Effect of Vacancy Defects on the Electronic Structure and Optical Properties of Bi₄O₅Br₂: First-Principles Calculations

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This article is devoted to the study of the first-principle calculations of vacancy defects in Bi₄O₅Br₂ semiconductor. The Bi_mO_yX_n catalysts are promising for photocatalytic reduction of CO₂, decomposition of organic pollutants, selective oxidation of biomass processing products and some other applications. The study is carried out at a good level, the calculated results will be in demand in the synthesis and application of new photocatalysts. The work can be published in the journal Coatings after responding to the following remarks and comments:

- Bi₄O₅Br₂ and other Bi_mO_yX_n materials are effective for photocatalytic CO₂ reduction (ref. 5,6). CO₂ reduction is an important promising direction in photocatalysis. It is proposed to point this out in the introduction and add references.

- The article should be supplemented with more recent references of similar theoretical studies, e.g., Sheng H., et. al First-Principles Study of Electronic Structure and Optical Properties of Ni-Doped Bi4O5Br2 doi: 10.3390/coatings14010067

- formula 1: the definition of n is missing. In line 141 it is said “𝑖 represents the number of vacancy atoms in the perfect crystal (𝑖=1 in the work)” – it seems that i comprises different types of atoms and not their number. Please, check.

- what was the self-consistent field tolerance during the calculations?

- what was the accuracy of calculation of the a parameter? why the values for VO1 and VO2 are so different? why in the case of O2 the a value increases, and in the case of O1 it rapidly decreases? In line 120, the values for parameters a, b, c are different to those presented in line “Unit cell” in Table 1. Please, check.

- please, move formulas 2-6 and their description to experimental section.

- based on Figure 3, the formation of Bi-Br bonds cannot be excluded and should be discussed. In the literature, such bonds are considered effective channels for electron transfer in BiOBr systems.

- line 283: “Figure 4(c) shows that the calculated adsorption edge of intrinsic Bi₄O₅Br₂ is around 460 nm” – the figure does not directly show such data.

Author Response

Comments 1: Bi₄O₅Br₂ and other Bi_mO_yX_n materials are effective for photocatalytic CO₂ reduction (ref. 5,6). CO₂ reduction is an important promising direction in photocatalysis. It is proposed to point this out in the introduction and add references.

Response: Thank you for your insightful comments and suggestions. We appreciate your observation regarding the effectiveness of Bi₄O₅Br₂ and other BimOyXn materials in photocatalytic CO₂ reduction, which is indeed a promising direction in photocatalysis. In response to your recommendation, we have expanded the introduction to highlight the significance of Bi₄O₅Br₂ in photocatalytic CO₂ reduction and have added references to the latest theoretical research on Bi₄O₅Br₂ applications have been included:

1. Yang W J, Sun K L, Wan J, Ma Y A, Liu J Q, Zhu B C, Liu L, Fu F. oosting Holes Generation and O₂ Activation by Bifunctional Nicop Modified Bi₄O₅Br₂ for Efficient Photocatalytic Aerobic Oxidation. Applied Catalysis B: Environmental. 2023,320,121978. doi: 10.1016/j.apcatb.2022.121978.
2. Zhao, L Y, Fang W L, Meng X C, Wang L, Bai H C, Li C H. In-Situ Synthesis of Metal Bi to Improve the Stability of Oxygen Vacancies and Enhance the Photocatalytic Activity of Bi₄O₅Br₂ in H2 Evolution. Journal of Alloys and Compounds. 2022,910,164883. doi: 10.1016/j.jallcom.2022.164883.
3. Sun J M, Li X L, Li J M, Mu M, Yin X H. Fabrication of Bi₄O₅Br₂-Decorated Rod-Like Mof-Derived MoS2 Hierarchical Heterostructures for Boosting Photocatalytic CO2 Reduction. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 2022, 653, 129940. doi: 10.1016/j.colsurfa.2022.129940.
4. Dong X Z. Cui, X. Shi, P. Yan, Z. Wang, A. C. Co, and F. Dong. Insights into Dynamic Surface Bromide Sites in Bi₄O₅Br₂ for Sustainable N2 Photofixation. Angew Chem Int Ed Engl. 2022, 61(19), 937. doi: 10.1002/anie.202200937.

These references provide additional context for our study and help us discuss the potential applications of Bi₄O₅Br₂ in photocatalytic more comprehensively.

Comments 2: The article should be supplemented with more recent references of similar theoretical studies, e.g., Sheng H., et. al First-Principles Study of Electronic Structure and Optical Properties of Ni-Doped Bi4O5Br2 doi: 10.3390/coatings14010067

 Response: Thank you for your insightful comments and suggestions. We have taken your advice into consideration and have added more recent references to our manuscript, specifically focusing on similar theoretical studies. We have included the reference suggested by you: Sheng H., et al. "First-Principles Study of Electronic Structure and Optical Properties of Ni-Doped Bi₄O₅Br₂," Coatings 2024, 14(1), 67. doi: 10.3390/coatings14010067. This reference provides valuable insights into the electronic structure and optical properties of Ni-doped Bi₄O₅Br₂, which is closely related to our work. We have ensured that all new references are properly cited within the text and listed in the bibliography. We believe that the inclusion of these updated references strengthens our paper and provides a more comprehensive understanding of the topic.

