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+title: "What Can ABACUS Do Too? | Research on the Multiple Hyperuniformity of High-Entropy Two-Dimensional Material MXene with More Than a Thousand Atoms"
+date: 2025-1-10
+categories:
+- ABACUS
+---
+
+Recently, doctoral student Yu Liu and Researcher Mohan Chen from the AI for Science Institute, Beijing and Peking University, used the domestic open-source density functional theory software ABACUS to conduct an in-depth study on the impact of multiple hyperuniform long-range order on the electronic properties of high-entropy two-dimensional material MXene. The two-dimensional materials optimized by density functional theory contain more than 1,500 atoms, indicating that ABACUS is suitable for handling large material systems. The relevant research results, titled "Multihyperuniformity in high-entropy MXenes", were published in Appl. Phys. Lett. 126, 013101 (2025) and were selected as Editor's pick by the editor (https://doi.org/10.1063/5.0246719).
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+
+## Research Background
+
+**MXene** is a new type of two-dimensional transition metal carbide (or nitride). Due to its unique two-dimensional structure, MXene exhibits excellent electrical conductivity, high capacitance, good mechanical properties, and hydrophilicity. Thanks to its outstanding performance, MXene has been widely studied in many application fields such as batteries, electromagnetic interference shielding, electrocatalysis, and supercapacitors. In 2021, the high-entropy strategy was extended to the design of MXene, further enhancing the tunability of the MXene structure. High-entropy MXene has great potential in energy storage and other fields due to its huge configurational space.
+
+Due to the difficulty in preparation, only a few high-entropy MXenes have been successfully synthesized so far. Considering that the strategy of combining the high-entropy concept with MXene is relatively new, the arrangement patterns of multiple transition metal atoms in high-entropy MXene remain unknown. Currently, the theoretical calculations of high-entropy MXene mainly adopt the random mixing method and the special quasirandom structure (SQS) model. These models essentially assume that different types of atoms in the MXene structure are randomly distributed at lattice sites. However, recent experimental studies have shown that the aggregation of the same type of transition metal atoms in MXene is inhibited. Atoms tend to have specific neighboring environments, which cannot be accurately captured by the random mixing method and the SQS model.
+
+Hyperuniformity[5] is a special type of long-range order, characterized by the vanishing of the static structure factor in the limit of infinite wavelength (or zero wave number), i.e.,
+
+<center><img src=https://dp-public.oss-cn-beijing.aliyuncs.com/community/Blog%20Files/ABACUS_10_01_2025/pic6.png pic_center width="10%" height="10%" /></center>
+
+where k is the wave number. Multiple hyperuniformity exists in multicomponent systems, where each component is hyperuniform, and thus the entire system is hyperuniform as a whole. To date, two examples of multiple hyperuniform systems have been reported, including the distribution of photoreceptor cones in the avian retina and high-entropy alloys. The emergence of multiple hyperuniformity in such systems is usually related to certain effective repulsive effects between the same kind of particles. Due to the similarity between high-entropy alloys and high-entropy MXene, a natural question arises: Can high-entropy MXene also be multiple hyperuniform in this case? To answer this question, the researchers conducted a comprehensive study on the multiple hyperuniformity of high-entropy MXene.
+
+## Research Results
+
+The researchers first adopted the image processing method[6] proposed by Jiao et al. to analyze the SEM image of the TiVCrMoC₃ high-entropy MXene experimental sample to detect the multiple hyperuniformity of the system. As shown in Figure 1(a), different types of transition metal atoms were identified, and their central positions were extracted and converted into point configurations. Figure 1(b) shows the static structure factors of all different types of transition metal atoms, indicating a weak power-law behavior α when k→0. The hyperuniformity exponents of different transition metal atom species are in the range of (0, 0.08), suggesting that high-entropy MXene is at least equivalently hyperuniform. The researchers noted that the SEM image may contain curved parts of the sample, reducing the degree of hyperuniformity obtained based on image analysis. The original sample may have a higher degree of hyperuniformity.
