Characterization of the continuous transition from atomic to molecular shape in the three-body Coulomb system

TL;DR

This paper introduces a new method to characterize the continuous transition from atomic to molecular shapes in a three-body Coulomb system by analyzing the evolution of a nonadiabatic potential energy surface as the mass ratio varies.

Contribution

It develops a unifying approach that extends traditional models to the nonadiabatic regime using marginal-conditional factorization and variational wavefunctions.

Findings

The potential energy surface reveals the shape transition as the mass ratio changes.

The approach unifies atomic and molecular shape descriptions beyond the Born-Oppenheimer approximation.

Shapes of marginal and conditional distributions evolve continuously with mass ratio.

Abstract

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.