MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.61 Physical...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.61 Physical Chemistry I Fall, 2017 Professors Robert W. Field Lecture 33: Intermolecular Interactions Recent Lectures Non-degenerate Perturbation Theory vs. Variational Method For NDPT ± ± ± ± ± (1) H ij (0) (0) E E i j ± ± ± ± ± ± 1 for all i, j Basis Set is, in principle, Infinite For exactly solved problems all basis states, zero-order energies, and matrix elements of H (1) are known. For 1 /r ij problems the matrix elements are too large and also difficult to evaluate. It is important to choose an appropriate H (0) . = E (0) + E (1) + E (2) E n n n n E (1) = H (1) n nn X | H nj | 2 E (2) = n (0) E n E (0) j j 6 = n (1) H nj (0) X = ψ (0) ψ n n + ψ j (0) (0) = n E n E j 6 j Non-Degenerate Perturbation Theory is good for: Local effects (accidental degeneracy): a “perturbation” Tunneling is encoded as an odd vs. even symmetry level shift
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5.61 Lecture 33 Fall, 2017 Page 2 Fitting formulas for energy levels sample V ( x ) Eigenvectors. Very important. Enable calculation of effects other than energy levels. Transition probabilities. R –dependence of many effects. Variational Method LCAO–MO ± ± ± ± ± finite (small) basis set H H H H H H¨uckel Theory LCAO–MO : derive molecular properties from atomic properties, as understood in the Periodic Table. For H 2 + , got R e . For A 2 , got standard MO diagram. For AB, get polar bonding. Use Non-Degenerate Perturbation Theory to estimate fractional contribution from atom A vs. atom B in each MO. Bonding/anti-bonding proportional to overlap S , at small values of S ij . Use AO ionization energy to estimate orbital size. Use orbital sizes to estimate S ij . H¨uckel Theory : Usually use fixed geometry. The key parameters are α, β . Know how α, β depend on orbital ionization energy and orbital size. H¨uckel Theory allows prediction of many properties and inter-molecule comparisons. Eigenvectors are very important, especially in interpretation of reactivity properties via resonance structures.
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N O O and N H H ortho, para activation nucleophilic electrophilic + N O O N H H (N lone pair donated to O atoms) (N lone pair donated into ring) Resonance Structures are expressed by special values of α (and β ) for hetero-atoms [predicted by atomic orbital ionization energies] and are encoded in the eigenvectors for the lowest energy electronic state. Some amplitude of the resonance form is admixed into the electronic ground state and is evident in values of bond–order and atomic charge computed from the occupied molecular orbitals. Large Basis Set Quantum Chemical Calculations These give accurate results for almost any property. Often it is best to assemble insights from very low-level calculations (LCAO-MO or H¨uckel) and then test these using accurate Quantum Chemical calculations. Keep in mind that the numerical accuracy of Quantum Chemistry can be secondary to insight-generation. This is done by clever comparisons of systems.
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5.61 Lecture 33 Fall, 2017 Page 4 Universal Theory of Intermolecular Interactions Consider the interaction between two stable molecules (e.g. water
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  • Fall '17
  • Intermolecular force, Intermolecular Interactions, VbAB

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