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Page 10 of 15 Wu et al. J. Mater. Inf. 2025, 5, 14 https://dx.doi.org/10.20517/jmi.2024.77

RESULTS AND DISCUSSION
Coverage-dependent adsorption energy on different indexed surfaces
Leveraging our trained model for predicting adsorption energies, we calculated the steady-state CO
adsorption energies for approximately 7 million configurations within the target configuration space,
plotting CO adsorption energy versus coverage spectra for eight Cu crystallographic surfaces [Figure 5]. It
was observed that each of the eight Cu surfaces corresponds to a unique CO coverage threshold, within
which the adsorption energy of the most stable adsorption configurations changes minimally. Beyond this
coverage threshold, the adsorption energy of the most stable configurations decreases significantly with
increasing coverage. This trend aligns with physical intuition: at low coverages, the CO molecules in steady-
state adsorption configurations are widely spaced, making non-bonding interactions between CO molecules
negligible; however, at medium to high coverages, the surface arrangement of CO molecules in steady-state
configurations becomes more compact, increasing molecular repulsion and thus increasing the system’s
potential energy, leading to decreased adsorption energies for CO molecules. Furthermore, aside from the
(100) and (111) surfaces (where all surface atoms have the same coordination number), CO molecules
preferentially occupy lower-coordination Cu sites that are energetically less favorable, and, with increasing
coverage, gradually cover higher-coordination Cu sites [Supplementary Figure 5]. At the same time, the
average coordination number of Cu atoms occupied by CO at each coverage level remains lower than the
average coordination number of surface Cu atoms, indicating a clear lowest-energy orientation for CO
adsorption. These computational results are consistent with previous research findings [58-60] . Understanding
the ease of C–C coupling on different Cu surfaces is crucial for developing Cu-based nanometal catalysts
with high selectivity for C products in CO RR reactions, as easier C–C coupling between CO molecules
2
2+
leads to higher selectivity for C products [61-65] .
2+
Here, we employed two straightforward metrics to evaluate the ease of C–C coupling on Cu surfaces. The
first metric is the mean minimum C–C distance (MMCD) within the set of most stable adsorption
configurations at various coverages, which serves as an indicator of the probability of C–C coupling. A
smaller MMCD suggests a higher likelihood of coupling. The second metric is the characteristic coverage of
the surface: taking the densely packed (111) surface as a reference and using its maximum adsorption
energy as a threshold, the maximum coverage achievable by other surfaces without falling below this
adsorption energy threshold is deemed their characteristic coverage. To facilitate successful C–C coupling,
CO must exhibit sufficient adsorption strength on Cu surfaces to prevent the reactants from desorbing,
which would interrupt the coupling reaction. Moreover, compared to the MMCD, the surface’s
characteristic coverage offers a more macroscopic dimension for representing the probability of C–C
coupling, providing a holistic view. As illustrated in Figure 6, we analyzed these two metrics across eight Cu
surfaces and found that the (310) surface exhibits the best C–C coupling performance, while the (111)
surface performs the worst. The performance ranking of (310) > (210) > (311) > (100) > (111) is largely in
agreement with experimental observations [40,60] . High-index surfaces tend to have smaller MMCDs and
greater characteristic coverages, indicating a higher probability of C–C coupling and better selectivity for C
2+
products. This finding aligns with our current theoretical and experimental research, which shows that
high-index surfaces offer a greater variety of surface sites and an abundance of low-coordination surface Cu
atoms. These features provide more stable adsorption sites and a superior surface electronic environment
conducive to C–C coupling [66,67] . Additionally, the (322) surface emerged as a potential candidate due to its
MMCD and characteristic coverage closely approaching those of the (310) surface, which has been
experimentally proven to exhibit excellent selectivity for C products .
[40]
2+
CONCLUSIONS
In this work, our investigation into the adsorption configurations of CO on Cu surfaces unveils critical