Molecular modeling and simulation in chemistry

Transcription

1 Molecular modeling and simulation in chemistry 1/20 Elements of modeling: Nuclei + electrons + photons: QED Nuclei + electrons: Schrödinger equation Auxiliary interaction centers (sites) Atoms classical molecular modeling (quantum corrections) Bigger groups (-CH 3 ): united (extended) atom Coarsed-grained models: meso/nanoscopic scale element = polyatomic group (surfactant = head + tail, polymer = [bead] n...) Microscopic scale (dispersions, granular materials) Continuum

2 Schrödinger equation 2/20...the theory of everything (in chemistry) In principle we can calculate the boiling point of water to 12 decimal digits using from these quantities: e, h, m e, m O, m H, c using QED. In reality it is a few % (after years of effort) Directly we can get with reasonable effort and precision: shape and energy of (small) molecules, spectra, kinetics K in gas phase a lot of stuff for crystals

3 Division of labor 3/20 nuclei electrons quantum mechanics quantum mechanics (quantum simulations) molecular model statistical mechanics macroscopic properties kinetic theory simulations

4 Before /20 molecular model statistical mechanics macroscopic properties kinetic theory

5 Classical molecular modeling 5/20 Static approach is based on energy as a function of coordinates Energy minimization (T = 0) molecular mechanics, structure optimization Refinement more accurate structure (from diffraction data) Biochemistry: molecular shape (lock and key), protein folding,...

6 Statistical thermodynamics 6/20 Averaged behavior of many particles...

7 Statistical thermodynamics 7/20... gives macroscopic properties

8 Molecular simulations molecular dynamics (MD) time development of a system composed of many molecules instantaneous forces acting on atoms cause their motion 8/20 Monte Carlo (MC); more precisely: Metropolis method and its variants a sequence of confiurations of the system is generated using random numbers an attempt is made to move a molecule (randomly with a certain distribution) this trial move is accepted or rejected so that its probability is the same as in real system kinetic Monte Carlo the simulated process is divided into elementary events (e.g., adsorption of an atom on a growing crystal, catalytical reaction) the event to happem is chosen according to a known probability quantum simulations MD, MC

9 What can be studied 9/20 Liquids: how structure affects properties (anomalies of water), solutions phase equilibria, solubility surfaces, interfaces, surfactants Solids: crystal structure, materials (defects) adsorption (zeolites) Biochemistry: proteins, nucleic acids, ion channels, lipid membranes Nanoobjects: micelles, polymers, self-assembly (coarse-grained models, lattices) Similar methods can be used for: granular materials, optimization, spreading of epidemies/species

10 [uvodsim/blend.sh] 10/20 Structure optimization (molecular mechanics) chair experiment: 28 kj/mol model: 26 kj/mol twist (skew) boat experiment: 45 kj/mol model: 53 kj/mol

11 [cd /home/jiri/tex/talks/letniskola; cytox.sh] 11/20 Electrospray of Cytochrome C Yi Mao, J. Woenckhaus, J. Kolafa, M.A. Ratner, M.F. Jarrold Electrospray: spray of charged aerosol Cross section is determined

12 Electrospray of Cytochromu C 12/20

13 Liquid water [cd /home/jiri/tex/talks/letniskola; showvid.sh] 13/ molecules 300K periodic in x,y adhesive pad nonadhesive lid

14 SIMOLANT [simolant-eng x] 14/20 Properties: 2D atoms (Lennard-Jones type potential) repulsive/attractive walls, gravity MC and MD constant energy and thermostat Phenomena: condensation of vapor freezing of a droplet crystal defects capilary action gas in a gravitational field

15 Self-assembly [janus.sh] 15/20 Supramolecular chemistry: assembling molecules using noncovalent forces (van der Waals, hydrogen bonds) to higher structural elements Show: bivalent particles in a solution Janus particles + tetravalent particles credit: wikipedie, pages/cassini credit: Atwood et al., Science 309, 2037(2005)

16 How to get energy minimum [uvodsim/min.sh] 16/20 Na 10 Cl 10 fast cooling (quenching) slow cooking (annealing)

17 [uvodsim/salesman.sh] 17/20 Optimization by simulated annealing We look for a global minimum of function U(A i ) (with many local minima) Configuration changes A i A j Metropolis MC simulation while decreasing temperature T Example: Traveling salesman problem 50 cities randomly in square 1 1 Configuration = sequence of cities U = path length Configuration change = interchange of 2 randomly chosen cities T = l = 5.37 T = 0 l = 7.93

18 (Plateau-)Rayleigh instability [../simul/rayleigh/show.sh] 18/20 A stream of water splits into droplets. Instability for kr < 1 (for perturbation sin(kz)), max. instability for kr = ln2.

19 Melting of nanoparticles [kroupa/kroupa.sh] 19/20 hail of 600 water molecules (ice Ih) heating simulation time = 5 ns

20 End of introduction a real lecture ahead... [showvid /home/jiri/macsimus/ray/dogrun/dogrun.vid] 20/20