There are several possible sources of entropic effects beyond SC-HA in CFF-AIMD, including the anharmonicity, configurational entropy of adsorbates, and vibrational entropy due to mobile surface atoms. The analysis on vibrational anharmonicity demonstrates that 2N*, N 2 *, and TS states are mostly harmonic (Figure ), though there can be other types of anharmonicity, such as the rotational entropy. Based on multiple 2N* states observed in CFF-AIMD simulations, we consider an ensemble of adsorbate configurations in HA, which we refer to as "multiple configuration HA (MC-HA)" (see Supporting Information). As illustrated in Figure , CFF-AIMD demonstrates better agreement in Δ𝐺 ‡ (𝑇) with MC-HA than with SC-HA, especially in the temperature-dependence of Δ𝑆 ‡ (𝑇). However, there is a minor change in ∆𝑆 3 (𝑇) between MC-HA and SC-HA because configurational entropies of N 2 * and 2N* states are comparable. To understand the remaining discrepancy between HA and CFF-AIMD, we include the vibrational entropy from both the nitrogen and the mobile surface atoms in the HA, called "multiple configurations with surface atoms (MCS-HA)" (see Supporting Information). For our 2x2 supercell of the Ru(0001) surface, we consider the surface phonons at the Γ < point, which also effectively includes boundary points of the surface Brillouin zone of the primitive cell (see Supporting Information for discussion on surface phonon modes). Comparing MCS-HA and CFF-AIMD results, we find a good agreement between the two methods even at higher temperatures.