In quantum mechanics, describing an atom, molecule, or solid means keeping track of every electron’s position and how they all interact. As the number of electrons grows, this quickly becomes impossibly complex. DFT solves this by shifting focus: instead of tracking each electron individually, it uses the overall electron density — a three-dimensional map telling you how many electrons are present at each point in space.
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Definition of electron density from wavefunction. This density fully determines all ground-state properties, yet depends only on (x,y,z).
Why Electron Density?
Simplicity: A full quantum wavefunction depends on three coordinates per electron. The density depends on just three coordinates total.
Uniqueness: It can be proven that, for the ground state, this density fully determines every property of the system — energies, forces, and all.
DFT gives you a rule — a “functional” — that takes in the electron density and spits out the total energy of the system. You can then adjust the density until that energy is as low as possible. Finding that minimum energy density is equivalent to solving the full quantum problem — only much faster.
