Behavior of Formaldehyde Adsorption on ZnO [1011] Facets: A DFT Study

Abstract

Formaldehyde is a toxic gas commonly found in industrial emissions, and ZnO is widely used for its detection due to its excellent gas-sensing properties. Most studies focus on non-polar or low-index ZnO surfaces, whereas investigations on high-index polar surfaces remain limited. In this work, density functional theory (DFT) was employed to study CH₂O adsorption on the ZnO [$10\overline{11}$] surface. By exploring various coverages, adsorption sites, and unit cell dimensions, ten stable configurations were identified. A maximum adsorption energy of −2.19 eV/CH₂O on configuration S1 was obtained, surpassing reported low-index surfaces. Strong adsorption originated from dual unsaturated Zn bonds, which promoted C–C formation between CH₂O molecules and induced synergistic Zn–O bonding. Adsorption further led to sp³-like hybridization and O 2p/Zn 3d orbital interactions, significantly narrowing the band gap. Electron redistribution, as evidenced by charge density analysis, revealed strong electronic modulation. This work clarifies the microscopic mechanism of ZnO high-index surfaces, offering insights for optimizing gas-sensing materials.

1. Introduction

Formaldehyde (CH₂O) is a well-recognized toxic gas that poses serious risks to human health. The medical community generally holds the belief that CH₂O possesses genotoxic properties, capable of causing DNA damage and inducing carcinogenesis [1]. Checkoway et al. [2] analyzed occupational health data from industrial workers with long-term exposure to CH₂O and revealed a significant positive correlation between CH₂O exposure and the incidence rates of nasopharyngeal carcinoma and leukemia. Over the past decade, several studies have further confirmed the multifaceted hazards of CH₂O, including carcinogenicity [3], DNA damage [4], respiratory disorders [5], neurological damage [6], and negative effects on children’s health [7]. These findings have highlighted the urgency of real-time monitoring and minimizing CH₂O exposure, thereby driving the development of low formaldehyde-emitting materials and efficient detection technologies. Currently, formaldehyde detection methods based on large-scale analytical instruments—such as gas chromatography–mass spectrometry (GC-MS) [8] and high-performance liquid chromatography (HPLC) [9]—are highly accurate but usually rely on expensive equipment, complex sample pretreatment, and professional operators. As a result, they present limitations such as poor portability, high cost, and long cycle times in practical applications [10], making real-time online monitoring difficult to achieve. In contrast, gas-sensitive sensor devices demonstrate significant advantages due to their compact size [11], especially metal oxide semiconductor gas-sensitive sensors, which are widely used for their excellent gas-sensing performance [12].

As an important group II–VI metal oxide semiconductor, ZnO typically possesses a large direct band gap of 3.37 eV, and its exciton binding energy is 60 meV [13,14]. As one of the earliest gas-sensing materials, ZnO has exhibited excellent sensitivity toward numerous reducing or combustible gases [15]. Furthermore, ZnO nanomaterials demonstrate superior gas-sensing performance due to their larger specific surface area [16], greater abundance of oxygen vacancies [17], and increased number of active sites [18]. For nanomaterials, gas-sensing reactions primarily occur at the material surface [19]. Consequently, numerous studies have examined the gas–molecule interactions governing the gas-sensing behavior of ZnO. For instance, Saniz et al. studied the adsorption mechanisms of hydroxyl groups (OH⁻) and carbon monoxide (CO) gas on the ZnO $[10\overline{1}0]$ surface, ultimately discovering that OH⁻ exhibits a higher binding energy on the surface [20]. Xiong et al. calculated the reaction process between perfluoroisobutyronitrile (C₄F₇N) gas and the ZnO $[10\overline{1}0]$ surface. Their results revealed that C₄F₇N exhibits significantly higher activity on the ZnO $[10\overline{1}0]$ surface compared to metallic Zn. These findings indicate that ZnO nanomaterials or two-dimensional films featuring $[10\overline{1}0]$ surfaces hold greater potential for gas-sensing applications [21]. Several theoretical investigations have focused on the gas-sensing response of ZnO to CH₂O molecules. For example, Chen et al. investigated the adsorption characteristics of CH₂O on the polar ZnO low-index surface [0001] and found that CH₂O molecules act as electron acceptors during the adsorption process, capable of capturing electrons from the ZnO surface [22]. Following CH₂O adsorption, impurity levels emerge within the band gap, exhibiting a tendency to narrow the band gap compared to pre-adsorption conditions. These electronic changes highlight ZnO’s promise in CH₂O gas sensors. Furthermore, Jin et al. studied the adsorption behavior of CH₂O molecules on the non-polar ZnO $[10\overline{1}0]$ surface [23]. Their findings revealed that CH₂O molecules exhibit a distinctive chain-like adsorption structure on the ZnO $[10\overline{1}0]$ surface. The polarized electrostatic interactions of the CH₂O molecule play a significant role in determining both the geometric structure and the system energy. Electronic property analyses showed that the C=O double bond in CH₂O was transformed into a C-O single bond, and the highest occupied molecular orbital (HOMO) of CH₂O was lifted into the ZnO band gap to become a hole trap center, which may be important for the degradation and detection of CH₂O.

