A Note on Units and Planck's Constant

Aside from *CHARMM* and *AMBER* `OPTIM` does no
unit conversions. These systems are treated differently, as explained below.
For all other cases `PATHSAMPLE` is
expecting to receive
in the `min.data`
and `ts.data` files. `PATHSAMPLE` converts to
using
, but also does no unit conversions.
The rate constants are therefore in natural frequency units of
, where is the unit of energy,
is the unit of mass, and is the unit of length.

For a system where all particles have equal masses, , the rate constants
calculated by `PATHSAMPLE` can therefore be converted to SI units
by multiplying by
.

For calculations involving free energy regrouping schemes we need to supply
a value for the Planck constant in reduced units via the *PLANCK* keyword.
Since the temperature is read in energy units, i.e. , so that
is in , we need to define in reduced units so that terms like
are dimensionless. If is in reduced time units then we
need divided by the unit of energy and the unit of time.
The reduced value of is therefore

(1) |

For *CHARMM* and *AMBER* we need to diagonalise the reciprocal
mass-weighted Hessian in `OPTIM`, where the various masses are known.
For convenience the frequency unit conversion is done in `OPTIM` as
well, so that the rate constants calculated in `PATHSAMPLE` are
in s and do not need to be converted.
The value required for the Planck constant is therefore different because
is not in reduced units. Instead, we need to convert
to kcal/mol, since these are the units of . Hence we need
,
where is one kcal/mol. Since 1kcal/mol is
J
the required value for the *PLANCK* keyword in regrouping calculations
is
.

David Wales 2019-02-15