Excited State Calculations of Cu-Doped Anatase TiO₂ (101) and (001) Nanofilms

Abstract

Excited state calculations are performed to predict the electronic structure and optical absorption characteristics of Cu-doped anatase Ti$O_2$ nanofilms, focusing on their (101) and (001) surface terminations. Using model structures that successfully represent the equilibrium positions of deposited Cu atoms on the Ti$O_2$ surface, a comprehensive analysis of the absorption spectra for each considered model is made. The proposed modeling reveals phenomena when photogenerated electrons from Ti$O_2$ tend to accumulate in the vicinity of the deposited Cu atoms exposed to photon energies surpassing the band gap of Ti$O_2$ (approximately 3.2 eV). The crucial transition states that are essential for the creation of potential photocatalytic materials are identified through detailed calculations of the excited states. These insights hold substantial promise for the strategic design of advanced photocatalytic materials. The obtained results provide a base for subsequent analyses, facilitating the determination of heightened surface reactivity, photostimulated water splitting, and antibacterial properties.

1. Introduction

In recent decades, heterogeneous photocatalysis has emerged as a promising pathway for advancing green technologies, particularly in the domains of photocatalytic water splitting, the degradation of hazardous organic pollutants, and the manifestation of robust antibacterial properties [1,2]. The comprehensive investigation underscores the significance of Ti$O_2$-based materials, attributing their appeal to environmentally benign attributes such as non-toxicity, stability, cost-effectiveness, and wide-ranging applicability [3,4,5,6,7,8,9,10,11,12,13,14,15]. Central to photocatalysis are mechanisms involving the generation of photogenerated charges, encompassing processes such as photo-induced charge separation, bulk and surface charge recombination, and surface charge reactions [16]. Subsequently, photogenerated electron–hole pairs engage with water, hydroxide groups, and molecular oxygen adsorbed on the Ti$O_2$ surface, yielding reactive oxygen species such as superoxide anions and hydroxyl radicals. These reactive oxygen species play a pivotal role in oxidation reactions that detrimentally affect the cell membranes, ribonucleic acid (RNA), deoxyribonucleic acid (DNA), proteins, lipids, and other cellular components, ultimately causing the demise of microorganisms [17,18].

Despite the numerous merits of Ti$O_2$, its wide band gap (ranging from 3.0 to 3.2 eV [19]) limits efficient photoabsorption in the visible light region of the solar spectrum. To overcome this, integrating 3d metal dopants, such as copper [3,4,16,20], into Ti$O_2$ has shown promise in boosting both its photocatalytic and antibacterial capabilities [21,22,23]. Copper introduces improvements by mitigating electron–hole pair recombination, thereby extending the lifespan of electrons and concurrently improving the photoresponse under visible light irradiation [18].

Although titanium dioxide has been the subject of wide experimental [9,24,25,26,27,28,29,30] and theoretical [31,32,33,34,35] investigations, the full scope of its photocatalytic and antibacterial properties, as well as their potential enhancements, remains an open field for exploration. State-of-the-art spectroscopy can analyze electronic structure at the atomic scale, including binding energies [36,37] and imaging reaction sites [38]. Nevertheless, the technology for synthesizing photocatalysts is still in need of improvement. From an experimental standpoint, measuring the absorption spectra of photocatalysts offers insights into solar energy utilization efficiency [36,37,39,40].