It has been observed that, whether concerning CH₂O or other gas molecules, research into the gas-sensing properties of ZnO material surfaces primarily focuses on non-polar surfaces or low-index polar surfaces. This choice is mainly due to the ease of preparing ZnO nanomaterials that typically expose these low-energy surfaces, while the synthesis of high-index surfaces has long remained a big challenge. With the development of crystal growth techniques, ZnO complex nanomaterials with high -index polar surfaces have been successfully obtained [24].For example, Lim et al. prepared a pyramidal array of ZnO nanomaterials with a $[11\overline{2}2]$ surface using chemical vapor deposition (CVD) and conducted experimental and theoretical analyses of their growth and photocatalytic activities [25]. The results showed a 73% performance improvement compared to ZnO nanomaterials with a $[10\overline{1}0]$ surface. Chang, Ahmed, and colleagues successfully synthesized pyramid-shaped ZnO nanocrystals with tip-exposed [$10\overline{1}1$] and base-exposed [$10\overline{11}$] surfaces, which enhanced the catalytic efficiency of dye-sensitized solar devices [26]. Mehta et al. performed systematic DFT studies on various ZnO crystal planes and found that high-index polar surfaces such as $[10\overline{1}3]$ and $[11\overline{2}2]$, characterized by step-like features, exhibit enhanced methanol adsorption, activation, and O-H bond dissociation compared with low-index non-polar surfaces [27]. Sun et al. discovered that, compared to the normal flat surface of ZnO, the photovoltaic properties of the polarized surface exhibited a marked change-over 230 times-in intensity range under 365 nm ultraviolet (UV) illumination [28]. Moreover, nanomaterials with high-index polar surfaces often outperform low-index non-polar ones due to higher surface activity and more adsorption sites. For instance, Zhang’s comparative research on the performance of different crystal faces in gas-sensitive sensors indicated that non-polar surfaces, lacking highly active sites, exhibit poorer gas-sensing capabilities [29]. Batyrev’s research revealed that under conditions of extremely low pressure, the low-index polar [0001] surface of ZnO undergoes structural changes, resulting in limitations to its gas-sensing performance [30].These studies highlight that such surfaces may not fully exploit the optimal gas-sensitive properties of the material due to factors such as low surface energy, few active sites, and flat structure. In this context, exploring the high-index polar facets of ZnO provides new opportunities to achieve both high activity and tunable selectivity. Our previous combined experimental and theoretical study showed that under Zn-rich conditions, Zn-terminated [$10\overline{11}$] surfaces can have lower energies than conventional low-index facets [31], enabling complex ZnO nanostructures-such as pagoda-shaped [32] and helical forms [33]— in agreement with Gibbs–Wulff theory [34,35]. Under Zn-rich chemical potential conditions, the ZnO [$10\overline{11}$] surface is characterized by a higher concentration of exposed Zn atoms and a partially polarized charge remains, which exhibit strong chemical activity. Meanwhile, the oxygen atom in the carbonyl group of CH₂O possesses high electronegativity and reactive lone-pair electrons. Therefore, the ZnO $[10\overline{11}]$ surface has strong potential for gas adsorption and sensing applications toward CH₂O molecues, which provides abundant active Zn sites that can effectively interact with the O atom of the –CHO group.

Therefore, it is readily apparent that utilizing ZnO nanostructures with $[10\overline{11}]$ surfaces expected to possess greater potential for CH₂O adsorption and gas-sensing performance. Although some research groups have successfully synthesized ZnO nanostructures with exposed [$10\overline{11}$] surfaces, their application in the gas-sensitive detection of CH₂O molecules remains scarcely documented. Studies on the interaction between ZnO $[10\overline{11}]$ surfaces and CH₂O molecules remain relatively scarce.

Accordingly, this study employed first-principles density functional theory (DFT) to systematically investigate the adsorption behavior of CH₂O molecules on the ZnO $\left[10\overline{11}\right]$ surface. The interaction mechanism between the two was analyzed in terms of adsorption configuration, electronic structural evolution, and charge transfer behavior. The study first determined the optimal adsorption configuration of CH₂O gas molecules on the ZnO surface through adsorption energy calculations. Subsequently, the underlying reaction mechanism between CH₂O molecules and the ZnO [$10\overline{11}$] surface was examined from the perspectives of surface band structure, density of states, and differential charge density. This research aims to provide theoretical guidance for further enhancing the gas-sensing properties of ZnO-based nanomaterials toward CH₂O molecules.

