Exclusion principle repulsion effects on the covalent bond beyond the Born-Oppenheimer approximation

The changes in the covalent bond of the hydrogen molecule limited in space by a spherical hard boundary are studied. The sphere is moved along an axis parallel or orthogonal to the molecular axis. The diffusion Monte Carlo approach is used to solve the Schrödinger equation with the relevant boundary conditions and to evaluate the changes in the bond energy versus the location of the sphere. The vertical and lateral quantum forces exerted on the sphere are evaluated by calculating the energy derivative versus the distances to the sphere. The results show that the quantum forces present an important dependence on the distance and vanish rapidly as the separation between the sphere and the molecule increases. In the limiting case the molecular bond breaks due to the electronic depletion induced in the covalent bond. An application of this study is the modelisation of the forces exerted on the passivated cantilever of an atomic force microscope probing the electron cloud in the contact mode in the Pauli exclusion regime.