Experimentally probing photon-induced electron transitions in single atoms or small clusters on semiconductor surfaces holds great promise, yet it is notably challenging, largely due to various constraints [4]. However, the swift advancement in computer technologies and the growing capabilities of supercomputers have globally opened new avenues for theoretical studies. These studies leverage quantum chemistry and density functional theory (DFT) as important tools for exploring charge transitions and photoabsorption at an atomic level. Time-dependent DFT (TDDFT) is an extension of density functional theory (DFT). The integration of TDDFT with the linear combination of atomic orbitals (LCAO) method has enabled simulations of structures comprising up to hundreds of atoms [41,42,43]. While DFT focuses on ground-state properties, TDDFT allows for the study of excited states and time-dependent phenomena. This approach achieves a balanced compromise between accuracy and computational efficiency. Moreover, the time propagation feature in LCAO TDDFT allows for the effective breakdown of Kohn–Sham wave functions. This breakdown is instrumental in representing transition states at specific energy levels. It could be used to simulate how electronic systems evolve over time under various conditions, such as in response to an external electromagnetic field providing a practical means to present the transition behavior from occupied to unoccupied Kohn–Sham orbitals [41,42,43,44].

Recent literature reviews [36,37,39] highlight the advantageous effects of noble metal clusters on the Ti$O_2$ surface, significantly boosting absorption in the photon spectrum ranging from visible to ultraviolet light. This enhancement of the absorption is primarily attributed to electron transitions within these noble metal clusters, which lead to the formation of excited states in the system. In the realm of TDDFT, the ground states are usually consistent with either structures that are optimized or those that represent minimal interactions among the components on the surface, as indicated in references [39,45]. However, there are geometric configurations that are close to the minimum energy of equilibrium models and that still fulfill the criteria for convergence in DFT calculations. Although the absorption spectrum might display similarities across different geometries, variations in the electronic orbitals due to such different geometries could cause noticeable differences in the localization patterns of the transitions [23].

In this paper, we perform the first-principles analysis of the optical absorption characteristics of Cu-doped anatase Ti$O_2$ surfaces, with a focus on the (101) and (001) surface terminations. The (101) and (001) surfaces of anatase Ti$O_2$ are the most thermodynamically stable and reactive surfaces, respectively. The (101) surface, being the most stable, is commonly observed in naturally occurring and synthetic anatase Ti$O_2$ particles. Its stability is crucial for applications that require long-term durability. The (001) surface, on the other hand, exhibits higher reactivity, making it particularly interesting for catalytic applications. The distinct properties of these surfaces influence the interaction with dopants like Cu, potentially altering the electronic structure and enhancing the material’s photocatalytic efficiency [10]. The study aims to predict and analyze the electronic structure of Cu-doped Ti$O_2$ surfaces and involves examining how the presence of copper dopants affects the electronic states and energy levels at the Ti$O_2$ surface; to examine the optical absorption properties of these structures to understand how the introduction of copper atoms affects the material’s ability to absorb light, particularly in the visible spectrum, which is crucial for photocatalytic applications; as well as to identify and discuss the crucial transition states and their implications for advanced photocatalytic material development. These states are important for understanding the behavior of photogenerated electrons in the presence of copper atoms and for the development of future photocatalytic materials.

2. Computation Details

The calculations in this study were performed using GPAW software [46,47], along with the Atomic Simulation Environment (ASE) library [48]. The electronic configurations of valence electrons for oxygen, titanium, and copper were specified as O$\left(2s^{2}2p^4\right)$, Ti$\left(3s^{2}3p^{6}3d^{2}4s^2\right)$, and Cu$\left(3d^{10}4s^1\right)$, respectively. Specifically, oxygen atoms were analyzed using the default Projector Augmented-Wave (PAW) dataset, version 0.9.20000, and the double-$\zeta$ polarized (dzp) basis sets provided in the GPAW package. To ensure precise modeling of absorption processes, both titanium and copper atoms were treated using the optimized double-$\zeta$ basis sets (p-valence) [49,50]. A critical aspect of these basis sets is their construction: for p-valence, the Gaussian polarization function, typically seen in dzp, is replaced with a bound, unoccupied p-type orbital and a split-valence wave function, providing a more accurate representation of the atomic orbitals.

