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2. Modeling of small systems

2. Modeling of small systems. Building the model What is the optimal conformation of a molecule? What is the relative energy of a given conformation? What does the charge distribution look like? Does a molecule form dimers? Does molecule A fit into a cavity of molecule B?

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2. Modeling of small systems

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  1. 2. Modeling of small systems Building the model What is the optimal conformation of a molecule? What is the relative energy of a given conformation? What does the charge distribution look like? Does a molecule form dimers? Does molecule A fit into a cavity of molecule B? How flexible is a molecule in solution? Sampling methods

  2. Modeling of small systems:building the model database (CSD, PDB, ICSD) molecular editor (Cerius, Sybyl, Molden) neighbor internet set of atoms connectivity hybridization molecule atom types charges atom types and charges depending on FF model

  3. Modeling of small systemswhat is the optimal conformation? optimal conformation: average geometry at room temperature optimal conformation: structure with the lowest MM energy optimizing a structure  minimizing the MM energy E = f (geometry) = f (ratom1, ratom2,ratom3,ratom4,……) [atomic coordinates] = f (bond lengths, bond angles, torsion angles) [internal coordinates]

  4. Modeling of small systemswhat is the optimal conformation? E = f (ratom1, ratom2,ratom3,ratom4,……) = f (bond lengths, bond angles, torsion angles) [internal coordinates] 3 d3 t3 d2 2 d1 c.f. QM: Z-matrix

  5. Modeling of small systemsoptimal molecular conformation:energy minimization energy Energy minimization may lead to…..: * the absolute E minimum * a local minimum * a saddle point; maximum * an area of almost constant energy geometric parameter

  6. Modeling of small systemsoptimal molecular conformation:energy minimization Common applications: ‘Cleaning up’ structures from the CSD ( remove errors in e.g. H positions) Identifying packing effects: what does the conformation of an isolated molecule look like?

  7. Modeling of small systemsWhat is the relative energy of a given conformation?  * calculate E() Calculate E, while setting  to 0, 15, 30, 45, ... ‘bumping atoms’ will cause unrealistic, high energy barriers.  relax (optimize) rest of structure, given  . * How likely is each conformation. * How easily can they interconvert.

  8. Modeling of small systemsconformational energy with/without solvent E()…. in water? in vacuum? in benzene?  No solvent included in simulation: * intra-molecular H bonds emphasized * molecule tends to contract

  9. Modeling of small systemsWhat does the charge distribution look like? * how polar is the molecule? * how large is the dipole moment? * which interactions can be anticipated? example: alizarine/NaCl

  10. Modeling of small systemsDoes a molecule form dimers? does a molecule dock well onto itself? * geometric fitting / steric hindrance: ‘close contacts’. * favorable electrostatics; H-bonds? energy minimization in vacuo

  11. Modeling of small systems Does molecule A fit into a cavity of molecule B? ligand -- protein additive -- crystal surface

  12. Modeling of small systems How flexible is a molecule in solution?Simulation of an organic salt in benzene or chloroform

  13. Modeling of small systems Simulation of an organic salt in solution Molecular Dynamics (MD): from still picture to movie. Atomic positions as a function of time, calculated by applying Newton’s equations of motion. r(t+ t) = r(t) + v(t+½t)t v(t+½t) = v(t-½t) + a(t)t a = F/m a r v r? v t+t t t+½t t-½t t~1fs * non-zero temperature  atomic motion * system has kinetic + potential energy * equilibrium properties at T, transport properties, conformational or ‘configurational’ search

  14. Modeling of small systems Simulation of an organic salt in solution * periodic boundary conditions to go from veeeeeeery smal droplet to ‘bulk’ * external forces/constraints: - nr. of particles - temperature - volume - pressure NVT, NPT simulations

  15. Modeling of small systemsresults from MD

  16. Sampling methods Obtaining a representative set of structures from a system with freedom in conformation/configuration. * Systematic: every combination of possible values of all DOF’s. * Random: a random subset of the above. * MD: ‘frames’ taken every n ps from an MD run. * MC: ‘frames’ taken from an MC run. Properties/features: simplicity completeness grid size speed efficiency birds’ eye view

  17. Next week: Crystals! Theorie: hoe zat dat ook al weer met die ruimtegroepen?? Experiment: wat bedoelt René de Gelder met R=6.2%? Modeling: hoe check ik mijn model in Cerius?

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