Hierarchical Simulations
       Multi-scale
           Years
           Yards                                Fossil Energy
                                       Cancer  Fuel Cells    Nanotechnology
                                       Research
                              Genetic                               Polymers
                              Engineering                                 Electronic         Design
                                          Organelle          Ceramics
          Seconds                         Modeling                        & Optical
                       2                                                  Materials
           Inches    Ñf=-r                               Specialty
                                              Receptor   Chemicals
                                              Modeling   & Catalysts      Metal 
                                                                          Alloys
                            Pharmaceuticals
                                                                                           Materials
        Microseconds                                Chemistry          Material 
                               Biochemistry                            Science
          Microns
                                     Molecular     Equilibrium    Meso-
                                   Self-Assembly     & Rate        scale
        Picoseconds                                 Constants    Modeling                 Molecules
         Nanometers  F=ma
                                                   Molecular 
                                                   Mechanics
                                                  Force Fields
        Femtoseconds  H = E                                                               Atoms
         Angstroms                                 QUANTUM
                                                  MECHANICS                                Electrons
                                                                    © W.A. Goddard III, M. Blanco, 1998
           Simulations
   Deterministic simulations: Molecular dynamics
   Stochastic simulations: Monte Carlo
                 Simulations
     Deterministic simulations: Molecular dynamics
            x1
                    Model         y1
            x2
                     f(x)
                                  y2
           ….
            xn
           What is an atom?
   Classical mechanics: a point particle
   Defined by its position (x,y,z) and its mass
   May carry an electric charge (positive or negative), 
    usually partial (less than an electron)
                                 Computing energy
                                        1                       2
                                                 (            )
                  U= å K b-b                                                                          Bonds
                                        2 b                 0
                            all bonds
                                           1                        2                                 Bond angles
                                                     (            )
                           + å Kqq-q0
                              all angles 2
                                              [             ( )]
                           + åKf1- cos nf                                                             Torsion angles
                              all torsions
                                                     éæ         ö12         æ        ö6ù
                                                          R                    R
                           +        å e êç ij÷ - 2ç ij ÷ ú                                            Vdw interactions
                                                  ij ê ç   r ÷              ç r ÷ ú
                              i, j nonbonded         ëè ij ø                è ij ø û
                                                    qq
                           +        å                 i   j                                           Electrostatics
                              i, j nonbonded 4pe er
                                                        0    ij