Universal steps in quantum dynamics with time-dependent potential-energy surfaces: Beyond the Born-Oppenheimer picture

It was recently shown [G. Albareda, Phys. Rev. Lett. 113, 083003 (2014)]PRLTAO0031-900710.1103/PhysRevLett.113.083003 that within the conditional decomposition approach to the coupled electron-nuclear dynamics, the electron-nuclear wave function can be exactly decomposed into an ensemble of nuclear wave packets effectively governed by nuclear conditional time-dependent potential-energy surfaces (C-TDPESs). Employing a one-dimensional model system, we show that for strong nonadiabatic couplings the nuclear C-TDPESs exhibit steps that bridge piecewise adiabatic Born-Oppenheimer potential-energy surfaces. The nature of these steps is identified as an effect of electron-nuclear correlation. Furthermore, a direct comparison with similar discontinuities recently reported in the context of the exact factorization framework allows us to draw conclusions about the universality of these discontinuities, viz., they are inherent to all nonadiabatic nuclear dynamics approaches based on (exact) time-dependent potential-energy surfaces.