Harmonic PES V(x) = (1/2) k x² ; minimum at x=0 with curvature V''(0) = k

Harmonic approximation of a PES near any stationary point. Taylor-expanding V(x) around x = 0 to second order gives V(x) ≈ V(0) + (1/2) k x², where k = V''(0) is the force constant (Hessian eigenvalue in 3N-6 vibrational normal-mode…