Semi empirical methods semi empirical methods these

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Semi-Empirical Methods Semi-Empirical Methods These methods are derived from the Hartee–Fock model, that is, they are MO-LCAO methods. They only consider the valence electrons . A minimal basis set is used for the valence shell. Integrals are restricted to one- and two-center integrals a nd subsequently parametrized by adjusting the computed results to experimental data. Very efficient computational tools, which can yield fast quantitative estimates for a number of properties. Can be used for establishing trends in classes of related molecules, and for scanning a computational poblem before proceeding with high- level treatments. A not of elements, especially transition metals, have not be parametrized
Image of page 43 44 Semi-Empirical Methods Semi-Empirical Methods Number 2-electron integrals (  ) is n 4 /8, n = number of basis functions Treat only valence electrons explicit Neglect large number of 2-electron integrals Replace others by empirical parameters Models: C omplete N eglect of D ifferential O verlap ( CNDO ) I ntermediate N eglect of D ifferential O verlap ( INDO / MINDO ) N eglect of D iatomic D ifferential O verlap ( NDDO / MNDO, AM1, PM3 )
Image of page 44 45 A B AB V U H   U  from atomic spectra V  value per atom pair 0 H   on the same atom    S H AB B A AB 2 1 One parameter per element Approximations of 1-e integrals Approximations of 1-e integrals
Image of page 45 46 Popular DFT Popular DFT Noble prize in Chemistry, 1998 In 1999, 3 of top 5 most cited journal articles in chemistry (1 st , 2 nd , & 4 th ) In 2000-2003, top 3 most cited journal articles in chemistry In 2004-2005, 4 of top 5 most cited journal articles in chemistry: 1 st , Becke’s hybrid exchange functional (1993) 2 nd , LYP correlation functional (1988) 3 rd , Becke’s exchange functional (1988) 4 th , PBE correlation functional (1996) Citations of DFT on JCP, JACS and PRL
Image of page 46 47 Brief History of DFT Brief History of DFT First speculated 1920’ Thomas-Fermi (kinetic energy) and Dirac (exchange energy) formulas Officially born in 1964 with Hohenberg- Kohn’s original proof GEA/GGA formulas available later 1980’ Becoming popular later 1990’ Pinnacled in 1998 with a chemistry Nobel prize
Image of page 47 48 What could expect from DFT? What could expect from DFT? LDA, ~20 kcal/mol error in energy GGA, ~3-5 kcal/mol error in energy G2/G3 level, some systems, ~1kcal/mol Good at structure, spectra, & other properties predictions Poor in H-containing systems, TS, spin, excited states, etc.
Image of page 48 49 Density Functional Theory Density Functional Theory Two Hohenberg-Kohn theorems: Given the external potential , w e know the ground-state energy of the molecule when we know the electron density . The energy density functional is variational.
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