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Liu et al. J. Mater. Inf. 2025, 5, 27 I http://dx.doi.org/10.20517/jmi.2024.105 Page 11 of 18

Figure 4. FTS reaction pathways on -Fe 5C 2(510) surface, including (A) dissociation of H 2 and CO on A-P5 site; (B) *CH-*C coupling
and following steps towards long-chain (C 2+) hydrocarbon products; (C) *CH-*H coupling steps towards CH 4 product; and (D) *CH-*CH
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coupling steps towards CH 2CH 2 product. In these plots, red line denotes that the PES calculations are done merely by FT DP, blue line
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denotes that the calculated data are acquired by single-point DFT calculation after FT DP optimization, purple line denotes that the PES
calculations are purely performed by DFT calculation, and C stands for carbon vacancy on A-P5 site. All the top views are for DFT-optimized
structures. Orange: Fe atoms; Grey: C atoms; White: H atoms; Red: O atoms. FTS: Fischer-Tropsch synthesis; PES: potential energy surface;
FT DP: fine-tuned Fischer-Tropsch deep potential; DFT: density-functional theory.
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corners) may differ significantly from that of regular surface atoms [12,74] , highlighting the importance of these
sitesin mechanistic research. In this section, four potential FeC active surfaces in iron-based Fischer-Tropsch,
i.e., -Fe 5C 2(510), -Fe 5C 2(021), -Fe 2C(111), and -Fe 3C(010) [Supplementary Figure 4], were considered
to investigate the surface morphology and stability of edge sites. Each surface was modeled using a slab with
a thickness of more than 10 Å, with the bottom two or three layers of FeC fixed during structural relaxations.
A vacuum layer of 20 Å was introduced to separate two neighboring slabs for all surfaces. To model the edge
sites, a ‘half-surface’ scheme was employed: half atoms of the top layer were removed, maximizing the distance
and simultaneously minimizing the interaction between two adjacent edge sites. This approach is particularly
useful for GA calculations, as it allows for two independent local searches on two edges to identify the most
stable reconstructed structure.

Before performing GA calculations, we first checked the accuracy of FT DP on large clean surfaces and unre-
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constructed edge structures. We used the FT DP model to optimize the structures and then calculated their
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single-point energies on the PBE level. In Supplementary Tables 3 and 4, we report the energy differences
between PBE single-point energies for FT DP and PBE-optimized structures. The energy differences for all
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tested structures are less than 1.2 meV/atom, indicating that FT DP is sufficiently accurate for investigating
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surface reconstructions of iron carbides.