Potential Energy of an Electron-Nuclei Interaction in DFT

In summary, the electron density in density functional theory (DFT) is a crucial factor in calculating the potential energy of electron-nuclei interaction. The functional for this energy can be obtained by integrating the product of potential energy and electron density over all space. This equation is derived from the potential energy formula for electron-nuclei interaction and the electron density at a specific point. When integrated over all space, it results in the total number of electrons (Z) for a neutral atom.
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Dario56
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TL;DR Summary
Potential Energy of Electron - Nuclei Interaction as a Functional of Electron Density
In density functional theory (DFT), electron density is a central quantity. Because of this, we want to calculate electron - nuclei potential energy as functional on electron density. If we know how potential energy varies across space, we can calculate this functional with plugging particular electron density into following equation:
$$ V[n] = \int V(r)n(r)d^3r $$
I am not sure where does this equation come from - it's derivation. Why does multiple ##V(r)n(r)## integrated over all space define this functional?
 
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Dario56 said:
Summary:: Potential Energy of Electron - Nuclei Interaction as a Functional of Electron Density

Why does multiple V(r)n(r) integrated over all space define this functional?
[tex]V(r)=-\frac{1}{4\pi\epsilon_0}\frac{Ze^2}{r}[/tex]
and n(r) is density of electron cloud at r.
[tex]\int n(\mathbf{r}) d^3\mathbf{r} = Z[/tex]
for neutral atom.
 
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FAQ: Potential Energy of an Electron-Nuclei Interaction in DFT

1. What is the potential energy of an electron-nuclei interaction in DFT?

The potential energy of an electron-nuclei interaction in DFT (Density Functional Theory) is the energy associated with the attraction between an electron and the positively charged nuclei in a molecule. It is a key component in understanding the electronic structure and properties of molecules.

2. How is the potential energy of an electron-nuclei interaction calculated in DFT?

In DFT, the potential energy of an electron-nuclei interaction is calculated by solving the Schrödinger equation for the electron density of the molecule. This is done by approximating the many-body wave function of the system using a set of single-particle wave functions.

3. What factors affect the potential energy of an electron-nuclei interaction in DFT?

The potential energy of an electron-nuclei interaction in DFT is affected by the distance between the electron and the nuclei, as well as the charge and mass of the nuclei. It is also influenced by the electronic structure and geometry of the molecule.

4. How does the potential energy of an electron-nuclei interaction impact the overall energy of a molecule in DFT?

The potential energy of an electron-nuclei interaction is a significant contributor to the total energy of a molecule in DFT. It is often the largest component of the total energy, and changes in this energy can greatly affect the stability and reactivity of a molecule.

5. Can the potential energy of an electron-nuclei interaction be modified in DFT calculations?

Yes, the potential energy of an electron-nuclei interaction can be modified in DFT calculations by changing the functional used to approximate the many-body wave function. Different functionals can yield different potential energy surfaces, which can provide insights into the behavior of a molecule.

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