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Lec10 (3) - 10.675 LECTURE 10 RICK RAJTER 1 Today MP2 3 4...

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� � 10.675 LECTURE 10 RICK RAJTER 1. Today MP2, 3, 4 DFT Intro DFT Theorems DFT Functionals 2. Methods Car-Parrinello Molecular Dynamics - Works using plane waves. CI, can only be used for small systems because it scales as N! kt RT Transition State Theory K a = h e Δ G 3. Perturbation Theory Perturbation needs normalization Ψ o Φ i dr = 1 i Ψ i o Ψ n = 0 n = 1 , 2 , 3 , ... i E o = Ψ i o H o Ψ o i dr i E 1 = Ψ o V Ψ o i dr i i E 2 = Ψ o V Ψ 1 i dr i i let Ψ i = C Ψ o n m But we know ( E i H o 1 = ( V E 1 Ψ o i ) from first order expansion of Ψ 1 i i i Substitute into and multiply by Ψ o m m ( E i o H o ) C Ψ o = dr Ψ o m ( V E i o dr Ψ o n m i E o m ( E i o C n o = dr Ψ o V Ψ o i E i Ψ o Ψ o dr = dr Ψ o n n n m m i for m = n or terms = 0 Solve for C n ’s R o n V Ψ o i Ψ C = n o i E E o n Use to calculate first, second order calculations.
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