The study is focused on a detailed examination of the pristine anatase TiO₂ surfaces, specifically the (101) and (001) facets. The (101) surface, consisting of 72 atoms (24 titanium and 48 oxygen atoms, slab thickness 9.2 Å), and the (001) surface, with 108 atoms (36 titanium and 72 oxygen atoms, slab thickness 9.1 Å), were modeled by slicing the bulk anatase crystal along the (101) and (001) directions. For the (101) surface, two distinct models were conceptualized (as shown in Figure 1b,c), due to variations in the positions of atoms used to cut the boundary in the x direction. To simulate an infinite surface, the periodic boundary conditions were applied in the x and y directions, while a substantial vacuum gap of 15 Å was introduced along the z direction to avoid interactions between the surfaces of the slab.

The vacuum gap of 15 Å has been kept fixed during the atomistic optimization procedure.

Structural optimization was performed using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm, which is widely used in numerical optimization, particularly for solving unconstrained nonlinear optimization problems [51]. It belongs to a class of iterative methods known as quasi-Newton methods, which are designed to find local minima or maxima of functions. At each step, it uses the gradient (first-order derivatives) of the function and an approximate inverse Hessian matrix to determine the next point to evaluate, without the need to compute the Hessian matrix (second-order partial derivatives of the function) directly. The key feature of BFGS is its way of updating the inverse Hessian matrix. It uses information from the gradient to refine this approximation at each step, making it more efficient than calculating the true Hessian.

For optimizing atomic coordinates, a grid-spacing parameter of 0.2 Å and the Perdew–Burke–Ernzerh (PBE) [52] exchange-correlation functional were employed to evaluate electronic densities and potentials. The k-point meshes, critical for sampling the Brillouin zone, were set at $3\times 3\times 1$ following the Pack–Monkhorst scheme. The optimization process was deemed complete when the maximal force on any atom was reduced to below 0.05 eV/Å.

For the electronic structure’s ground state calculations, the linear combination of atomic orbitals (LCAO) method was utilized [53], incorporating the Gritsenko–van Leeuwen–van Lenthe–Baerends orbital-dependent functional, meaning it explicitly uses information from the Kohn–Sham orbitals, with a solid-state modification (GLLB-SC) [54]. One of the key advantages of the GLLB-SC functional is its ability to correct the self-interaction error, a common challenge in many traditional DFT functionals. Due to its strengths in band gap prediction and treatment of exchange-correlation energy, this functional is widely used in the study of the electronic properties of materials. The GLLB-SC functional also is computationally more efficient than many-body perturbation theories like GW approximation, making it a practical choice for larger systems [55]. To model dynamic electronic behavior, real-time propagated wave functions were generated for the surface models by applying a weak $\delta$-kick of a dipole electric field in each Cartesian coordinate direction (x, y, and z). The propagation spanned 1500 time steps, each lasting 20 attoseconds, summing up to a total duration of 30 femtoseconds. The resulting time-dependent dipole moments were then transformed via Fourier analysis to create the absorption spectrum, utilizing Gaussian function broadening with a parameter $\eta =0.07$ eV. The difference in absorption in the x–y and z directions stems from the reduced periodicity along the (z direction of the chosen multi-slab model). The visualization of pseudo-wave functions was conducted using VESTA software [56], and for comprehensive data analysis and the generation of graphical representations, Python’s NumPy [57] and Matplotlib [58] packages were employed.

3. Results and Discussion

3.1. Pristine Surfaces

Computing the band gap of Ti$O_2$ with the GLLB-SC functional provides a more accurate representation of titanium’s d-orbitals. However, this method, which samples reciprocal space only at the Gamma point due to GPAW code constraints, can underestimate the band gap compared to experimental data and more comprehensive k-point sampling using the GLLB-SC functional. To address the noted discrepancy, the Hubbard DFT+U scheme is applied, enhancing the representation of localized electrons. The DFT+U methodology augments the standard DFT Hamiltonian with an additional term, known as the Hubbard U parameter [59]. This U term serves as a correction factor, specifically targeting the on-site Coulomb interactions among electrons in localized states, such as d- or f-orbitals. Its primary function is to impose an energy penalty on these systems when they exhibit fractional electron occupations. This penalty is designed to more accurately reflect the energetic cost associated with electron localization. In the context of this study, the adjustment of the Hubbard $U_{Ti\left(d\right)}$ parameter for titanium d-orbitals to 4.2 eV is implemented as recommended by Tritsaris et al. [60].

