Topocatalysis: A Topological Catalysis Overview

• Topocatalysis is a catalysis paradigm defined by leveraging global topological properties, such as symmetry-protected surface states and network connectivity, for enhanced reactivity.
• It integrates quantum, membrane, and network phenomena to dynamically modulate active sites and reaction phases, offering improved performance and robustness.
• Case studies in quantum materials and biomimetic systems demonstrate its potential to optimize processes like hydrogen evolution and catalytic transitions through topological control.

Topocatalysis is the emerging paradigm in catalysis that emphasizes the critical role of geometric, electronic, or network topology in defining and enhancing catalytic activity. Distinct from traditional structure–activity relationships, topocatalysis focuses on how topological features—such as symmetry-protected surface states, long-range site connectivity, or membrane topology—mediate reactivity, robustness, and dynamic function across chemical, biological, and solid-state platforms.

1. Fundamental Concepts and Definitions

Topocatalysis refers to catalysis fundamentally governed or enhanced by topological properties of a system, rather than solely by local atomic coordination or chemical composition. Central to this approach are features such as:

• Symmetry-protected surface or edge states (as in topological materials) that provide robust, high-mobility conduction channels.
• Topological phase transitions in crystalline solids, which facilitate dynamic rearrangement of active sites.
• Complex spatial organization or network connectivity in catalytic systems, where the underlying topology determines reaction phase behavior and transitions.
• Topological changes in biological membranes, where structure-driven lowering of activation barriers for molecular reconfiguration enables phenomena such as protocell fission.

Topocatalysis is distinct yet often complementary to classical geometric/chemical catalysis in that it leverages global or mesoscale topological invariants—such as the presence of Fermi arcs, helical edge states, or toroidal nanoholes—rather than, or in addition to, local chemistry.

2. Topological States in Quantum Materials and Catalysis

Topological quantum materials (e.g., topological insulators, electrides supporting multiple-fold fermions, and two-dimensional topological insulators) have been shown to possess symmetry-protected electronic states that fundamentally impact catalytic performance.

Example: Electride C₁₂A₇:4e

• C₁₂A₇:4e is a nanoporous electride with localized interstitial electrons in cage-like sublattices.
• Symmetry analysis and first-principles calculations identify sixfold (SDP) and fourfold (FDP) degenerate points near the Fermi energy, originating from band crossings at high-symmetry Brillouin zone points due to these interstitial electrons.
• These multiple-fold fermions give rise to extraordinarily long Fermi arcs on the (001) surface—much longer than those in typical Weyl or Dirac semimetals.
• Fermi arcs confer high chemical activity and low Gibbs free energy for hydrogen adsorption (ΔG_H* ≈ 0.24 eV), resulting in enhanced HER catalysis.
• The position of topological degeneracy points relative to the Fermi level is crucial; shifts caused by hole doping or lattice strain significantly increase ΔG_H*, reducing catalytic efficiency (Meng et al., 2021).

Example: 2D Topological Insulator LiMgAs

• LiMgAs in the 2D limit exhibits robust helical edge states with high carrier density, protected by topology even under stress or surface disorder.
• First-principles calculations demonstrate that these edge states facilitate ideal H adsorption, yielding ΔG_H ≈ –0.02 eV—closer to the Sabatier optimum than conventional HER catalysts.
• Structural stability in both pristine and strained forms is confirmed via ab initio molecular dynamics.
• This suggests high electron transfer rates, surface robustness, and resistance to site poisoning, generalizable to other 2D TIs (Sattigeri et al., 2022).

Example: Topological Insulators as Robust Platforms

• Current-induced molecular dissociation can be greatly enhanced on topological insulator substrates (modeled by the Kane–Mele Hamiltonian) versus conventional metallic ones.
• Non-equilibrium Green's function (NEGF) calculations reveal that the localized edge states of TIs enable strong electron–molecule hybridization and maintain high molecular level occupation even with significant substrate vacancy disorder.
• The net non-equilibrium force facilitating molecular bond breaking is more robust and effective, due to edge state protection, than on extended-state metals like graphene (Mehring et al., 2 Sep 2025).

3. Network, Membrane, and Phase Topology Effects

Topocatalysis encompasses phenomena beyond quantum materials, extending into networked or biomimetic systems where topology mediates reactivity at the mesoscale.

