Does financial development lower energy intensity?

Abstract

The growth-induced effects of financial development have been well-established in the empirical literature, as well as the significance of financial development to energy demand behavior. However, the empirical evidence on the relationship between financial development and energy intensity remains sparse in the literature. Given the multifaceted nature of the effects of financial development, the proposed relationship seems a complex one and warrants an empirical investigation. Using the case of Ghana, this study provides an empirical answer to the question: does financial development lower energy intensity? To provide solid grounds for either rejection or acceptance of the null hypothesis, this study performed several robustness checks. Generally, the evidence revealed that financial development lowers energy intensity. Further, the results revealed that the price of energy, trade liberalization and industry structure play significant roles. These results have important implications for the design of macro energy efficiency policies and the creation of a ‘Green Bank’.

Keywords

financial development / energy intensity / energy efficiency / Ghana

1 1 Introduction

Photocatalysis has gained significant attention due to its potential as an alternative energy source and its ability to address the energy crisis [1]. Among various materials considered for photocatalysis, two-dimensional (2D) materials are of great significance due to their excellent properties, including large specific surface area, high electrical conductivity, abundant reactive sites, and suitable electronic structures for photocatalytic reactions such as water splitting and CO₂ reduction [2–8]. The explosive popularity of 2D materials in catalytic applications can be attributed not only to their intrinsic properties but also to the flexibility to tune their properties. Among various tuning methods, defect engineering holds great promise as it can effectively tailor the electronic structures, promote charge separation, and increase the active sites of 2D materials [9–12].

The effective and rational design of 2D defects for photocatalysis necessitates a thorough understanding of the electronic structures, optical properties, and reaction mechanisms of the materials. Besides, to facilitate the exploration of novel photocatalysts, it is essential to establish descriptors that enable the computational screening of materials. First-principles calculations employing the density functional theory (DFT) can be utilized to gain insights into the mechanism and guide the material design and discovery for photocatalysis [13,14]. Furthermore, by using appropriate descriptors, the discovery of 2D defective photocatalysts can be accelerated by screening, especially when combined with machine learning (ML) techniques [15].

In this mini-review, defect engineering for 2D photocatalysis is explored from a first-principles design perspective. 2D defects and their capability to tune the intrinsic properties are briefly introduced, followed by useful descriptors to appropriately describe the stability, electronic, optical, and catalytic properties of 2D defect systems, as well as their limitations. In addition, the application of ML techniques in accelerating photocatalyst design is also explored. While the primary focus is on photocatalytic water splitting, the insights provided here apply to other redox reactions as well. This review aims to offer a comprehensive understanding of the computational design of 2D materials for photocatalysis.

2 2 Defects in 2D materials

2D materials for photocatalysis can be broadly classified into three categories: 2D metal oxides, including TiO₂, Bi₂WO₆, and perovskite oxides; 2D metal chalcogenides, such as MoS₂, SnS₂, and WSe₂; and metal-free photocatalysts like graphitic carbon nitride (g-C₃N₄) and hexagonal boron nitride (h-BN) [16–19]. The fabrication of 2D materials inevitably introduces imperfections in the structures. Common defects in 2D materials include point defects (e.g., vacancies, dislocations, and dopants), line defects (e.g., grain boundaries, phase boundaries, and lateral heterostructures), and planar defects (e.g., van der Waals heterostructures and Janus structures) (Fig.1). These defects play an important role in modifying the intrinsic properties of 2D materials and ultimately impacting their photocatalytic performance.

Fig.1 Defects in 2D materials, using 2D TMDCs as examples (defects being categorized by their dimensionality).

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2.1 2.1 0D defects

2D materials, such as 2D transition metal dichalcogenides (TMDCs), have been extensively investigated for catalyzing water splitting [20,21]. However, theoretical and experimental work have shown that their active sites are located at the edges other than the basal plane [22,23]. The introduction of point vacancies in 2D materials can activate the basal plane and enhance catalytic activity [24–26]. For instance, introducing sulfur vacancies modifies the electronic structure of 2H-MoS₂, creating defective states in the gap near the Fermi level that contribute to the enhanced hydrogen binding at the vacancy sites [27]. In addition to modifying catalytic activity, vacancies in atomically thin metal oxide sheets also regulate the band edge position, bandwidth, and photo-induced carrier migration kinetics to improve the photocatalytic activity [28–30]. Doping is also an effective method to enhance the photocatalytic performance of 2D materials [31,32]. For example, Co doping in In₂S₃ enhances photocatalytic water splitting by increasing the density of states at the conduction band minimum (CBM), which significantly boosts visible-light absorption [33]. While doping introduces foreign atoms into the lattice, creating new energy states within the band structure, vacancies arise from the absence of atoms, typically generating defect states within the band gap. These differences lead to varying modifications in electronic structures, and recent studies suggest that a synergistic combination of vacancies and dopants can further enhance photocatalytic performance [31,34].

