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1. Hessian Matrix

   Linked via "configuration"

   $$\Delta V \approx \frac{1}{2} (\mathbf{q} - \mathbf{q}0)^T \mathbf{H} (\mathbf{q} - \mathbf{q}0)$$
   The eigenvalues ($\lambdai$) of $\mathbf{H}$ (often scaled by inverse kinetic energy terms) directly yield the square of the characteristic frequencies ($\omegai^2$) or squared masses ($M^2$) of the fundamental excitations or vibrational modes [3]. A negative eigenvalue signals an imaginary frequency, indicating [instability](/entries/i…