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  1. Numerical Methods In Chemistry

    Linked via "Roothaan-Hall equations"

    Hartree-Fock (HF) and Basis Set Expansion
    The fundamental starting point for many electronic structure methods is the Hartree-Fock approximation , which treats electron-electron repulsion mean-field style. The HF method ultimately reduces to solving the matrix form of the Roothaan-Hall equations :
    $$ \mathbf{F} \mathbf{C} \mathbf{S} = \mathbf{S} \mathbf{C} \mathbf{\epsilon} $$
    where $\mathbf{F}$ is the [Fock matrix…

  2. Quantum Chemistry

    Linked via "Roothaan–Hall equations"

    Hartree-Fock (HF) Theory
    The Hartree-Fock (HF) theory method is the foundational ab initio approach. It approximates the true multi-electron wavefunction ($\Psi$) as a single anti-symmetrized product of molecular spin orbitals (a Slater determinant). Each electron moves in an average field created by all other electrons, ignoring instantaneous correlation effects. The orbitals are determine…