Potential Energy Surface & Molecular Graphics


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this is the work on PES done by me referencing all available molecular modelling books And it also contains Molecular graphics as its second part

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Potential Energy Surface & Molecular Graphics

  3. 3. Wave function <ul><li>Describe the physical system </li></ul><ul><li>Deals about a function of the possible states of the system </li></ul><ul><li>Molecule : the possible configurations of all the electrons and the wave function describes the probabilities of those configurations. </li></ul>
  4. 4. <ul><li>Computation of the energy and wave function of a molecule </li></ul><ul><li>Born–Oppenheimer approximation allows the wave function of a molecule to be broken into its electronic and nuclear motions </li></ul><ul><li>Ψ total = product function </li></ul>Born–Oppenheimer approximation Ψ total = Ψ electronic x Ψ nuclear
  5. 5. H ψ = E ψ For a general quantum system Describes how the quantum state of a physical system changes in time Schrödinger equation i imaginary unit Ψ(r, t ) wave function ħ Planck constant Hamiltonian operator
  6. 6. Also considers Electronic Energy Of Each Of These Orientations
  7. 7. A potential energy surface must be created to take into account : 1.Every possible orientation of the reactant molecules 2.Every possible orientation of the product molecules 3.The electronic energy of the reactant molecules 4.The electronic energy of the product molecules
  8. 8. <ul><li>Let us consider a system comprising M nuclei and N </li></ul><ul><li>electrons. By including only electrostatic interactions, </li></ul><ul><li>the Hamiltonian of the system is given by </li></ul>M Nucleus N Electrons r Electronic coordinates { r 1 , r 2 , . . . . . , r N } R Nuclear coordinates { R 1 , R 2 , . . . .. . ., R M } σ Electronic Spin Coordinates { σ 1 , σ 2 , . . . . . . σ N } V(r,R) All electrostatic interactions M α Mass of the nucleus α m e Mass of the electron e
  9. 9. The time-independent Schrödinger equation In the Born-Oppenheimer approximation the wave function     is written as a product function                                 ψ E (r, σ ,R) ψ B.O = ψ e (r, σ ;R) Φ (R)
  10. 10. Equation for electronic motion: Remember: r Electronic Coordinates R Nuclear Coordinates The Potential Energy Surface (PES) depends parametrically on the position of the nuclei R
  11. 11. The electronic wavefunction    is a solution of the electronic Schrödinger equation                                                              The Schrödinger equation for the nuclear wave function    
  12. 12. Transition state The state corresponding to the highest energy along the reaction coordinate Reaction Coordinate Coordinate of a geometric parameter that changes during the conversion of one or more molecular entities bond length, bond angle , bond order, . . . . . . . . . .
  13. 13. LOCAL MINIMA LOCAL MAXIMA Ethane Dihedral Motion
  14. 14. CH 2 Cl-CH 2 Cl Dihedral Motion GLOBAL MINIMUM
  15. 15. Saddle Points {Minimum in all variables except one variable, Maximum in this Excepted variable} Saddle Point 2 minima & a Saddle point This corresponds to a transition state in theories of reaction mechanisms
  16. 16. Minima, Maxima & Saddle Points
  17. 17. COURTESY : Molecular Modeling:Geometry Optimization-Introduction to Cheminformatics II by Kelsey Forsythe Cyclohexane
  18. 18. The Real Picture….
  19. 19. What these points tell us ? Global Minimum Energy value corresponds to the most stable nuclear configuration Reaction Coordinate The path along the potential energy surface that the atoms &quot;travel&quot; during the chemical reaction Saddle Points or Correspond to transition Local Maxima states Local Minima Reactive Intermediates
  20. 20. It’s the Right time to define the Potential Energy Surface. . . . A geometric hyper surface on which the potential energy of a set of reactants is plotted as a function of the coordinates representing the molecular geometries of the system
  21. 21. A PES displays the energy of a molecule as a function of its geometry Potential Energy Geometric Coordinate e.g. bond length Potential Energy Geometric Coordinate s e.g. bond length, bond order 1-D 3-D