Comments 3: formula 1: the definition of n is missing. In line 141 it is said “? represents the number of vacancy atoms in the perfect crystal (?=1 in the work)” – it seems that i comprises different types of atoms and not their number. Please, check.

Response: Agree. There is a problem of unclear expression of symbols in formula 1. We have made detailed modifications to this problem, and the modification results are as follows:

Defect formation energies are defined as [28, 29]:

                                      (1)

where E(defect) represents the total energy of the supercell in which the defect is formed, E(bulk) denotes the total energy of the bulk material, and  represents the chemical potentials. The chemical potential of the oxygen atom is represented by half the energy of an oxygen molecule. Here, i represents the different types of atoms, represents the number of vacancy atoms in the perfect crystal (i,n=1 in the work).

Comments 4: what was the self-consistent field tolerance during the calculations?

Response: Thank you for your inquiry regarding the self-consistent field (SCF) tolerance used in our calculations. We appreciate your attention to the computational details of our study.In response to your question, the SCF tolerance employed during our calculations was set to 1.0 × 10^-6 eV/atom. This value ensured reliable convergence of the SCF cycles, leading to accurate results in our computational simulations. In addition, we have added the following sentence to the manuscript calculation details section:  "The self-consistent field (SCF) calculations were performed with a tolerance of 1.0 × 10^-6 eV/atom to ensure convergence."

Comments 5: what was the accuracy of calculation of the a parameter? why the values for VO1 and VO2 are so different? why in the case of O2 the a value increases, and in the case of O1 it rapidly decreases? In line 120, the values for parameters a, b, c are different to those presented in line “Unit cell” in Table 1. Please, check.

Response: Thank you for your meticulous review and insightful questions regarding the details of our computational work. We have carefully examined each point and have made the following revisions and clarifications:

1. Accuracy of the Calculation of the 'a' Parameter: We have ensured that the calculation accuracy of the lattice parameter 'a' is very high, reaching an accuracy of 10^-6 Å, which is precise to three decimal places as presented in this paper.
2. Differences in Values for V_O1 and V_O2: The lattice parameters for V_O1 are indeed a=14.621 Å, b=5.660 Å, c=10.902 Å, and for V_O2, they are a=14.600 Å, b=5.647 Å, and c=10.943 Å. The differences in these values are primarily due to the distinct positions and bonding environments of oxygen atoms O1 and O2 within the unit cell, which lead to variations in the optimized lattice parameters after computational cell relaxation.
3. Variation in a Values for O2 and O1: The increase in the 'a' value for O2 and the rapid decrease for O1 can be attributed to the differential response of these atoms to the optimization process. O2, being in a different local chemical environment, experiences a distinct stress field that leads to an expansion along the 'a' axis. Conversely, O1 experiences a contraction due to the stronger covalent interactions and electron delocalization effects in its vicinity.
4. Inconsistency in Parameters a, b, c in Line 120 and Table 1: Upon reviewing the manuscript, we identified the discrepancy you pointed out. The values of parameters 'a', 'b', and 'c' in line 120 did not match those in the "Unit cell" row of Table 1. This inconsistency has been corrected, and the parameters in line 120 now accurately reflect the optimized values presented in Table 1.

Comments 6: please, move formulas 2-6 and their description to experimental section.

Response: Thank you for your valuable comments and suggestions. I appreciate your guidance on enhancing the clarity and structure of the manuscript. You have suggested moving formulas 2-6 and their description to the experimental section. I understand your intention is to ensure that the methods and theoretical calculations are clearly described and easily accessible for readers. In my manuscript, all the content is computational, and there is no experimental section present. However, to address your suggestion and improve the presentation of the paper, I have created a new section titled "Computational Methods" where I have included formulas 2-6 and their detailed descriptions. This section now provides a comprehensive overview of the theoretical framework and computational strategies employed in this study. I have made sure that all references to these formulas in the rest of the manuscript have been updated to reflect this change.

Comments 7: based on Figure 3, the formation of Bi-Br bonds cannot be excluded and should be discussed. In the literature, such bonds are considered effective channels for electron transfer in BiOBr systems.

