POTENTIAL ENERGY SURFACE (PES)

MOLECULAR GRAPHICS

Presentation By S.Prasanth Kumar

POTENTIAL ENERGY SURFACE (PES)

Wave function

Describe the physical system Deals about a function of the possible states of

the system Molecule : the possible configurations of all the

electrons and the wave function describes the probabilities of those configurations.

Computation of the energy and wave function of a molecule

Born–Oppenheimer approximation allows the wave function of a molecule to be broken into its electronic and nuclear motions

Ψtotal = product function

Born–Oppenheimer approximation

Ψtotal = Ψ electronic x Ψ nuclear

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 unitΨ(r,t) wave function ħ Planck constant Hamiltonian operator

Also considers Electronic Energy Of Each Of These Orientations

A potential energy surface must be created to take into account :

1.Every possible orientation of the reactant molecules2.Every possible orientation of the product molecules 3.The electronic energy of the reactant molecules4.The electronic energy of the product molecules

Let us consider a system comprising M nuclei and N

electrons. By including only electrostatic interactions,

the Hamiltonian of the system is given by

M Nucleus

N Electrons

r Electronic coordinates { r1, r2, . . . . . , rN }

R Nuclear coordinates { R1, R2 , . . . .. . ., RM}

σ Electronic Spin Coordinates {σ1 , σ2 , . . . . . . σN }

V(r,R) All electrostatic interactions

Mα Mass of the nucleus α

me Mass of the electron e

The time-independent Schrödinger equation

In the Born-Oppenheimer approximation the wave function     is written as a product function                                

ψE (r, σ,R) ψB.O = ψe (r, σ;R)Φ(R)

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

The electronic wavefunction    is a solution of the electronic Schrödinger equation                                                            

The Schrödinger equation for the nuclear wave function    

Transition state The state corresponding to the highest energy along the reaction coordinate

Reaction CoordinateCoordinate of a geometric parameter that changes during the conversion of one or more molecular entities

bond length, bond angle , bond order, . . . . . . . . . .

LOCAL MINIMA

LOCAL MAXIMA

Ethane Dihedral Motion

CH2Cl-CH2Cl Dihedral MotionGLOBAL MINIMUM

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

Minima, Maxima & Saddle Points

COURTESY: Molecular Modeling:Geometry Optimization-Introduction to Cheminformatics II by Kelsey Forsythe

Cyclohexane

The Real Picture….The Real Picture….

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 "travel" during the chemical

reaction

Saddle Points or Correspond to transition Local Maxima states

Local Minima Reactive Intermediates

It’s the Right time to define the Potential Energy It’s the Right time to define the Potential Energy Surface. . . .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

A PES displays the energy of a molecule A PES displays the energy of a molecule as a function of its geometryas a function of its geometry

Potential E

nergy

Geometric Coordinate

e.g. bond length

Potential E

nergy

Geometric Coordinates

e.g. bond length, bond order

1-D 3-D

KEY FEATURES OF PES Equilibrium molecular structures correspond to the positions of the minima

Energetics of reactions can be calculated from the altitudes of the minima for reactants and products

A transition structure is the highest point on the lowest energy path

Reaction rates can be obtained from the height and profile of the potential energy surface around the transition structure

The shape of the valley around a minimum determines the vibrational spectrum

APPLICATIONS

ADVANTAGES

LIMITATIONS

The structure, energetics, properties, reactivity, spectra and dynamics of molecules can be readily understood in terms of potential energy surfaces

Stability and reactivity are not precise concepts

Resonance, nucleophilicity, leaving group ability not considered

MOLECULAR GRAPHICS

MOLECULAR GRAPHICS: The discipline and philosophy of studying molecules and their properties through graphical representations

MILESTONESMILESTONES

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" 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)

Vector Graphics

◙ No 3-D renderings used

◙ Hence, Geometrical attributes like bond length, torsional angle cannot be used

◙ a.k.a 1-D Diagram

3-D Rendered Image

x,y,z coordinates should be known

All geometric transformations (rotation, scaling, etc) can be done

Reference frames

Drawing molecules requires a transformation between molecular coordinates and the screen

Molecular transformations requires: Scaling of the display (but not the molecule). Translations of the molecule and objects on the screen. Rotations about points and lines

Ambient occlusion

Ambient occlusion is a global lighting techniqueConcept : 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

Ambient occlusion applied to Proteins

WITHOUT AMBIENT OCCLUSION WITH AMBIENT OCCLUSION

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

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)

DIFFERENT MODELS USED IN VISUALIZATION

SOFTWARES

Ribbon Model

Structure of Hemagglutinin

Ligand: Sialic Acid

Alpha Helices

Carbon Oxygen Nitrogen

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 "cloud" of negative electrons. The electron cloud defines an approximate size for the molecule

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

NegativePositiveNeutral

Stick Model

Space-Fill Model

Cylindrical or "Licorice" modes

Cylindrical-Med

But Not the least, The Animation

RasMol

Swiss PDB viewer

Molscript

Ribbons

Grasp

VMD

WebMol

Chime

Cn3D

PyMol

QMol

Structure Visualization & Manipulation Softwares

References:

POTENTIAL ENERGY SURFACE (PES)

Molecular Modelling : Principles and Applications by Andrew R LeechMolecular Modelling for Beginners by Alan Hinchliffe, UMIST, Manchester, UKPotential energy surfaces and applications for CmHn by Bastiaan J. BraamsEmory 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.HurrayAmbient Occlusion and Edge Cueing for enhancing Real Time Molecular Visualization by Marco Tarini, Paolo Cignoni, Claudio MontaniOnline Programs: PDB, JMol,

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