Computational Chemistry

Molecular Modeling

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.

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

History - Big Picture Handheld molecular models

Think organic chemistry Pauling discovery helix & sheets Watson & Crick discovery DNA

X-ray crystal structures (experimental) Computer graphics

More Specifically3 Dimensional structures of molecules and

associated physicochemical properties Generation Manipulation Representation

Four Stages Structure building Structure analysis Structure comparison Structure prediction

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

NH

O NH

OH

Computer Graphics

Relationship to ExperimentExperiment Computation

Define Problem

Design experimental specify and buildprocedure and setup modelsapparatus

Do experiment Do calculationAnalyze Results

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

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!!!

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

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

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

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

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

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

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.)

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 + ….

Molecular Mechanics Programs Amber Charmm Discover MM2 MM3 MM4 Tripos

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

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

Computational Battle What is the goal of the project?

Small vs. Large molecular systems Accuracy vs speed