Abstract
Accuracy of the Born–Oppenheimer adiabatic approximation to the ground state of a hydrogenlike molecule (M+M+m-m−) is examined in comparison with the exact results obtained by diffusion Monte Carlo simulations, fully incorporating quantum fluctuations. For the mass ratio m⁄M<0.1, the relative error in the ground-state energy is found to be less than 1%. We discuss the change in nature of the binding mechanism of this system with the increase of m⁄M from the usual chemical bonding at m⁄M<<1 to the one in which nonadiabatic effects such as the retardation of electron response to proton motion play a crucial role.
