With the continuous advancement and refinement of research methodologies， structural chemistry should evolve from the traditional exploration of “the relationship between reactants-products and chemical reactions” to the higher level of revealing and utilizing “the relationship between the dynamic structure of matter in condensed states and its chemical reactions”. When discussing chemical reactions within condensed matter systems， we cannot disregard the significant influences of the dynamic evolutions in their structures and the coupling of environmental factors. To elucidate the connection between the spatial dimensions of solid material systems and chemical reactions， we introduce the spatial dimension of crystal materials by starting from Bloch theory. Changes in spatial dimensions， surface configurations， and heterostructures can significantly alter their physical properties， thereby affecting the related chemical reactions， and even modifying the reaction pathways. In this review， we will discuss the ways in which spatial confinement effects can influence catalytic reactions， as demonstrated by the performance of carbon nanotubes in the asymmetric hydrogenation of ethyl propionate. Under reaction conditions， the intrinsic structure of solid surfaces， as well as the defects and catalyst particles distributed on them， undergo a series of dynamic changes. Beyond temperature and pressure， the environmental conditions of the reaction system （including pH-values， external electric/magnetic fields， optical fields， etc.） can also dynamically influence the geometric and electronic configurations of defects and catalytically active sites. Through a comprehensive introduction to these examples， we aim to clearly and concisely demonstrate how the dimensionality and dynamic changes in solid material structures affect chemical reactions， thereby emphasizing the importance and essentiality of research in condensed matter structural chemistry.
Ran Jia, Chuipeng Kong, Wenfu Yan.
Dimensions of Solid-State Material Systems and Their Chemical Reactions.
Progress in Chemistry, 2026, 38(1): 23-39 DOI:10.7536/PC20250908
The perspectives and research methodologies of chemistry and physics differ fundamentally. Physics seeks to observe and understand physical phenomena, attempting to explain and unify them through mathematical frameworks. In contrast, chemistry initially focused on identifying substances but later evolved toward synthesizing new materials. Chemistry provides the material basis for physics to discover or realize physical phenomena. Over several decades, and even nearly a century, physics—particularly condensed matter physics—has developed a robust theoretical foundation. Meanwhile, chemistry has progressively elucidated the relationship between the structure of chemical substances and their properties by drawing upon disciplines such as quantum mechanics and crystallography. This has led to the development of important theories and research methods, including valence bond theory, molecular orbital theory, ligand field theory, spectroscopy, and computational chemistry［1-2］. However, the central focus of chemical research lies in reactions, especially the reaction process itself; therefore, structural chemistry should not be confined solely to the structures of substrates, intermediates, transition states, and products. A chemical reaction is a dynamic process influenced by the local environment at the reaction site. Moreover, numerous factors—including the instantaneous structures, concentrations, and orientations of all participating species—affect the transient conditions at that site. As early as the 1990s, studies revealed a close correlation between surface reconstruction capabilities and reactivity［3-5］. During crystal growth or dissolution, the interface between the crystal and the solution remains in a dynamic state due to the continuous adsorption and desorption of solute molecules on the crystal surface. Depending on the solution concentration, this interface can exhibit different growth mechanisms or topological configurations［6-8］. Consequently, the study of structural chemistry should transcend the framework of static material structures and instead investigate the dynamic relationships between multi-level material structures and the reaction process, thereby advancing to the level of condensed matter structural chemistry.
Condensed-state chemistry is still in its infancy and requires extensive research and further development by a broad community of scholars［9-10］. In this paper, we begin with the most fundamental, simplest, and easily understandable crystal structures. By examining the partitioning of ordered structural systems in three-dimensional space and the influence of spatial topological dimensions on chemical reactions, we illustrate the importance of the spatial dimensions and structural hierarchies of solid materials for chemical reactivity. Based on the fundamental theories of condensed matter physics, this paper introduces methods for partitioning the spatial dimensions of a system and elucidates how various structural characteristics—such as the environment, spatial dimensions, spatial confinement, and defects—influence the course of chemical reactions. Unlike previous review articles, this work does not focus on a specific material system or chemical reaction. Instead, by emphasizing the role of the spatial structure of chemical systems and its dynamic nature in shaping both the process and outcome of chemical reactions, it aims to stimulate interest and attention toward condensed-state chemistry, particularly condensed-state structural chemistry, thereby fostering the advancement of this emerging discipline.
2 Spatial Dimensions of Solid-State Systems
Solid-state material systems, owing to their relatively stable structures or shapes and minimal temporal variations, serve as a readily accessible and clearly definable starting point for addressing scientific questions. Over the years, remarkable achievements have been made in chemical research fields closely associated with solid-state materials, including solid-state chemistry, heterogeneous catalysis, and chemical synthesis. Since quantum mechanics was introduced to elucidate the structure, properties, and reactivity of chemical systems, our understanding of chemistry at the atomic scale has significantly deepened. The microscopic structure of a material determines the chemical properties it can exhibit. However, local microscopic properties do not necessarily correspond exactly to the macroscopic chemical properties manifested by the entire system, as macroscopic properties are statistical manifestations resulting from the interplay of multiple factors acting on all microscopic behaviors. In solid-state systems, three primary structural forms are commonly encountered: crystalline, amorphous, and quasicrystalline. To facilitate an explanation of the necessity of condensed-phase structural chemistry, we will primarily focus on crystalline material systems.
2.1 Reciprocal Space and Dimensions
When conducting theoretical research using quantum chemical methods, particularly for crystalline material systems, it is often necessary to understand not only the real-space configuration of the system but also its reciprocal-space structure. To explain the necessity of reciprocal space, we must first introduce the general form of single-electron orbitals under periodic potential energy—the so-called Bloch theory. Bloch theory was originally developed for periodic ring systems (Figure 1a) and was later extended to non-ring periodic systems. When a linear system is sufficiently long, treating it as a ring system with an infinitely large radius does not introduce significant errors. Of course, this approach is clearly inappropriate for short-chain systems. In Bloch theory, the single-electron eigenfunctions under the action of a ring-shaped periodic potential should be expressed as Equation (1).
in the equation: ; j is an integer; is the coordinate (angle) of a periodic unit in the cyclic structure. If the symmetry of this cyclic system belongs to the point group , then . This is the so-called Bloch equation. Suppose we define a rotation operator to represent performing a rotation operation by qtimes , then we obtain Equation (2).
if we choose another integer to replace j in the above equation, we will find that regardless of the value of N, the eigenvalue of this rotation operator remains unchanged at . In other words, for any given j, this rotation operator possesses an infinite number of degenerate wave functions. By taking a linear combination of these degenerate wave functions, we can obtain Equation (3).
It can be seen that at this point, the is actually a Fourier series expansion of a periodic function, and its properties are determined by the coefficients .
When the Bloch theory is extended to linear periodic structures (Figure 1b), we replace the angle in the ring system with the coordinate x, conventionally substituting jwith k, and should obtain the same eigenfunctions and eigenvalues. If the ring system comprises nperiodic units separated by a distance d, then the range of the coordinate xin the non-cyclic linear periodic system—namely, (0, nd]—corresponds to the variation range of the angle in the ring periodic system, which is (0, 2π]. Moving ssteps in the ring system implies an increase (or decrease) of the exponent in the exponential function by s. Correspondingly, in the linear system, the change in the exponent should be s. From this, we derive a very important relation, expressed as Equation (4).
because the e-exponential function can be expressed as a combination of sine and cosine functions, and assuming that the wavelength is less than 2d, i.e., , considering that the range of values for k should correspond to the angular range in a ring structure , therefore , which is the First Brillouin zone of a one-dimensional linear periodic system. The wave function in a linear periodic system will repeat with this period. Thus, we obtain the Bloch function for a non-ring-shaped 1D periodic system (Equation (5)).
