Current Science Research Bulletin

Density Functional Theory (DFT) is currently one of the most powerful and widely employed quantum mechanical methods in modern materials science, condensed matter physics, and computational chemistry. Due to its capability to accurately describe the electronic structure of materials at the atomic level with relatively moderate computational cost, DFT has become an essential theoretical framework for investigating a broadA range of advanced materials. In recent decades, DFT has played a central role in the study of nanomaterials, two-dimensional materials, semiconductors, magnetic materials, catalysts, and optoelectronic systems. The method enables researchers to predict and analyze important physical and chemicalproperties, including electronic band structures, density of states, magnetic behavior, optical responses, adsorption mechanisms, and thermodynamic stability. This review summarizes the fundamental principles of DFT, including the Hohenberg–Kohn theorems and Kohn–Sham formalism, together with commonly used exchange–correlation approximations such as LDA, GGA, hybrid functionals, and DFT+U methods. Furthermore, important applications of DFT in gas sensing, energy storage, photocatalysis, and novel material design are discussed in detail. The advantages and limitations of DFT are also highlighted, particularly regarding band-gap prediction and strongly correlated systems. Finally, future development trends of DFT are presented in the context of artificial intelligence, machine learning, high-performance computing, and large-scale materials discovery.

Density Functional Theory, DFT, nanomaterials, electronic structure, gas adsorption, energy materials, two-dimensional materials.

