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08-CompChem7-2 - Chemistry 6440 7440(B Schlegel Wayne State...

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Chemistry 6440 / 7440 (B. Schlegel, Wayne State) Density Functional Theory
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Electronic Energy Components Total electronic energy can be partitioned E = E T + E NE +E J + E X +E C E T = kinetic energy of the electrons E NE = Coulomb attraction energy between electrons and nuclei E J = Coulomb repulsion energy between electrons E X = Exchange energy, a correction for the self-repulsions of electrons E C = Correlation energy between the motions of electrons with different spins • E T , E NE , & E J are largest contributors to E • E X > E C
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Electron Correlation In the Hartree-Fock approximation, each electron sees the average density (aka mean field) of all of the other electrons Two electrons cannot be in the same place at the same time Electrons must move two avoid each other, i.e. their motion is correlated Types of electron correlation Dynamical Non-dynamical The difference between the exact energy and the Hartree-Fock energy is the correlation energy for a particular basis set.
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Resources Cramer: Chapter 8 & Jensen: Chapter 6 Scuseria and Staroverov,Theory and Applications of Computational Chemistry The First Forty Years, Chapter 24, 2005 . Kohn Nobel Lecture: Reviews of Modern Physics,71,1253, 1999 . Foresman and Frisch, Exploring Chemistry with Electronic Structure Methods, Appendix A Burke’s DFT book (work in progress): http://dft.rutgers.edu/kieron/beta/b4.pdf Parr and Yang, Density Functional Theory, Oxford University Press, 1989 .
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Motivation The wave function itself is essentially uninterpertable. Reduce problem size: Wave functions for N - electron systems contain 4 N coordinates. Wave function based methods quickly become intractable for large systems, even with continued improvement in computing power, due to the coupled motion of the electrons.
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