，
by decomposing the vector k along its independent translational symmetry directions, one can obtain the Bloch-form wave functions for both 2D and 3D periodic systems using the aforementioned method.
To aid in understanding, we return once again to the 1D system. It can be observed that the periodicity of the scalar is related to the reciprocal of the unit cell length in this one-dimensional periodic structure. We may thus regard as being periodic in the reciprocal space corresponding to the 1D real space. By generalizing this concept to higher-dimensional systems, we arrive at the corresponding definition of reciprocal space. Then, how is the dimensionality of a system in real space defined? Taking single-walled carbon nanotubes (SWCNTs) as an example, the carbon atoms within the nanotube unit cell are distributed in three-dimensional space, unlike a linear single-atom chain that is arranged along only one direction. However, SWCNTs exhibit translational symmetry—or, equivalently, periodicity—only along a single axis. Consequently, the single-electron wave function of SWCNTs derived from the aforementioned Bloch theory involves a that is purely one-dimensional. For this reason, SWCNTs are classified as one-dimensional periodic systems. To further illustrate this point, consider the case of 6,6,12-graphdiyne and its corresponding nanotubes. As shown in Figure 1c, due to the diverse orbital hybridization states that carbon atoms can adopt—namely sp, sp2, and sp3—a wide variety of two-dimensional carbon materials with a single-atom thickness similar to graphene can be formed. The unit cell of 6,6,12-graphdiyne possesses rectangular pmm symmetry; accordingly, its first Brillouin zone in reciprocal space is also rectangular, as depicted in Figure 1d. When such a two-dimensional material system is rolled up along one edge of the rectangular lattice to form a nanotube, although the carbon atoms still occupy distinct spatial coordinates in three-dimensional space, periodicity no longer exists in the direction perpendicular to the nanotube axis. In other words, periodic mirror images appear only at infinity. Therefore, according to the definition of reciprocal-space lattice vectors, the three spatial dimensions are projected onto the axial direction of the nanotube, resulting in a one-dimensional Brillouin zone, represented by the line segment ΓX or ΓX′ labeled in Figure 1d. Similarly, graphene and sodium chloride crystals possess two-dimensional and three-dimensional reciprocal spaces, respectively, and are thus classified as 2D and 3D systems. In contrast, non-periodic systems such as molecules and nanoclusters have their reduced to a single point in reciprocal space. Such systems are commonly referred to as zero-dimensional (0D) systems, even though the distribution range of atomic coordinates in real space may be quite extensive. It should be noted that we do not discuss amorphous systems here. Although they may manifest as macroscopic three-dimensional entities in real space, their lack of translational symmetry in reciprocal space causes them to be treated as a single point. This presents significant challenges for theoretical research and computational simulations, as the abundance of inequivalent sites can lead to a sharp increase in computational costs. Nevertheless, amorphous systems are of great importance in chemical research, owing to their large number of active sites that facilitate reaction processes. Moreover, the complex and highly variable microenvironments surrounding these active sites constitute both a challenge and a focal point for future studies in condensed-phase structural chemistry.
2.2 Surface and Edge
Due to their well-defined structure, 3D crystals can serve as an entry point for understanding the relationship between the structure of solid-state materials and chemical reactions. In chemical systems, reactions typically occur at the surfaces or interfaces of 3D crystals. From a theoretical perspective, crystal surfaces/interfaces should be treated as 2D systems because translational symmetry is broken in one direction. Figure 2a shows the three most common crystal faces in rock salt (or table salt, NaCl) crystals. In a rock-salt crystal, each Na atom has six Cl atoms as its nearest neighbors. However, the coordination number of a Na atom varies depending on the specific crystal face. A Na atom located on the (100) surface has five nearest-neighbor Cl atoms, whereas on the (110) and (111) surfaces, its coordination number decreases to four and three, respectively. This also results in the (100) surface having a significantly lower surface energy than the other two surfaces, making it more stable. Of course, the polarity of the NaCl crystal’s (111) surface is another reason for its higher surface energy. Clearly, once surface atoms are exposed from the bulk of the crystal, they experience markedly different interactions compared with those within the crystal due to the loss of some of their original neighboring atoms. Consequently, the atomic configurations at crystal surfaces undergo a certain degree of relaxation, manifesting as contraction or expansion of surface atoms/ions along the surface normal. Naturally, the extent of relaxation differs among surfaces with different crystal orientations for the same reasons. These differences in coordination numbers and degrees of relaxation also lead to variations in the effective charges of surface atoms, which may in turn result in distinct chemical reactivity. Taking the nonpolar (100) and (110) surfaces of NaCl crystals as examples, simple DFT-PBE calculations reveal that, relative to the bulk phase, the distance d12between the outermost and second-to-outermost layers contracts by 1.45% and 6.79%, respectively, while the change in the distance d23between the second-to-outermost layer and the layer below is minimal; the Hirshfeld charges of the outermost atoms also increase significantly. Specifically, on the (100) surface, QNa= 0.26e and QCl= −0.26e, whereas on the (110) surface, QNa= 0.33e and QCl= −0.32e. By contrast, the Hirshfeld charges of Na and Cl in the bulk phase are both approximately ±0.20 e. Even for the same crystal surface with identical spatial symmetry and similar geometric structures—for example, the (100) surfaces of BaTiO3and PbTiO3—the directions of atomic relaxation in the outermost three layers differ substantially［12］.
In the vast majority of real chemical systems, even the surface of a single crystal cannot perfectly align with a specific crystallographic direction; steps, defects, and atomic/molecular adsorption are commonly observed. Figure 2Part b illustrates several typical surface configurations. In theoretical studies, researchers often use step structures on specific surfaces as initial models to construct the aforementioned surface features, such as the NaCl(501) surface shown in Figure 2part c. Here, we primarily focus on the influence of surface steps, step kinks, and step-edge atom adsorption on chemical reactions, while other surface configurations will be discussed later. Step-like structures frequently appear on crystal surfaces. Due to the lower coordination number of edge atoms compared with that of the corresponding surface atoms, the effective charge distribution at the edges undergoes significant changes, thereby enhancing their chemical reactivity. These factors markedly affect the kinetics of nearby chemical reactions, including adsorption and desorption processes, reaction rates, and selectivity. As early as 1925, Hugh Stott Taylor pointed out in his article on surface catalysis theory that the catalytic activity is determined only by a small portion of the surface and depends on the arrangement and properties of surface atoms［13］. It was found that surface steps indeed can accelerate chemical reactions occurring on single-crystal surfaces; however, the true location of catalytic activity has long been debated. Early theoretical studies suggested that the electrons in high-coordination-number metal atoms located at the lower edges of transition-metal surface steps exhibit the greatest fluctuations, making these atoms the active sites for catalysis［14］. This conclusion clearly contradicted Taylor’s earlier notion of “low coordination number—high activity.” It was not until the late 20th century, through scanning tunneling microscopy (STM) studies of the NO dissociation reaction catalyzed by the Ru(0001) surface, that it was determined that the catalytic active sites should be the low-coordination-number atoms at the upper edges of the steps. The rationale provided by subsequent theoretical research was that the d-band of low-coordinated transition metals narrows, and the backbonding interaction between the d-orbitals and the antibonding π* orbital of NO is strengthened, thereby weakening the N—O bond strength［15］. In the early 21st century, studies on the activation of ethylene on the Ni(111) surface further demonstrated that the step edges of the Ni(111) surface exhibit higher catalytic activity toward ethylene activation and significantly greater selectivity for C—C bond cleavage over C—H bond cleavage［16］.
Compared with bulk materials, nano-clusters composed of the same constituents exhibit exceptionally high catalytic activity. In addition to quantum confinement effects and abundant surface defects, another crucial factor is the rich stepped-edge configurations present on the cluster surfaces. Figure 3a illustrates the surface configuration of MgO nanoparticles composed of (100), (010), and (001) facets. To approximate a spherical particle shape, the surface displays numerous stepped edges and curved structures. According to the dimensional classification of material systems mentioned earlier, nanoparticles should be categorized as 0D systems; therefore, we will provide a detailed discussion in subsequent sections.
