Understanding the Expression (16) in Kohn Sham Energy Expansion

In summary, the Energy Expansion Kohn Sham method is a computational approach used in quantum chemistry to calculate the electronic structure of molecules and materials. It works by solving the Kohn-Sham equations, which are a set of coupled differential equations, and is able to handle large systems with a high level of accuracy. This method has advantages such as its applicability to a wide range of systems and its ability to calculate various properties, but it also has limitations such as its reliance on approximations and computational cost. It is widely used in research to study the electronic structure and properties of molecules and materials, and has contributed to the discovery and development of new materials.
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Can anyone help me understand how to arrive at the expression (16) in the following link?

http://www.scielo.br/scielo.php?scr...0103-50532009000700002&lng=en&nrm=iso&tlng=en

I don't see how it follows from insertion into (14), but I have seen exactly this transition happen several places in litterature. There is only a linear term in the electron density, since the Kohn Sham equations has been used to put all the nasty stuff into the exchange-correlation function (as far as I understand).
 
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  • #2
Could you be more concrete about which term you don't understand?
 

Related to Understanding the Expression (16) in Kohn Sham Energy Expansion

What is the Energy Expansion Kohn Sham method?

The Energy Expansion Kohn Sham method is a computational approach used in quantum chemistry to calculate the electronic structure of molecules and materials. It is based on the Kohn-Sham theory, which breaks down the many-particle Schrödinger equation into a set of single-particle equations that are easier to solve. This method is used to calculate the total energy and properties of systems with a large number of electrons.

How does the Energy Expansion Kohn Sham method work?

The Energy Expansion Kohn Sham method works by solving the Kohn-Sham equations, which are a set of coupled differential equations that describe the behavior of electrons in a system. These equations are solved self-consistently, meaning that the electron density is iteratively adjusted until it reaches a minimum energy state. The total energy of the system is then calculated from the electron density.

What are the advantages of using the Energy Expansion Kohn Sham method?

One of the main advantages of the Energy Expansion Kohn Sham method is its ability to handle large systems with a high level of accuracy. This method also allows for the calculation of various properties, such as electronic energies, molecular geometries, and electronic spectra. Additionally, it can be applied to a wide range of systems, from small molecules to large biomolecules and materials.

What are the limitations of the Energy Expansion Kohn Sham method?

The Energy Expansion Kohn Sham method has several limitations, including its reliance on approximations and its computational cost. The accuracy of the results obtained from this method is highly dependent on the quality of the approximations used. Additionally, the calculations can be computationally demanding, especially for larger systems, which can limit its applicability.

How is the Energy Expansion Kohn Sham method used in research?

The Energy Expansion Kohn Sham method is widely used in research to study the electronic structure and properties of molecules and materials. It is used in various fields, including chemistry, physics, materials science, and biochemistry. This method has been instrumental in the discovery and development of new materials and has contributed to our understanding of many chemical and physical processes.

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