Fig. 3: Free energy profiles and representative structures for CO₂ activation process on Cu(100) surface.

a Free energy profile and representative initial state (IS), transition state (TS), and final state (FS) structures for the CO₂ adsorption process in the pure water (Cu–*CO₂–H₂O) system without M⁺. The gray dashed lines indicate the zero value. b Corresponding free energy gradient with error bar at each calculated collective variable. Crossover points with dashed baseline indicate the positions of IS, TS, and FS. The error bars represent standard errors of free energy gradients calculated using block average at the corresponding collective variable. c–f Free energy profiles and representative structures at IS, TS, and FS for CO₂ adsorption with different cations (Cu–*CO₂–M⁺) of c Li⁺, d Na⁺, e K⁺, and f Cs⁺. The shadows in all five free energy profiles represent the cumulative errors ( ~ 0.01 eV at TS) estimated with the block average method (Supplementary Notes 2 and 3). In the local structures, CO₂ molecules are depicted as gray and red spheres, Cu substrates are shown as reddish-brown spheres, H₂O molecules are illustrated as red and white sticks, and M⁺, including Li⁺, Na⁺, K⁺, and Cs⁺ are represented by green, yellow, purple and blue spheres, respectively. The magenta dashed lines around M⁺ illustrate their coordination with O atoms in the first solvation shells.