Extended Data Fig. 4: Time-dependent potential barriers.

Time-dependent potential barriers between C3 and H3 at t = 0fs (A), 10fs (B), and 14fs (C), where one of the atoms carries a charge of +1 and the other one is neutral, respectively. The donor energy levels E_D(C 2p) and E_D(H 1s) are based on the atomic orbital energies, influenced by the electrostatic interaction with the other atom, using Eq. (3) in Methods. The potential shown, \(V(x)=-\frac{1}{| x| }-\frac{1}{| x-R| }\) (where R is the average C3–H3 distance at time t (see Fig. 2C)), corresponds to a charge of +1 on both atomic sites, as the electron on the neutral atom considered for the charge transfer does not feel its own shielding of the nuclear charge. Filled areas indicate forbidden regions (no tunneling included in the model). For t < 10 fs (A), electron transfer is possible in both directions; for 10 < t < 14 fs (B), electron transfer is only possible from C to H⁺, but not from H to C⁺; for t > 14 fs (C), the potential barrier exceeds both energy levels, and no electron transfer can occur. The one-way electron transfer between 10 fs and 14 fs explains the decrease of the average hydrogen charges in the same time period in Fig. 2D.