Table 1. The band gap (in eV) calculated for (101)- and (001)-terminated pristine nanofilms of anatase TiO₂ with and without applied $U_{Ti\left(d\right)}$.

	${\mathit{U}}_{\mathit{Ti}\left(\mathit{d}\right)}=0$ eV	${\mathit{U}}_{\mathit{Ti}\left(\mathit{d}\right)}=4.2$ eV
TiO2 (101) surface type A	3.32	4.18
TiO2 (101) surface type B	3.31	4.17
TiO2 (001) surface	2.55	3.39

illustrates the variance in the band gap for TiO₂ (101) and (001) surfaces, both with and without the application of the $U_{Ti\left(d\right)}$ parameter. Generally, instances where the Hubbard correction is applied exhibit larger band gaps compared to those without the $U_{Ti\left(d\right)}$ adjustment. On TiO₂ surfaces, the Hubbard correction induces a more pronounced localized attraction among electrons, effectively broadening the band gap.

Further, the electronic structure, specifically the density of states (DOS) for each case shown in Table 1, is graphically represented in Figure 2. The experimentally measured band gap for anatase TiO₂ is 3.2 eV. In comparison with these theoretical findings, the band gap of the TiO₂ (101) surface with the Hubbard correction tends to overestimate this value, while the TiO₂ (001) surface without the Hubbard correction underestimates it. This discrepancy can be attributed to surface dangling bonds, as discussed by Deng et al. [61], which introduce additional states between the valence band maximum (VBM) and the conduction band minimum (CBM) that are absent in the bulk phase. Moreover, the Ti$O_2$ (101) surface, having a reduced atomic count, presents fewer states, in contrast to the densely populated Ti$O_2$ (001) surface.

The DOS calculated for the Ti$O_2$ (101) surface shows distinct variations when comparing type A and B surfaces, both at $U_{Ti\left(d\right)}$ = 0 eV and 4.2 eV. For type A with $U_{Ti\left(d\right)}$ = 0 eV (Figure 2a), the DOS shows a baseline electronic structure that is significantly altered when $U_{Ti\left(d\right)}$ is increased to 4.2 eV (Figure 2b), indicating a shift in energy levels with the introduction of new states due to the potential applied. Similarly, for type B surfaces, the change in $U_{Ti\left(d\right)}$ from 0 (Figure 2c) to 4.2 eV (Figure 2d) reflects in the DOS due to the inherent differences between surface types A and B. These differences manifest in the energy distribution of states, the presence or absence of specific peaks, and the overall shape of the DOS curves. The DOS for the Ti$O_2$ (001) surface at $U_{Ti\left(d\right)}$ = 0 eV (Figure 2e) and 4.2 eV (Figure 2f) provides a basis for comparison with the (101) surfaces. The (001) surface exhibits distinct electronic characteristics that are reflected in its DOS profile. The impact of applying $U_{Ti\left(d\right)}$ = 4.2 eV to the (001) surface offers insights into how different crystal orientations respond to electronic modifications. This comparison highlights the complexity and variability of the electronic structure in Cu-doped Ti$O_2$ surfaces, emphasizing the importance of DOS analysis in understanding material properties for photocatalytic applications.

