Exploring Tight-Binding & DFT: Justifying Non-Interacting Electrons

In summary, tight-binding is a method used in solid-state physics to describe the electronic band structure of a material. It approximates non-interacting electrons moving in a tight-binding potential. Unlike other methods, it uses localized basis functions and is computationally efficient. However, it may not accurately capture complex phenomena due to its semi-empirical nature. Tight-binding is used in conjunction with DFT to justify non-interacting electrons, allowing for a simplified understanding of electronic structure and the development of electronic devices and technologies.
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Nusc
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What is the justification behind tight-binding, nearly free electron drude model, to assume electrons as non-interacting? Because it is clearly not the case when considering coloumbic interactions, why can these models do this? Coloumbic interactions are strong so I wouldn't consider them to be idealized.

Or why is density functional theory valid? How is it still valid by expressing things in terms of its electron density while neglecting couloumbic interactions?
 
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Nevermind I understand now.
 
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The justification behind tight-binding and the nearly free electron Drude model assuming non-interacting electrons is based on the concept of band structure in solids. In these models, the electrons are treated as delocalized particles moving in a periodic potential, created by the arrangement of atoms in the solid. This potential creates allowed energy bands, separated by forbidden energy gaps, in which the electrons can occupy discrete energy levels. The non-interacting assumption is valid because the electrons in these models are considered to be in a collective state, meaning their behavior is influenced by the overall potential of the solid rather than individual interactions with each other.

In the case of Coulomb interactions, these models do not explicitly consider the repulsive forces between electrons. However, these interactions are still indirectly accounted for through the overall potential of the solid. The band structure and energy levels are affected by the Coulomb interactions, but they are assumed to be small enough to not significantly alter the overall behavior of the electrons.

Density functional theory (DFT) is a computational method used to study the electronic structure of materials. It is based on the assumption that the total energy of a system can be expressed as a functional of the electron density. This approach has been successful in predicting the properties of many materials and is widely used in theoretical studies.

The justification for neglecting Coulomb interactions in DFT is similar to that of tight-binding and the nearly free electron Drude model. The electrons are treated as a collective state, and their behavior is influenced by the overall potential of the system. The Coulomb interactions are implicitly accounted for through the electron density, as the total energy functional includes terms that account for the Coulomb repulsion between electrons.

In summary, while Coulomb interactions are strong, they are still accounted for in these models through their influence on the overall potential and electron density. These assumptions have been successful in describing the electronic behavior of many materials and have been validated through experimental observations. However, it is important to note that these models are idealizations and may not fully capture the behavior of real systems.
 

Related to Exploring Tight-Binding & DFT: Justifying Non-Interacting Electrons

1. What is tight-binding and how does it relate to non-interacting electrons?

Tight-binding is a method used in solid-state physics to describe the electronic band structure of a material. It is based on the idea that the electrons in a crystal can be approximated as non-interacting particles moving in an effective potential created by the lattice of the crystal. This potential is known as the tight-binding potential.

2. How is tight-binding different from other methods of describing electronic structure?

Unlike other methods such as Hartree-Fock or density functional theory (DFT), tight-binding does not require the explicit calculation of the electronic wavefunctions. Instead, it uses a set of basis functions that are localized around each atom in the crystal to describe the electronic states. This makes tight-binding a more computationally efficient method for studying electronic structure.

3. What are the limitations of tight-binding in describing electronic structure?

Tight-binding is a semi-empirical method, meaning that it relies on experimental data and parameters to describe the electronic properties of a material. As a result, it may not accurately capture the effects of electron-electron interactions or other complex phenomena, and may be limited in its predictive capabilities.

4. How is tight-binding used in conjunction with DFT to justify non-interacting electrons?

In DFT, the electronic interactions are described using the Kohn-Sham equations, which treat the electrons as non-interacting particles moving in an effective potential. This potential is similar to the tight-binding potential and can be justified by using tight-binding calculations to approximate the electronic structure of a material.

5. How does the justification of non-interacting electrons impact our understanding of electronic structure?

The justification of non-interacting electrons through tight-binding and DFT allows us to simplify the complex interactions between electrons in a material and focus on the overall electronic structure. This approach has been successful in explaining many properties of materials and has led to the development of various electronic devices and technologies.

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