  Molecular dynamics are extremely complex, yet understanding the slow
components of their dynamics is essential to understanding their macroscopic
properties. To achieve this, one models the molecular dynamics as a stochastic
process and analyses the dominant eigenfunctions of the associated
Fokker-Planck operator, or of closely related transfer operators. So far, the
calculation of the discretized operators requires extensive molecular dynamics
simulations. The Square-root approximation of the Fokker-Planck equation is a
method to calculate transition rates as a ratio of the Boltzmann densities of
neighboring grid cells times a flux, and can in principle be calculated without
a simulation. In a previous work we still used molecular dynamics simulations
to determine the flux. Here, we propose several methods to calculate the exact
or approximate flux for various grid types, and thus estimate the rate matrix
without a simulation. Using model potentials we test computational efficiency
of the methods, and the accuracy with which they reproduce the dominant
eigenfunctions and eigenvalues. For these model potentials, rate matrices with
up to $\mathcal{O}(10^6)$ states can be obtained within seconds on a single
high-performance compute server if regular grids are used.