2.2 2.2 1D defects

In addition to point defects, line defects also have a significant impact on activating the basal plane of 2D materials [11,35–37]. Similar to point defects, the presence of boundaries in 2D materials influences the electronic properties, thereby modifying the chemical properties [11]. More importantly, introducing boundaries is an effective approach for creating separate domains for different functions on the surface, while still maintaining structural integrity. One good example is multiphasic 2D MoS₂ nanosheets for photocatalytic HER [38]. In this study, light absorption and charge generation were achieved by the 2H phase, efficient charge separation occurred at the 1T'/2H interface, and HER was favored in the 1T' phase. The well-balanced compositions of different domains on MoS₂ sheets result in an optimal photocatalyst that exhibits excellent optical, electronic, and chemical properties.

2.3 2.3 2D defects

Another advantage of 2D materials is their ability to form van der Waals heterostructures [39,40]. 2D materials serve as building blocks for heterostructures, and when held together by van der Waals forces, they can create materials with desirable physical and chemical properties for photocatalysis. Such face-to-face construction allows an intimate interface to promote the transfer and separation of photogenerated charge carriers, thus improving photocatalytic efficiency [41–43]. Moreover, these multi-stacked structures can include layers with various functions, such as semiconductor or cocatalyst layers. The reactivity of cocatalyst layers can be further enhanced by introducing point or line defects in their basal planes [44].

Among various defects in 2D materials, point defects, such as vacancies, are most extensively studied due to their controllability and versatility [45,46]. However, the impact of any given defect on photocatalytic efficiency is highly material-specific and depends on several factors, including defect concentration, interactions with the electronic structure of the material, and synergistic effects among multiple defects. Therefore, a comprehensive understanding of these factors is essential for optimizing photocatalytic performance in 2D materials via defect engineering.

3 3 Descriptors for defect engineering in 2D materials for photocatalytic applications

To computationally design materials with enhanced photocatalytic performance through defect engineering, it is essential to identify key material properties for accurate and efficient analysis. This is particularly important for high-throughput computational screening in the design of 2D photocatalysts. To utilize 2D defects for photocatalytic applications, certain conditions must be met, and suitable descriptors are needed to characterize these properties (Fig.2).

Fig.2 Descriptors for defect engineering in 2D materials for photocatalysis. Descriptors arise from the structural properties (defect formation energy, aqueous Pourbaix diagram, etc.), electronic properties (band gap, band edge positions, etc.), optical properties (excited states, light absorption coefficient, etc.), and catalytic properties (intermediate adsorption energy and band center), among others.

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3.1 3.1 Structural properties

Stability is the first essential requirement for designing materials for any application. One direct and effective descriptor for stability is the formation energy. The formation energy of a 2D defect comprises two significant components: the formation energy of the monolayer from the bulk materials, and the formation energy of the defect on the 2D materials. The calculation of the formation energy of a specific 2D defect using DFT is well-established and straightforward [49–51]. Similar to defects in bulk materials, 2D defects are typically modeled in a supercell and repeated periodically throughout space. However, for charged defects, this supercell approach may introduce errors due to electrostatic interactions between the defect and its periodic images as well as the background charge (Fig.3(a)). As a result, careful model construction and energy correction are required to obtain accurate formation energies of 2D charged defects [51,52]. Additionally, while each defect can be accurately addressed and calculated individually, the computational exploration of a broad range of potential 2D host materials and defect configurations is still challenging. This difficulty arises from the extensive chemical space, the high computational cost due to the large supercell required for defect calculations, and the lack of defect generation methods and data sets. In recent years, considerable effort has been devoted to evaluating formation energies for 2D materials through high-throughput screening [53–57], and several databases for 2D defects have been established [58,59]. In addition to thermodynamic stability, it is important to consider the corrosion of 2D materials in aqueous solutions for photocatalytic applications. The corrosion of 2D materials is usually examined using Pourbaix diagrams (Fig.3(b)) [60], and the interaction between the surface and solution can be accounted for using implicit or explicit solvation models [61,62]. Additionally, other key descriptors, such as phonon dispersion for evaluating dynamic stability and bond length deviations for assessing structural changes, can offer further insights into the structural properties of materials [63, 64].