2. Computational Models and Methods

This study is based on density functional theory (DFT) [36] and all calculations were performed using Vienna Ab initio Simulation Package (VASP) [37,38], version 6.1.0. The exchange-correlation energy was treated using the Perdew-Burke-Ernzerhof (PBE) generalization [39] under the generalized gradient approximation (GGA) [40]. The electron-ion interactions were described by the projector augmented wave (PAW) method [41], and the cutoff energy (ENCUT) was set to 500 eV to ensure convergence of the calculations. For the Brillouin zone integrals, the Monkhorst–Pack grid centered at the Γ point was used for sampling, and the k-point grid was set to 3 × 3 × 1 to ensure a balance between computational accuracy and cost.

During the structural optimization process, the conjugate gradient (CG) method was used for atom relaxation, with the energy convergence criterion set at 10⁻⁵ eV and the force convergence criterion set to a maximum residual force on all atoms not exceeding 0.02 eV/Å. During model construction, to avoid interactions between neighboring layers due to periodic boundary conditions, a vacuum layer of 15 Å was introduced in the c-axis direction, which effectively isolated the interactions between the periodic mirrors.

Finally, the computational data obtained from VASP were post-processed using the VASPKIT program (version 1.4) [42], including the energy band structure and density of states.

For adsorption energy, the adsorption energy per CH₂O molecule is defined by Equation (1):

$${\mathrm{E}}_{\mathrm{ads}} = {\displaystyle \frac{1}{\mathrm{N}}}\left({\mathrm{E}}_{\mathrm{total}}-{ \mathrm{E}}_{\mathrm{slab}}-\mathrm{N}{\mathrm{E}}_{\mathrm{gas}}\right)$$

(1)

where E_total is the total energy of the model after adsorption, E_slab is the total energy of the pure surface model, without CH₂O gas molecules, before adsorption, E_gas is the total energy of a single CH₂O molecule, and N is the number of CH₂O molecules.

The charge density difference is defined by Equation (2):

$$\mathsf{\Delta }\mathsf{\rho } = {\mathsf{\rho }}_{\mathrm{total}}-{\mathsf{\rho }}_{\mathrm{slab}}-{\mathsf{\rho }}_{\mathrm{gas}}$$

(2)

where ${\mathsf{\rho }}_{\mathrm{total}}$ is the charge density of the total system, while ${\mathsf{\rho }}_{\mathrm{slab}}$ and ${\mathsf{\rho }}_{\mathrm{gas}}$ represent the surface charge density of the pure ZnO [$10\overline{11}$] surface without adsorbed gases and the charge density of the gas molecules, respectively.

The optimized ZnO lattice parameters of a = 3.24927 Å and c = 5.320544 Å are in better agreement with the experimental values of the lattice parameters [43], which also demonstrates the reliability of the computational method used in this paper. In prior research by Yan et al. [44], it was shown that surface coverage affects molecular adsorption behavior. Building upon this, 1 × 1 and 2 × 1 supercells of the ZnO [$10\overline{11}$] plane were constructed. Within this model, the adsorption characteristics of CH₂O molecules were investigated at coverages of 0.5 ML and 1 ML.

Our model used a ZnO [$10\overline{11}$] surface supercell structure consisting of eight atomic layers, where the lower six layers were fixed and the upper two layers were allowed to relax. The dimensions of the 1 × 1 surface supercell were 3.25 × 6.14 × 33.69 Å, comprising 16 Zn atoms and 16 O atoms. The [$10\overline{11}$] surface contained two Zn atoms—one with two dangling bonds and the other with one dangling bond.

The 2 × 1 supercell dimensions were 6.50 × 6.14 × 33.69 Å. The 2 × 1 supercell was created by extending the 1 × 1 supercell by one lattice unit along the x-axis and contained 32 Zn atoms and 32 O atoms.

As shown in Figure 1a,b the ZnO [$10\overline{11}$] surface consisted of a longitudinal alternation of Zn atoms with double dangling bonds and Zn atoms with a single dangling bond. In the research group’s prior work, it was proposed that the stable structure of the ZnO [$10\overline{11}$] surface, under a 2 × 1 periodicity, involved two Zn atoms with double dangling bonds moving laterally toward each other to form the Zn dimer structure shown in Figure 1b [45]. Zn-terminated surfaces are more likely to form than O-terminated ones because oxygen vacancies are the most prevalent intrinsic defects in ZnO. In this work, the ZnO $\left[10\overline{11}\right]$ surface was formed under Zn-rich chemical potential conditions, where the Zn-terminated configuration becomes thermodynamically stable. Under these conditions, the 2 × 1 supercell undergoes surface reconstruction, forming Zn–Zn dimer structures that effectively reduce the number of dangling bonds and improve surface stability.