It should be emphasized that the surface step configuration is not beneficial for all reactions or all processes therein. For example, a research group recently reported on the synthesis of HBC-GDY nanosheets—graphdiyne-like derivatives centered on hexabenzocoronene (HBC)—via thermally induced dehydrogenative coupling reactions catalyzed by the Au(111) surface［17］. In this atomically precise nanomaterial synthesis process, after the reaction precursors are deposited onto the Au(111) surface, they migrate to the step edges and are stably adsorbed, as shown in Figure 3b. As the precursors accumulate along the step edges, they predominantly form head-to-head coupled aggregates. This aspect is highly advantageous for the precise synthesis of such materials. However, the area of the step terraces is extremely limited; consequently, only nanoscale fragments constrained by the terrace area can be obtained, making it impossible to produce larger-area HBC-GDY materials. The terrace area and the number of surface step edges constitute a pair of competing factors: the greater the number of step edges, the smaller the terrace area becomes. The former influences the size of the product, whereas the latter affects the reaction efficiency.
The importance of surface steps for reactions is not absolute; it is related to the activation energy of the reaction on the catalyst surface. Figure 4a illustrates two different scenarios of CH4 dissociation catalyzed by the Ni(111) surface (including both the clean surface and the surface step edges passivated by S atoms), whereas Figure 4b shows the dissociation of CO catalyzed by the same surface. By examining the coverage of the dissociation products on the surface, it can be observed that passivation of the step edges indeed reduces the extent of the dissociation reaction; however, the impact on CH4 dissociation is significantly less pronounced than that on CO dissociation. This indicates that the CO dissociation reaction predominantly occurs at the step edges of the Ni(111) surface, whereas for CH4 dissociation, the activation energy on the Ni(111) surface is sufficiently low such that this reaction can also take place on the terrace sites. This phenomenon is also referred to as “structural sensitivity of the reaction”［18］.
The environmental atmosphere can have a strong influence on surface step configurations. Studies have shown that the stepped structure of the Pt(557) surface gradually transforms into triangular nanoparticles under a CO atmosphere［19］. Taking the NaCl crystal as an example, the (100) face is its most stable surface with the lowest surface energy. Conversely, the NaCl (111) surface is a polar surface with high surface energy and is generally unstable. When the NaCl (111) surface is exposed from the crystal—for instance, during the formation of nanoclusters—it undergoes surface reconstruction to produce non-1∶1 stoichiometric compounds, thereby reducing the surface dipole moment and surface energy. Theoretical studies have indicated that, under sodium-rich and chlorine-rich surface conditions, the NaCl (111) surface will respectively exhibit NaCl6-(111) and Na3Cl-(111). Among these, Na3Cl-(111) displays a sawtooth-like structure, with the platforms of the sawteeth reproducing the (100) face of the NaCl crystal［20］.
2.3 pH Value
The exposure of a crystal surface depends on the magnitude of its surface energy. According to the classical Griffith theory, fracture toughness［21］can be defined asEquation (6).
in the equation: denotes the surface energy; and represent the shear modulus and Poisson’s ratio of the crystal, respectively. The surface energies of different crystallographic planes are not identical, and both the shear modulus and Poisson’s ratio are direction-dependent in anisotropic systems. Consequently, the fracture toughness varies among different crystal planes in crystalline materials. In other words, certain crystal planes are more readily exposed than others. In theoretical studies, the definition of surface energy is closely related to the chemical potentials of the constituent elements (Equation (7)).
in the equation: represents the total energy of the surface system; is the chemical potential of the ith element; and is the number of atoms of the ith element in the system. It should be emphasized that the chemical potential of an element is not a constant; it varies with changes in its surrounding environmental factors. In the same crystal, the chemical potential of a particular element located within the bulk phase is actually different from that of the same element on the surface. In addition to variations in local environmental factors such as the coordination number, external conditions also have a significant impact on the chemical potential of surface atoms. For example, changes in the pH value of the solution in contact with the crystal surface can affect the chemical potential of surface atoms, thereby influencing the surface energy and the corresponding fracture toughness. Consequently, this can affect the formation of crystal faces during dissolution or crystallization processes. Another definition of surface energy or surface potential more intuitively incorporates the influence of environmental factors by introducing the dielectric constant and the surface charge density［22］(Equation (8)).
in the equation: denotes the Boltzmann constant; represents the volumetric concentration of salt in the solution; and correspond to the relative permittivities of vacuum and the medium, respectively; indicates the surface charge density. The growth rates of the KDP (100) and (101) faces exhibit significant differences in response to varying pH values. Furthermore, atomic force microscopy (AFM) studies on the morphology of the KDP (100) face have demonstrated that pH can regulate both the morphology of the (100) crystal face and the crystal growth mechanism. At pH = 4.2, the KDP (100) surface displays a stepped configuration with curved edges; however, when the pH is reduced to 2.8 or 3.2, the step height and width increase accordingly. Upon further lowering the pH to 2.4, the crystal growth transitions to a two-dimensional nucleation-controlled mechanism［23］. For semi-organic complex crystals, pH also influences the crystallization process, leading to variations in morphology and physical properties. Investigations on L-histidine tetrafluoroborate (L-HFB) have revealed that its nonlinear optical properties are optimal at pH = 3.2, with the crystal developing faces such as (001), (012), (010), (210), (212), (130), and (140). As the pH decreases, the (210), (212), and (012) faces completely disappear; conversely, upon increasing the pH, the dominance of (010) and (012) face growth results in the disappearance of the (212), (012), (210), (140), and (130) faces［24］. A substantial portion of these pronounced differences in crystal face growth rates can be attributed to the localized supersaturation enhancement induced by pH variations.
Charging is a fundamental property of mineral solid–solution interfaces. The charge on different crystal faces depends on their surface chemical composition. In the field of heterogeneous catalysis, the photo/electrochemical water-splitting reaction serves as a very typical example. At the interface formed between a semiconductor crystal and water, changes in pH can be used to determine the concentrations of species such as H+, OH-, and H2O on the crystal surface. This involves the definition of the so-called “point of zero charge” (PZC): the pH value at which the average surface charge is zero. For instance, suppose that the surface of a TiO2 crystal exposes NTiTi atoms and NOO atoms to the aqueous environment; then the pH of this surface relative to the PZC is given by Equation (9)［25］。
in the equation: denotes a proton H+ in water adsorbed onto an Os atom on the TiO2 surface; represents a water molecule adsorbed onto a Ti atom on the surface. It has been found that different crystal phases and crystal facets of TiO2, under varying pH conditions, exhibit distinct surface species and charge types (Figure 5a). Theoretical studies on the (010) surface of BiVO4 in contact with liquid water have provided a more detailed description of the relationship between surface acid–base species concentrations and interfacial pH (Figure 5b). From these two examples, it is clear that one key focus in condensed-phase structural chemistry lies in the fact that the microenvironment of reactive sites significantly influences the structure of reaction species and their chemical reactivity.