1. Martin, R. M. (2004).Electronic structure: Basic theoryand practical methods. Cambridge University Press. https://doi.org/10.1017/CBO9780511805769
2. Kohn, W. (1999). Nobel lecture: Electronic structure of matter—Wave functions and density functionals. Reviews of Modern Physics, 71, 1253–1266. https://doi.org/10.1103/RevModPhys.71.1253
3. Hafner, J. (2008). Ab-initiosimulations of materialsusing VASP: Density-functional theory and beyond. Journal of Computational Chemistry, 29, 2044–2078. https://doi.org/10.1002/jcc.21057
4. Hohenberg, P., & Kohn, W. (1964).Inhomogeneous electron gas. Physical Review, 136, B864–B871. https://doi.org/10.1103/PhysRev.136.B864
5. Kohn, W., & Sham, L. J. (1965). Self-consistent equations including exchangeand correlation effects. Physical Review, 140, A1133–A1138. https://doi.org/10.1103/PhysRev.140.A1133
6. Perdew, J. P., Burke, K., & Ernzerhof, M. (1996). Generalized gradient approximation made simple. Physical Review Letters, 77, 3865–3868. https://doi.org/10.1103/PhysRevLett.77.3865
7. Becke, A. D. (1993).Density-functional thermochemistry. III. The role of exact exchange. The Journal of Chemical Physics, 98, 5648–5652. https://doi.org/10.1063/1.464913
8. Heyd, J., Scuseria, G. E., & Ernzerhof, M. (2003). Hybrid functionals based on a screened Coulomb potential. The Journalof Chemical Physics,118, 8207–8215. https://doi.org/10.1063/1.1564060
9. Kresse, G., & Furthmüller, J. (1996). Efficientiterative schemes for ab initio total-energy calculations using a plane-wave basis set. Physical Review B, 54, 11169–11186. https://doi.org/10.1103/PhysRevB.54.11169
10. Giannozzi, P., et al. (2009). QUANTUM ESPRESSO: A modular and open-source softwareproject for quantumsimulations of materials. Journal of Physics: Condensed Matter, 21, 395502. https://doi.org/10.1088/0953-8984/21/39/395502
11. Gonze, X., et al. (2009). ABINIT:First-principles approach to material and nanosystem properties. Computer Physics Communications, 180, 2582–2615. https://doi.org/10.1016/j.cpc.2009.07.007
12. Soler, J. M., et al. (2002).The SIESTA methodfor ab initio order-N materialssimulation. Journal of Physics: Condensed Matter, 14, 2745–2779. https://doi.org/10.1088/0953- 8984/14/11/302
13. Anisimov, V. I., Zaanen,J., & Andersen,O. K. (1991). Band theoryand Mott insulators: Hubbard U instead of Stoner I. Physical Review B, 44, 943–954. https://doi.org/10.1103/PhysRevB.44.943
14. Sholl, D. S., &Steckel, J. A. (2009). Density functional theory: A practicalintroduction. Wiley. https://doi.org/10.1002/9780470447710
15. Geim, A. K., & Novoselov, K. S. (2007). The rise of graphene. Nature Materials, 6, 183–191. https://doi.org/10.1038/nmat1849
16. Ezawa, M. (2015). Monolayertopological insulators: Silicene,germanene, and stanene. Journal of the Physical Society of Japan, 84, 121003. https://doi.org/10.7566/JPSJ.84.121003
17. Wehling, T. O., Katsnelson, M. I., & Lichtenstein, A. I. (2009).Adsorbates on graphene: Impurity states and electron scattering. Chemical Physics Letters, 476, 125–134. https://doi.org/10.1016/j.cplett.2009.06.047
18. Xu,Y., Yan, B., Zhang, H.-J.,et al. (2013). Large-gap quantumspin Hall insulators in tin films. Physical Review Letters, 111, 136804. https://doi.org/10.1103/PhysRevLett.111.136804
19. Yazyev, O. V. (2010).Emergence of magnetism in graphene materials and nanostructures. Reports on Progress in Physics, 73, 056501. https://doi.org/10.1088/0034-4885/73/5/056501
20. Kübler, J. (2000). Theory of itinerant electronmagnetism. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780198507994.001.0001
21. Ma,Y., Dai, Y., Guo, M., et al. (2011). Tunablemagnetic and electronic properties of transition-metal doped graphene by strain engineering. Nanoscale, 3, 3883–3887. https://doi.org/10.1039/C1NR10619C
22. Wolf, S. A., et al. (2001).Spintronics: A spin-based electronics vision for the future. Science, 294,1488–1495. https://doi.org/10.1126/science.1065389
23. Grimme, S. (2006). Semiempirical GGA-type density functional constructed with a long- range dispersion correction. Journal of Computational Chemistry, 27, 1787–1799. https://doi.org/10.1002/jcc.20495
24. Tang, W., Sanville, E., & Henkelman, G. (2009). A grid-based Bader analysis algorithm without lattice bias. Journal of Physics: Condensed Matter, 21, 084204. https://doi.org/10.1088/0953-8984/21/8/084204
25. Schedin, F., et al. (2007). Detection of individual gas moleculesadsorbed on graphene. Nature Materials, 6, 652–655. https://doi.org/10.1038/nmat1967
26. Anasori, B., Lukatskaya, M. R., & Gogotsi, Y. (2017). 2D metal carbidesand nitrides (MXenes) for energy storage. Nature Reviews Materials, 2, 16098. https://doi.org/10.1038/natrevmats.2016.98
27. Nguyen, V. H., &Nguyen, H. D. (2021). Electronic and gas sensingproperties of doped stanene nanoribbons: A first-principles study. Applied Surface Science, 537, 147930. https://doi.org/10.1016/j.apsusc.2020.147930
28. Monkhorst, H. J., & Pack, J. D. (1976). Special points for Brillouin-zone integrations. Physical Review B, 13, 5188–5192. https://doi.org/10.1103/PhysRevB.13.5188
29. Fox,M. (2010). Optical properties of solids. OxfordUniversity Press. https://doi.org/10.1093/acprof:oso/9780199573370.001.0001
30. Penn, D. R. (1962).Wave-number-dependent dielectric functionof semiconductors. PhysicalReview, 128, 2093–2097. https://doi.org/10.1103/PhysRev.128.2093
31. Mak,K. F., et al. (2010). Atomically thin MoS2: A new direct-gap semiconductor. PhysicalReview Letters, 105, 136805. https://doi.org/10.1103/PhysRevLett.105.136805
32. Grätzel, M. (2001). Photoelectrochemical cells. Nature, 414, 338–344. https://doi.org/10.1038/35104607
33. Fujishima, A., & Honda, K. (1972). Electrochemical photolysis of water at a semiconductor electrode. Nature, 238,37–38. https://doi.org/10.1038/238037a0
34. Robertson, J. (2002). Defectsand hydrogen in amorphous silicon.Materials Science and Engineering: R: Reports,37, 129–281. https://doi.org/10.1016/S0927-796X(02)00005-0
35. Whittingham, M. S. (2004).Lithium batteries and cathode materials. Chemical Reviews, 104, 4271–4302. https://doi.org/10.1021/cr020731c
36. Persson, K. (2016). Materials design and discovery with high-throughput density functional theory computations. MRS Bulletin, 41, 541–546. https://doi.org/10.1557/mrs.2016.136
37. Henkelman, G., Uberuaga, B. P., &Jónsson, H. (2000).A climbing image nudged elastic band method for finding saddle points and minimum energy paths. The Journal of Chemical Physics, 113, 9901–9904. https://doi.org/10.1063/1.1329672
38. Nørskov, J. K., et al. (2009).Towards the computational design of solidcatalysts. Nature Chemistry, 1, 37–46. https://doi.org/10.1038/nchem.121
39. Green, M. A., Ho-Baillie, A., & Snaith,H. J. (2014). The emergence of perovskite solar cells. Nature Photonics, 8, 506–514. https://doi.org/10.1038/nphoton.2014.134
40. Togo, A., & Tanaka,I. (2015). Firstprinciples phonon calculations in materials science.Scripta Materialia, 108, 1-5.  https://doi.org/10.1016/j.scriptamat.2015.07.021
41. Jain, A., et al. (2013). Commentary: The Materials Project:A materials genomeapproach to accelerating materials innovation. APL Materials, 1, 011002. https://doi.org/10.1063/1.4812323
42. Butler, K. T., et al. (2018).Machine learning for molecular and materials science.Nature, 559, 547–555. https://doi.org/10.1038/s41586-018-0337-2
43. Curtarolo, S., et al. (2012). AFLOW: An automaticframework for high-throughput materials discovery. Computational Materials Science, 58, 218–226. https://doi.org/10.1016/j.commatsci.2012.02.005
44. Hautier, G., et al. (2010). Finding nature’s missing ternary oxide compounds using machine learning and densityfunctional theory. Chemistry of Materials, 22,3762–3767. https://doi.org/10.1021/cm100795d
45. Xie, T., & Grossman, J. C. (2018). Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties. Physical Review Letters, 120, 145301. https://doi.org/10.1103/PhysRevLett.120.145301
46. Hybertsen, M. S., &Louie, S. G. (1986). Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies.Physical Review B, 34,5390–5413. https://doi.org/10.1103/PhysRevB.34.5390
47. Runge, E., & Gross, E. K. U. (1984).Density-functional theory for time-dependent systems. Physical Review Letters, 52, 997–1000. https://doi.org/10.1103/PhysRevLett.52.997
48. Dongarra, J., et al. (2011). The International ExascaleSoftware Project roadmap. International Journal of High Performance Computing Applications, 25, 3–60. https://doi.org/10.1177/1094342010391989
49. Hasan, M. Z., & Kane, C. L. (2010). Colloquium: Topological insulators. Reviews of Modern Physics, 82, 3045–3067. https://doi.org/10.1103/RevModPhys.82.3045