Quantum Many-Body Simulations of Catalytic Metal Surfaces

TL;DR

Confronts the cost-accuracy dilemma in modeling catalytic reactions on metal surfaces by introducing FEMION, a fragment-embedding framework that treats metallic environments with nonlocal screening (RPA) and active sites with high-accuracy many-body methods (AFQMC). The method relies on a smearing-adapted bath construction to handle partially filled states and combines global RPA with fragment corrections to achieve systematic improvability. Across benchmarks (Li, Al cohesive energies; CO adsorption on Cu(111); H2 desorption on Cu(111); ten-electron rule in 3d SAAs), FEMION delivers chemical accuracy and resolves long-standing discrepancies that plague DFT and simpler embedding approaches. This work establishes a scalable, first-principles route for predictive catalysis on metal surfaces and opens avenues for improved trial-wavefunctions and basis sets.

Abstract

Quantum simulations of metal surfaces are critical for catalytic innovation. Yet existing methods face a cost-accuracy dilemma: density functional theory is efficient but system-dependent in accuracy, while wavefunction-based theories are accurate but prohibitively costly. Here we introduce FEMION (Fragment Embedding for Metals and Insulators with Onsite and Nonlocal correlation), a systematically improvable quantum embedding framework that resolves this challenge by capturing partially filled electronic states in metals. FEMION combines auxiliary-field quantum Monte Carlo for local catalytic sites with a global random phase approximation treatment of nonlocal screening, yielding a scalable approach across diverse catalytic systems. Employing FEMION, we address two longstanding challenges: determining the preferred CO adsorption site and quantifying the H2 desorption barrier on Cu(111). Furthermore, our calculations demonstrate that the recently discovered 10-electron-count rule can also be extended to the single-atom catalysis processes on 3d metal surfaces, resolving the controversies arising from density functional theory calculations. We thus open a predictive, first-principles route to modeling complex catalytic systems.

Figures (5)

• Figure 1: FEMION workflow, features, and performance. The framework combines global RPA with fragment AFQMC (workflow), incorporates smearing adaptation, beyond-RPA accuracy, and systematic improvability (features), and achieves state-of-the-art performance from bulk to adsorption and bond breaking, surpassing prior methods (performance).
• Figure 2: Benchmarking the Accuracy of the FEMION Embedding Scheme on Pure Metals.(A) Deviations of embedding RPA and AFQMC total energy from their corresponding conventional counterparts, using HF and PBE ($\sigma = 0.2-0.8$ eV) as mean-field wavefunctions, decrease with tighter $\varepsilon_\mathrm{occ}$ and consistently approach the conventional limit, with only weak dependence on the smearing parameter $\sigma$. (B) Cohesive energies for simple metallic systems: lithium in the body-centered cubic (BCC) structure and aluminum in the face-centered cubic (FCC) structure, demonstrating agreement with high-level theory. The detailed reference values are listed in Table \ref{['SI-tab:li_al_properties']} of the Supplementary Information.
• Figure 3: Application of the FEMION Framework to CO Adsorption on Cu(111). (A) Atop and fcc configurations for the CO@Cu(111) system. (B) Absolute adsorption energies at the atop site, with our results (empty circles) compared against a range of methods from DFT to QMC. Detailed definitions for the DFT methods are provided in Table \ref{['SI-tab:COCu_data']}. FEMION results are shown at three computational settings (from bottom to top): (1) 3×3 $k$-mesh with $\varepsilon_{\text{occ}} = 0.005$ and $\varepsilon_{\text{vir}} = 0.0005$; (2) 3×3 $k$-mesh with $\varepsilon_{\text{occ}} = 0.005$ and $\varepsilon_{\text{vir}} = 0.00005$; and (3) 4×4 $k$-mesh with $\varepsilon_{\text{occ}} = 0.005$ and $\varepsilon_{\text{vir}} = 0.0005$. The gray band indicates the experimental range. (C) Energy difference between fcc and atop configurations using the same methods as in panel (B); a positive value indicates correct preference for the atop site, consistent with experiment. (D) Left: schematic of the two dominant interactions between CO and Cu: $\sigma$ donation and $\pi$ back-donation. housecroftInorganicChemistry2005hieringerBlyholderModel2020 Right: bar plots of Mayer bond orders for these interactions (C–O and C–Cu) in both atop and fcc configurations. The experimental value is corrected for ZPE and detailed reference values are listed in Table \ref{['SI-tab:COCu_data']} of the Supplementary Information.
• Figure 4: Application of the FEMION Framework to H2 Dissociation on Cu(111). (A) Schematic of the reaction pathway from the adsorbed reactant state to the transition state for H2 dissociation on the Cu(111) surface. (B) Calculated energy barriers (bottom) using various methods, including the FEMION embedding, DFET-MRPT2, DFT-based cluster embedding (XYG3@PBE, B3LYP@PBE), RPA, and PBE. The dashed line indicates the experimental barrier, with the gray band representing the chemical accuracy of 1 kcal/mol. The experimental value is corrected for zero-point energy (ZPE) and detailed reference values are listed in Table \ref{['SI-tab:H2Cu_data']}.
• Figure 5: Application of the FEMION framework to 3d transition-metal–doped single-atom alloys $X@\text{M–Cu}(111)$.(A) Structure of $X@\text{M–Cu}(111)$; (B) Orbital scheme illustrating the ten-electron rule for $X=$ C, N, O; (C) Adsorption energy as a function of dopant (Sc–Ni) across methods, with thin dashed lines indicating each method’s minimum; The yellow panel marks the element where the ten-electron rule predicts the strongest binding.