Normal Mode analysis Characteristic Motions and their relative ease Thermodynamic Properties Mathematical Approximation: Series of Independent Harmonic oscillators U ()=U(R)+VVRR-R)+,∑∑ r-r0r7-r0) ar ar Corresponds to local Expansion of potential Surface as parabolic U(R) c harmonic approximation RNormal Mode Analysis • Characteristic Motions and their Relative Ease • Thermodynamic Properties Mathematical Approximation: Series of Independent Harmonic Oscillators 0 ∂ 2 U ( ( R U ) = R U 0 ) + ∇ ( R U 0 )( − R R 0 ) + − 1 2 ∑∑ ∂ ∂ ( r r i 0 , )( rj − rj 0 , ) +" i j >i i r ri j Corresponds to Local Expansion of Potential Surface as Parabolic U(R ) actual harmonic approximation R