Applying the Hubbard correction to the band gap calculations for pure TiO₂ (101) surfaces, both types A and B (Figure 1b,c), affects their absorption spectra, leading to band gap increase. The absorption spectra of pure TiO₂ (101) surfaces with and without Hubbard correction are illustrated in Figure 3. When the Hubbard U parameter for titanium d-orbitals $U_{Ti\left(d\right)}=4.2$ eV is incorporated, the resulting optical absorption spectrum shows a red shift compared to neglect of the Hubbard correction. Interestingly, despite these adjustments, our analysis reveals that there is no significant difference in the absorption characteristics between the TiO₂ surfaces with and without the Hubbard correction [23,62,63]. This finding suggests that the Hubbard correction does not markedly alter the absorption properties of these surfaces, at least within the range of our study. To ensure a consistent approach in our study, we have opted to calculate the electronic structures of both pure and doped TiO₂ surfaces using the Hubbard correction $U_{Ti\left(d\right)}$ equal to 4.2 eV. This consistency in methodology allows for a more accurate comparison and understanding of the electronic properties across different TiO₂ surface configurations.

3.2. Doped Surfaces

Experimental strategies for doping Ti$O_2$ include the hydrothermal method, sol-gel method, co-precipitation method, and electrochemical anodization method. Computational simulation, particularly using DFT and classical molecular dynamics, is also a promising alternative method for studying metal doping in Ti$O_2$ nanotubes [64]. Doping in Ti$O_2$ is primarily done to improve its photocatalytic properties by modifying its electronic structure [65]. Research has focused on doping Ti$O_2$ with transition metals and non-metals to lower the threshold energy for photoexcitation [66]. Various modification strategies for Ti$O_2$ doping include constructing heterojunctions [67]. Metal-doped Ti$O_2$ has shown enhanced photocatalytic activity for dye degradation compared to undoped Ti$O_2$ [68]. In this study, internal positions of Cu in the (101) surfaces of titanium were not considered primarily due to the focus on surface doping effects and their direct impact on the photocatalytic properties of Ti$O_2$. The preference for doping Cu at the surface positions, especially in the (001) surfaces, is based on the significant influence these positions have on enhancing optical absorption and photocatalytic efficiency. Surface doping, particularly in the configuration where Cu substitutes Ti in the surface layer, introduces new mid-gap states that are crucial for lowering the band gap and enhancing light absorption below the band gap of the pure surface. This is particularly important for applications like water splitting and hydrogen production, where efficient light absorption and charge carrier separation are critical. In contrast, internal doping positions might not offer the same level of interaction with incident light or the same degree of influence on the electronic structure at the surface, which is where the photocatalytic reactions predominantly occur. Therefore, this theoretical investigation emphasizes surface doping strategies that directly modify the surface properties of Ti$O_2$ to optimize its photocatalytic performance.

For the copper-doped TiO₂ (101) surface based on the models of types A and B, the DOS is illustrated in Figure 4. When a copper atom is introduced onto the TiO₂ (101) surface using both type A and B models, the resulting changes in the DOS are not significantly different. We observe the formation of mid-gap states caused by the doped Cu atoms that emerged between the original VBM and CBM of the TiO₂ (101) surface.

Table 2. The band gap width ($E_g$ in eV) and position of defect induced levels in the in-gap state with respect to the top of the valence band ($\delta$ in eV) as calculated for (101)- and (001)-terminated Cu-doped nanofilms of anatase TiO₂.

	$E_{\mathit{g}}$	$\mathit{\delta }$
TiO2 (101) surface type A	3.97	0.75
TiO2 (101) surface type B	4.00	0.77
TiO2 (001) surface type I	3.32	0.33
TiO2 (001) surface type II	3.15	0.41
TiO2 (001) surface type III	3.17	0.27
TiO2 (001) surface type IV	3.25	0.30

