Potential Energy Surface & Molecular Graphics

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

1. POTENTIAL ENERGY
SURFACE (PES)
MOLECULAR GRAPHICS
Presentation By S.Prasanth Kumar

2. POTENTIAL ENERGY
SURFACE (PES)

3. Wavefunction

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

4. 
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
Ψ

total
=
product function
–
Born Oppenheimerapproximation

Ψ
total
=

Ψ
electronic
x Ψ
nuclear

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. Also considers Electronic Energy Of Each Of These Orientations

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. 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 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
Mα
Mass of the nucleus
α
m
e
Mass of the electron e

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. :
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. The electronic wavefunction    is a solution of the

electronic Schrödinger equation                     


The Schrödinger equation for the nuclear wave function

12. Transitionstate


The state corresponding to the highest energy along the

reaction coordinate


ReactionCoordinate

Coordinate of a geometric parameter that changes during the

conversion of one or more molecular entities
, , , . . . . . . . . . .
bond length bond angle bond order

13. LOCALMINIMA

LOCALMAXIMA

EthaneDihedralMotion

14. CH
2
Cl-CH
2
Cl Dihedral Motion
GLOBAL MINIMUM

15. SaddlePoints
{ ,
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. Minima, Maxima & Saddle Points

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

18. ….
TheRealPicture
….
TheRealPicture

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 "travel"
during the chemical
reaction
Saddle Points or Correspond to transition
Local Maxima states
Local Minima Reactive
Intermediates

20. 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

21. APESdisplaystheenergyofamoleculeasa

APESdisplaystheenergyofamoleculeasa

functionofitsgeometry

functionofitsgeometry
P
o
t
e
n
t
ia
l
E
n
e
r
g
y
Geometric Coordinate
e.g. bond length
P
o
t
e
n
t
ia
l
E
n
e
r
g
y
Geometric Coordinates
e.g. bond length, bond order
1-D
3-D

22. 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

23. APPLICATIONS

25. ADVANTAGE
S
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

26. MOLECULAR GRAPHICS

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

28. 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)

29. Vector Graphics
◙ No 3-D renderings
used
◙ Hence, Geometrical
attributes like bond
length, torsional angle
cannot be used
◙ a.k.a 1-D Diagram

30. 3-D Rendered Image
x,y,z coordinates should be known
All geometric transformations (rotation, scaling, etc)
can be done

31. 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

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

33. Ambient occlusion applied to Proteins
WITHOUT AMBIENT OCCLUSION WITH AMBIENT OCCLUSION

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

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. DIFFERENT MODELS USED IN
VISUALIZATION SOFTWARES

37. RibbonModel
Structure of Hemagglutinin
Ligand: Sialic Acid
Alpha Helices
Carbon
Oxygen
Nitrogen

38. -
Space FillModels
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

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

40. Stick Model
Space-Fill Model

41. Cylindrical or
"Licorice" modes
Cylindrical-Med

42. ,
ButNottheleast TheAnimation

43. RasMol
Swiss PDB viewer
Molscript
Ribbons
Grasp
VMD
WebMol
Chime
Cn3D
PyMol
QMol

Structure Visualization & Manipulation Softwares

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 enhancing Real Time Molecular
Visualization by Marco Tarini, Paolo Cignoni, Claudio Montani
Online Programs: PDB, JMol,

45. FOR YOUR ATTENTION