Quantum confinement of the covalent bond beyond the Born-Oppenheimer approximation

Dirichlet boundary conditions with different symmetries, spherical and cylindrical impenetrable surfaces, are imposed on the covalent electron pair of a molecular bond. Accurate results for different observable like energy and interparticle distances are calculated using quantum Monte Carlo methods beyond the Born-Oppenheimer approximation. The spherical confinement induces a raise in the bond energy and shortens the internuclear distances even for a relatively soft confinement. When cylindrical symmetry is considered, similar qualitative behavior is observed though only the electrons are confined. A compression followed by a relaxation process of the confined bond is shown to induce a vibrationally excited state. Finally, a brief qualitative discussion based on a simplified picture of the role of compression/relaxation cycles in enzyme catalysis is given.