+
+<center><img src=https://dp-public.oss-cn-beijing.aliyuncs.com/community/Blog%20Files/ABACUS_10_01_2025/pic1.png pic_center width="60%" height="60%" /></center>
+
+*Figure 1 (a) Distribution of each type of transition metal atom and (b) static structure factor S(k) obtained by analyzing the SEM image [7] of the TiVMoCrC₃ high-entropy MXene experimental sample. The unit of the wave number k is 0.1 nm⁻¹.*
+
+As shown in Figure 2(a), the researchers constructed a multiple hyperuniform model and a random structure of a three-layer high-entropy MXene structure (TiVZrMo)₂C without terminal groups as simulation systems to study the multiple hyperuniformity of high-entropy MXene. As shown in Figure 2(b), the multiple hyperuniform model clearly exhibits a higher degree of hyperuniformity than the original experimental sample. The limited resolution of the SEM image, the curvature of the original experimental sample, and defects may lead to this difference. In contrast, the random structure shows an almost constant static structure factor, which is significantly different from that obtained from the analysis of the original experimental image. Therefore, the static structure factor characteristics of the original experimental sample are closer to those of the multiple hyperuniform model, indicating that it is a reasonable inference that the original experimental sample has multiple hyperuniformity.
+
+<center><img src=https://dp-public.oss-cn-beijing.aliyuncs.com/community/Blog%20Files/ABACUS_10_01_2025/pic2.png pic_center width="60%" height="60%" /></center>
+
+*Figure 2 (a) Top view (upper) and side view (lower) of the multiple hyperuniform model (left) and random mixing structure (right) of (TiVZrMo)₂C high-entropy MXene, containing a total of 1536 atoms. (b) Static structure factors S(k) of the multiple hyperuniform model and the random mixing structure. The unit of the wave number k is 0.1 nm⁻¹.*
+
+To further analyze the energy stability of the multiple hyperuniform high-entropy MXene, the researchers used ABACUS to calculate the total energies of the multiple hyperuniform structure and the random mixing structure systems. As shown in Figure 3, the energy per atom of the multiple hyperuniform structure is 8.1 meV lower than that of the random mixing structure, indicating that the multiple hyperuniform structure has higher energy stability than the random mixing structure. In addition, the calculation results show that the multiple hyperuniform structure exhibits a smaller Vegard's law deviation than the random structure. The researchers found that the distortion parameter Δh (0.613 Å) of the multiple hyperuniform structure is much smaller than that of the random structure (1.286 Å). The multiple hyperuniform structure shows significantly smaller lattice distortion and thus has a more stable energy state than the random mixing structure, which can be attributed to the suppression of density fluctuations.
+
+<center><img src=https://dp-public.oss-cn-beijing.aliyuncs.com/community/Blog%20Files/ABACUS_10_01_2025/pic3.png pic_center width="60%" height="60%" /></center>
+
+*Figure 3 Energy per atom E, width d, and distortion parameter Δh of the multiple hyperuniform and random structures of (TiVZrMo)₂C high-entropy MXene obtained by structural optimization using ABACUS. The width d represents the distance between the centers of two transition metal layers. The distortion parameter Δh is defined as the average width of the transition metal layer.*
+
+The researchers also studied the impact of multiple hyperuniform long-range order on the electronic structure of (TiVZrMo)₂C high-entropy MXene. Previous studies have shown that mechanical strain can affect the electronic properties of graphene, leading to the opening and closing of the bandgap, which is similar to the findings in high-entropy MXene. According to the PDOS in Figure 4, the DOS near the Fermi level mainly comes from the d orbitals of transition metal atoms, indicating that the electrical conductivity mainly comes from the contribution of outer d electrons. In addition, the d orbitals of transition metal atoms and the p orbitals of carbon atoms overlap between -6 and -3 eV below the Fermi level, indicating a strong hybridization between them.
+
+<center><img src=https://dp-public.oss-cn-beijing.aliyuncs.com/community/Blog%20Files/ABACUS_10_01_2025/pic4.png pic_center width="60%" height="60%" /></center>
+
+*Figure 4 Density of states (top) and projected density of states (bottom) of the multiple hyperuniform and random structures of (TiVZrMo)₂C high-entropy MXene. The Fermi level is shifted to 0 eV.*
+
+Finally, the researchers used the Bader charge analysis method to study the charge transfer of multiple atomic species in the multiple hyperuniform and random structures of (TiVZrMo)₂C high-entropy MXene. As shown in Figure 5, carbon atoms gain valence electrons, while transition metal atoms mainly lose d electrons. These electrons bond with the p electrons of C atoms, resulting in strong hybridization between them, which is consistent with the analysis results of the density of states.