According to the electron counting principle, this structure effectively reduced surface hanging bonds, thereby lowering surface energy and enhancing stability. This structure was reproduced in the present work. Calculations indicated that the bond length of the Zn dimer was 2.50 Å, which was shorter than the Zn–Zn bond length of 2.66 Å in metallic zinc. This decrease suggested stronger interactions between the two zinc atoms in ZnO with the chrysotile-like structure.

The study of CH₂O molecule adsorption on the ZnO [$10\overline{11}$] surface was conducted based on this structure.

3. Results and Discussion

3.1. 1 ML Adsorption Behavior Study

Within a 1 × 1 unit cell, different configurations were selected for the adsorption of a single CH₂O molecule onto a supercell.

Table 1. Adsorption energies of various adsorption configurations and O-Zn bond lengths.

Configuration	dO-Zn (Å)	Eads (eV)	Coverage	Size
A1	2.03	−1.09	1	1 × 1
A2	2.03	−0.87	1	1 × 1
A3	2.09	−0.73	1	1 × 1
B1	2.07	−1.43	0.5	2 × 1
B2	1.20	−1.39	0.5	2 × 1
B3	2.24	−1.16	0.5	2 × 1
B4	2.24	−0.95	0.5	2 × 1
S1	2.24	−2.19	1	2 × 1
S2	1.99	−1.96	1	2 × 1
S3	1.99	−1.79	1	2 × 1

presents the adsorption energies, bond lengths, and other related data for configurations A1, A2, and A3. Calculations yielded the three most stable adsorption configurations, as depicted in Figure 2. These configurations were ranked in descending order of adsorption energy as A1 > A2 > A3. In all adsorption configuration figures presented in this work, the top profile shows the top view and the bottom profile shows the side view.

Figure 2a shows that configuration A1 exhibited the highest adsorption energy among the three. The CH₂O molecule was positioned above two Zn atoms with double dangling bonds, with the oxygen atom forming bonds with two distinct Zn atoms on different lattice planes. The Zn–O bond length measured 2.03 Å. The CH₂O molecule lay approximately parallel to the ZnO surface. The carbon atom in the C=O bond was attracted toward the surface Zn atom, causing the entire C=O bond to tilt toward the rear Zn atom. The shape of the CH₂O molecule transformed from its original sp² planar configuration to a distorted sp³-type tetrahedral configuration, with an adsorption energy of −1.09 eV/CH₂O.

Figure 2b depicts that in configuration A2, the CH₂O molecule adsorbed at two bridging sites with Zn atoms bearing single dangling bonds. The oxygen atom bonded to two Zn atoms, each with double dangling bonds, with an O–Zn bond length of 2.03 Å. CH₂O molecules were aligned parallel to the [$11\overline{2}0$] crystal direction, exhibiting a distinct bridging adsorption configuration. The CH₂O molecules largely retained their original planar configuration, with no significant structural deformation, and the structure remained stable. However, only the oxygen atoms interacted with surface atoms, yielding an adsorption energy of −0.87 eV/CH₂O for this configuration.

For configuration A3, CH₂O molecules were arranged parallel to the [$11\overline{2}0$] crystal direction and perpendicular to the surface. They interacted with a surface Zn atom bearing a single dangling bond to form a covalent bond, with a bond length of 2.09 Å. The CH₂O molecule adsorbed in a terminal manner directly above this Zn atom, maintaining its original planar configuration with no significant structural distortion. The adsorption energy for this configuration was −0.73 eV/CH₂O.

In a 2 × 1 supercell, the coverage of one CH₂O molecule per 1 ML was investigated, specifically examining the adsorption of two CH₂O molecules per supercell. Three stable adsorption configurations were obtained from the calculations, each exhibiting a novel feature: following adsorption, two CH₂O molecules formed covalent bonds with each other, connected exclusively by C–C bonds. The three adsorption configurations were ranked in descending order of adsorption energy as S1 > S2 > S3. Table 1 presents the adsorption energies, bond lengths, and other related data for configurations S1, S2, and S3.

In configuration S1, which had the highest adsorption energy (Figure 3a), two CH₂O molecules adsorbed above two bonded Zn atoms to form bridging adsorption sites. The oxygen atoms in each CH₂O molecule disrupted the original Zn dimer structure on the surface and bonded with two Zn atoms, respectively. The CH₂O molecules transitioned from their original planar configuration to a quasi-tetrahedral structure, forming a stable C–C single bond between the two molecules with a bond length of 1.55 Å. This bond length was consistent with that observed in common saturated hydrocarbons such as ethane. The formation of this C–C bond enabled intermolecular interactions between CH₂O molecules, enhancing the stability of the adsorption. The bond lengths between the oxygen atom in the CH₂O molecule and the surface zinc atoms were 1.998 Å and 2.040 Å, respectively. This saturates the dangling bond created by the disruption of the surface zinc dimer. The adsorption energy for this configuration was calculated to be −2.188 eV/CH₂O.

