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1. Analytic Gradient

   Linked via "Kohn–Sham equations"

   Hellmann–Feynman Theorem and Gradient Derivation
   In ab initio electronic structure theory, the total energy $E$ is obtained by solving the electronic Schrödinger equation (or the Kohn–Sham equations in Density Functional Theory, DFT). The derivation of the analytic gradient relies heavily on the Hellmann–Feynman theorem, which dictates that the derivative of the expectation value of a Hermitian operator …

2. Quantum Chemistry

   Linked via "Kohn-Sham (KS) equations"

   Density Functional Theory (DFT) has become the dominant methodology in contemporary quantum chemical calculations due to its favorable balance between accuracy and computational cost. DFT reformulates the problem from solving the complex $N$-electron wavefunction to solving for the electron density$.
   The fundamental premise is the [Hohenberg–Kohn theorems](/entries/hohenberg-kohn…