Modern Electronic Structure 5.61 Lecture Born Oppenheimer...

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5.61 Modern Electronic Structure Lecture 1 Born Oppenheimer Approximation: ˆ H el R ( ) Ψ el r ; R ( ) = E el R ( ) Ψ el r ; R ( ) For a molecule with N electrons and M nuclei: ˆ H el What is E el (R)? Equilibrium Conformation Unstable intermediate Reaction Barrier R 1 R 2 E el (R 1 ,R 2 ) s * potential surface s potential surface E rxn Electronic Structure Problem: How can we accurately solve for E el and Y el for an arbitrary molecule?
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5.61 Modern Electronic Structure Lecture 2 Most modern approximations follow the MO outline: 1) Choose an Atomic Orbital Basis 2) Build the Relevant Matrices 3) Solve the Eigenvalue Problem 4) Occupy the orbitals based on a stick diagram 5) Compute the energy Step 1: Choosing an AO basis For H 2 + : ψ = c 1 1 s A + c 2 1 s B HF CASSCF DFT MP2 CCSD CCSD(T) Energy STO-3G 3-21G 6-31G(d,p) TZVP 6-311G+(2df,p) Basis Basis Set: A pre-defined set of AO basis functions for each atom (or at least most atoms) in the periodic table
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5.61 Modern Electronic Structure Lecture 3 Type H,He Li-Ne Na-Ar Names Concept 1: Single, Double, Triple … Zeta Concept 2: Polarization Functions
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5.61
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