1. Computational Chemistry
Molecular Modeling

2. Molecular Modeling Requires mastering a broad range of fields
Chemistry, Physics, Mathematics, Computer science, Biology, Pharmacology, serendipity
Molecular Modeling is the generation, manipulation and representation of three dimensional structures of molecules and associated physicochemical properties.

3. What is Molecular Modeling?
Term used to describe computer based methods which give both quantitative and qualitative insight into the way molecules interact and react.
Within this definition are many possible methods
Empirical
Quantum
Dynamics

4. History - Big Picture Handheld molecular models Computer graphics
Think organic chemistry
Pauling discovery  helix &  sheets
Watson & Crick discovery DNA
X-ray crystal structures (experimental)
Computer graphics

5. More Specifically
3 Dimensional structures of molecules and associated physicochemical properties
Generation
Manipulation
Representation
Four Stages
Structure building
Structure analysis
Structure comparison
Structure prediction

6. How should a molecule be represented?
Theory H = E
Chemical formula C14H20N2O2
2D structure
Models
Computer graphics
Black and white line representation, color line drawing, color ball and stick model, space filling model, Van der Waals dot surface, wire surface, electrostatic potential energy surface

7. Computer Graphics

8. Relationship to Experiment
Experiment Computation
Define Problem
Design experimental specify and build
procedure and setup models
apparatus
Do experiment Do calculation
Analyze Results

9. Computational Approaches
Quantum chemical
Ab initio
Semi empirical
Density functional theory
Molecular Mechanics
Force field calculations
Requires use of the Born-Oppenheimer Theorem
Electrons move in stationary field of the nuclei; electronic and nuclear motion are separable

10. Quantum Theory
Solving Schrodinger wave equation to minimize the electronic energy of the system
Fundamental Equation Ĥ  = E 
 = wave function of system (eigenfunction)
Ĥ = Hamiltonian operator
E = energy eigenvalue
Each wave function (that is a solution to the Schrodinger equation) must meet certain mathematical restrictions and corresponds to a different stationary point of the system. The stationary point with the lowest energy eigenvalue is the ground state of the system.
VERY HARD TO DO!!!

11. Hartree Fock Theory
Using MO theory, define simplified wave functions (Hartree-Fock wave functions) which can be further broken down into a linear combination of one-electron atomic orbitals (LCAO-MO).
Choice of atomic orbitals is important since they define the basis set (gaussian type orbitals)
Take a linear combination of gaussian orbitals to define electron conditions. (Noble Prize to John Pople 1998)
Use Self Consistent Field Method to calculate total electronic Energy

12. Limitations of Hartree Fock
Use of simplified wave function
Single assignment of electrons to orbitals
Need to expand on the configuration interaction of electrons
Other ab initio methods
Moller-Plesset Perturbation Theory
Typically terminated at the second order
MP2, MP4
Coupled Cluster Theory

13. Semi-Empirical Methods
Use simplifying assumptions to solve the energy and wave function of molecular systems.
Use simpler Hamiltonian operator
Use empirical parameters for some of the two-electron integrals
Complete or partial neglect of other electron integrals

14. Semi-Empirical Methods
CNDO – Complete Neglect of Differential Overlap
Bonding not calculated
MINDO – Modified Intermediate Neglect of Differential Overlap
MNDO – Modified Neglect of Differential Overlap
Fix is AM1 method
Allow for faster calculations
Allow for bigger chemical systems
Obvious problems with accuracy

15. Density Functional Theory
Replace complicated multi-electron wave function and the Schrodinger equation with simpler equation for calculation of electron density of the molecular system.
Local density approximation where electronic properties are determined as functions of the electron density through the use of local relationships.
Nobel Prize to Walter Kohn in 1998

16. DFT
One to one correspondence between ground state wave function and ground state electron density
Simpler to calculate G. S. electronic wave function from G. S. electronic density
Faster and greater Accuracy than conventional ab initio
Problematic with excited state systems
Newest method – not standardized

17. Molecular Mechanics Based on Born-Oppenheimer Approximation
Electrons move in stationary field of the nuclei; electronic and nuclear motion are separable
Calculating position of nuclei only
Through set of simple equations called a force field
Uses the notion that molecules have “natural” bond lengths and bond angles
Molecules will adjust their nuclear positions to take up these natural values
In a strained system, the molecule will deform in predictable ways to minimize the strain (and allow for the strain energy of the molecule to be calculated.)

18. Molecular Mechanics Classical mechanics approach
Develop a set of potential functions called the force field which contains adjustable parameters that are optimized to obtain the best match to the experimental properties.
Mathematical approach in an attempt to reproduce molecular structures, potential energies and other features
Etotal= Es + Eb + Etor + Evdw + Eele + ….

19. Molecular Mechanics Programs
Amber
Charmm
Discover
MM2 MM3 MM4
Tripos

20. Limitations of Molecular Mechanics
Parameters for a particular class of compounds must be in the program
Parameters and equations must be accurate
Extrapolation to “new” molecular structures may be dangerous
Does not deal with electrons
FOR ALL METHODS
Local minimum problem
Over interpreting results – looking at individual components

21. Applications of Molecular Modeling
Understanding Mechanisms
Understanding Conformations
Understanding Biological Activity
Understanding the Pharmacophore
Understanding Protein Structures

22. Computational Battle What is the goal of the project?
Small vs. Large molecular systems
Accuracy vs speed