+
+<center><img src=https://dp-public.oss-cn-beijing.aliyuncs.com/community/Blog%20Files/ABACUS_10_01_2025/pic5.png pic_center width="60%" height="60%" /></center>
+
+*Figure 5 Bader charge analysis of the multiple hyperuniform and random structures of (TiVZrMo)₂C high-entropy MXene. Δ𝑛 represents the average value of the change in the number of valence electrons, and σ represents the standard deviation of the valence electron numbers of different atoms of the same element.*
+
+The researchers found that the multiple hyperuniform long-range order has a significant impact on the charge transfer of (TiVZrMo)₂C high-entropy MXene. Taking Zr as an example, Δ (1.145) in the multiple hyperuniform structure is greater than Δ (1.100) in the random structure. The local aggregation of Zr in the random structure leads to a local atomic environment composed of Zr and C atoms. However, in the multiple hyperuniform structure, the multiple hyperuniform long-range order suppresses the local aggregation of the same kind of atoms, resulting in the presence of other transition metal atoms at the adjacent positions of Zr. Therefore, Zr atoms with the lowest electronegativity tend to lose additional valence electrons, which are then transferred to other types of adjacent transition metal atoms. Similarly, the charge transfer of other transition metals can be understood in the same way. In addition, the researchers used the standard deviation σ of the valence electron numbers of different atoms of the same element to measure the valence state fluctuations. Notably, σ in the random structure is greater than that in the multiple hyperuniform structure. The suppressed valence state fluctuations in the multiple hyperuniform structure can be attributed again to the multiple hyperuniform long-range order, as the local aggregation of the same kind of atoms is suppressed, leading to a more stable local atomic environment.
+
+
+## Conclusion
+
+This work proposed a multiple hyperuniform model of high-entropy MXene and conducted an in-depth first-principles large-system calculation study taking (TiVZrMo)₂C high-entropy MXene as an example. Due to the hidden long-range order, the multiple hyperuniform model has lower energy and smaller Vegard's law deviation compared to the existing random model. The SEM image analysis of the experimental sample shows that the transition metal atoms tend to be hyperuniformly distributed, which is consistent with the theoretical modeling results. In addition, the multiple hyperuniform structure shows significantly smaller lattice distortion, which has an important impact on the electronic properties (such as the density of states and charge distribution) of high-entropy MXene. The above work was supported by multiple projects of the National Natural Science Foundation of China.
+
+## References
+
+[1]Chen Mohan, Guo Guang-Cheng, He Lei, Systematically improvable optimized atomic basis sets for ab initio calculations, J. Phys.: Condens. Matter 22, 445501 (2010).
+
+[2]Li Peng, Liu Xin, Chen Mohan, Lin Peng, Ren Xin, Lin Lei, Yang Chao, He Lei, Large-scale ab initio simulations based on systematically improvable atomic basis, Computational Materials Science 112, 503 (2016).
+
+[3]Naguib M., Kurtoglu M., Presser V., Lu J., Niu J., Heon M., Hultman L., Gogotsi Y., Barsoum M.W., Two-Dimensional Nanocrystals Produced by Exfoliation of Ti₃AlC₂, Advanced Materials 23, 4248 (2011).
+
+[4]Nemani S.K., Zhang B., Wyatt B.C., Hood Z.D., Manna S., Khaledialidusti R., Hong W., Sternberg M.G., Sankaranarayanan S.K.R.S., Anasori B., High-Entropy 2D Carbide MXenes: TiVNbMoC₃ and TiVCrMoC₃, ACS Nano 15, 12815 (2021).
+
+[5]Torquato S., Stillinger F.H., Local density fluctuations, hyperuniformity, and order metrics, Phys. Rev. E 68, 041113 (2003).
+
+[6]Jiao Yang, Berman H., Kiehl T.-R., Torquato S., Spatial Organization and Correlations of Cell Nuclei in Brain Tumors, PLOS ONE 6, e27323 (2011).
+
+[7]He Xin, Qian Yang, Wu Chen, Feng Jun, Sun Xin, Zheng Qian, Li Xin, Shen Jun, Entropy-Mediated High-Entropy MXenes Nanotherapeutics: NIR-II-Enhanced Intrinsic Oxidase Mimic Activity to Combat Methicillin-Resistant Staphylococcus Aureus Infection, Advanced Materials 35, 2211432 (2023).