lists positions of levels induced by defects with respect to the top of the valence band as well as the calculated band gap width. Factors contributing to the formation of mid-gap states in Cu-doped Ti$O_2$ surfaces include the localized electronic states of the doped Cu atoms and their interactions with the Ti$O_2$ lattice. The presence of Cu atoms between the original VBM and CBM of the Ti$O_2$ surface leads to the formation of mid-gap states, which are caused by the doped Cu atoms and result in increased absorption below the original band gap of the undoped surface, particularly in the x direction. These mid-gap states are crucial for enhancing the absorption in the visible light regions, which is essential for photocatalytic applications. The absorption spectrum of the doped and undoped TiO₂ (101) surfaces for both types A and B is demonstrated in Figure 5. The presence of doped Cu atoms leads to increased absorption below the original band gap of the undoped surface, with the most significant difference observed in the x direction. Additionally, we find that the absorption effect is more pronounced in type A surfaces with Cu doping.

In Figure 6, the DOS for the doped TiO₂ (001) surface is depicted, utilizing four distinct models that differ in the arrangement of the copper atom, which is incorporated in place of titanium. Models I and IV feature copper incorporation in the Ti position within the surface layer of the TiO₂ (001) slab, while models II and III incorporate copper in the subsurface layers.

Models of types I to IV exhibit minimal discrepancies in DOS around the VBM. Table 2 lists positions of defect induced levels with respect to the top of the valence band as well as the calculated band gap width. The pristine TiO₂ (001) surface’s VBM edge is characterized by well-defined oxygen states. When examining Cu dopant positions at the top (type I) and bottom (type IV) of the slab, we note the absence of additional states between Cu states and these sharp oxygen states, in contrast with types II and III when Cu is incorporated inside in subsurface layers. The additional tiny oxygen states appear to be split from the original sharp O states of the pure TiO₂ (001) surface.

To understand the impact of this doping, we also examined the absorption spectrum of the doped TiO₂ (001) surface, as illustrated in Figure 7. Similar to the phenomena observed on the (101) surface, the doped Cu atom also induces increased absorption below the original band gap of the pure surface. However, a notable distinction for the TiO₂ (001) surface is that the enhancement in absorption is not confined to the x direction; it extends to the y and z directions as well. The observed slight red shift in the calculated absorption spectra aligns with our recent theoretical investigation involving Cu, Ag, and Au adatoms deposited onto the rutile Ti$O_2$ (110) surface [23]. In cases where the noble metal adatom is not strongly bonded to the surface oxygen or other nearest host surface atoms, the calculated electronic structure of the pristine rutile Ti$O_2$ (110) surface closely resembles that of the surface with an attached adatom. This similarity arises from the contribution of the d-orbital of the noble metal adatom, which plays a role in hybridizing the surface states. Specifically, the sp-orbitals of the adatom overlap with orbitals at the conduction band of the pristine Ti$O_2$ surface. This hybridization pattern closely mirrors that predicted for Cu-doped anatase Ti$O_2$ surfaces in the current study (see Figure 4 and Figure 6). Consequently, the process of depositing adatoms on the rutile Ti$O_2$ surface, as well as Cu-doped anatase thin films, can induce localized effects in the optical spectrum.

Considering the absorption properties, three distinct types of transitions can arise from a doped or adsorbed Cu atom. Firstly, the most pronounced enhancement of absorption occurs during the transition from the occupied sp-orbitals of Cu to the unoccupied states of the host nanofilm’s surface. These transitions result in Cu-induced charge transfer to the Ti$O_2$ surface, closely resembling the optical signatures near the resonance peak of a single Cu atom at approximately 4.8 eV [23]. Secondly, there are transitions from the occupied Cu d-orbitals to the unoccupied states of the Ti$O_2$ nanofilm. Given the sufficiently short bond length between Cu and surface oxygen, the optical response of a single Cu atom becomes indistinct or may even be dispelled. Consequently, the occupied Cu d-orbitals introduce new transition states at relatively low energies. Thirdly, transitions arise from the occupied states of Ti$O_2$ to the unoccupied Cu sp-orbitals. Due to the odd number of Cu electrons, a single occupation occurs at the sp-orbitals. This results in the photogenerated electrons of Ti$O_2$ accumulating around the Cu atom. The predicted broader absorption profile underscores the influence of copper doping on the optical properties of TiO₂ surfaces, highlighting the crucial role of surface orientation and doping in modulating the material’s absorption characteristics.