Response: Thank you for your valuable comments on our work. The discussion you pointed out regarding the formation of Bi-Br bonds and their role in electron transfer in BiOBr systems is highly relevant. We acknowledge that this aspect has not been adequately explored in previous articles, and we apologize for this oversight. According to the literature, the formation of Bi-Br bonds is indeed considered an efficient mechanism for electron transfer in BiOBr systems. The crystal structure of BiOBr differs from that of Bi₄O₅Br₂. Typically, BiOBr exhibits a tetragonal structure with a space group of P4/nmm and lattice parameters of a=b=3.923A, c=8.105A. It possesses a layered structure consisting of two Br layers sandwiching quadrilateral [Bi₂O₂]²⁺ layers to form a [-Br-Bi-O-Bi-Br -] sandwich structure held together by van der Waals forces. On the other hand, Bi₄O₅Br₂ has a monoclinic crystal structure with a space group of P21 and a more complex arrangement. In this structure, there is an increased presence of both Bi and O atoms, resulting in the involvement of O 2p, Br 4p, and Bi 6p states at dispersed energy levels within valence and conduction bands. This configuration facilitates charge transfer. Regarding the influence of the Bi-Br bond on transport within the framework of Bi₄O₅Br₂'s structure, we will calculate its transmission spectrum using quantum transport computing software (ATK). Through analysis based on this transmission spectrum data, we aim to determine the specific role played by the Bi-Br bond in facilitating electron transport processes.

Comments 8: line 283: “Figure 4(c) shows that the calculated adsorption edge of intrinsic Bi₄O₅Br₂ is around 460 nm” – the figure does not directly show such data.

Response: Thank you for your helpful suggestion regarding the x-axis label in Figure 4. We have carefully considered your feedback and have made the following revisions to ensure clarity and consistency within our manuscript. In Figure 4, eV units are used for horizontal coordinates, while nm units are used in the paper. Although these two units have a conversion relationship of λ=hc/E, it is easy to cause confusion for reading. Considering that this value is not important in the paper, we deleted 460nm.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The reviewed paper presents DFT-based studies on the influence of selected point defects on the electronic structure and optical properties of Bi4O5Br2 semiconductor compound. The Authors analyse single vacancies of Bi, O, and Br atoms, taking into account possible various coordination of bismuth and oxygen atoms in the unit cell. The calculation results provide formation energies of the studied defect, the band structure of the defected compound, density of states function, effective mass of charge carriers, and the optical characteristics such as the dielectric function, absorption and reflection coefficients. These findings shed light on the photocatalytic performance of Bi4O5Br2 in the visible light range, which has an important technological aspect. However, I have some doubts about the model used for the research, and hence the provided results. Additionally, there are several issues that need to be improved, or clarified.

1.       The statement “ relatively negative conduction band position” in line 46 is unclear. Please reformulate this sentence.

2.       It is not written how big is the supercell used in calculations with respect to the primitive unit cell of Bi4O5Br2 compound? In other words, how many atoms there are in the primitive unit cell of pristine Bi4O5Br2, and how many atoms there are in the supercell model? Did you enlarge the primitive unit cell in a, b, c crystallographic direction by the same number? How many times?

3.       It is not clear what kind of lattice constants are there in Table 1, row 2. You reported experimental values in line 101 and first row of Table 2, the lattice constants after the geometry optimization (line 120/121), while those in Table 1 are different. This needs clarification and modification of the Table caption.

4.       Did you perform a preliminary test showing changes in the formation energy values of a vacancy atom introduced to the supercell versus the total number of atoms in the system? Please provide information about the results of such test and demonstrate that the formation energy of the defects remains stable for the supercell size used for calculations. This issue is crucial to justify the obtained band structure results.

5.       Please add information about the choice of chemical potentials of Bi and Br atoms after Equation (1); which structure was used to calculate their values?

6.       Reformulate the sentence in line 174: “Figure 2(b) illustrates the band structure of VO1”. In reality, this figure presents the band structure of the whole Bi4O5Br2 with the presence of VO1, instead of a single VO1. Such simplifications appear throughout the whole manuscript and they should be corrected.

7.       In my opinion, the reported bandgap values in lines 176/177 are wrong. The band gap value of the Bi4O5Br2 compound cannot be so drastically reduced by the presence of one vacancy in the supercell (from 2.38 to e.g. 0.75 eV). In reality, the vacancy level which appeared in the band gap should be non-dispersive, and the non-zero dispersion of the defect level shown in Fig. 2b, 2c is rather due to a small size of the supercells used in calculations. This issue requires deeper study.

8.       You use the statement “shallow energy level defects” in line 174. However, when the defect levels are located in the middle of the band gap, as it follows from Fig. 3, it is hard to call them "shallow". Please, reformulate the sentence.

9.       The statement “The band structure of the VBr defect” in line 190 should be reformulated.

10.   Equation (5): a notation of the photon energy should be corrected, as well as the superscript  in the second wave function.

11.   The static dielectric constant Epsilon is a dimensionless quantity contrary to what is written in line 273.

12.   Please, correct the description of the x-axis in Fig. 4 so that the physical quantity corresponds to its unit.

Technical remarks:

1.       Remove an extra full-stop in line 74 after Bi4O5Br2

2.       Correct two surnames in line 88

3.       Replace the word "One" with "one" in lower case in line 133

Comments on the Quality of English Language

Some minor language corrections should be done throughout the whole manuscript.

