Hydrogen molecule ion: Path-integral monte carlo approach

The path-integral Monte Carlo approach is used to study the coupled quantum dynamics of the electron and nuclei in hydrogen molecule ion. The coupling effects are demonstrated by comparing differences in adiabatic Born-Oppenheimer and nonadiabatic simulations, and inspecting projections of the full three-body dynamics onto the adiabatic Born-Oppenheimer approximation. Coupling of the electron and nuclear quantum dynamics is clearly seen. The nuclear pair correlation function is found to broaden by 0.040a(0), and the average bond length is larger by 0.056a(0). Also, a nonadiabatic correction to the binding energy is found. The electronic distribution is affected less than the nuclear one upon inclusion of nonadiabatic effects.