Given the nuclear joint probability ρ nuc (R), the probability density for observing a molecule in a certain labeled configuration is given by a rotationally integrated nuclear probability density ρ nuc,rot ([R] rot ) = ρ nuc (UR)dU, where the integration is over all possible rotations U. Since ρ nuc,rot is invariant under the permutation of positions of identical particles, the probability density for observing an unlabeled configuration is ρ nuc,rot,perm ([R] rot,perm ) =