Author Response

Comments 1: The statement “ relatively negative conduction band position” in line 46 is unclear. Please reformulate this sentence.

Response: Thank you for your constructive feedback. We have revised the sentence as suggested to enhance clarity and precision. The revised sentence now reads: Among the various compositions in the BimOyXn system, Bi₄O₅Br₂, an n-type semiconductor photocatalyst, has attracted significant attention. This attention is due to its suitable band gap, tunable morphology, good chemical stability, and satisfactory performance in visible light-driven photocatalysis. Moreover, the conduction band (CB) of Bi₄O₅Br₂ has a negative position relative to Normal Hydrogen Electrode, which can effectively activate molecular oxygen to generate O^2- active groups.

Comments 2: It is not written how big is the supercell used in calculations with respect to the primitive unit cell of Bi4O5Br2 compound? In other words, how many atoms there are in the primitive unit cell of pristine Bi4O5Br2, and how many atoms there are in the supercell model? Did you enlarge the primitive unit cell in a, b, c crystallographic direction by the same number? How many times?

Response: Thank you for your meticulous review and for raising an important point regarding the unit cell used in our calculations. In response to your query, we would like to clarify the following details about the pristine Bi₄O₅Br₂ compound:

1. The primitive unit cell of Bi₄O₅Br₂ contains 16 bismuth (Bi) atoms, 20 oxygen (O) atoms, and 8 bromine (Br) atoms, totaling 44 atoms per unit cell.
2. Given the relatively large volume of the primitive unit cell for Bi₄O₅Br₂, we have not enlarged the primitive unit cell to construct a supercell for our defect models. Our calculations were performed directly using the primitive unit cell.

We hope this provides the necessary clarification. We appreciate your interest in our work and are grateful for the opportunity to address your questions.

Comments 3:    It is not clear what kind of lattice constants are there in Table 1, row 2. You reported experimental values in line 101 and first row of Table 2, the lattice constants after the geometry optimization (line 120/121), while those in Table 1 are different. This needs clarification and modification of the Table caption.

    Response: Thank you for your meticulous review. After carefully checking our computational data, we discovered an error in the values listed in line 120. We have made the necessary corrections to ensure consistency with the content of the second row in Table 1.

Comments 4:    Did you perform a preliminary test showing changes in the formation energy values of a vacancy atom introduced to the supercell versus the total number of atoms in the system? Please provide information about the results of such test and demonstrate that the formation energy of the defects remains stable for the supercell size used for calculations. This issue is crucial to justify the obtained band structure results.

Response: Thank you for your insightful comments and for bringing attention to the importance of vacancy formation energy in our calculations. We understand the significance of ensuring that the supercell size used in our calculations is appropriate and does not affect the accuracy of the formation energy values for the defects.

Following your suggestion, we conducted additional preliminary tests to study the stability of the defect model after the introduction of vacancy defects. We considered different sizes of supercells and calculated the formation energy in each case to ensure its stability.

The formation energy (Ef) of a vacancy is calculated using the formula:

where E(defect) represents the total energy of the supercell in which the defect is formed, E(bulk) denotes the total energy of the bulk material, and  represents the chemical potentials，i represents the different types of atoms, represents the number of vacancy atoms in the perfect crystal.

In order to ensure the stability of the formation energy, we tested the different size of the supercell. The results show that with the increase of the supercell, the defect structure can exist stably, and the defect formation energy changes little, indicating that the size of the supercell does not have a significant effect on the defect formation energy. In addition, we listed the formation energy data of the defect model in Table 2.

Comments 5:      Please add information about the choice of chemical potentials of Bi and Br atoms after Equation (1); which structure was used to calculate their values?

Response: Thank you for your valuable feedback and for giving us the opportunity to clarify the details regarding the choice of chemical potentials for Bi and Br atoms in our manuscript.

In response to your request, we have now included additional information after Equation (1) regarding the selection of chemical potentials for Bi and Br atoms. The chemical potentials were calculated based on the most stable structures of the respective elements in their standard state. For Bi, we considered the rhombohedral structure, and for Br, we used the molecular form (Br₂) as the reference state.

The chemical potentials (μ) were determined using the following approach:

For Bi:   μ_Bi=μ_{Bi, rhombohedral}=

For Br:   μ_Br=μ_{Br2, molecular}=

Where EBi, rhombohedral​ and EBr2, molecular​ are the total energies of the rhombohedral Bi and molecular Br₂, respectively, calculated using density functional theory (DFT) within the generalized gradient approximation (GGA). The values natoms in the formula unit​ and n_Br atoms in Br2​ represent the number of atoms in the formula unit for Bi and Br₂, respectively. We have added this information after Equation (1) in the manuscript to provide clarity on the methodology used to determine the chemical potentials.