Another important structure-related analytical method in the field of electrochemistry is the Pourbaix diagram, also known as the potential–pH or stability-area diagram. This method is named after the Belgian chemist Marcel Pourbaix and was proposed in the 1930s［27］. Initially, it was used to study metal corrosion; with the electrode potential (E) plotted on the vertical axis and the pH value on the horizontal axis, it is a thermodynamic diagram that indicates the most stable species under specific conditions, enabling the prediction and understanding of metal corrosion, passivation, dissolution, and other behaviors.Figure 6a shows the most stable species of Ti in an aqueous solution at 25 ℃ under various conditions of potential and pH［28］. Subsequently, the application scope of the Pourbaix diagram has been extended to the study of redox reactions, metallurgy, electrochemical synthesis, geochemistry, and other fields. Hansen et al.［29］introduced the Pourbaix diagram into the research on platinum-catalyzed oxygen reduction reaction (ORR) to identify the stable interfaces of catalysts under different reaction conditions, thereby providing theoretical predictions for selecting optimal reaction conditions.Figure 6b illustrates the theoretical predictions regarding how different potentials and pH values affect the stable forms of a Pt cluster with a radius of 0.5 nm in an aqueous environment. As the potential increases, the surface of the Pt cluster becomes progressively covered by various species, eventually existing in the form of oxides or ions. With the market share of new energy sources increasing substantially year by year, the recycling and treatment of waste batteries have become pressing issues that require serious consideration. Currently, the most common LiFePO4cathode material can typically be processed via hydrothermal leaching to recover lithium metal. Analyzing the Pourbaix diagram for LiFePO4is conducive to selectively controlling the process conditions of this reaction［30］.
Taking the photocatalytic water splitting reaction as an example, the pH value can influence the reaction in the following three ways: (1) altering the surface charge properties of the photoelectrode; (2) regulating the concentrations of reactants and products on the photoelectrode surface; (3) modifying the stability of intermediates and the reaction pathway. Clearly, when the pH value of the solution is lower than the point of zero charge (PZC), the catalyst surface becomes protonated and thus positively charged; conversely, it tends to be deprotonated and therefore negatively charged. Due to these differences in surface charge, the energy bands of semiconductor catalysts undergo bending in different directions, which in turn facilitates the migration of photogenerated electrons or holes, thereby enhancing the corresponding half-reactions. Moreover, the distinct surface charge characteristics also determine the types of species enriched at the surface (H− or OH+), thereby accelerating the respective hydrogen evolution or oxygen evolution half-reactions. In addition, the pH value can affect the reaction rate by altering the adsorption energies of intermediates, changing the rate-determining step, and consequently modifying the microscopic reaction pathway.
2.4 Low-dimensional Materials
We generally refer to systems with dimensions lower than 3D as low-dimensional materials, including: 2D layered materials, 1D nanotubes and nanowires/nanorods, and 0D isolated molecules and clusters. For 2D and 1D systems, there should theoretically be two and one periodic directions, respectively. In practice, when the dimensions of nanosheet systems and nanowire or nanorod systems are sufficiently large, they can be regarded as 2D and 1D material systems, because the quantum confinement effects in the corresponding dimensions have become negligible. 2D layered materials, exemplified by single-layer graphene (G) with a thickness of a single atom, possess a much larger specific surface area than their 3D bulk counterparts. Moreover, through van der Waals (vdW) interactions, they can be flexibly combined with different materials to form functional vdW heterostructures, thereby providing more possibilities and conveniences for chemical research. We sometimes also refer to 2D layered materials with multilayer structures as slab systems. Similar to the aforementioned criteria for identifying 2D and 1D material systems, once the thickness of a 2D slab material reaches a certain level and exhibits several repeating units along that direction, the quantum confinement effects imposed by the de Broglie wavelength (also known as the “matter wave wavelength”) can be disregarded. Consequently, in theoretical studies, such materials can be treated as 3D periodic systems.
The existing common 2D material systems are mainly classified into the following seven categories: (1) elemental 2D materials (Xenes), including graphene (G), silene, phosphorene, borophene, etc.; (2) transition metal dichalcogenides (TMDs), such as MoS2 and WS2; (3) transition metal carbides/nitrides (MXenes), such as Ti3C2 and Mo2C; (4) graphene-like materials, such as monolayer hexagonal boron nitride (h-BN monolayer), g-C3N4, and graphdiyne (GDY); (5) metal–organic frameworks (MOFs) and covalent organic frameworks (COFs); (6) metal oxides, such as TiO2, MoO3, Fe2O3, and Al2O3; and (7) heterostructures composed of the aforementioned materials. The tunability of their electronic structures is another important reason why 2D material systems have attracted the attention of chemists. Introducing defects or impurities into 2D material systems through defect engineering leads to a redistribution of charge within the material, thereby altering its electronic structure—an effective approach to enhancing chemical reaction performance. Constructing heterojunctions between different 2D materials is also a common strategy for improving charge carrier separation within the system. 2D materials can form heterojunctions in various ways: one method involves van der Waals interactions to create vdW heterojunctions, while another uses chemical bonds to connect two or more 2D materials into a planar heterojunction, as shown in Figure 7. These two types of heterojunctions are respectively referred to as “vertical heterojunctions” and “in-plane heterojunctions.”
First, in vertically stacked vdW heterostructure systems, the overall properties of the system can be flexibly tuned by adjusting factors such as the composition, thickness, and stacking order of each layer. Furthermore, due to the weak interlayer interactions in vdW heterostructures, external strain can induce interlayer twisting, thereby forming a specific Moiré superlattice that leads to band structure reconstruction and periodic modulation of charge carriers. The Moiré potential can trap photogenerated charge carriers, resulting in the formation of Moiré excitons at the interface. This phenomenon effectively suppresses charge carrier dissociation. However, from another perspective, the Moiré potential can, under certain conditions, enhance charge carrier transport along specific directions, thereby facilitating separation. A typical example is the so-called "magic-angle bilayer graphene," which exhibits superconductivity［31］. Of course, due to lattice mismatch, a Moiré superlattice can also emerge even without interlayer twisting, as seen in TMD/h-BN heterostructures［32］. Based on the band structure and band-edge positions of semiconductor materials, semiconductor heterojunctions can be classified into three types: straddling gap (type-I), staggered gap (type-II), and broken gap (type-III). It is generally believed that in type-II heterojunctions, different types of photogenerated charge carriers are influenced by the built-in electric field and migrate to different semiconductors, providing a driving force to prevent recombination and achieve charge carrier separation, thus enhancing photocatalytic reaction efficiency. When Coulombic interactions between charge carriers are strong, even though different types of carriers are transferred to distinct material layers in a type-II heterojunction, only limited interlayer excitons may form. In addition, vdW heterostructures possess numerous other factors that can effectively improve catalytic performance, including intrinsic electric fields and interfacial electronic coupling states. Due to lattice mismatch between the semiconductor materials in vdW heterostructures, 2D in-plane strain is induced in the two-dimensional materials on either side of the heterojunction, which in turn exerts a certain degree of control over the electronic structure of the material system. At the interface of vdW heterostructures, charge redistribution and orbital hybridization may give rise to a localized interfacial dipole layer, thereby generating an additional local electric field. Depending on the direction of this local electric field, the built-in electric field of the vdW heterostructure can be either enhanced or weakened, subsequently affecting charge carrier separation and transport properties. Naturally, real-world vdW heterostructures often contain various in-plane defects and edge-active sites. These sites, in conjunction with other factors such as the built-in electric field and interfacial states, can synergistically produce more pronounced catalytic activity.
