc. |
Pathways can also be calculated using entirely second derivative based steepest-descent methods:
| PATH | |
| CONVERGE | 0.01 0.000001 |
| STEPS | 500 |
| SEARCH | 5 |
| PUSHOFF | 0.04 |
| DUMPPATH | |
| POINTS | |
| etc. |
Alternatively, the eigenvector for which a PUSHOFF is required can be calculated by a full diagonalisation of the Hessian followed by a gradient only based minimisation:
| PATH | |
| CONVERGE | 0.01 0.000001 |
| STEPS | 500 |
| SEARCH | 0 |
| BFGSMIN | 0.00001 |
| PUSHOFF | 0.04 |
| DUMPPATH | |
| POINTS | |
| etc. |
A more complicated example for a CONNECT run using NEB to generate transition state guesses and BFGSTS for transition state searches. NOIT or NOHESS could also be used in conjunction with BFGSTS. The maximum number of transition state searches allowed is 20, and BFGSTS searches are started from guesses generated by NEB using a small number of images and a sloppy convergence criterion. Pathways will be calculated by LBFGS energy minimisation with 2000 steps allowed, whereas only 300 steps are allowed in the transition state searches.
| CONNECT | 20 |
| NEB | 100 5 0.02 |
| PATH | 3 |
| BFGSTS | 100 3 20 0.01 |
| BFGSMIN | 0.000001 |
| PUSHOFF | 0.05 |
| BFGSSTEPS | 2000 |
| STEPS | 300 |
| POINTS | |
| etc. |
In the next example hard sphere moves are used for the initial transition state guesses, using a displacement vector based upon the initial and final geometries of the two minima in question at the given step, if they are initially less than 2.5 distance units apart. Steepest-descent pathways are calculated by Runge-Kutta integration.
| CONNECT | 30 |
| PATH | 3 |
| FIXD | 0.70 2.5 |
| BFGSTS | 100 3 20 0.01 |
| BFGSCONV | 0.000001 |
| RKMIN | 0.00001 0.1 |
| NOIT | |
| PUSHOFF | 0.05 |
| STEPS | 2000 |
| POINTS | |
| etc. |
The pathways can also be calculated using the Page-McIver second-order steepest-descent approach:
| CONNECT | |
| NEB | 100 5 0.02 |
| PATH | 3 |
| SEARCH | 6 |
| MAXSTEP | 0.05 |
| MAXMAX | 0.1 |
| TRAD | 1.0 |
| BFGSTS | 100 3 20 0.01 |
| BFGSCONV | 0.000001 |
| NOIT | |
| PUSHOFF | 0.05 |
| STEPS | 2000 |
| POINTS | |
| etc. |
A collection of example odata and the corresponding output files can be found in the newtests directory.