In the context of dissociation by photogenerated electrons, this study introduces an alternative strategy that addresses not only enhancements in light absorption but also considerations regarding the final state of electron transitions. It is crucial to comprehend the transition behavior for various deposited elements on the surface, as this understanding plays a pivotal role in harnessing the solar spectrum for future photocatalysts.

It also should be noted that states in the band gap were predicted recently for another promising photocatalytic material used for water splitting and hydrogen production—SrTi$O_3$ nanoparticles doped with Al impurities [69]. These first-principles calculations have shown that Al-induced states serve as hole traps, thus reducing recombination of mobile electrons and holes and respectively increasing the hydrogen production yield. This prediction indeed was confirmed experimentally [70]. In light of these findings, it is reasonable to hypothesize that a similar mechanism might be at play in the case of Ti$O_2$ doped with Cu. This process likely involves carrier trapping, potentially leading to an increase in the efficiency of bacteria destruction. However, this hypothesis warrants further investigation, both theoretically and experimentally.

In summary, the copper doping in TiO₂ surfaces leads to the formation of mid-gap states and thus enhances optical absorption. Incorporating Cu in the surface layer is preferred, as it introduces new mid-gap states that enhance optical absorption below the band gap of the pure surface, which is crucial for photocatalytic applications. It also leads to a broader absorption profile, highlighting the role of surface orientation and doping in modulating the material’s light absorption characteristics for applications like water splitting and hydrogen production. It highlights the significance of the preferred doping position for enhancing the photocatalytic efficiency and broadening the application potential of Cu-doped Ti$O_2$ materials. The distinct absorption patterns for different surface orientations and types underscore the complex interplay between doping, surface structure, and optical properties.

4. Conclusions

The performed study presents a comprehensive analysis of the electronic structure and optical absorption characteristics of Cu-doped anatase Ti$O_2$ nanofilms, focusing on the (101) and (001) surface terminations. Through state-of-the-art computational methods, we have explored the impact of copper doping on the optical properties of the Ti$O_2$ surface.

The effect of copper-doped surfaces on titanium dioxide can be primarily assessed in terms of energy levels both below and above the band gap of the pure surface. Firstly, a notable enhancement in absorption is observed in both the copper-doped (101) and (001) surfaces for excitation energies below the band gap of the dopant-free surface. This enhancement is attributed to the introduction of new states by the doped Cu atom between the VBM and CBM of the pure surface. Additionally, since the electronic configuration of a single Cu atom occupies states, the TiO₂ surface with a doped Cu atom is conducive to increased absorption in the region below the band gap of the pure surface.

Secondly, doping the TiO₂ surface with copper results in a red shift in the optical absorption spectrum. Analyzing the DOS, it is evident that the doped copper atom brings new hybridizations at the VBM edges, particularly between copper and oxygen states. This hybridization results in smoother oxygen states around the VBM compared to the states of the pure surface, leading to a slightly red-shifted absorption. Additionally, the absorption peak associated with a single Cu atom is located at 4.8 eV [71]. Therefore, the combination of reduced oxygen states around the VBM and the resonance peak of copper contributes to this red shift, especially when the excitation energy surpasses the band gap of the pure surface.

Lastly, Ti$O_2$ nanofilms doped with transition metals like copper hold promise for enhanced photocatalytic and antibacterial properties, consistent with results published previously [72]. These enhancements are crucial, offering significant implications for public health by mitigating the spread of harmful microorganisms and presenting opportunities for the development of novel photocatalytic materials, particularly for applications such as water splitting and hydrogen production.