Fig.3 Defect engineering in 2D materials for photocatalysis.

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3.2 3.2 Electronic properties

The potential of 2D defect systems as photocatalysts relies heavily on their electronic structures, specifically the band gaps and band edge positions [13]. For efficient photocatalysis in 2D systems, the band gap must be greater than 1.23 eV, which is the reaction energy for water splitting [65]. Furthermore, the energy of the CBM should be higher than the reduction potential of H⁺/H₂ (−4.44 eV at pH = 0), and the energy of the valence band maximum (VBM) should be lower than the oxidation potential of O₂/H₂O (−5.67 eV at pH = 0) [20]. It is important to note that these potentials shift by approximately 0.059 eV per pH unit as pH increases, which can either enhance or hinder photocatalytic efficiency depending on the alignment of the CBM and VBM with the redox potentials. A wide range of 2D materials exhibit suitable band gaps and band edge positions for water splitting and CO₂ reduction (Fig.3(c)). These properties can be calculated using DFT. However, it is known that there is a trade-off between efficiency and accuracy when it comes to the exchange-correlation functionals used. Standard functionals such as local density approximation (LDA) and Perdew-Burke-Ernzerhof (PBE) can calculate electronic properties with low computational cost, but they tend to significantly underestimate band gaps [66,67]. On the contrary, traditional hybrid functionals such as PBE0 and HSE06 can provide more accurate results [68] but are computationally more expensive, especially for models that involve defects, which typically contain at least dozens of atoms. Recently developed functionals such as SCAN meta-GGA have the potential to improve the accuracy of band gap calculations while maintaining affordable efficiency [69]. In addition to these energy-based considerations, other properties such as charge separation and charge carrier mobility are also important electronic factors for photocatalytic systems, and several descriptors have been developed to evaluate these properties [70].

3.3 3.3 Optical properties

The efficiency of light harvesting is one of the most important factors that determines the overall photocatalytic performance. Materials used for photocatalysis should be able to absorb a substantial fraction of the visible light spectrum, as it accounts for over 40% of solar energy [60]. The evaluation of light absorption typically requires the determination of optical band gaps. However, to accurately compute the optical band gaps, hybrid functionals or GW approximations are necessary. Furthermore, excitonic effects are generally more pronounced in 2D systems due to quantum confinement, and thus it is important to include the excitonic effects (Fig.3(d)) [71–74]. One key metric for evaluating the excitonic effects is the exciton binding energy (EBE) [75]. A lower exciton binding energy promises easier generation of free electrons and holes, which is advantageous for photocatalytic processes. The accurate calculations of EBE have been achieved by the Bethe-Salpeter Equation (BSE) formalism for both bulk and 2D materials [76,77]. However, the BSE formalism demands significant computational resources. Given the inevitably increased size of the 2D defect system, the challenge in obtaining its optical properties lies in selecting accurate methods that are also computationally affordable.

3.4 3.4 Catalytic properties

In terms of the catalytic activity of materials, several descriptors have been established in the past few decades, including adsorption energies, work function, coordination numbers, and band centers [78]. Detailed discussions of these descriptors have been covered in several review papers [79–81]. Among these descriptors, the band center is particularly important for understanding and predicting the catalytic activity of materials [24,82,83]. The key properties of a catalyst are fundamentally determined by its electronic structure, as described by the band center. Typically, a band center closer to the Fermi level results in stronger adsorbate-surface interactions, leading to enhanced adsorption. This model provides valuable insights into how electronic properties dictate catalytic performance and is widely used in catalyst design. However, due to the complexity of the defect configurations, descriptors that were successfully applied to simple models may no longer be suitable for 2D defect structures. One example is the failure of band center models to accurately describe the hydrogen adsorption at the defect sites of 2D TMDCs, highlighting the need for new descriptors for adsorption (Fig.3(e)) [11,24,84]. This failure can be attributed to the different contributions of atomic orbitals at the defect site to the adsorbed hydrogen atom, and the variability in the hydrogen adsorption geometry. In fact, this could be beneficial for catalyst design, as the failure of simple descriptors sometimes also indicates the breaking of ‘scaling relations’ for reactions, which limits the enhancement of catalytic activity [85]. However, the failure of descriptors is also a challenge for rational design and screening of the 2D defect systems. It is necessary to understand the catalytic reactions on 2D defects and develop new descriptors for them.