In-plane heterostructures are typically connected by chemical bonds and therefore do not undergo relative twisting under small stresses. Due to the close lattice match between graphene (G) and monolayer h-BN, these two materials can be flexibly combined to fabricate single-atom-thick 2D in-plane heterostructure materials with various patterns. Studies have successfully synthesized, via chemical vapor deposition, 2D in-plane heterostructure materials in which h-BN patterns of different shapes are embedded within graphene［33-34］. It should be emphasized that, in the design and application of G/h-BN in-plane heterostructures, the boundary configurations at the material domain boundaries must be considered; the two simplest types are zigzag and armchair boundaries. Atomic-scale STM images have demonstrated that zigzag boundaries are more readily formed than armchair boundaries, accounting for over 77% of all boundaries［35］. However, experimental observations regarding the dominant boundary composition differ. Some studies suggest that B–C bonds constitute the primary boundary type, as B–C boundaries possess a theoretical energy advantage of 0.04 eV per atom over N–C boundaries［35］. In contrast, another experimental study found that the edges of the obtained G/h-BN in-plane heterostructures predominantly consist of N–C bonds［36］. It is important to note that the synthesis methods used in these two experiments were different: B–C bond boundaries appeared in experiments conducted on an Rh(111) substrate, whereas N–C bond boundaries were observed under graphene-supported conditions. This difference in substrates likely represents the primary reason for the divergent experimental findings. In other words, the choice of substrate material during the synthesis of G/h-BN in-plane heterostructures may significantly influence the chemical structure of the heterojunction, which aligns with key principles in condensed matter structural chemistry. Theoretical studies further indicate that B–C boundaries result in a larger band gap compared to N–C boundaries［37］. Consequently, by modulating the chemical composition of the boundaries in G/h-BN in-plane heterostructures, it is possible to flexibly tune the electronic band structure and thereby regulate the material’s chemical properties.
In more complex in-plane heterojunction systems, the effect of internal stress is even more pronounced. For example, in the in-plane heterojunction formed by MoS2 and α-MoC, lattice parameter mismatch between the two materials induces stress through chemical bonds at their interface, thereby altering the electronic configuration of MoS2. As a result, the Gibbs free energy required for proton adsorption and desorption becomes very close to that of Pt-based metal catalysts. Due to the direct synergistic interaction between the two materials, this in-plane heterojunction exhibits a higher catalytic activity for the hydrogen evolution reaction (HER) in both neutral and alkaline conditions than Pt does［38］. Such an in-plane heterojunction overcomes the typical pH dependence of electrocatalytic HER, achieving pH-independent tolerance for the catalyst. In-plane heterojunctions can also be constructed between different phases of the same material, leveraging differences in crystal structure to introduce internal stress at the grain boundaries. The metallic 1T-MoS2 possesses excellent electrical conductivity, making it well-suited for electrocatalytic HER; however, its large-scale synthesis remains limited by current chemical and physical methods. By annealing 2H-MoS2 and doping it with phosphorus to expand its lattice, a partial transformation from the 2H phase to the 1T phase can be induced, thereby generating a stable nested 1T/2H self-heterojunction of MoS2［39］. Benefiting from the high electrical conductivity, highly exposed active sites, and hydrophilicity exhibited by this self-heterojunction, the in-plane 1T/2H-MoS2 heterojunction can significantly enhance the electrocatalytic performance of HER in alkaline electrolytes. Overall, in-plane stress modulates the band structure and alters lattice vibrational modes, which in turn affects carrier mobility and may even induce phase transitions. All of these factors have a significant impact on the chemical reactions involving the material system.
For 1D material systems, carrier transport is restricted in two directions; the most typical example is the carbon nanotube (CNT). CNTs can be further classified into single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs). As early as 1952, Soviet scientists L.V. Radushkevich and V.M. Lukyanovich published clear images of carbon tubes with a diameter of 50 nm［40］. In the early 1990s, Japanese scientist Sumio Iijima made a major contribution by developing a transition-metal-catalyzed method to synthesize SWCNTs, which subsequently sparked a surge of research activities in this field［41］. Carbon fibers were first fabricated more than 160 years ago and can, in fact, be regarded as bundles of MWCNTs. Research on SWCNTs has been extensively conducted in the chemical field. Depending on their chirality, SWCNTs exhibit distinct electronic properties and, consequently, different responses to chemical reactions. Moreover, due to the curvature-induced differences between the inner and outer surfaces, the electronic states inside and outside the tube are not entirely identical. Therefore, the inner and outer walls of SWCNTs display different adsorption behaviors toward certain small-molecule chemicals［42-43］. Theoretically, as the diameter of a nanotube gradually increases, its properties should progressively approach those of its parent 2D material. However, it is important to emphasize that a nanotube cannot have an infinitely large diameter. Studies have shown that both carbon nanotubes and graphene nanotubes tend to collapse when their radii reach approximately 3 nm［11, 44］. Due to the spatial constraints within the CNT cavity, chemical reactions occurring inside exhibit superior reactivity. This aspect will be discussed in greater detail later. With the increasing synthesis of 2D layered materials, corresponding 1D nanotube materials have also been designed, including boron nitride nanotubes, graphyne nanotubes, TiO2nanotubes, MoS2and WS2nanotubes, silicon nanotubes, and organic nanotubes, among others［44-49］. 1D nanotubes not only significantly enhance the specific surface area of the respective materials but also introduce additional tunable parameters—such as chirality, tube diameter, surface stress, and defect sites—thereby creating favorable conditions for their applications in the chemical field.
0D materials encompass molecules, clusters, and cage-like structures, with fullerenes being a quintessential example. Initially discovered in sooty carbon evaporation residues, fullerenes primarily consist of C60, also known as buckminsterfullerene or "Buckyballs" ［50］. Subsequently, scientists identified naturally occurring C60and C70［51］in nature and even detected their presence in outer space ［52］. Following these discoveries, fullerene species of various sizes were synthesized, with the smallest being C20. Theoretical predictions suggest that the largest single-layer fullerene could comprise up to n=104carbon atoms ［53］. Another class of 0D materials commonly encountered in catalytic research comprises metal or metal oxide nanoclusters. Experimental evidence indicates that when Pt clusters are dispersed on SiO2, an appropriately controlled reduction temperature can not only maintain a high surface area of the Pt clusters but also enhance their catalytic activity in the dehydrogenation of propane ［54］. Researchers have attributed this enhancement to the strong interfacial interactions between the Pt clusters and the SiO2support; however, due to limitations in experimental techniques, the precise mechanisms and origins of these significant interfacial effects remain unclear. Furthermore, 0D fullerenes can be covalently bonded to 1D carbon nanotubes to form carbon nanobuds, thereby integrating the properties of both fullerenes and carbon nanotubes ［55］. Chinese researchers have also successfully linked 0D C60molecules via covalent bonds to construct a monolayered 2D fullerene network exhibiting a bandgap of approximately 1.6 eV, which is near ideal for visible-light absorption ［56］. Such low-dimensional composites offer a novel avenue for the application of low-dimensional materials. It is important to emphasize that reducing material dimensionality leads to a more pronounced delocalized dielectric shielding effect. Consequently, low-dimensional materials exhibit heightened sensitivity to their dielectric environment, resulting in distinct electronic properties across different media ［57-58］, thereby facilitating their versatile applications. However, whether combining low-dimensional materials to increase their overall dimensionality can mitigate the environmental sensitivity of individual components remains an open question. These dynamic environmental and microenvironmental effects constitute key research priorities in the development of condensed-phase structural chemistry.