  22. 22. KEY FEATURES OF PES <ul><li>Equilibrium molecular structures correspond to the positions of the minima </li></ul><ul><li>Energetics of reactions can be calculated from the altitudes of the minima for reactants and products </li></ul><ul><li>A transition structure is the highest point on the lowest energy path </li></ul><ul><li>Reaction rates can be obtained from the height and profile of the potential energy surface around the transition structure </li></ul><ul><li>The shape of the valley around a minimum determines the vibrational spectrum </li></ul>
  24. 25. ADVANTAGES LIMITATIONS The structure, energetics, properties, reactivity, spectra and dynamics of molecules can be readily understood in terms of potential energy surfaces <ul><ul><li>Stability and reactivity are not precise concepts </li></ul></ul><ul><ul><li>Resonance, nucleophilicity, leaving group ability not considered </li></ul></ul>
  25. 26. <ul><li>MOLECULAR GRAPHICS </li></ul>
  26. 27. MOLECULAR GRAPHICS : The discipline and philosophy of studying molecules and their properties through graphical representations
  27. 28. MILESTONES Early Cathode ray tube screens or through plotters drawing on paper 1966 Display of a protein molecule (Project MAC) - Cyrus Levinthal and Robert Langridge Realistic&quot; Rendering Of Macromolecules Using Reflecting Spheres - Nelson Max 1982 Molecular Graphics Society (MGS) in UK 1980s Programs for calculating molecular properties (such as molecular dynamics and quantum mechanics) Molecular Graphics and Modelling Society (MGMS)
  28. 29. <ul><li>Vector Graphics </li></ul><ul><li>No 3-D renderings used </li></ul><ul><li>Hence, Geometrical attributes like bond length, torsional angle cannot be used </li></ul><ul><li>a.k.a 1-D Diagram </li></ul>
  29. 30. 3-D Rendered Image x,y,z coordinates should be known All geometric transformations (rotation, scaling, etc) can be done
  30. 31. Reference frames Drawing molecules requires a transformation between molecular coordinates and the screen <ul><li>Molecular transformations requires: </li></ul><ul><li>Scaling of the display (but not the molecule). </li></ul><ul><li>Translations of the molecule and objects on the screen. </li></ul><ul><li>Rotations about points and lines </li></ul>
  31. 32. Ambient occlusion Ambient occlusion is a global lighting technique Concept : light each point p with normal vector with its computed irradiance. Irradiance : the quantity of light reaching p from any direction… Local lighting Ambient Occlusion
  32. 33. Ambient occlusion applied to Proteins WITHOUT AMBIENT OCCLUSION WITH AMBIENT OCCLUSION
  33. 34. DIFFERENT ATTRRIBUTES TRANSLATION :A translation moves an object into a different position in a scene SCALING : A scaling changes the size of an object with two scale factors, Sx and Sy
  34. 35. ROTATION : Using the trigonometric relations, a point rotated by an angle about the origin SHEARING : A shearing affects an object in a particular direction (in 2D, it’s either in the x or in the y direction)
  36. 37. Ribbon Model Structure of Hemagglutinin Ligand: Sialic Acid Alpha Helices Carbon Oxygen Nitrogen
  37. 38. Space-Fill Models Structure of Formic Acid Atoms are drawn to suggest the amount of space they occupy CPK Model = Corey, Pauling, Koltan The quantum mechanical representation of molecules, there are only (positively charged) nuclei and a &quot;cloud&quot; of negative electrons. The electron cloud defines an approximate size for the molecule
  38. 39. Isosurface Zirconocene where part (left) is rendered as ball-and-stick and part (right) as an isosurface. Isosurfaces that have been coloured to show quantities such as electrostatic potential Negative Positive Neutral
  39. 40. Stick Model Space-Fill Model
  40. 41. Cylindrical or &quot;Licorice&quot; modes Cylindrical-Med
  41. 42. But Not the least, The Animation
  42. 43. RasMol Swiss PDB viewer Molscript Ribbons Grasp VMD WebMol Chime Cn3D PyMol QMol Structure Visualization & Manipulation Softwares
  43. 44. References: POTENTIAL ENERGY SURFACE (PES) Molecular Modelling : Principles and Applications by Andrew R Leech Molecular Modelling for Beginners by Alan Hinchliffe, UMIST, Manchester, UK Potential energy surfaces and applications for CmHn by Bastiaan J. Braams Emory University with Joel M. Bowman MOLECULAR GRAPHICS (MG) History of Visualization of Biological Macromolecules by Eric Martz and Eric Francoeur. Brief History of Molecular Mechanics/Graphics in LSU CHEM7770 lecture notes Desktop Molecular Modeling by Peter L.Hurray Ambient Occlusion and Edge Cueing for e nhancing Real Time Molecular Visualization by Marco Tarini, Paolo Cignoni, Claudio Montani Online Programs: PDB, JMol,