4 4 Machine learning (ML) techniques for accelerating 2D material design for photocatalysis

While descriptors offer an effective approach for the high-throughput design of 2D materials for photocatalysis, the substantial computational costs of first-principles methods remain challenging. ML presents a promising solution to these issues. For example, ML techniques have been employed to enhance prediction accuracy for electronic and optical properties of 2D materials, bypassing the need for time-consuming functionals [87,88]. Recent studies show that ML-assisted models, whether using PBE band gaps as features or not, can predict band gaps of 2D materials with accuracy comparable to the GW method, but at significantly lower computational cost [89–91]. Additionally, ML models can serve as efficient pre-screening tools, enabling rapid prediction of material properties, such as vacancy formation energies, without exhaustively sampling the entire configurational and compositional space of defect systems [92,93]. Furthermore, machine-learned interatomic potentials, including descriptor-based and moment tensor potentials, have been developed to predict energies and forces in atomic structures with high precision across various material systems [94–96]. These potentials substantially reduce computational costs while maintaining accuracy, facilitating the exploration of large defect systems [97–99].

By leveraging these advanced ML techniques, researchers can efficiently screen and design 2D materials with desired photocatalytic properties. However, challenges in applying ML to 2D materials with defects include the need for high-quality, diverse data sets for training robust models, and the development of interpretable models that offer insights into underlying physical mechanisms. Several efforts have been devoted to addressing these challenges [58,100].

5 5 Discussion and future prospects

Defect engineering offers an effective method for tuning the electronic, optical, and chemical properties of 2D materials for photocatalytic applications. In this mini-review, a brief introduction to various defects in 2D materials and their impact on photocatalytic properties was provided. Common descriptors used for the computational design of photocatalysts were discussed, focusing on their stability, electronic, optical, and catalytic properties, as well as their limitations. Additionally, ML techniques for accelerating catalyst design were explored.

While this mini-review primarily focuses on photocatalytic water splitting, the modification methods and descriptors discussed are fundamental to photocatalyst design and are broadly applicable to various redox reactions. Defect engineering has received extensive attention and has been widely explored in various photocatalytic fields, including CO₂ reduction, nitrogen fixation, and organic synthesis [101–104]. A notable example is the use of defect-rich ultrathin ZnAl-layered double hydroxide nanosheets as photocatalysts for CO₂ reduction to CO [105]. The introduction of oxygen vacancies generates coordinatively unsaturated Zn⁺ centers in the nanosheets, leading to high photocatalytic activity. For these photocatalytic reactions, key descriptors such as band gaps and band centers have been investigated to better understand and predict the photocatalytic performance of 2D materials [6,106].

It is worth noting that the limitations of first-principles methods in modeling defect properties can be mitigated through multiscale modeling [107,108]. Molecular dynamics (MD) simulations enable the exploration of larger systems and longer timescales than DFT, offering insights into nanoscale phenomena like molecule adsorption and diffusion [109,110]. Additionally, kinetic Monte Carlo (kMC) simulations allow for simulations of system dynamics over extended timescales that are challenging for traditional MD methods, effectively modeling material properties, including defect diffusion, charge transport, and reaction kinetics [111–113].

In prospect, there are still several challenges that need to be addressed in this field. First, it is crucial to bridge the gap between theory and experiments. While computational methods are mature and widely used to predict the atomic structures and properties of materials, identifying true atomic structures under realistic working conditions remains a significant challenge [106]. Secondly, although water splitting represents a fundamental and relatively simple reaction, the complexity of most reactions is far beyond the scope of correlations and descriptors, which hinders the feasibility of large-scale computational screening [114]. Considering defects in the atomic models adds complexity to the computations, necessitating cautious use and development of new descriptors. A promising avenue for future research involves leveraging ML techniques to predict properties and design descriptors for defects in 2D materials, which could provide promising approaches to accelerate the discovery of photocatalytic materials. Nonetheless, challenges such as the lack of defect databases and the limited interpretability of ML models remain significant obstacles that need to be addressed. Overall, gaining a deeper understanding of the electronic structures of defects in 2D materials and how they impact the mechanisms of photocatalytic reactions is crucial. Only then can it be possible to identify the origins of these phenomena and guide the future computational design of 2D defective systems for photocatalysis.

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