2.5 Reactions in Confined Spaces
When a reaction takes place in a confined space, it may differ drastically from the general case. Confined spaces typically refer to smaller environments, often at the nanoscale. Carbon nanotubes (CNTs) are among the first materials that come to mind. Open-ended CNTs provide channels for the entry and exit of reactants and products, thereby ensuring the continuity of the reaction. By selecting the chirality of CNTs, one can obtain tubes of specific dimensions to serve as reactors. In practice, CNT bundles are commonly used, which spatially divide the system into intratubular, extratubular, and inter-tube regions. To clearly demonstrate the influence of confined space on reactions, we focus on a single isolated CNT, where the system comprises only the confined intratubular space and the unconfined extratubular space.In organic synthetic chemistry, product separation is a crucial step, particularly in the synthesis of chiral molecules. Homogeneous asymmetric catalysis suffers from difficulties in both product purification and catalyst recovery. To address these challenges, constructing a chiral microenvironment on the surface of active metals has emerged as a relatively effective heterogeneous asymmetric catalytic strategy. However, issues such as insufficient activity or selectivity in heterogeneous chiral catalysts continue to severely hinder their practical application. In 2011, a study first reported the use of CNTs as supports for chiral-modified Pt nanoparticles, leveraging their spatial confinement to significantly enhance the enantioselectivity of asymmetric hydrogenation reactions［59］.Figure 8a illustrates the catalytic performance and turnover efficiency (TOC) of Pt nanoparticles chiral-modified with cinchonidine when dispersed on both the inner and outer walls of CNTs in the asymmetric hydrogenation of α-ketoesters. Figure 8b provides a more detailed comparison of the catalytic effects of Pt clusters distributed within the tube, on the outer surface, and in activated carbon during the hydrogenation of ethyl pyruvate. It is evident that CNTs themselves exhibit no catalytic activity in this reaction. Notably, when Pt clusters are located inside the CNT, the enantioselectivity of the hydrogenation reaction reaches its highest level. Furthermore, according to the report, under the same reaction conditions, the Pt/CNT (in) system with a 5% mass fraction loading demonstrates catalytic activity even surpassing that of the renowned Pt/Al2O3catalyst. Another typical example involves Pt–Ru alloy catalysts housed within CNTs for the hydrogenation of cinnamaldehyde to cinnamyl alcohol, achieving a selectivity of 95%, far exceeding the 35% selectivity observed with isolated alloy nanoparticles［60］.We can gain a better understanding of how the confined space within CNTs influences reaction selectivity through a simple schematic diagram, as shown in Figure 9. In an unconstrained environment, the orientation of cinnamaldehyde molecules adsorbed on the catalyst surface is random, resulting in roughly equal probabilities of contact between the aldehyde oxygen atom and either of the adjacent carbon atoms. Given that the carbon atom bearing the double bond is more readily reducible, the unconstrained catalytic hydrogenation process yields only approximately one-third cinnamyl alcohol. Conversely, within the confined space of the CNT, cinnamaldehyde molecules align parallel to the catalyst surface, tending to orient the less sterically hindered aldehyde-containing end toward the catalyst. This alignment significantly enhances the selectivity toward cinnamyl alcohol. In confined systems, the initial state of the reaction is inherently more ordered than in bulk-phase reactions. Consequently, the initial entropy value S0in confined conditions is substantially lower than that in bulk-phase systems. According to the fundamental laws of thermodynamics, the change in Gibbs free energy (∆G)Equation (10)determines the direction of a chemical reaction.
The entropy decrease during the reaction process leads to an increase in ∆G, thereby hindering the reaction. However, confined systems that initially possess a higher S0 value result in a weakened entropy decrease during the reaction (∆S ≈ 0). Furthermore, strong interactions between the edge materials of the system and the reacting species can reduce the activation energy of the reacting species, making the enthalpy change ∆H more negative and thus lowering ∆G overall. Finally, the increased local concentration of the reacting species within the confined space significantly enhances the frequency of effective collisions, while the selective adsorption of the reacting species by the confined system itself can effectively remove the reaction products, thereby reducing the reverse reaction.
Although confined spaces are not exclusive to one-dimensional nanomaterials such as CNTs, they are also prevalent in other low-dimensional material systems and even in three-dimensional systems. Due to its inherent cavity structure, fullerene can also be utilized as a 0D nanoreactor. However, its closed structure hinders the exchange of reactants and products between the interior and exterior, thereby limiting reaction efficiency. In microdroplets, differences in the distribution of species, polarity, and stress environment between the interior and the surface result in markedly different reaction efficiencies compared with those observed in bulk solutions. It has been reported that the rates of common organic reactions occurring within water microdroplets can increase by 1 to 6 orders of magnitude. The primary acceleration occurs at the droplet surface, mainly because the electric field strength along the free O—H groups on the droplet surface is significantly higher than its average value inside the droplet［61］. Such alterations in the microenvironment arising from spatial confinement substantially influence chemical reaction processes, which falls precisely within the scope of condensed-phase structural chemistry. Given that this aspect lies beyond the solid-state system discussed in this paper, it will not be elaborated upon here.
Layered materials generally exhibit only weak interlayer interactions. Therefore, by employing specific methods to overcome these interlayer interactions and appropriately modulate the interlayer spacing, an ideal two-dimensional (2D) confinement space can be obtained for controlling factors such as the concentration and distribution of reaction species. By selectively modifying the surface polarity of the layered materials on both sides of the 2D space, a built-in electric field can be introduced into the 2D space, thereby enabling the regulation of the spatial orientation of reaction species or the enantioselectivity of the reaction.
3D confined spaces are primarily composed of the pore channels within 3D material systems. By employing specific synthesis methods, 2D graphene nanosheets can be assembled into a 3D graphene foam system featuring abundant pore channels［62］. Zeolites are typical examples of 3D material systems possessing micro- and mesopores. With pore sizes ranging from 0.3 to 10 nm, zeolites offer the flexibility to create confined spaces of varying dimensions. Currently, zeolites are predominantly utilized in adsorption–separation and catalytic reaction applications. Due to their unique pore dimensions, zeolites can achieve molecular sieving through spatial geometric constraints. Furthermore, the surface activity of zeolite pore channels can be modulated via ion exchange or the addition of templating agents, thereby enhancing the adsorption of specific molecules, improving intrinsic catalytic efficiency, or facilitating the loading of transition metals. For instance, in a 2020 report on the catalytic dehydrogenation of propane using Pt–Zn bimetallic clusters encapsulated within zeolites, we employed Silicalite-1 (S-1) to confine the size of Pt–Zn clusters within its sub-nanometer-scale internal pores. This approach not only improved the stability of the metal clusters but also yielded an exceptionally high propylene selectivity of 99.3%, effectively preventing over-dehydrogenation［63］. The diversity and inequivalence of active sites within zeolite pore channels confer significant tunability to these materials. Recently, in our research on ammonia-selective catalytic reduction (NH3-SCR) targeting major nitrogen oxide pollutants during the cold-start phase of diesel engines, we utilized SSZ-39 zeolite. By employing K+as the sole inorganic structure-directing agent, we promoted the incorporation of framework aluminum atoms into the eight-membered rings of the zeolite［64］. This strategy enhanced the formation of [Cu(OH)]+-species with low-temperature activity within the eight-membered rings, consequently doubling the nitrogen oxide reduction efficiency of copper-based SSZ-39 zeolite at temperatures between 150 and 225 ℃.
In summary, within a confined space, the local reactant concentration increases significantly, leading to an increase in effective pressure and even altering the physical properties of the reactant molecules, thereby enhancing the rate of chemical reactions. Furthermore, the reaction pathway may change due to the interactions between the materials forming the confined space and the reacting species. Although this introduces additional transition states—specifically, the two steps of reactant entry into and exit from the confined space—the appropriate spatial confinement can modify the stabilities of reactants, transition states, and products, reduce the entropy change of the reaction system, and enhance the enthalpy change. As a result, the energy barrier of the main reaction is lowered, while the energy barriers of competing reactions are raised through factors such as polarity, size, and adsorption energy, ultimately achieving the goal of improving reaction selectivity.
