Calculating Pathways

Pathways are calculated by starting a minimisation of some sort after stepping off the
transition state specified in `odata`.
Using *MODE* values of 1 and will give the two sides of the path.
With *SEARCH* 0 (or 3) or LBFGS minimisation
the resulting pathway will only be an approximation to a true
gradient line. For search type 6 (or 7) and *RKMIN* or *BSMIN*
the results should be close 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,[80] has now been implemented, but not in the BFGS
minimisation or hybrid EF/BFGS routines.

From svn revision 24173 it is possible to follow a transition state search by a
pathway calculation automatically. The transition state search can be specified
by *BFGSTS*, including *NOIT* and *NOHESS*, or full eigenvector-following
using *SEARCH 2*.
The default minimisation uses eigenvector-following if no other method is specfied.
Otherwise the paths can be calculated by specifying *BFGSMIN*,
*PMPATH*, *BBRSDM*, *RKMIN*, or *BSMIN*.
Example input and output can be found at http://www-wales.ch.cam.ac.uk/examples/OPTIM/.
The following input is for a gradient-only hybrid eigenvector-following transition state
search with pathways calculated using LBFGS energy minimisation:

MAXBFGS | 0.2 0.2 |

DUMPALLPATHS | |

PATH | 1000 0.0 |

MAXSTEP | 0.1 |

MAXMAX | 0.2 |

TRAD | 0.2 |

BFGSTS | 100 3 25 0.001 |

UPDATES | 10 10 |

NOHESS | |

BFGSMIN | 1.0D-7 |

CONVERGE | 1.0D-4 1.0D-7 |

PUSHOFF | 0.02 |

STEPS | 200 |

BFGSSTEPS | 5000 |

POINTS | |

etc. |

The *DUPALLPATHS* keyword results in a `path.info` file being created, which
can be read into a discrete path sampling database for PATHSAMPLE using the
*ADDPATH* keyword for that program.

David Wales 2018-06-23