where ξ is the displacement of the coordinate x and p = mv is the corresponding momentum of the nucleus along the coordinate. By choosing a fixed σ x we can parameterize the sampling procedure that fulfills the uncertainty principle along each given degree of freedom in the molecule. The construction of the Wigner distribution requires solving the quantum-mechanical problem. Alternatively, we can try to apply heuristic considerations to make a self-sustained procedure for generating such distributions. As a starting point, we need to consider that the uncertainties of the coordinate and momentum should at least fulfill the Heisenberg equality principle (σ x • σ p = h/2). This principle makes both distributions for the coordinate ρ x and the momentum ρ p dependent on each other: the larger is the uncertainty for the momentum, the smaller it is for the coordinate, and vice versa. We can think of the uncertainty as the amount of information we have about x and p. As a guiding principle, we require the same amount of information for x and p, i.e. the uncertainty in the distributions ρ x and ρ p should be approximately the same.