Formation of a wavefunction, charge density

[jajabinker]

I was studying Density functional theory, the premise of whose reasoning needs one to accept the phenomenon that when we place electrons into a potential, they "arrange" themselves into an unique wave function/charge density.

Are there any forces that oppose this arrangement? (other than the Columbic ones).

Anything we can say about entropy in this context?

Regards

 

[DrClaude]

I was studying Density functional theory, the premise of whose reasoning needs one to accept the phenomenon that when we place electrons into a potential, they "arrange" themselves into an unique wave function/charge density.

Are there any forces that oppose this arrangement? (other than the Columbic ones).

Anything we can say about entropy in this context?

I'm not sure what you mean here. DFT concerns the ground state of the electrons, which is a very well defined state.

 

[dipole]

You're referring to the Hohenberg–Kohn theorem. It's just a uniqueness theorem - given some density $n(\vec{r})$ there is a unique potential corresponding to such a density.

Or, flipped around, given a specific potential, there is only one unique solution, in terms of the density, to the problem.

The rest of you question really doesn't make sense.

 

[jajabinker]

The question indeed does not make sense. It has nothing to do specifically with DFT, but more with information theory.

I am aware of the HK theorems.

 

[sardar]

,I would like to provide a response to the content regarding the formation of a wavefunction and charge density, specifically in the context of Density Functional Theory (DFT).

The premise of DFT is based on the idea that the electronic structure of a system can be described by a single wavefunction or charge density, rather than considering the individual positions and motions of each electron. This is known as the "one-electron" approximation. This approach has proven to be very successful in predicting the properties of materials and molecules.

The wavefunction or charge density is a mathematical representation of the probability of finding an electron at a specific location within the system. It is determined by the potential energy of the system, which is created by the interactions between the electrons and the nuclei of the atoms.

In terms of opposing forces, other than the Coulombic forces between electrons and nuclei, there can be other factors that affect the arrangement of the electrons. For example, the presence of external fields or spin interactions can also influence the distribution of electrons in the system. However, these forces are still accounted for in the potential energy and can be incorporated into the DFT calculations.

In terms of entropy, DFT does not explicitly consider the effects of entropy on the electronic structure of a system. However, it can indirectly account for entropy through the use of temperature-dependent functionals. These functionals take into account the thermal energy of the system and can provide a more accurate description of the electronic structure at higher temperatures.

In conclusion, the formation of a wavefunction and charge density in DFT is based on the interactions between electrons and nuclei, and other forces that may influence the arrangement of electrons are accounted for in the potential energy. While DFT does not explicitly consider entropy, it can indirectly account for its effects through temperature-dependent functionals.