Comments 6:     Reformulate the sentence in line 174: “Figure 2(b) illustrates the band structure of VO1”. In reality, this figure presents the band structure of the whole Bi4O5Br2 with the presence of VO1, instead of a single VO1. Such simplifications appear throughout the whole manuscript and they should be corrected.

Response: Thank you for your careful reading of our manuscript and for pointing out the need for clarification in the sentence mentioned. We understand your concern and agree that it is important to accurately represent the content of the figures and the context in which they are presented. To streamline the representation of the defect model, we have indicated in lines 116-118 that 'V' signifies the defect model and the subscript represents the type of defective atom. Consequently, V_O1 denotes the overall Bi₄O₅Br₂ system with an O₁ defect. In Figure 2(b), V_O1 is used to represent the band structure of Bi₄O₅Br₂ that contains an O₁ defect. We appreciate your guidance in helping us improve the clarity and accuracy of our manuscript.

Comments 7:      In my opinion, the reported bandgap values in lines 176/177 are wrong. The band gap value of the Bi4O5Br2 compound cannot be so drastically reduced by the presence of one vacancy in the supercell (from 2.38 to e.g. 0.75 eV). In reality, the vacancy level which appeared in the band gap should be non-dispersive, and the non-zero dispersion of the defect level shown in Fig. 2b, 2c is rather due to a small size of the supercells used in calculations. This issue requires deeper study.

Response: Thank you for your review comments on the band gap value of Bi₄O₅Br₂ in our paper. The point you made about the possibility of an error in the band gap value is important, and we recognize that introducing a vacancy defect in a semiconductor material does not generally reduce the band gap significantly. Band gap width is a basic physical property of semiconductor materials, which is closely related to the electronic structure and chemical composition of the material. Vacancy defects may introduce local states in the band gap that can act as traps for electrons or holes and thus affect the optical properties of the material, but they usually do not significantly change the band gap width itself, and a significant reduction in the band gap value after the introduction of a defect may not be justified, especially if only one vacancy is introduced in the supercell. Therefore, we have corrected the band gap value in the manuscript.

Comments 8:       You use the statement “shallow energy level defects” in line 174. However, when the defect levels are located in the middle of the band gap, as it follows from Fig. 3, it is hard to call them "shallow". Please, reformulate the sentence.

Response:Thank you for your careful review and insightful comment regarding the terminology used to describe the defect levels in our manuscript. We appreciate your expertise and agree that the term "shallow energy level defects" may not be the most accurate choice given the context of our findings. In response to your suggestion, we have revised the sentence in line 185 to better reflect the nature of the defect levels as presented in Figure 3. The new sentence now reads: "It can be concluded that the formation of defect energy levels is due to the introduction of oxygen vacancy defects, which disrupts the periodic potential field generated by the atomic arrangement."

Comments 9:       The statement “The band structure of the VBr defect” in line 190 should be reformulated.

Response: Thank you for your insightful review and constructive comments on our manuscript. We have carefully considered your suggestion regarding the statement on line 190.The original text: "The band structure of the V_Br defect" has been revised to: " The band structure of the V_Br is shown in Figure 2(d)" to provide clearer information and reference. We believe this amendment enhances the clarity and precision of our presentation regarding the band structure of the V_Br.

Comments 10:   Equation (5): a notation of the photon energy should be corrected, as well as the superscript  in the second wave function.

Response: Thank you for your insightful comments and suggestions on our manuscript. Upon your recommendation, we have carefully reviewed and amended Equation (5) as follows:

1. We have corrected the notation for the photon energy to ensure it is consistent with the standard notation used in the field.
2. Additionally, we have revised the superscript in the second wave function to match the notation used in our referenced literature.

We have cross-checked the revised equation with the formulas cited in our references to ensure accuracy and conformity with the established scientific conventions. The corrected equation now reads as:

We trust that these revisions meet the requirements and enhance the clarity of our presentation. We are grateful for the opportunity to improve our manuscript and appreciate your guidance.

Comments 11: The static dielectric constant Epsilon is a dimensionless quantity contrary to what is written in line 273.

Response: Thank you for your careful review and for pointing out the inconsistency regarding the static dielectric constant (ε) in our manuscript. You are correct that the static dielectric constant is indeed a dimensionless quantity, and we appreciate you bringing this to our attention. We acknowledge the error in line 273, where it incorrectly suggests that the static dielectric constant has units. We have corrected this mistake in the manuscript and have now properly represented the static dielectric constant as a dimensionless quantity. To ensure the accuracy of our work, we have also reviewed the entire manuscript and supporting information to confirm the consistent use of the static dielectric constant throughout.

Comments 12:   Please, correct the description of the x-axis in Fig. 4 so that the physical quantity corresponds to its unit.

