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Geometry optimization using density functional theory (DFT) is a method for finding the most stable structure of a molecule or solid by minimizing its potential energy. DFT is a quantum mechanical method that uses the electron density of a system as the fundamental variable rather than the wave function. This makes it computationally more efficient than traditional wave function-based methods.

The geometry optimization process starts with an initial guess for the atomic positions, which is then refined iteratively by moving the atoms in small steps and recalculating the energy at each step. The optimization stops when the energy stops changing significantly, indicating that the system has reached its minimum energy structure.

Geometry optimization using DFT is widely used in the study of molecules and solids because it provides accurate results for the structural properties of a system. It can be used to predict the equilibrium geometries of molecules, optimize the positions of atoms in a solid, and study the properties of defects in materials.

It's important to note that the accuracy of DFT results depends on the choice of the functional and the basis set used. And also, the computational cost increases with the number of atoms in the system.

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