Post on 19-Dec-2015
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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
Modeling of small systems:building the model
database
(CSD, PDB, ICSD)
molecular editor
(Cerius, Sybyl, Molden)
neighbor
internet
set of atoms
molecule
model
connectivityhybridization
atom typescharges
atom types and chargesdepending on FF
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]
Modeling of small systemswhat is the optimal conformation?
E = f (ratom1, ratom2, ratom3, ratom4,……) = f (bond lengths, bond angles, torsion angles) [internal coordinates]
d1
d22
d3
t3
3
c.f. QM: Z-matrix
Modeling of small systemsoptimal molecular conformation: energy minimization
energy
geometric parameter
Energy minimization may lead to…..:* the absolute E minimum* a local minimum* a saddle point; maximum* an area of almost constant energy
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 theconformation of an isolated molecule look like?
Modeling of small systems What 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.
Modeling of small systems conformational 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
Modeling of small systems What 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
Modeling of small systems Does 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
Modeling of small systems Does molecule A fit into a cavity of molecule B?
ligand -- proteinadditive -- crystal surface
Modeling of small systems How flexible is a molecule in solution?
Simulation of an organic salt in benzene or chloroform
Molecular Dynamics (MD): from still picture to movie.
Atomic positions as a function of time, calculated by applyingNewton’s equations of motion.
r(t+ t) = r(t) + v(t+½t)tv(t+½t) = v(t-½t) + a(t)ta = F/m
Modeling of small systems Simulation of an organic salt in solution
* non-zero temperature atomic motion* system has kinetic + potential energy* equilibrium properties at T, transport properties, conformational or ‘configurational’ search
t-½t t+½tt t+t
r v r?a
v
t~1fs
Modeling of small systems Simulation of an organic salt in solution
* periodic boundary conditionsto go from veeeeeeery smal dropletto ‘bulk’
* external forces/constraints: - nr. of particles - temperature - volume - pressure
NVT, NPT simulations
Modeling of small systemsresults from MD
Sampling methods
* 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 sizespeed efficiency birds’ eye view
Obtaining a representative set of structures from a system withfreedom in conformation/configuration.
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?