In configuration S2, depicted in Figure 3b, the Zn dimer structure on the ZnO surface was also disrupted by the adsorption of CH₂O molecules. An oxygen atom from one CH₂O molecule formed a chemical bond with one of the Zn atoms in the Zn dimer. This bonding action caused the two originally connected Zn atoms to be pulled apart laterally. Simultaneously, another pair of surface Zn atoms bearing dangling bonds each formed a bond with an oxygen atom from a separate CH₂O molecule, establishing end-on adsorption. Furthermore, the stable C–C single bond between the two CH₂O molecules persisted, transforming their conformation from planar to a tetrahedral-like shape. The calculated adsorption energy for configuration S2 was −1.956 eV/CH₂O.

In configuration S3 (Figure 3c), the surface Zn dimer structure was similarly disrupted by CH₂O molecules. This configuration resembled, but did not entirely match, configuration S2: one oxygen atom from one CH₂O molecule bonded with each of the two Zn atoms forming the dimer, while the other CH₂O molecule bonded with two Zn atoms bearing single dangling bonds, establishing a bridging adsorption mode. The O–Zn bond lengths at the surface were 1.902 Å and 1.976 Å, respectively. The adsorption energy for this configuration was −1.7856 eV/CH₂O.

3.2. 0.5 ML Adsorption Behavior Study

At a coverage of 0.5 ML, a 2 × 1 surface supercell adsorbed one CH₂O molecule. Four stable adsorption configurations were established, all of which represented stable integral adsorption structures. Arranged in descending order of adsorption energy, the configurations were B1 > B2 > B3 > B4. Table 1 presents the adsorption energies, bond lengths, and other related data for configurations B1, B2, B3 and B4.

Figure 4a shows that the configuration B1 possessed the highest adsorption energy among the four. In this configuration, the CH₂O molecule underwent bridging adsorption with two Zn atoms bearing a single dangling bond, with the oxygen atoms forming bonds with the two Zn atoms, respectively, yielding a bond length of 2.07 Å. The original Zn dimer on the surface disappeared due to the mutual attraction between the carbon atom in the CH₂O molecule and the Zn atom. The CH₂O molecule’s geometry transitioned from its original planar configuration toward a distorted sp³-type tetrahedral structure. The C=O bond tilted toward the surface due to the attraction exerted by the Zn atoms on the carbon atom. The calculated adsorption energy was −1.43 eV/CH₂O for this configuration.

In configuration B2 (Figure 4b), a CH₂O molecule adsorbed onto a surface Zn atom bearing a dangling bond, with a bond length of 1.20 Å. The C=O bond in the CH₂O molecule lay nearly parallel to the surface. The adsorption energy for this configuration was calculated to be −1.39 eV/CH₂O.

For configuration B3, depicted in Figure 4c), the CH₂O molecule adsorbed between two previously bonded zinc atoms. The CH₂O molecule formed bonds with the two Zn atoms that previously constituted a dimer structure, thereby disrupting the original Zn dimer. The newly formed Zn–O bond had a bond length of 2.24 Å. The CH₂O molecule retained its original planar configuration and lay perpendicular to the surface along the [$11\overline{2}0$] crystal direction. The surface underwent deformation during adsorption, with the O–Zn–O bond angle changing from 74.64° to 96.93°. It was evident that the polar surface became flatter after adsorption compared to its original state. The calculated adsorption energy for this configuration was −1.16 eV/CH₂O.

Figure 4d displays that configuration B4 was similar to B2 in that the oxygen atom in CH₂O bonded with another surface Zn atom bearing a single dangling bond, with a bond length of 2.07 Å. Unlike B1, the CH₂O molecule retained its planar configuration, exhibiting an overall adsorption pattern without deformation. Compared to configuration B1, this configuration exhibited a longer Zn–O bond length and a lower adsorption energy of −0.95 eV/CH₂O.

3.3. Electronic Property

3.3.1. Band Structure

To elucidate the mechanism of CH₂O molecule adsorption on the ZnO [$10\overline{11}$] polar plane and its impact on the gas-sensing properties of the material, it was necessary to conduct a systematic analysis of the evolution of the electronic structure of the system before and after adsorption.

Electronic structural parameters—particularly the band structure, density of states, and charge distribution—not only reflected the strength of interactions between the surface and gas molecules but also directly determined the electron transport characteristics and gas response capability of gas-sensitive materials. Therefore, we investigated the modulation of CH₂O adsorption on the polar ZnO surface, including energy band structure, density of states distribution, and charge transfer behavior. Five representative adsorption configurations were considered to elucidate the underlying microscopic mechanisms.