Response: Thank you for your helpful suggestion regarding the x-axis label in Figure 4. We have carefully considered your feedback and have made the following revisions to ensure clarity and consistency within our manuscript. In Figure 4, eV units are used for horizontal coordinates, while nm units are used in the paper. Although these two units have a conversion relationship of λ=hc/E, it is easy to cause confusion for reading. Considering that this value is not important in the paper, we deleted 460nm.

Technical remarks:

1. Remove an extra full-stop in line 74 after Bi4O5Br2
2. Correct two surnames in line 88
3. Replace the word "One" with "one" in lower case in line 133

Thank you for your meticulous review and valuable suggestions on our manuscript. We have made the following corrections as per your technical remarks:

1. We have removed the extra full-stop after "Bi₄O₅Br₂" on line 74.
2. We have corrected the two surnames on line 88.
3. We have replaced the word "One" with the lowercase "one" on line 133.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

In the present paper, the effects of O and Br vacancy defects on the electronic and optical properties of Bi4O5Br2 have been investigated using ab initio state-of-the-art code. The modifications of the geometrical structure, the band structure and the optical spectra have been calculated and the related physics has been discussed.

The main finding is that three coordinated O vacancies give rise to high effective electron-hole pair mass ratio, and enhanced absorption and reflection coefficients in the visible-light spectrum.

The manuscript reports quite interesting results while using a sound approach. The findings are properly discussed.

The paper can be considered for publication once the following issues have been addressed:

1) The maximum of the valence band and the minimum of the conduction band are uniquely identified for the pristine Bi4O5Br2 (band structure in figure 2a), and the effective mass of electrons and holes is calculated according to equation (3). Regarding the band structures of the systems with vacancy defects (figures 2b-d), which occupied bands have been used as valence band to calculate the effective mass? Indeed, for V_O1 and V_O2 is possible to consider as valence band the defect band(s) just below the Fermi level, localized on Bi as calculated with PDOS, or the occupied band below the defect band(s) (indeed, there are two defect bands for V_O1 and one defect band for V_O2), delocalized on the crystal. Also, same question for the conduction band. Some ambiguity is also present for the metallic system V_Br with a semi-occupied conduction band (figure 2d). Indeed, the concept of effective mass is more functional for semiconductors.

2) One defect per unit cell has been introduced. Which is the defect density of the model? Which are typical defect densities in experiments? How much the model is able to capture the physics of the experiments?

3) For some weird mistake, the static dielectric constant values for Bi4O5Br2, V_O1, V_O2, and V_Br are expressed in eV (line 273 on page 8). The static dielectric constant is adimensional.

Comments on the Quality of English Language

English is quite good. Just minor editing is required.

Author Response

Comments 1: The maximum of the valence band and the minimum of the conduction band are uniquely identified for the pristine Bi4O5Br2 (band structure in figure 2a), and the effective mass of electrons and holes is calculated according to equation (3). Regarding the band structures of the systems with vacancy defects (figures 2b-d), which occupied bands have been used as valence band to calculate the effective mass? Indeed, for V_O1 and V_O2 is possible to consider as valence band the defect band(s) just below the Fermi level, localized on Bi as calculated with PDOS, or the occupied band below the defect band(s) (indeed, there are two defect bands for V_O1 and one defect band for V_O2), delocalized on the crystal. Also, same question for the conduction band. Some ambiguity is also present for the metallic system V_Br with a semi-occupied conduction band (figure 2d). Indeed, the concept of effective mass is more functional for semiconductors.

Response: Thank you for your questions about defect levels and bands near Fermi levels in our paper. The questions you ask are critical to understanding the electronic properties of the material.

In the defenceless Bi₄O₅Br₂, the valence band top and conduction band bottom are clearly distinguished, and the effective masses of the electrons and holes are calculated accordingly. However, in systems containing defects, especially in the presence of V_O1 and V_O2 defects, the band structure near the Fermi level becomes more complex. For these defects, we consider the following steps to determine the energy band used to calculate the effective mass:

1. Location of the defect level: We first determined the position of the defect level relative to the Fermi level. For V_O1 and V_O2, we find defect bands close to Fermi levels that are localized on Bi atoms, as shown in the PDOS calculations.
2. Determination of valence band and conduction band: for V_O1 and V_O2, we look for the maximum occupation band that exists right below Fermi level and defect level, and then regard it as valence band. For conduction bands, we take the opposite approach, looking for the minimum unoccupied band above the Fermi level.
3. Calculation of effective mass: After determining the valence and conduction bands, we calculate the effective mass of electrons and holes according to these energy bands. We use the appropriate effective mass formula, taking into account the non-parabolic properties of the bands, especially near the bands where the defects are introduced.
4. Treatment of metallic systems: We are particularly careful with V_Br systems that exhibit metallic properties because the Fermi level crosses the semi-occupied conduction band. In this case, we consider the band near the Fermi level as the conduction band and calculate the corresponding effective mass.

