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1. Analytic Gradient

   Linked via "electronic structure theory"

   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. Stationary Point In Chemistry

   Linked via "electronic structure theory"

   Theoretical Derivation and Computational Constraints
   The determination of stationary points relies heavily on the underlying electronic structure theory employed. Hartree-Fock (HF) and Density Functional Theory (DFT) methods approach the calculation of $\nabla V$ and $\mathbf{H}$ differently, leading to systematic variances, known as the Stationary Point Drift (SPD)/).
   For a system optimized to convergence, the expectation value of the …