CHEM6670Notes10 - Basics of molecular dynamics 1 CHEM 6670...

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Unformatted text preview: Basics of molecular dynamics 1 CHEM 6670 omputational Chemistry & Biophysics Computational Chemistry & Biophysics Molecular dynamics Feb 19, 2008 Course instructor: Dr. Jana Khandogin [email protected] Course web site: http://ccb.ou.edu/teaching.aspx Simulations of model systems • Potential energy of an N atom system can be generally written s as • A good approximation ) , , ( ) , ( ) ( 3 2 1 ⋅ ⋅ ⋅ + + + = ∑∑ ∑ ∑∑ ∑ > > > > j i j i j k k j i i i j j i i i r r r v r r v r v V r r r r r r 2 ∑∑ ∑ > + ≈ i i j j i eff i i r r v r v V ) , ( ) ( 2 1 r r r Idealized model potentials • Hard ‐ sphere potential • Square well potential ⎩ ⎨ ⎧ ≥ < ∞ = ) ( ) ( ) ( σ σ r r r v HS 3 ⎪ ⎩ ⎪ ⎨ ⎧ ≥ < ≤ − < ∞ = ) ( ) ( ) ( ) ( 2 2 1 1 σ σ σ ε σ r r r r v HS Lennard ‐ Jones potential • For simulation of liquids, Lennard ‐ Jones (van der Waals) 6 ‐ 12 otential is often used. potential is often used. [ ] 6 12 ) / ( ) / ( 4 ) ( r r r v LJ σ σ ε − = 4 Basics of molecular dynamics 2 Molecular force field • Assumptions 5 Force field bonded terms • Bonded energy terms • Between bonded atoms (improper torsion) – Maintain planarity and chirality 6 Force field nonbonded terms • Columbic and Lennard ‐ Jones potentials • 1 ‐ 2 and 1 ‐ 3 are excluded from non ‐ bonded calculations 7 Non ‐ bonded interaction • Electrostatic interactions decay with distance 8 Basics of molecular dynamics 3 Simple truncation 9 Truncate and shift 10 Switching function 11 Truncation artifacts • Ion ‐ ion radial distribution function Auffinger and Beveridge Chem Phys Lett, 1995 36 Na and Cl, 1531 H2O 36 Å cubic cell 9 ‐ 16 Å twin ‐ range cutoff artifact 12 Basics of molecular dynamics 4 Periodic boundary conditions • Question: how to obtain ulk properties from a bulk properties from a small number of particles? • Solution: use a box • Problem: too particles interact with the walls (surface artifacts) • Solution: periodic boundary conditions 13 Periodic boundary conditions • Solution: periodic boundary conditions y • Box (primary cell) is replicated periodically • When a primary particle leaves the box, an image particle enters the box • nic particles: sum to Ionic particles: sum to infinity in PBC. Thus, counter ions need to be introduced to make total charge neutral....
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CHEM6670Notes10 - Basics of molecular dynamics 1 CHEM 6670...

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