Emergent Rate Laws for Collective Lying-Standing Transitions

Lying-standing transitions in the first molecular monolayer at organic-inorganic interfaces strongly influence interface dipoles, energy-level alignment, and growth modes, yet their collective kinetics remain difficult to predict. Here, we establish a quantitative adsorbate-to-kinetics relationship for such transitions using first-principles-based kinetic Monte Carlo simulations combined with a mean-field-type coarse-graining strategy. Focusing on the prototypical system tetracyanoethylene on Cu(111), we show that the collective transition rate cannot be inferred from any single elementary step but instead emerges from a small set of coupled microscopic processes, including reorientation, adsorption, and diffusion. A local two-step reorientation mechanism captures the diffusion-limited regime, while diffusion of lying molecules accelerates the transition in diffusion-enhanced regimes by sterically suppressing back-reorientation via vacancy-molecule decoupling. This effect is captured by a regime-dependent geometric factor that quantitatively accounts for deviations between single-molecule and collective rate constants. By systematically varying molecular size and footprint ratio, we demonstrate that geometry provides a powerful intrinsic control parameter. While the collective rate scales approximately proportionally with molecular area, increasing the footprint ratio between lying and standing configurations leads to order-of-magnitude accelerations due to enhanced vacancy creation and diffusion-assisted stabilization. Based on these results, we derive an explicit analytical expression for the collective reorientation rate constant that links temperature- and pressure-dependent microscopic rate constants to geometric parameters. The resulting formulation quantitatively reproduces the simulation results across kinetic regimes and provides transferable design principles for engineering lying-standing transition time scales at organic-inorganic interfaces.