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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
Molecular Modeling: Semi-Empirical Methods

C372

Introduction to Cheminformatics II

Kelsey Forsythe

semi empirical methods
Semi-Empirical Methods
  • Advantage
    • Faster than ab initio
    • Less sensitive to parameterization than MM methods
  • Disadvantage
    • Accuracy depends upon parameterization
semi empirical methods3
Semi-Empirical Methods
  • Ignore Core Electrons
  • Approximate part of HF integration
estimating energy
Estimating Energy
  • Recall Eclassical quantal
approximate methods
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 energy6
Estimating Energy
  • Want to find c’s so that
estimating energy7
Estimating Energy
  • F simulataneous

equations gives a

matrix equation

matrix algebra
Matrix Algebra
  • Finding determinant akin to rotating matrix until diagonal ( )
huckel theory
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
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 c3h512
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
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
Beyond One-Electron Formalism
  • HF method
    • Ignores electron correlation
    • Effective interaction potential
    • Hatree Product-

Fock introduced exchange – (relativistic quantum mechanics)

hf exchange
HF-Exchange
  • For a two electron system
  • Fock modified wavefunction
slater determinants
Slater Determinants
  • Ex. Hydrogen molecule
beyond one electron formalism17
Beyond One-Electron Formalism
  • HF method
    • Ignores electron correlation
    • Effective interaction potential
    • Hatree Product-

Fock introduced exchange – (relativistic quantum mechanics)

neglect of differential overlap ndo
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 methods19
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 methods20
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
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
Complete Neglect of Differential Overlap (CNDO)
  • Overlap integrals, S, is assumed zero
neglect of differential overlap ndo23
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 cndo24
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
Intermediate Neglect of Differential Overlap (CNDO)
  • Overlap integrals, S, is assumed zero
eigenvalue equation
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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