We recognize that in semiconductors containing defects, the band structure near the Fermi level can become complex, especially when the defect level intersects or approaches the Fermi level. In these cases, the traditional concept of effective mass may need to be revisited, and more complex models may be required to accurately describe the carrier's behavior.

Thank you again for your valuable comments and we look forward to your further guidance.

Comments 2: One defect per unit cell has been introduced. Which is the defect density of the model? Which are typical defect densities in experiments? How much the model is able to capture the physics of the experiments?

Response: Thank you for your questions regarding the defect density in our paper. The questions you have raised are crucial for understanding the physical properties of materials and experimental observations.

Firstly, we have developed a model that incorporates a defect in the unit cell, resulting in an exceptionally high theoretical defect density, surpassing what is typically observed in experiments. In reality，experimentally observed defect densities usually range from 10¹⁶ cm^-3 to 10²⁰ cm^-3, whereas our model demonstrates a higher defect density. However, this high-defect-density model aids us in comprehending the impact of individual defects on material properties at the atomic scale. With this model, we can meticulously study the local structure of defects, their electronic structure, and their interaction with surrounding atoms aspects that are challenging to directly observe through experiments.

To better capture physical phenomena observed during experiments, we will undertake supplementary work as follows:

1. Adjusting the defect density: We will introduce an appropriate number of defects into a larger supercell to simulate a defect density closer to experimental conditions.
2. Comparison with experimental data: We will gather relevant experimental data and compare it with our calculated results to verify the accuracy of our model.

We acknowledge that high defect densities in theoretical models may not directly reflect actual experimental conditions; however, such models serve as powerful tools for understanding how defects fundamentally affect material properties. By gradually reducing the defect density within our model simulation, we can better replicate and comprehend phenomena observed during experiments. This provides theoretical guidance for experimentation and supports further research on material design.

Once again, thank you for your valuable comments and we eagerly await your continued guidance.

Comments 3:  For some weird mistake, the static dielectric constant values for Bi4O5Br2, V_O1, V_O2, and V_Br are expressed in eV (line 273 on page 8). The static dielectric constant is adimensional.

Response: Thank you for pointing out this error in our paper. Indeed, we made a mistake in reporting the static permittivity of Bi₄O₅Br₂ and related defects, incorrectly expressing it as electron-volt (eV) units, when in fact the static permittivity is a dimensionless physical quantity that should not have any units. We have rechecked our calculations and made sure that the value of the static dielectric constant is dimensionless. We apologize for this oversight and thank you for pointing out this error. We have corrected this in the revised manuscript and ensured that all relevant discussions and conclusions are based on correct values for static dielectric constants. Thanks again for your careful review and valuable comments, we believe that after this amendment, our paper will be more accurate and reliable.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have revised their original manuscript and addressed some of the issues raised in the first review. Unfortunately, there are still places in the manuscript that have not been corrected or require further study. Therefore, the manuscript cannot be published in its present form.

1. The Authors did not correct two surnames related to PBE pseudopotential, line 93. Please check e.g. the original paper of these authors in order to correct them properly:

DOI:https://doi.org/10.1103/PhysRevLett.77.3865

2. The Authors explained in their answer that due the relatively large volume of the primitive unit cell for Bi4O5Br2, they have not enlarged the primitive unit cell to construct a supercell for calculations, and hence the calculations were performed directly using the primitive unit cell. This approach could be accepted provided that the Authors present the results of tests showing a stable formation energy of defects studied in the manuscript for different sizes of supercells. This problem was raised in my previous Comment 4, but the Authors did not show any results of such test, claiming only that “the defect formation energy changes little” in their test. Please, report separate data showing the formation energies of all studied defects versus the size of the enlarged supercell. Write explicite the accuracy of the formation energy. To confirm your statements I would like to see the corresponding band structures of the enlarged systems having one defect, in the area of the band gap. As I wrote previously, the dopant level shown in Figure 2 exhibits a dispersion, which can indicate that the cell size, chosen for calculations, is too small. Only then can I accept the selection of the appropriate unit cell’s size.

3. Equation (5) needs a correction concerning the wave function. Since the absorption process takes place between different quantum states |i> and |j> in the valence and conduction bands, it cannot be described by only one wave function, as it follows from your equation. Please refer to a textbook for further clarification.

4. The horizontal axis in Figure 4 is still wrongly described. An electronvolt is not a unit of frequency.  Please refer to a textbook for further clarification.

Author Response

Comments 1: The Authors did not correct two surnames related to PBE pseudopotential, line 93. Please check e.g. the original paper of these authors in order to correct them properly:

DOI:https://doi.org/10.1103/PhysRevLett.77.3865

Response: Thank you for your attention to detail and for pointing out the need for correction regarding the surnames associated with the PBE pseudopotential on line 93. Upon reviewing the original paper by the authors, we have made the necessary corrections to ensure accuracy in our citation. The surnames have been corrected to Perdew-Burke-Ernzerhof. We appreciate your thorough review and hope that this amendment addresses your concerns satisfactorily.

