Quantum rate calculations proceed via an instanton which is equivalent to the transition state on the ring-polymer surface.
These stationary points are computed using a quasi-Newton saddle-point search with Powell's Hessian update.
Because of the known symmetry of the final geometry (that the ring polymer folds back on itself), only half of the beads need be specified.
The geometry of the transition state should be specified with the geometry keyword,
and the classical TST rate through this point is compared with the rate computed from the instanton.
The action of the instanton, its fluctuations and rotations are printed to the output file.
MOLPRO computes the tunnelling factor which is the ratio of these rates and the rate itself can be calculated if the reactant partition function is known.
It is necessary to converge the results in the large- limit.
References for the ring-polymer instanton method are:
- J. O. Richardson and S. C. Althorpe.
“Ring-polymer molecular dynamics rate-theory in the deep-tunneling regime: Connection with semiclassical instanton theory.”
J. Chem. Phys. 131, 214106 (2009).