3 Dimensions of Defects and Impurities
Defects are locations that disrupt the regularity of a periodic system. Clearly, the defects we have been discussing are primarily found in crystalline systems characterized by periodic structures and symmetry. In contrast, amorphous systems—more common in nature—are riddled with defects compared to crystals. This is also the fundamental reason why amorphous systems generally exhibit higher chemical reactivity. The main structural defects in crystals include vacancies, topological defects, dislocations, grain boundaries, stacking faults, and voids. Impurities, or doping, are another frequent structural feature in crystal lattices. Doping can occur as substitutional doping, interstitial doping, or mixed-type doping, depending on whether foreign dopant atoms occupy lattice sites, interstitial positions, or both. Dopants are not limited to specific elements; they may be chosen to match the original element’s valence state for isoelectronic doping, or their electron-donating or -accepting behavior can be exploited to achieve donor or acceptor doping. In physics research, defects, impurities, or defect–impurity complexes are often intentionally introduced into target systems to tune their electrical, optical, and mechanical properties. In chemistry, beyond these physical property modifications, changes in the electronic structure at the surface or interface of such materials significantly alter their chemical reactivity. Consequently, these approaches are widely used to control the course, rate, conversion efficiency, and selectivity of chemical reactions. Of course, the concentration of defects and dopants is a key factor in modulating both the physical and chemical properties of a system. When multiple elements are doped in near-equal molar ratios, high-entropy solid solutions or compounds can form. These systems promote catalytic reactions through various mechanisms, including multi-site synergy, lattice distortion effects, and entropy stabilization. Methods that deliberately introduce defects and impurities to manipulate a material’s physicochemical properties are commonly referred to as defect engineering. Moreover, “topological defects” and “doping” are often collectively termed crystal defects for convenience.
3.1 0D: Point Defects
According to the dimensional classification of crystalline material systems, a defect is considered a 0D defect when it lacks translational symmetry in all three spatial dimensions over a sufficiently large real-space region. In other words, 0D defects are localized at a single lattice site or within a finite neighborhood around it. Of course, for crystals containing 0D defects—particularly in computational simulation studies—the overall structure can still exhibit translational symmetry on a larger scale. Therefore, in theoretical studies of 0D defects within crystals, these defects do not possess translational symmetry within the corresponding supercell. Typically, 0D defects involve only a single atom or a small number of atoms; they are spatially confined and induce only local atomic-scale perturbations in the system’s geometric configuration. However, due to their influence on the material’s electronic structure, they can lead to significant changes in its physicochemical properties, making them an important fundamental factor in modulating the structure–property relationship.
We classify typical point defects into five categories, as shown in Figure 10. The most common 0D defect in crystals is the vacancy. In molecular crystals, the absence of a molecule at a lattice site may occur, whereas in ionic crystals, either anion or cation vacancies can arise. When both anions and cations are missing from their normal lattice sites in an ionic crystal, this is referred to as a Schottky defect. Conversely, if anions or cations leave their regular lattice positions and move into interstitial sites within the crystal lattice, such defects are known as Frenkel defects. Some crystals, due to the presence of internal 0D defects, selectively absorb specific wavelengths of light, thereby exhibiting particular colors; these are traditionally termed color centers in condensed matter physics.
The emergence of point defects leads to local structural distortions in crystals and causes a redistribution of charges within the crystal, forming local potential barriers or potential wells, which subsequently affects their chemical activity. Based on the magnitude of the impact brought by these defects, we can classify the defect states into deep defect states and shallow defect states［65-66］. To facilitate comparison, we take the oxygen vacancies (Oxygen-vacancy, VO) in WO3crystals reported in the literature as an example. As shown in Figure 11a, for the VO-WO3system without structural optimization, a large amount of bound charge (localized charge) appears at the VOsite, thereby forming polarons. The corresponding defect band emerges near the middle of the band gap, resulting in a deep defect state. Conversely, after structural optimization, as depicted in Figure 11b, the charges in the defect system become more diffuse, and the defect band shifts closer to the band edge, forming a shallow defect state. It can be seen that, in the case of a shallow defect state, the energy difference between the defect band and the conduction band minimum (CBM) is extremely small, typically less than 50 meV. Therefore, under room-temperature conditions (kBT≈26 meV), such defects can be easily thermally excited. These two systems with distinctly different defect states will obviously exhibit different chemical activities. It should be emphasized, however, that the same type of defect cannot simultaneously manifest both types of defect states within the same crystal. We use this example solely to compare and illustrate the differences caused by various defect states while excluding other factors. Defects within a crystal are subject to dynamic changes under chemical reaction conditions, a view that has been substantiated by numerous studies［67］. According to the fundamental principles of thermodynamics, defects tend to disperse throughout the crystal to satisfy the entropy-increasing requirement. However, enthalpy changes arising from defect–defect interactions may serve as a driving force for defect aggregation. Consequently, by manipulating different reaction conditions, it is possible to control the distribution and configuration of defects within a crystal. For instance, CeO2, a widely used metal oxide catalyst in industry, possesses highly efficient “oxygen storage capacity” due to its rapid formation and elimination of surface oxygen vacancies［68］. The ability of CeO2to act as an oxygen buffer and active carrier primarily stems from its surface oxygen vacancies, with subsurface oxygen vacancies playing a crucial role in the formation of surface oxygen vacancy clusters. High-resolution scanning tunneling microscopy (STM) can be employed to observe the configuration and distribution of oxygen vacancies on the CeO2(111) surface. STM observations reveal that, following multiple sputtering processes and annealing cycles at 900 ℃ under vacuum conditions, the oxygen vacancy defects on the CeO2(111) surface transition from a state where they were predominantly dispersed individually across the surface and subsurface layers to a configuration in which they form linearly arranged vacancy clusters distributed only on the outermost surface layer. Meanwhile, the number of oxygen vacancies in the subsurface layer significantly decreases as they migrate toward the outermost surface［69］.
Introducing heteroatoms with different electronic configurations into a crystal can also alter its physical properties due to local lattice distortions, electron redistribution, and other factors, thereby regulating its chemical activity. When appropriate elements are sufficiently dispersed on the surface of the system, they can exhibit optimal catalytic performance owing to their full exposure. However, the substrate material does not merely serve as a dispersing agent; rather, through interactions between the substrate and the dispersed elements, it can exert a non-negligible influence on the electronic structure of the dispersed elements that function as catalytic active centers. This precisely reflects the single-atom catalysis theory proposed by Tao Zhang’s research group within the framework of condensed-phase structural chemistry. A typical example is provided by previous studies on Au single-atom catalysis of the CO oxidation reaction, as illustrated in Figure 12. The research team created oxygen vacancies on the pristine TiO2 surface and then dispersed Au atoms in a single-atom form onto these vacancies, using the oxygen vacancies as adsorption sites for the Au atoms. The strong interaction between the oxygen vacancies and the Au atoms not only prevents the migration and even aggregation of Au atoms during the reaction but also further modifies the electronic configuration of the Au atoms via Coulombic interactions and electron transfer. As shown in Figure 12(b), experimental results indicate that pristine TiO2 lacks the ability to catalyze this reaction. When Au single atoms are dispersed on the intact TiO2 surface, the system exhibits only limited catalytic activity at temperatures above 200 °C, requiring high temperatures to activate the Au atoms, and there remains a significant risk of Au atom aggregation during the reaction. In contrast, the synergistic effect between defects and single-atom Au can substantially lower the onset temperature of the catalytic reaction. At 100 °C, the catalytic activity is already markedly higher than that observed at 200 °C for the system consisting of Au atoms dispersed on a complete TiO2 surface, with a significant reduction in the activation energy.
As with surface defects, transition metal elements that are dispersed on the carrier surface in atomic form as catalysts or co-catalysts undergo a dynamic transformation process throughout the reaction. This is a key point that condensed-phase structural chemistry needs to emphasize and focus on. Both theoretical and experimental studies have provided abundant relevant evidence. Taking the Cu-mTiO2 photocatalytic CO2 reduction reaction as an example, when Cu species are dispersed at the atomic scale on the mesoporous TiO2 surface, in-situ observations under illumination reveal temporal changes: the Cu species initially present as Cu(OH)2 gradually transform into CuO, after which their oxidation state continues to decrease. After 2 hours of illumination, the oxidation state further declines to Cu2O, and with sufficient irradiation time, they eventually reduce to Cu(0) [71]. This serves as a typical example of how reaction conditions continuously act upon catalytic species during a reaction, inducing dynamic structural transformations.
