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 Computer graphics Think organic chemistry Pauling discovery  helix &  sheets Watson & Crick discovery DNA X-ray crystal structures (experimental) Computer graphics

More Specifically 3 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

Computer Graphics

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