Molecular Modeling and Informatics C371 Introduction to Cheminformatics Kelsey Forsythe

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

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

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

MMFF Potential E = E bond + E angle + E angle-bond + E torsion + E VDW + E electrostatic E = E bond + E angle + E angle-bond + E torsion + E VDW + E electrostaticE bondE angleE angle-bond E torsionE VDWE electrostaticE bondE angleE angle-bond E torsionE VDWE electrostatic

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

Classical vs. Quantum Trajectory Trajectory Real numbers Real numbers Deterministic (“The value is ___”) Deterministic (“The value is ___”) Variables Variables Continuous energy spectrum 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 - Hamiltonian operator - Hamiltonian operator Gravity? Gravity?

Hydrogen Molecule Hamiltonian Born-Oppenheimer Approximation Born-Oppenheimer Approximation Now Solve Electronic Problem Now Solve Electronic Problem

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

Hydrogen Molecule HOMO HOMO LUMO LUMO

Hydrogen Molecule Bond Density Bond Density

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

Approximate Methods SCF (Self Consistent Field) Method (a.ka. Mean Field or Hartree Fock) 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 (V external) Pick single electron and average influence of remaining electrons as a single force field (V 0 external) Then solve Schrodinger equation for single electron in presence of field (e.g. H-atom problem with extra force field) 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 Perform for all electrons in system Combine to give system wavefunction and energy (E Combine to give system wavefunction and energy (E) Repeat to error tolerance (E Repeat to error tolerance (E i+1 -E i )

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

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

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

Comparison to Experiments Electronic Schrodinger Equation gives bonding energies for non-vibrating molecules (nuclei fixed at equilibrium geometry) at 0K Electronic Schrodinger Equation gives bonding energies for non-vibrating molecules (nuclei fixed at equilibrium geometry) at 0K Can estimate G=  S using frequencies Can estimate G=  S using frequencies E out NOT  H f ! E out NOT  H f ! Bond separation reactions (simplest 2-heavy atom components) provide path to heats of formation Bond separation reactions (simplest 2-heavy atom components) provide path to heats of formation

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

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

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

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

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

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

Modeling Programs Spartan ( Spartan ( MacroModel ( MacroModel ( Sybyl ( Sybyl ( Gaussian ( Gaussian ( Jaguar ( Jaguar ( Cerius2 and Insight II ( Cerius2 and Insight II ( Quanta Quanta CharMM CharMM GAMESS GAMESS PCModel PCModel Amber Amber

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

Next Time QSAR (Read Chapter 4) QSAR (Read Chapter 4)

MMFF Energy Stretching Stretching Stretching

MMFF Energy Bending Bending Bending

MMFF Energy Stretch-Bend Interactions Stretch-Bend Interactions Stretch-Bend Interactions Stretch-Bend Interactions

MMFF Energy Torsion (4-atom bending) Torsion (4-atom bending) Torsion (4-atom bending) Torsion (4-atom bending)

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

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

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