3.2 1D: Line Defects
When defects in a crystal are arranged more closely along specific crystallographic directions, they exhibit linear translational symmetry within a certain range. We refer to such defects as 1D line defects. The most common type of line defect in crystals is the dislocation, where atoms deviate from their original positions along a linear path, thereby reducing the crystal’s symmetry and disrupting the continuity of its lattice pattern. This linear periodicity breaking gives rise to strain or lattice distortion in the vicinity (Figure 13), leading to significant changes in mechanical, optical, electrical, and magnetic properties, and consequently affecting the overall chemical properties and behavior of the system. The Burgers vector (b) is commonly used to describe the geometric configuration of a dislocation. There are two primary types of dislocations in crystalline materials: edge dislocations and screw dislocations. Figure 13 illustrates schematic diagrams of these two typical dislocations in a crystal. As can be seen, the Burgers vector of an edge dislocation is perpendicular to the dislocation line, whereas in a screw dislocation, the Burgers vector is parallel to the dislocation line. Distinct regions of compressive and tensile strain exist near edge dislocations, while screw dislocations primarily induce shear strain. The structure and properties of edge dislocations are relatively straightforward to understand, and plastic deformation can occur through slip motion. In contrast, the structure of screw dislocations is comparatively complex; nevertheless, they are quite prevalent during crystal growth［72-73］. Of course, purely edge or screw dislocations are relatively rare. In most cases, dislocations in crystals are coupled forms that combine both types, forming more complex mixed dislocations that possess characteristics of both basic dislocation types, with Burgers vectors oriented neither perpendicular nor parallel to the dislocation line［74］.
The strain at the core of a dislocation can sometimes exceed 10%［75］, leading to a significant reduction in the atomic coordination number and the formation of unsaturated bonds. This results in an increase in local energy, thereby creating highly reactive adsorption sites or catalytic active centers. The lattice distortion and local chemical environment changes induced by dislocations can modulate the electronic structure of the system, significantly influencing the local band structure. Consequently, one-dimensional shallow defect levels may form, the d-band center can be altered, and quantum wells capable of effectively capturing charge carriers can be established［76-77］. Theoretical studies on spiral dislocations within MgO crystals reveal that their optical absorption spectra differ markedly from those of the crystal surface topography, and they play a role in enhancing light absorption intensity［78］. Furthermore, the relatively open space and low-coordination environment in dislocation regions can substantially accelerate the diffusion of atoms or ions, giving rise to the so-called "pipe diffusion" phenomenon［79］. As a typical representative of two-dimensional materials, graphene can have linearly arranged five- to seven-membered or five- to eight-membered rings introduced through defect engineering, forming one-dimensional defects. Additionally, grain boundaries formed during the synthesis of graphene due to changes in the crystal growth direction are also fundamentally one-dimensional defects［80］.
Recent research in condensed matter physics has discovered that in chiral magnets such as MnSi or Cu2OSeO3, the magnetization can vary helically along a single spatial direction, resulting in layered order. Consequently, these materials are referred to as 3D helical magnets and are also regarded as a type of linear defect. The far-field behavior of these helical dislocations exhibits universal and typical lamellar ordering, enabling a rich variety of dislocation core structures［81］. Such specialized magnetic materials may lead to broader applications within the field of physics; however, the chemical implications of this phenomenon have yet to be addressed. Magnetic fields, as a typical environmental factor, exert significant influences on the reactivity of chemical substances, the mechanisms of chemical reactions, as well as reaction rates and selectivity. Moreover, chiral structures can affect the enantioselectivity of certain chemical reactions through their responses to spin or circularly polarized light. Therefore, the impact of helical magnets that couple both magnetic and chiral properties on chemical reactions represents a scientific question that warrants thorough investigation in future studies of condensed matter structural chemistry.
In addition to the previously mentioned "pipe diffusion" phenomenon, impurities may also segregate along the larger spaces created by linear defects, thereby forming 1D linear doping within the crystal. This phenomenon is driven by the local strain field induced by dislocations and significantly alters the local chemical environment, thus affecting material properties. The most typical example is the experimentally observed segregation of boron at edge-type dislocations in boron-doped diamond films［82］. Such linear segregation can influence the reconstruction of chemical bonds on atoms located at the dislocation core, hindering dislocation motion. Research on such doping systems remains very limited, particularly with few reports on their applications in the chemical field. As a new hotspot in "dopant-mediated defect engineering," this 1D linear doping system still requires in-depth theoretical and experimental exploration.
3.3 2D: Grain Boundaries
2D defects, also known as planar defects, exhibit greater extentiveness than 0D point defects and 1D line defects, possessing two-dimensional translational symmetry within a certain range. The main types of 2D defects include grain boundaries, antiphase boundaries, and stacking faults. Among these, grain boundaries and stacking faults have been more commonly and thoroughly studied. A grain boundary is an interface formed when two grains of the same crystal structure with different orientations meet during growth. Based on the orientation difference between the grains, it can be classified into low-angle grain boundaries (<10°~15°) and high-angle grain boundaries (>15°)［83］. Atoms located in the grain boundary region exhibit a certain degree of disorder and unsaturated coordination, making them sites with relatively high chemical activity. One specific type of grain boundary characterized by a particular orientation angle difference is the twin boundary. Twin boundaries are introduced during crystal deformation or heat treatment through the formation of a mirror-symmetry plane; the atomic arrangements on either side of the boundary are mirror images of each other, yet the coordination number of atoms at the interface remains unchanged. In ordered alloy systems, antiphase boundaries can be observed, where, despite the preservation of crystallographic orientation, a phase-order reversal occurs across the boundary due to atomic positional shifts. In layered materials, stacking faults may arise from the insertion (extrinsic) or removal (intrinsic) of certain atomic layers, as well as from dislocation motion. During material synthesis, particularly in vapor-phase deposition processes, erroneous atomic deposition can also lead to the formation of stacking faults. Similar to 1D linear dislocations, the lower atomic coordination and larger interstitial spaces at grain boundaries not only provide effective pathways for mass transport but also facilitate segregation phenomena, potentially resulting in the formation of 2D doping layers［84-85］. Furthermore, grain boundaries and stacking faults can influence the electronic structure of a material system, thereby affecting its overall electronic and phononic properties. High-angle grain boundaries can significantly increase the number of electrochemically active sites, promote electron transfer, and alter the work function of the material system, thus optimizing the activity, selectivity, and stability of noble-metal-based catalyst systems［86］. As antiphase boundaries in ordered alloys modify the local atomic coordination environment, they may induce changes in the magnetic properties of the system［87-88］, influencing interactions with surface-adsorbed species and consequently regulating the course of related chemical reactions. There are numerous research papers and review articles exploring the effects of defects of various dimensions on chemical reaction activity and kinetics, from which readers can obtain more comprehensive and detailed information［89］.
4 Conclusion and Future Work
In this paper, by distinguishing and briefly introducing the dimensions of crystalline material systems from those of their internal defects, we attempt to inductively summarize the relationship between the spatial dimensions of material systems and chemical reactions. Through this approach, we aim to deepen the understanding of relevant researchers, particularly scholars in the field of chemistry, regarding the importance of condensed-phase structural chemistry. Based on the simplest and most readily understandable crystalline materials, we illustrate, using several typical examples across different spatial dimensions, how condensed-phase structural factors such as space and microenvironment influence chemical reactions. The study of condensed-phase structures should not be confined to the investigation of their physical properties; rather, it ought to be extended to chemical research focused on the creation and generation of new substances. Future chemical research should also transcend traditional research paradigms, conducting thorough and in-depth investigations into the pivotal roles of ubiquitous condensed-phase factors—such as structural hierarchies and microenvironments—in chemical reactions, with the ultimate goal of designing reaction system architectures to control reaction processes. With the continuous development and advancement of experimental techniques like in situ characterization and computational simulation methods, we are confident that, in the near future, condensed-phase structural chemistry will undoubtedly propel the discipline of chemistry forward, elevating it to new heights.
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