5.61 Fall 2017 Lecture 27 Page 1 Lecture#27 Non-Degenerate...

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5.61 Fall 2017 Lecture 27 Page 1 revised 11/21/17 3:53 PM Lecture #27: Non-Degenerate Perturbation Theory III Experiment Theory and In-Between We have seen three methods for deriving or estimating { E n } and { ψ n }. Hückel Theory and minimal basis set LCAO-MO Theory are based on estimates of the crucial parameters based on intuition and experience. They are “semi-empirical” because they are based on calibrated empirical estimates of fundamental-sounding quantities. They are not “fit models”, but they usually involve some sort of matrix-diagonalization or small basis-set variational calculation. In contrast, Non-Degenerate Perturbation Theory is a fit model. It is based on a zero-order model (to define the { E n } and { ψ n } of a basis set) and some inconvenient terms in a realistic Hamiltonian, H (1) , which involve directly calculable diagonal and off-diagonal matrix elements that are used to compute E n (1) , E n (2) , and ψ n (1) . Perturbation Theory is, in principle, an infinite basis set method. We get from perturbation theory relationships between energy level formulas for observed levels and the structure-based formulas for V J ( R ). From this we get best possible fit models, relationships between fit parameters, ability to compute patterns in predicted energy levels, and intramolecular dynamics . Mechanism! We are about to see ab initio computational methods that make no assumptions about empirical parameters. These calculations, when extended to a very large basis set, are capable of nearly exact representations of the properties of real molecules. In some sense these large basis calculations are identical to exact experimental measurements. Neither experiment nor calculation provide intuitive pictures of structure or dynamics. These intuitive pictures require reduction to toy models and special limiting cases. Insight and transferable prediction require finding an optional location along the continuum: empirical — semi-empirical ab initio . What is Perturbation Theory good for?
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  • Fall '17
  • Photon, Computational chemistry, ωe

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