Firstly, in order to better compare the adsorption properties of polar surfaces, the most stable and highest adsorption energy configurations of DB [23] for CH₂O adsorption on the non-polar ZnO [$10\overline{1}0$] surface with the same size and equal coverage, calculated in previous work, were reproduced (Figure 5d), and energy band structure calculations were carried out on them (Figure 5b). The band structure was illustrated with a band gap of 0.66 eV, the conduction band bottom at 0.25 eV, and the valence band top at −0.41 eV. It exhibited typical direct semiconductor characteristics, conducive to maintaining favorable intrinsic semiconductor properties.

The polar surface configuration A1, on the other hand, exhibited a narrower indirect band gap (0.36 eV) and a further downward shift of the Fermi energy level, showing more significant surface state hybridization and electronic structure rearrangement. Thus, it was evident that the polar surface was susceptible to electron excitation and dense surface states after adsorption.

Compared with the pure ZnO surface energy band diagram (Figure 5a), the configuration A1 significantly modulated the energy band structure of ZnO (Figure 5b). On the pure surface, ZnO retained a relatively wide direct band gap and intrinsic semiconductor properties. Following adsorption on the polar surface, the band gap narrowed and transitioned to an indirect band gap, with newly induced hybrid states partially inserted into the band gap region.

Near the valence band top, additional energy band branches emerged, increasing the band density. The valence band width expanded, while the distribution of lower-energy bands beneath it became more complex and densely packed. The conduction band base exhibited a greater concentration of low-energy levels, with some bands shifting downward, causing the valence band to cross the Fermi level. The spacing between bands at the conduction band edge narrowed, resulting in localized band interleaving. The overall distribution at the top of the conduction band became denser. New hybrid states emerged near the Fermi level, causing the band gap to narrow and transition from direct to indirect. The Fermi level shifted slightly relative to the pristine surface, approaching the newly introduced hybrid bands.

3.3.2. Projected Density of States

To further analyze the surface electronic properties and charge transfer behavior, projected density of states calculations and differential charge density calculations were carried out for configuration A1, as shown in Figure 6. It was observed that the intrinsic electronic structure of ZnO was still dominated by Zn 3d and O 2p orbitals in the valence band region, while the conduction bands were mainly contributed by the Zn 4s, Zn 3p, and C 2p orbitals. The overlap of the Zn 4s and O 2p orbitals occupied almost the entire conduction band, reflecting the strong Zn–O bonding.

The introduction of the CH₂O molecule produced three significant peaks at the valence band positions of the C 2p state, indicating strong orbital hybridization with the ZnO surface. Although the carbon atom did not bond with the surface Zn atom, this explained why the C=O bond was nearly parallel to the surface—resulting from the presence of a weak van der Waals adsorption between the C and Zn atoms.

The density of states near the Fermi energy level changed, with new states appearing in the 0–1 eV region, suggesting that CH₂O molecular adsorption induced charge redistribution and a significant narrowing of the band gap.

Differential charge density calculations were also performed for configuration A1, and the differential charge density diagram of the most stable configuration of the CH₂O molecule in a 1 × 1 cell on the ZnO [$10\overline{11}$] surface is shown in Figure 7, where yellow indicates the electron accumulation region and cyan indicates the electron depletion region.

A clear electron overlap region was formed between the oxygen atoms of the CH₂O molecule and the two Zn atoms with double dangling bonds, corresponding to the formation of Zn–O bonds. The original planar configuration (sp² hybridization) of the CH₂O molecule was distorted by the influence of surface Zn atoms, transitioning toward a tetrahedral-like (sp³ hybridization) structure.

Due to the rear Zn atom’s attractive interaction, the C=O bond was displaced, resulting in electron accumulation behind the carbon atom, as observed in the charge density map. The CH₂O molecule also showed electron accumulation around the two hydrogen atoms, resulting from weak electrostatic or hydrogen bonding interactions with the ZnO surface.

Although the hydrogen atoms were not directly involved in the surface coordination bonding process, charge reconstruction occurred near their positions, suggesting that the overall charge distribution of the entire CH₂O molecule changed significantly during adsorption. This change may have enhanced the molecule’s polarizability and increased its dipole interactions with the surface, further stabilizing the adsorption configuration.

In the 2 × 1 supercell configurations, projected density of states (PDOS) calculations were performed for configuration B1, as shown in Figure 8. Analysis revealed that a strong peak dominated by Zn 3d and O 2p orbitals appeared at approximately −1 eV, representing the intrinsic deep energy level in the ZnO valence band and indicating that Zn 3d electrons were primarily involved in the construction of the Zn–O bonds.

