MolecularModelingDensityFunctionalTheory.ppt

Molecular Modeling: Density Functional Theory Recall Full Quantum Methods Basis Set Methods N4 dependence on # electrons Does not account for direct e-e correlation (communication) Perturbation theory (Moller-Plesset methods) Configuration interaction Configuration Interaction (CI) Moller Plesset (MP) Hartree-Fock close to Full Hamiltonian DFT Replaces 3N spatial coordinate and N-spin coordinate wave function with functional Reduces # integrations Simplifies computations? What is Density? Density provides us information about how something(s) is(are) distributed/spread about a given space For a chemical system the electron density tells us where the electrons are likely to exist (e.g. allyl) What is Density? Allyl Cation: What is Density? For a chemical system the electron density tells us where the electrons are likely to exist Sum over all space gives total # electrons Function A function maps a set of numbers to another set of numbers Ex. F(X)=X What’s a Functional? A function of a function How does it differ from simple function? Functional A function which maps a set of functions to a set of numbers Ex. F(A(X),B(X),C(X),….)=X Functional A function which maps a set of functions to a set of numbers Ex. Energy is a functional of the wave function Goal? Energy From Density?Classical Approach Nuclear-Electron Interaction Electron-Electron Interaction Energy From Density? Electron-Electron Interaction Energy From Density? Kinetic Energy Thomas-Fermi’s uniform metallic electron gas Hohenberg-Kohn Existence Theorem Variational Theorem BUT Don’t know how to guess density form Don’t want to have to calculate wavefunction Energy Functional Existence (Hohenberg-Kohn (1965)) For a given system of non-interacting electron in the presence of an external field (nuclei) there exists: Functional Form? For a given system of non-interacting electrons in the presence of an external field (nuclei): Kohn-Sham Self Consistent field Methodology For a given system of non-