molecular modeling l.
Skip this Video
Loading SlideShow in 5 Seconds..
Molecular Modeling PowerPoint Presentation
Download Presentation
Molecular Modeling

Loading in 2 Seconds...

play fullscreen
1 / 28

Molecular Modeling - PowerPoint PPT Presentation

  • Uploaded on

Molecular Modeling. Part I. A Brief Introduction to Molecular Mechanics. Molecular Modeling (Mechanics). Calculation of preferred (lowest energy) molecular structure and energy based on principles of classical (Newtonian) physics

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

PowerPoint Slideshow about 'Molecular Modeling' - Sharon_Dale

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
molecular modeling

Molecular Modeling

Part I.

A Brief Introduction to

Molecular Mechanics

molecular modeling mechanics
Molecular Modeling (Mechanics)
  • Calculation of preferred (lowest energy) molecular structure and energy based on principles of classical (Newtonian) physics
  • “Steric energy” based on energy increments due to deviation from some “ideal” geometry
  • Components include bond stretching, bond angle bending, torsional angle deformation, dipole-dipole interactions, van der Waals forces, H-bonding and other terms.
components of steric energy
Components of “Steric Energy”

E steric = E stretch + E bend + E torsion + E vdW + E stretch-bend + E H- bonding + E electrostatic + E dipole-dipole + E other

bond stretching energy
Bond Stretching Energy
  • A Morse potential best describes energy of bond stretching (& compression), but it is too complex for efficient calculation and it requires three parameters for each bond.

n(l) = De{1- exp [-a (l - l0)]}2

if: De = depth of potential energy minimum,

a = w(m/2De) where m is the reduced mass and w is related to the bond stretching frequency by w = (k/m)

morse potential hooke s law
Morse potential & Hooke’s Law
  • Most bonds deviate in length very little from their equilibrium values, so simpler mathematical expressions, such as the harmonic oscillator (Hooke’s Law) have been used to model the bond stretching energy:

n(l) = k/2(l - l0)2

bond stretching energy6
Bond Stretching Energy

Estretch = ks/2 (l - l0)2

(Hooke’s law force...

harmonic oscillator)

graph: C-C; C=O

higher order terms give better fit
Higher order terms give better fit

With cubic and higher terms:

n(l) = k/2(l - l0)2 [1- k’(l - l0)

- k’’(l - l0)2

- k’’’(l - l0)3 - …]

(cubic terms give better fit

in region near minimum; inclusion

of a fourth power term eliminates the maximum in the cubic fcn.)

bond angle bending energy
Bond Angle Bending Energy

Ebend = kb/2 (q - q0)2

graph: sp3 C-C-C

(Likewise, cubic and higher

terms are added for better fit

with experimental observations)

torsional energy
Torsional Energy
  • Related to the rotation “barrier” (which also includes some other contributions, such as van der Waals interactions).
  • The potential energy increases periodically as eclipsing interactions occur during bond rotation.





torsional energy10
Torsional Energy

Etorsion = 0.5 V1 (1 + cos f) + 0.5 V2 (1 + cos 2f) +

0.5 V3 (1 + cos 3f)

van der waals energy
van der Waals Energy

EvdW = A/r12 - B/r6

Lennard-Jones or

6-12 potential

combination of a repulsive

term [A] and an attractive term [B]

van der waals energy14
van der Waals Energy...

EvdW = A (B/r ) - C/r6

Buckingham potential

(essentially repulsion only, especially at short distances)

hydrogen bonding energy
Hydrogen Bonding Energy

EH-Bond = A/r12 - B/r10

(Lennard-Jones type,

with a 10, 12 potential)

electrostatic energy
Electrostatic Energy

E electrostatic = q1q2 / cer

(attractive or repulsive, depending on relative signs of charge; value depends inversely on permitivity of free space, or the dielectric constant of the hypothetical medium)

dipole dipole energy
Dipole-Dipole Energy

Calculated as the three dimensional vector sum of the bond dipole moments, also considering the permitivity (related to dielectric constant)of the medium (typical default value is 1.5)

(this is too complicated to demonstrate!!!)

use of cut offs
Use of Cut-offs
  • Van der Waals forces, hydrogen bonding, electrostatic forces, and dipole-dipole forces have dramatic distance dependencies; beyond a certain distance, the force is negligible, yet it still “costs” the computer to calculate it.
  • To economize, “cut-offs” are often employed for these forces, typically somewhere between 10 and 15Å.
properties calculated
Properties Calculated
  • Optimized geometry (minimum energy conformation)
  • Equilibrium bond lengths, bond angles, and dihedral (torsional) angles
  • Dipole moment (vector sum of bond dipoles)
  • Enthalpy of Formation (in some programs).
enthalpy of formation
Enthalpy of Formation
  • Equal to “steric energy” plus sum of group enthalpy values (CH2, CH3, C=O, etc.), with a few correction terms
  • Not calculated by all molecular mechanics programs (e.g., HyperChem and Titan)
  • Calculated values are generally quite close to experimental values for common classes of organic compounds.
bond lengths
Bond Lengths

Sybyl MM+ MM3Expt


C-C 1.554 1.532 1.531 1.526

C-H 1.095 1.115 1.113 1.109


C-C 1.518 1.517 1.516 1.522

C-H 1.107 1.114 1.111 1.110

C=O 1.223 1.210 1.211 1.222

bond angles
Bond Angles

Sybyl MM+ MM3


H-C-C 109.5 111.0 111.4

H-C-H 109.4 107.9 107.5


C-C-C 116.9 116.6 116.1

H-C-H 109.1 108.3 107.9

C-C-O 121.5 121.7 122.0

common force fields
Common Force Fields
  • MM2 / MM3 (Allinger) best; general purpose
  • MMX (Gilbert) added TS’s, other elements; good
  • MM+ (Ostlund) in HyperChem; general; good
  • OPLS (Jorgenson) proteins and nucleic acids
  • AMBER (Kollman) proteins and nucleic acids +
  • BIO+ (Karplus) CHARMm; nucleic acids
  • MacroModel (Still) biopolymers, general; good
  • MMFF (Merck Pharm.) general; newer; good
  • Sybyl in Alchemy2000, general (poor).
molecular modeling programs
Molecular Modeling Programs
  • HyperChem (MM+, OPLS, AMBER, BIO+)
  • Spartan(MM3, MMFF, Sybyl; on SGI or via x-windows from pc)
  • Titan (like Spartan,but faster; MMFF)
  • Alchemy2000 (Sybyl)
  • Gaussian 03 (on our SGIs linux cluster and on unix computers at NCSU and ECU; no graphical interface; not for molecular mechanics; MO calculations only)
steps in performing molecular mechanics calculations
Steps in Performing Molecular Mechanics Calculations
  • Construct graphical representation of molecule to be modeled (“front end”)
  • Select forcefield method and termination condition (gradient, # cycles, or time)
  • Perform geometry optimization
  • Examine output geometry... is it reasonable?
  • Search for global minimum.
energy minimization
Energy Minimization
  • Local minimum vs global minimum
  • Many local minima; only ONE global minimum
  • Methods: Newton-Raphson (block diagonal), steepest descent, conjugate gradient, others.

local minima

global minimum