A new peak appeared near the Fermi energy level (0 eV), jointly contributed by Zn 4s, C 2p, and O 2p orbitals, indicating that significant orbital hybridization and charge redistribution between the CH₂O molecule and the ZnO surface. These new states provided additional electronic channels for electrons, enhancing the conductivity and charge responsiveness of the system.

Multiple distinct peaks appeared in the conduction band in the range of 1–2.5 eV, mainly composed of Zn 4s, Zn 3p, and C 2p orbitals, indicating that adsorption induced the structural complexity of the conduction band and the formation of multiple excited states.

Figure 9 shows the differential charge density profiles of configuration B1. The oxygen atoms in the CH₂O molecule formed a bridge adsorption with two neighboring Zn atoms, and the two Zn–O coordination bonds exhibited obvious electron redistribution. Strong electron accumulation occurred in the bonding region, which indicated that electrons were significantly transferred from the Zn atoms to the O atoms, thus enhancing the bonding effect.

This accumulation confirmed that there was a significant transfer of electrons from Zn atoms to O atoms, which enhanced the bonding effect and reflected the strong adsorption characteristics. At the same time, a pronounced electron depletion region (cyan area) appeared under the Zn–O coordination bond and between the Zn atoms, indicating that these Zn atoms had lost part of their valence electrons for coordination bonding with the O atoms.

The carbon atom in the CH₂O molecule also exhibited attraction toward surface Zn atoms with single dangling bonds. Consequently, the C=O bond tilted toward the surface after adsorption, a behavior attributed to weak attraction between Zn and C. As shown in the Figure 9, the C=O bond lost electron density, which dispersed toward the three atoms bonded to the carbon atom, leading to hybridization.

Under adsorption, partial electron orbitals of the carbon atom underwent new hybridization with surface Zn atomic orbitals, transforming its sp² hybridization into sp³ hybridization. This sp³-like hybridization manifested as a spatial redistribution of the carbon atom’s orbitals, with its non-bonding orbitals pointing more toward the adsorption surface while simultaneously affecting the electron density bonded to the hydrogen atom. The electron cloud distribution along the C–H bond direction became more concentrated and localized, resulting in a more pronounced electron accumulation zone around the hydrogen atom (manifested as electron accumulation in the differential charge density map). This adjustment increased the σ bond electron density on the hydrogen atom, leading to the observed electron accumulation.

Projected density of states calculations were performed for configurations S1, S2, and S3 under 2 × 1 supercell with 1 ML coverage. Figure 10a illustrates the PDOS profile for configuration S1, and the overall density of states distribution for the system was relatively smooth. Zn 3d orbitals formed a density-of-states peak near −2 eV, which provided the main contribution to the valence band. The O 2p and C 2p orbitals were mainly distributed in the region of 0–2.5 eV, suggesting a certain degree of orbital hybridization between adsorbed molecules and surface atoms.

Similar to configuration B1, several small density-of-state peaks were observed near the Fermi energy level, which were mainly contributed by the Zn 4s, O 2p, and C 2p orbitals. These peaks indicated that CH₂O molecular adsorption introduced new electronic states, disrupted the complete forbidden band structure of the pristine ZnO surface, and blurred the edges of the energy bands. Although these new states did not exhibit high concentration and strong orbital hybridization, they reflected the mild coupling between molecular orbitals and surface states, as well as local state splitting phenomena. Combined with a clear charge accumulation region between the oxygen atom of the CH₂O molecule and the Zn atoms on the ZnO surface in the differential charge density map, this suggested that a charge transfer process occurred from the lone electrons of the oxygen atom to the Zn atomic orbitals on the surface.

This medium-strength electronic coupling corresponded to several small density-of-state peaks near the Fermi energy level in the PDOS profile, indicating that such localized state splitting did not occur near the bottom of the conduction band, even though adsorption did not introduce a strong heterogeneous state.

Figure 11 displays the differential charge density profile for configuration S1, where yellow isosurfaces represented electron-rich regions and cyan regions indicated electron-deficient areas. The oxygen atom in each CH₂O molecule formed bridging adsorption with two adjacent Zn atoms. Zn–O coordination bonds exhibited distinct electron redistribution, with strong electron accumulation occurring in the bond-connecting regions and noticeable depletion zones present on the surface Zn atoms. This distribution indicated that these Zn atoms had lost part of their valence electrons due to coordination with the oxygen atoms.

This process achieved electronic passivation of the surface double-dangling or single-dangling bonds. It confirmed a significant electron transfer from Zn atoms to O atoms, thereby enhancing bonding interactions and demonstrating strong adsorption characteristics.