Membrane Topology and Protocell Fission

• Toroidal nanoholes in lipid bilayer protocell membranes puncture the separation between inner and outer leaflets, drastically lowering the activation energy for lipid translocation ("flip-flop").
• Force balance between repulsive electrostatic contributions and attractive bending elasticity stabilizes these nanoholes at intermediate radii.
• Temperature gradients between inner and outer leaflets drive asymmetric molecular flux, exponential growth of surface area, and eventual vesicle fission.
• The interplay of topological membrane defects and thermally induced dynamics is thus catalytic for protocell self-reproduction (Attal, 2022).

Complex Networks and Reaction Phase Behavior

• The topology of a catalytic "surface" affects phase transitions in reaction models such as the Yaldram–Khan (YK) scheme.
• Monte Carlo simulations on random network topologies (Erdős–Rényi, random geometric graphs) show that long-range or spatially constrained randomness modifies both the critical boundaries and the order (continuous or discontinuous) of phase transitions between reactive and inactive regimes.
• For spatially correlated random graphs, reducing connectivity can turn first-order transitions into continuous ones, illustrating fine-tunability of catalytic onset via network topology (Gomes et al., 4 Jun 2025).

4. Dynamic Topotactic Transitions in Functional Oxides

Topotactic transitions—structural phase changes mediated by the ordering or migration of atoms (often oxygen)—represent a form of topocatalysis where dynamic topology modification creates new active phases.

• Methods such as chemical reduction (e.g., CaH₂), controlled annealing, hydrogenation, voltage bias, and electron beam irradiation enable the formation of ordered vacancy patterns and unusual metal coordination environments while retaining overall crystallinity.
• Such transitions can induce superconductivity (e.g., infinite-layer nickelates), high ionic/electronic conductivities for energy devices, and improved redox-active surfaces for catalysis.
• Dynamic, reversible control of these topotactic processes allows real-time tuning of material properties central to catalysis, drawing explicit connections to topocatalysis by leveraging ordered atomic rearrangements to modify activity (Meng et al., 2023).

5. Theoretical Frameworks: Spatial and Temporal Integration

Unified models of catalysis now explicitly incorporate spatial and temporal topology.

• The Active Catalytic Space (ACS) framework generalizes catalytic activity as an integrated field over space and time:

$$\mathrm{TOF}(t) = \int_V p(\mathbf{r}) \cdot f(\mathbf{r}, t) \cdot k_{\text{local}}(\mathbf{r}, t) \, dV$$

where $p(\mathbf{r})$ is the local site density, $f(\mathbf{r}, t)$ dynamic modulation of activity, and $k_{\text{local}}$ the site-specific rate.

• This approach unites the treatment of homogeneous, heterogeneous, and enzymatic catalysis, and places topocatalysis on rigorous footing by quantifying the role of spatial arrangement, dynamic modulation, and localized reactivity.
• In this perspective, topocatalysis is rationalized as a direct outcome of varying $p(\mathbf{r})$ and $k_{\text{local}}$ via topological engineering—be it in surface states, site distribution, or network/phase topology (Crespilho, 2 May 2025).

6. Applications and Implications for Catalyst Design

Topocatalytic principles underpin key advances across disparate catalytic fields:

• Catalysts based on topological electrides and 2D TIs enable highly efficient HER, outperforming conventional precious metal systems and offering defect-tolerant, high-mobility surfaces.
• Topologically engineered catalysts (e.g., via topotactic transitions) offer dynamically reconfigurable active site populations and phases for next-generation membranes, superconductors, sensors, and energy devices.
• Network and membrane topology tailoring (e.g., controlling defect populations or network connectivity) facilitates precise modulation of catalytic onset, stability, and robustness—crucial for real-world, disordered environments.

A plausible implication is that future catalyst design will increasingly rely on intentional topological manipulation, moving beyond static structure–activity paradigms to leverage defects, edge and surface state engineering, and dynamic phase transitions for optimal performance.

7. Outlook and Research Directions

Topocatalysis connects quantum topology, mesoscale physics, and catalytic reaction engineering. The field is marked by:

• Increasing integration of computational, spectroscopic, and in situ structural probes to resolve topological features during catalytic turnover.
• Expansion of topocatalytic materials from quantum topological phases (e.g., Weyl semimetals, higher-order TIs) to soft-matter and biomimetic contexts (e.g., membrane vesicles, synthetic active networks).
• Greater focus on disorder and resilience: leveraging topological protection to maintain catalytic activity despite defects, poisoning, or environmental fluctuations.
• Development of meshable multi-scale theories, such as the ACS framework, to connect local site attributes with global topology-driven dynamics.

Topocatalysis thus constitutes a central organizing principle in contemporary and future catalyst research, shaping both fundamental understanding and technological implementation.