MolMod C371

Molecular Modeling and Informatics: 

Molecular Modeling and Informatics C371 Introduction to Cheminformatics Kelsey Forsythe

Characteristics of Molecular Modeling: 

Characteristics of Molecular Modeling Representing behavior of molecular systems Visual (tinker toys – LCDs) rendering of molecules Mathematical rendering (differential equations, matrix algebra) of molecular interactions Time dependent and time independent realms

Molecular Modeling : 

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

Empirical Models: 

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

MMFF Potential: 

MMFF Potential

Atomistic Model History: 

Atomistic Model History Atomic Spectra Balmer (1885) Plum-Pudding Model J. J. Thomson (circa 1900) Quantization Planck (circa 1905) Planetary Model Neils Bohr (circa 1913) Wave-Particle Duality DeBroglie (circa 1924) Schrodinger Wave Equation Erwin Schrodinger and Werner Heisenberg

Classical vs. Quantum: 

Classical vs. Quantum Trajectory Real numbers Deterministic (“The value is ___”) Variables Continuous energy spectrum Wavefunction Complex (Real and Imaginary components) Probabilistic (“The average value is __ ” Operators Discrete/Quantized energy Tunneling Zero-point energy

Schrodinger’s Equation: 

Schrodinger’s Equation - Hamiltonian operator Gravity?

Hydrogen Molecule Hamiltonian: 

Hydrogen Molecule Hamiltonian Born-Oppenheimer Approximation Now Solve Electronic Problem

Electronic Schrodinger Equation: 

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)

Hydrogen Molecule: 

Hydrogen Molecule HOMO LUMO

Hydrogen Molecule: 

Hydrogen Molecule Bond Density

Ab Initio/DFT: 

Ab Initio/DFT Complete Description! Generic! Major Drawbacks: Mathematics can be cumbersome Exact solution only for hydrogen Informatics Approximate solution time and storage intensive Acquisition, manipulation and dissemination problems

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)

Correcting Approximations: 

Correcting Approximations Accounting for Electron Correlations DFT(Density Functional Theory) Moller-Plesset (Perturbation Theory) Configuration Interaction (Coupling single electron problems)

Geometry Optimization: 

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

Modeling Programs : 

Modeling Programs Observables Equilibrium bond lengths and angles Vibrational frequencies, UV-VIS, NMR shifts Solvent Effects (e.g. LogP) Dipole moments, atomic charges Electron density maps Reaction energies

Comparison to Experiments: 

Comparison to Experiments Electronic Schrodinger Equation gives bonding energies for non-vibrating molecules (nuclei fixed at equilibrium geometry) at 0K Can estimate G= H - TS using frequencies Eout NOT DHf! Bond separation reactions (simplest 2-heavy atom components) provide path to heats of formation

Ab Initio Modeling Limits: 

Ab Initio Modeling Limits Function of basis and method used Accuracy ~.02 angstroms ~2-4 kcal N HF - 50-100 atoms DFT - 500-1000 atoms

Semi-Empirical Methods: 

Semi-Empirical Methods Neglect Inner Core Electrons Neglect of Diatomic Differential Overlap (NDDO) Atomic orbitals on two different atomic centers do not overlap Reduces computation time dramatically

Other Methods: 

Other Methods Energetics Monte Carlo Genetic Algorithms Maximum Entropy Methods Simulated Annealing Dynamics Finite Difference Monte Carlo Fourier Analysis

Large Scale Modeling (>1000 atoms): 

Large Scale Modeling (>1000 atoms) Challenges Many bodies (Avogardo’s number!!) Multi-faceted interactions (heterogeneous, solute-solvent, long and short range interactions, multiple time-scales) Informatics Split problem into set of smaller problems (e.g. grid analysis-popular in engineering) Periodic boundary conditions Connection tables

Large Scale Modeling: 

Large Scale Modeling Hybrid Methods Different Spatial Realms Treat part of system (Ex. Solvent) as classical point particles and remainder (Ex. Solute) as quantum particles Different Time Domains Vibrations (pico-femto) vs. sliding (micro) Classical (Newton’s 2nd Law) vs. Quantum (TDSE)

Reference Materials: 

Reference Materials Journal of Molecular Graphics and Modeling Journal of Molecular Modelling Journal of Chemical Physics THEOCHEM Molecular Graphics and Modelling Society NIH Center for Molecular Modeling “Quantum Mechanics” by McQuarrie “Computer Simulations of Liquids” by Allen and Tildesley

Modeling Programs: 

Modeling Programs Spartan (www.wavefun.com) MacroModel (www.schrodinger.com) Sybyl (www.tripos.com) Gaussian (www.gaussian.com) Jaguar (www.schrodinger.com) Cerius2 and Insight II (www.accelrys.com) Quanta CharMM GAMESS PCModel Amber

Summary: 

Summary Types of Models Tinker Toys Empirical/Classical (Newtonian Physics) Quantal (Schrodinger Equation) Semi-empirical Informatic Modeling Conformational searching (QSAR, ComFA) Generating new potentials Quantum Informatics

Next Time: 

Next Time QSAR (Read Chapter 4)

MMFF Energy: 

MMFF Energy Stretching

MMFF Energy: 

MMFF Energy Bending

MMFF Energy: 

MMFF Energy Stretch-Bend Interactions

MMFF Energy: 

MMFF Energy Torsion (4-atom bending)

MMFF Energy: 

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

Intermolecular/atomic models: 

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

MMFF Energy: 

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