Comments 2: The Authors explained in their answer that due the relatively large volume of the primitive unit cell for Bi4O5Br2, they have not enlarged the primitive unit cell to construct a supercell for calculations, and hence the calculations were performed directly using the primitive unit cell. This approach could be accepted provided that the Authors present the results of tests showing a stable formation energy of defects studied in the manuscript for different sizes of supercells. This problem was raised in my previous Comment 4, but the Authors did not show any results of such test, claiming only that “the defect formation energy changes little” in their test. Please, report separate data showing the formation energies of all studied defects versus the size of the enlarged supercell. Write explicite the accuracy of the formation energy. To confirm your statements I would like to see the corresponding band structures of the enlarged systems having one defect, in the area of the band gap. As I wrote previously, the dopant level shown in Figure 2 exhibits a dispersion, which can indicate that the cell size, chosen for calculations, is too small. Only then can I accept the selection of the appropriate unit cell’s size.

Response: Thank you for your valuable comments. We have performed additional calculations based on your suggestion to test the effect of different supercell sizes on the defect formation energy. We understand your concern that smaller supercells could lead to mirror charge interactions, which could affect the energy and stability of the defect. Therefore, we expanded the size of the supercell and performed the following calculations. In the primitive unit cell of Bi₄O₅Br₂, there are 44 atoms. We first attempted to expand it to a 2×2×1 supercell, which would increase the number of atoms to 176, which is already the limit of our server's computational capacity. Despite applying for an extension for the revised manuscript, we ultimately only obtained the calculation results for the oxygen defect in the 2×1×1 and 2×2×1 supercells. These calculation results have been included in Table 1.

Table 1. Total energies and formation energies of Bi₄O₅Br₂ with vacancy.

The calculations show that as the volume of the supercell increases, the formation energy of the defects decreases. This finding is consistent with the literature discussions on the relationship between semiconductor defect stability and supercell size (DOI:10.7498/aps.73.20231960). Specifically, in the 2×1×1 supercell, the defect formation energy is smaller than that of the defects in the primitive cell, and in the 2×2×1 supercell, the formation energy is almost the same as that in the 2×1×1 supercell. This indicates that as the size of the supercell increases, the calculated defect formation energy tends towards a stable value, which helps us better understand the behavior of defects in real materials.

In addition, according to your requirements, we built the O₂ defect model of 2×2×1 supercell and optimized its structure. Then, we calculated the band structure of the model, and the calculation results are shown in the figure 1. The calculation results show that there are indeed defect levels near the Fermi level, which indicates that the defect levels shown in the band structure diagram in the manuscript are not the result of the interaction of the defect charge with its mirror charge. We believe that this can rule out the concerns you mentioned earlier about the possible small size of the supercell. We hope that this additional data and analysis will meet your requirements and prove that the size of the primitive cell we have chosen is feasible. We appreciate your guidance and look forward to your further feedback.

Figure 1. Band structure of O₂ defect model of 2×2×1 supercell

Comments 3: Equation (5) needs a correction concerning the wave function. Since the absorption process takes place between different quantum states |i> and |j> in the valence and conduction bands, it cannot be described by only one wave function, as it follows from your equation. Please refer to a textbook for further clarification.

Response: Thank you for your insightful comments regarding Equation (5). We appreciate your guidance on the need for a more accurate description of the wave function in the context of the absorption process between different quantum states |i> and |j> in the valence and conduction bands.

We have revised Equation (5) to better represent the transition between these states. The corrected equation is now:

ℏ

This formulation takes into account the contributions from all possible transitions between the valence and conduction bands, as suggested by your feedback.

We have also referred to relevant textbooks for further clarification and have ensured that our approach aligns with the standard theoretical framework in the field.

Comments 4: The horizontal axis in Figure 4 is still wrongly described. An electronvolt is not a unit of frequency.  Please refer to a textbook for further clarification.

Response: Thank you for your valuable feedback. We acknowledge that the description of the horizontal axis in Figure 4 was indeed misleading, as the electron volt (eV) is a unit of energy, not frequency. In the calculation of optical properties using Materials Studio software, although the horizontal axis is displayed as frequency (Frequency), what we intended to represent was the energy corresponding to the frequency. This representation is based on the relationship between the energy of a photon and its frequency, which is given by E=hν, where E is the energy, ν is the frequency, and h is the Planck constant.

To avoid confusion, we have changed the horizontal axis from "Frequency" to "Energy" in Figure 4, following the conventions of most academic journals. We believe that this modification will accurately convey our data and eliminate any potential misunderstandings.

We appreciate your patient guidance, and we hope that this correction meets your requirements.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have satisfactorily addressed the reviewers' comments. Therefore, I recommend publication of this manuscript.

Author Response

Thanks for the review's approval of the modification