A distinct electron density accumulation (yellow region) appeared in the C–C bond area, distributed between the two carbon atoms and displaying typical covalent bond features. This characteristic clearly indicated that two CH₂O molecules had formed a stable molecular dimer structure. Electron depletion zones on both sides of the C–C bond extended outward around the carbon atoms, indicating electron redistribution from the local region to the bonded area, further reinforcing the bonding nature of the C–C σ bond. This electron rearrangement behavior demonstrated that CH₂O molecules underwent significant orbital reorganization during adsorption, thereby altering their original molecular electronic structure.

Figure 10b illustrates that configuration S2 showed clear features of localized states, especially in the 0–1 eV range, where two sharp peaks dominated by the C 2p and O 2p orbitals were clearly visible. This localization suggested that the carbon atom orbitals of the CH₂O molecule made a strong contribution at the bottom of the conduction band, forming a significant hybridization with the Zn 4s and Zn 3p orbitals. This new state was located close to the Fermi energy level, and the adsorption process not only altered the conduction band structure but also drastically improved the electron-leaping efficiency and conductivity.

Figure 10c shows that in configuration S3, the C 2p orbitals formed an isolated and strong peak near 0.8 eV and became the main contributing orbitals at the bottom of the conduction band, displaying highly selective orbital coupling behavior. The density of states of the remaining Zn and O orbitals was relatively smooth, and the original spike of up to 5.2 eV in the 0–0.7 eV region was transformed into a number of broader and lower energy peak small peaks contributed by the C 2p, Zn 4s, and O 2p orbitals on the ZnO surface. The peaks were generally lower than those in configuration S2.

Thus, configuration S3 had the lowest adsorption energy of the three, even though it was the configuration with the highest number of dangling bonds passivated on the 2 × 1 supercell at 1 ML coverage. The hybridized states of this configuration indicated that the CH₂O molecule was not coupled at a single point in configuration S3, but rather was electronically reconfigured with moderate strength through multiple low-energy orbitals.

The presence of these multiple hybridized states reflected the process of passivating multiple surface dangling bonds while maintaining the stability of the electronic structure of the system.

The adsorption of CH₂O molecules significantly modulated the band structure and local density of states on the polar surface of ZnO, while also introducing surface hybrid states and novel electronic states. This modulation led to a narrowing of the system’s band gap and enhanced carrier activation capability.

Analysis of the projected density of state and differential charge density further revealed the microscopic essence of strong orbital hybridization, charge rearrangement, and the formation of hybrid bonds between CH₂O molecules and the ZnO surface. The electronic restructuring and emergence of new energy bands triggered by the adsorption process provided a crucial electrical foundation for the application of ZnO polar surfaces in gas recognition, sensing, and surface catalysis.

From the perspective of gas-sensing mechanism, the Zn-rich $\left[10\overline{11}\right]$ surface provides abundant electron-donating Zn sites, which can strongly interact with electron-withdrawing species such as CH₂O. During adsorption, the electron transfer from Zn surface atoms to the O atom of CH₂O decreases the local electron concentration of the conduction band, thereby modulating surface conductivity. Such conductivity modulation is directly related to the sensing performance of ZnO-based devices. A stronger adsorption interaction, as reflected by the larger adsorption energy obtained in this study, enhances charge transfer efficiency and amplifies the change in surface conductivity upon gas exposure, which translates to higher sensor sensitivity. The adsorption-induced narrowing of the band gap facilitates carrier excitation and accelerates the recovery of the sensor signal once the gas molecule desorbs.

4. Summary

In this paper, the adsorption behavior and electronic structural changes of CH₂O molecules on the ZnO [$10\overline{11}$] high index polar surface were systematically investigated using density functional theory. Multiple adsorption configurations revealed strong CH₂O binding accompanied by significant surface reconstruction and electron transfer from Zn to O, forming stable Zn–O bonds and, in some cases, C-C single bonds between adjacent CH₂O molecules. The most stable configuration (S1) has the highest adsorption energy of −2.19 eV per CH₂O. The adsorbed CH₂O also experiences rehybridization toward an sp³-like state. The adsorption induced pronounced orbital hybridization between C/O 2p and Zn 3d/O 2p states, leading to new electronic states near the Fermi level and a narrower band gap compared with ZnO [$10\overline{1}0$] low-index surfaces.

Therefore, the electronic responses predicted from our DFT calculations—large adsorption energies, significant charge redistribution, and reduced band gap—collectively indicate that the ZnO $\left[10\overline{11}\right]$ surface is highly active toward CH₂O detection, exhibiting strong sensitivity and fast response characteristics desirable for high-performance gas-sensing applications. This study has not only uncovered the physical mechanism of CH₂O gas sensitization on the ZnO [$10\overline{11}$] polar surface but has also provided a theoretical foundation for the design and optimization of ZnO-based gas-sensitive devices and surface catalytic materials.