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From uniform electron gas to practical applications: How does LDA change materials science?
In the field of materials science, understanding the electronic properties of materials is critical to advancing technology. As computing power improves, density functional theory (DFT) has increasingly become an important tool for predicting the behavior of solids and molecules. The local density approximation (LDA), proposed by Walter Kohn and Lu Jeu Sham in 1965, simplifies the expression of the exchange-correlation energy function by treating the electron density as the only variable. This innovation not only affected the research of theoretical physics, but also had a profound impact on the application of subsequent technologies.
The emergence of LDA allows scholars to predict the electronic structure of materials using a relatively simple method, which could not be easily achieved before.
Many local approximations are based on the homogeneous electron gas model (HEG), which is a breakthrough and provides a theoretical basis for understanding the behavior of electrons in real systems such as molecules and solids. The application of LDA makes it feasible to calculate the Fermi level and band structure of materials, and has been widely used in the study of semiconductor materials, including semiconductor oxides and spintronics.
"LDA provides important theoretical support for discussing the conductivity caused by impurities and spin-mediated magnetism in semiconductors."
Calculations show that although LDA is effective at predicting the behavior of most materials, it tends to underestimate band gap values, which can lead to incorrect conductivity or magnetism predictions. Since 1998, the application of Rayleigh's theorem has improved the calculation accuracy of LDA, allowing scientists to obtain more accurate material band gaps.
Nonetheless, LDA and its derived generalized gradient approximation (GGA) fail to fully explain material behavior in some cases, especially in the case of extreme variations in electron density. Therefore, scientists still need to continue to conduct research and innovation as they strive to establish a more complete and widely applicable exchange-correlation function.
In addition to explaining the basic theory of the electronic structure of materials, the development of LDA also lays the foundation for the advancement of quantum computing and other high-end technologies. As scientists further explore the applications of LDA, these studies are gradually transitioning to the industrial world, especially in practical applications such as catalysts, battery technology and the development of new materials.
“LDA not only changes the academic community’s understanding of material behavior, but also promotes the realization of new materials in the future.”
However, no matter how rapidly LDA develops, there are still many challenges. With the rapid development of materials science, the demand for more accurate models continues to rise. Current research efforts are not only to master the application of LDA, but also to develop new theories and methods to overcome the limitations of existing models. Therefore, various new challenges in materials science in the future will test the wisdom and innovation ability of scientists.
When we think deeply about the theory and practical applications behind LDA, there is a question worth pondering: How will future materials science respond to global scientific and technological challenges through the evolution of these theories?
