  We present an alternative, univocal characterization of the continuous
transition from atomic to molecular shape in the Coulomb system constituted by
two identical particles and a third particle with the opposite charge, as the
mass ratio of the particles varies. Applying a marginal-conditional exact
factorization to a variationally optimized wavefunction, we construct a
nonadiabatic potential energy surface for the relative motion between the
single particle and each of the identical particles in the ground state. The
transition is revealed through the evolution with the mass ratio of the
topography of such surface and of the shapes of the associated marginal and
conditional distributions. Our approach unifies and extends to the nonadiabatic
regime the Born-Oppenheimer and charge-distribution pictures of molecular
shape.
