Extended Data Fig. 1: Schematic of photoinduced bond formation in [Au(CN)₂⁻]₃.

Upon laser excitation (with energy represented by hv), wavepackets are created in both of the ground and excited states. The excited-state wavepacket in the \({{\rm{T}}}_{1}^{{\prime} }\) state is prepared in the FC region after the ultrafast intersystem crossing from the initially excited singlet state (S₁) to a triplet excited state (\({{\rm{T}}}_{1}^{{\prime} }\)). The excited-state wavepacket created in the FC region should move towards the equilibrium structure of \({{\rm{T}}}_{1}^{{\prime} }\), which has two equivalent covalent Au–Au bonds between adjacent gold atoms (right inset, yellow spheres; blue and white spheres denote N and C atoms, respectively). The trajectory of the wavepacket from the FC region to the equilibrium structure of \({{\rm{T}}}_{1}^{{\prime} }\) eventually determines the reaction trajectories of the ultrafast bond formation and hints towards its reaction mechanism. Three candidate reaction mechanisms of bond formation (paths 1, 2 and 3), described in the text, are represented by blue arrows on the nuclear coordinates of R_AB versus R_BC. In short, path 2 represents a concerted bond formation mechanism and path 1 and path 3 represent asynchronous bond formation mechanism. Path 1 and path 3 are distinct, depending on which bond is formed first between the A–B pair and the B–C pair. The initial motion of the excited-state wavepacket affects the initial motion of the ground-state wavepacket in the S₀ state, because impulsive Raman scattering generating the ground-state wavepacket can occur non-impulsively, owing to the finite pulse duration (~100 fs), as described in Supplementary Information. After the initial motions of the wavepackets in the ground and excited states, the wavepackets oscillate around their equilibrium structures.