A few procedures must be defined.
`beadpot` defines the method for computing the potential energy of a single bead geometry.
`beadgrad` gives the method for computing the gradient for a bead using the `force` command.
`beadfreq1`, `beadfreq2` and `beadfreq3` define methods for computing frequencies of the transition state/well minimum, of the initial (pre-optimized) ring-polymer beads and of the final (optimized) beads.
Because the procedure `beadfreq1` is only called once directly after `beadpot`, it is not necessary to recalculate the wavefunction in this case.
For the tunnelling-splitting calculations, `beadfreq2` is not used as the L-BFGS optimization proceeds without a Hessian.

molpro@molpro.net 2019-06-17