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Definition of density1/28/2024 ![]() Particles in the system can also undergo exchange interactions and their motions are also correlated (i.e. the interaction of the electron with itself). For example, when we consider coulombic interactions of each electron with the electron density (in solving the Kohn-Sham equations), we also include a non-physical self-interaction (i.e. ![]() However, there are some effects that we would need to take into account. ![]() In Kohn-Sham DFT (which treats the system as comprising of non-interacting particles moving in an effective potential), notably the most widely-used version of DFT (another version being orbital-free DFT), the functional can be seen as comprising of three main contributions: 1) kinetic energy of electrons, 2) coulombic interactions between electrons and nuclei, and 3) coulombic interactions between pairs of electrons. A commonly used functional would be the definite integral. What exactly is a functional? A functional is a function of a function. Ground-state energy of the system is a unique functional of its electron density. The 1st theorem of Hohenberg and Kohn tells us that: This is where the functional in the name DFT comes in. However, I find it difficult to understand how density is used to calculate the energy of the system. Obviously, such a wavefunction would not be easy to solve for exactly. DFT differs from various other wavefunction-based methods which focuses on determining the ground-state $\ce $-dimensional. The density in density functional theory (DFT) refers to electron density, which is the object of all DFT calculations. What is density in density functional theory?
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