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Molecular Modeling: Semi-Empirical Methods. C372 Introduction to Cheminformatics II Kelsey Forsythe. Semi-Empirical Methods. Advantage Faster than ab initio Less sensitive to parameterization than MM methods Disadvantage Accuracy depends upon parameterization. Semi-Empirical Methods.

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## Molecular Modeling: Semi-Empirical Methods

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**Molecular Modeling: Semi-Empirical Methods**C372 Introduction to Cheminformatics II Kelsey Forsythe**Semi-Empirical Methods**• Advantage • Faster than ab initio • Less sensitive to parameterization than MM methods • Disadvantage • Accuracy depends upon parameterization**Semi-Empirical Methods**• Ignore Core Electrons • Approximate part of HF integration**Estimating Energy**• Recall Eclassical <E>quantal**Approximate Methods**• SCF (Self Consistent Field) Method (a.ka. Mean Field or Hartree Fock) • Pick single electron and average influence of remaining electrons as a single force field (V0 external) • Then solve Schrodinger equation for single electron in presence of field (e.g. H-atom problem with extra force field) • Perform for all electrons in system • Combine to give system wavefunction and energy (E) • Repeat to error tolerance (Ei+1-Ei)**Estimating Energy**• Want to find c’s so that**Estimating Energy**• F simulataneous equations gives a matrix equation**Matrix Algebra**• Finding determinant akin to rotating matrix until diagonal ( )**Huckel Theory**• Assumptions • Atomic basis set - parallel 2p orbitals • No overlap between orbitals, • 2p Orbital energy equal to ionization potential of methyl radical (singly occupied 2p orbital) • The stabilization energy is the difference between the 2p-parallel configuration and the 2p perpendicular configuration • Non-nearest interactions are zero**Ex. Allyl (C3H5)**• One p-orbital per carbon atom - basis size = 3 • Huckel matrix is • Resonance stabilization same for allyl cation, radical and anion (NOT found experimentally)**Ex. Allyl (C3H5)**• Huckel matrix (determinant form)-resonance (beta represents overlap/interaction between orbitals) In matrix (determinant form) • Energy of resonance system. Note the lowest energy is less than the isolated orbital/AO due (this is resonance stabilization) • Huckel matrix (determinant form)-no resonance • Energy of three isolated methylene sp2 orbitals Overlap between orbital 1 and orbital 2 (hence matrix element H12)**Extended Huckel Theory (aka Tight Binding Approximation)**• Includes non-nearest neighbor orbital interactions • Experimental Valence Shell Ionization Potentials used to model matrix elements • Generally applicable to any element • Useful for calculating band structures in solid-state physics**Beyond One-Electron Formalism**• HF method • Ignores electron correlation • Effective interaction potential • Hatree Product- Fock introduced exchange – (relativistic quantum mechanics)**HF-Exchange**• For a two electron system • Fock modified wavefunction**Slater Determinants**• Ex. Hydrogen molecule**Beyond One-Electron Formalism**• HF method • Ignores electron correlation • Effective interaction potential • Hatree Product- Fock introduced exchange – (relativistic quantum mechanics)**CNDO (1965, Pople et al)**MINDO (1975, Dewar ) MNDO (1977, Thiel) INDO (1967, Pople et al) ZINDO SINDO1 STO-basis (/S-spectra,/2 d-orbitals) /1/2/3, organics /d, organics, transition metals Organics Electronic spectra, transition metals 1-3 row binding energies, photochemistry and transition metals Neglect of Differential Overlap (NDO)**Semi-Empirical Methods**• SAM1 • Closer to # of ab initio basis functions (e.g. d orbitals) • Increased CPU time • G1,G2 and G3 • Extrapolated ab initio results for organics • “slightly empirical theory”(Gilbert-more ab initio than semi-empirical in nature)**Semi-Empirical Methods**• AM1 • Modified nuclear repulsion terms model to account for H-bonding (1985, Dewar et al) • Widely used today (transition metals, inorganics) • PM3 (1989, Stewart) • Larger data set for parameterization compared to AM1 • Widely used today (transition metals, inorganics)**General Reccommendations**• More accurate than empirical methods • Less accurate than ab initio methods • Inorganics and transition metals • Pretty good geometry OR energies • Poor results for systems with diffusive interactions (van der Waals, H-bonded, radicals etc.)**Complete Neglect of Differential Overlap (CNDO)**• Overlap integrals, S, is assumed zero**Neglect of Differential Overlap (NDO)**Gives rise to overlap between electronic basis functions of different types and on different atoms**Complete Neglect of Differential Overlap (CNDO)**• One-electron overlap integral for different electrons is zero (as in Huckel Theory) • Two-electron integrals are zero if basis functions not identical**Intermediate Neglect of Differential Overlap (CNDO)**• Overlap integrals, S, is assumed zero**Eigenvalue Equation**• Matrix * Vector = Matrix (diagonal) * Vector • Schrodinger’s equation! The solutions to this differential equation are equal to the solutions to the matrix eigenvalue equation

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