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Molecular Modeling Fundamentals: Modus in Silico

Molecular Modeling Fundamentals: Modus in Silico. C372 Introduction to Cheminformatics II Kelsey Forsythe.

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Molecular Modeling Fundamentals: Modus in Silico

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  1. Molecular ModelingFundamentals: Modus in Silico C372 Introduction to Cheminformatics II Kelsey Forsythe

  2. "Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit in chemistry. If mathematical analysis should ever hold a prominent place in chemistry - an aberration which is happily almost impossible - it would occasion a rapid and widespread degeneration of that science." A. Comte (1830) 1992 Nobel Prize in Chemistry Rudolph Marcus (Theory of Electron Transfer) 1998 Nobel Prize in Chemistry John Pople (ab initio) Walter Kohn (DFT-density functional theory)

  3. Characteristics of Molecular Modeling • Representing behavior of molecular systems • Visual rendering of molecules • Tinker toys • Tinker Program (Washington Univ. St. Louis) • Mathematical rendering of molecular interactions • Newton’s Laws - Kinetic Theory of Gases • Matrix Algebra - Quantum Theory Graph Theory? Informatics!!

  4. Molecular Modeling Valence Bond Theory + = Underlying equations: empirical (approximate, soluble) -Morse Potential ab initio (exact, insoluble (less hydrogen atom)) -Schrodinger Wave Equation

  5. Energy Energy = ? E=KE + PE Depends on underlying equations/assumptions: Energy of all/some of particles? Energy = 0? EMMFFNOT EHF

  6. Electrostatics • Coulombs Law • Permittivity used for vacuum • Point particles? • Solvent effects • Poisson Equation • Used to calculate electronic properties

  7. Atomic Units

  8. Thermodynamics • How might we compute relevant thermodynamic quantities? • Equipartition Theorem • Harmonic Oscillator Approximation

  9. Quantum Mechanics • All chemical properties for a system are given by the Schrodinger equation • No closed form solutions for systems of more than two-bodies (H-atom) • Number of equations too numerous for computation/storage (informatics problem?)

  10. Schrodinger’s Equation • - Hamiltonian operator • Gravity?

  11. Hydrogen Molecule Hamiltonian • Born-Oppenheimer Approximation • Now Solve Electronic Problem

  12. Electronic Schrodinger Equation • Solutions: • , the basis set, are of a known form • Need to determine coefficients (cm) • Wavefunctions gives probability ( ) of finding electrons in space (e. g. s,p,d and f orbitals) • Molecular orbitals are formed by linear combinations of electronic orbitals (LCAO)

  13. Statistical Mechanics • Molecular description of thermodynamics • Temperature represents average state for system of molecules • Energy of system is not energy of each molecule - distribution • Condensed Phase - Ideal Gas Law not applicable. • Boltzmann averaging • Use Monte Carlo for spatial/configurational averaging or molecular dynamics to average a property (ergodic hypothesis)

  14. Geometry Optimization • First Derivative is Zero - At minimum/maximum • As N increases so does dimensionality/complexity/beauty/difficulty • Multi-dimensional (macromolecules, proteins) • Conjugate gradient methods • Monte Carlo methods

  15. Empirical Models • Simple/Elegant? • Intuitive?-Vibrations ( ) • Major Drawbacks: • Does not include quantum mechanical effects • No information about bonding (re) • Not generic (organic inorganic) • Informatics • Interface between parameter data sets and systems of interest • Teaching computers to develop new potentials from existing math templates

  16. MMFF Potential E = Ebond+ Eangle+ Eangle-bond + Etorsion+ EVDW + Eelectrostatic Merck Molecular Force Field -Common organics/biopolymers

  17. MMFF Energy • Stretching

  18. MMFF Energy • Bending

  19. MMFF Energy • Stretch-Bend Interactions

  20. MMFF Energy • Torsion (4-atom bending)

  21. MMFF Energy • Analogous to Lennard-Jones 6-12 potential • London Dispersion Forces • Van der Waals Repulsions

  22. Intermolecular/atomic models • General form: • Lennard-Jones Van derWaals repulsion London Attraction

  23. MMFF Energy • Electrostatics (ionic compounds) • D – Dielectric Constant • d - electrostatic buffering constant

  24. Hydrogen Molecule • Bond Density

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