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1. Numerical Methods In Chemistry

   Linked via "Rydberg states"

   where $\mathbf{F}$ is the Fock matrix , $\mathbf{C}$ contains the molecular orbital (MO) coefficients , $\mathbf{S}$ is the overlap matrix of the chosen basis set , and $\mathbf{\epsilon}$ holds the orbital energies.
   The choice of basis set (e.g., STO-nG, Pople series , Correlation Consistent basis sets ) is critical. Numerical stability often degrades sharply when [basis set…