lec11 - CHE596M Multi-Scale Modeling of Matter Instructor...

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NC STATE CHE596M Multi-Scale Modeling of Matter Instructor: Keith E. Gubbins Lecture 11: Composite pair potentials and force fields
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NC STATE Outline induction forces Introduction to Force Fields. General features of force fields Pair potentials for small molecules Potentials for large, flexible molecules. Intramolecular contributions - Bond stretching - Bond bending - Bond rotation (torsion) - Cross terms Class I, II and III force fields. Some common force fields United atom models Mesoscopic models
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NC STATE Induction Interactions So far we assumed the charge distribution was rigid. In reality the molecules are polarizable – their charge cloud will adjust in response to an applied field, e.g. that due to neighboring molecules. • Thus a dipole is induced, μ ind , due to an electric field E ( r ) ( 29 E α r μ ind = where = α molecular polarizability tensor The induction interaction energy will be ( 29 2 2 2 1 1 : 2 2 ind xx x yy y zz z u EE E E E α = - = - + + in the principal axes
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NC STATE Induction Interactions • For 2 dipoles μ 1 and 2 separated by r , the potential φ ( r ) at molecule 2 ( 29 2 1 ~ r μ r φ , so that the electric field ( 29 φ r E - = is ( 29 3 1 ~ r μ r E • The interaction energy between 1 and ind is 1 2 1 1 3 1 2 1 6 ~ ~ ind ind ind u r u u r μ α μ μ μ = , or due to 1 is • Thus the ratio of u ind / u elec for 2 dipoles is ~ α / r 3 . Usually / σ 3 ~ 0.03 – 0.06, so for 2 isolated dipoles induction is a small effect compared to electrostatic interactions However, in dense fluids and liquids, many-body effects are important for induction, and can be 20 – 40% of electrostatic interaction (see Gray and Gubbins, sec. 2.10)
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NC STATE Force Fields Methods • In these methods we use classical force fields to describe the interactions between atoms, molecules or particles • Force field methods rely on the Born-Oppenheimer approximation, ignore electronic motions and calculate the energy of a system as a function of nuclear positions only → simulations of much larger systems can be performed → up to billions of atoms possible on the largest supercomputers (nearly a cubic micrometer - beyond that should not need to resolve everything at the atomic or molecular level)! •Force fields rely on: – Relatively “simple” expressions that capture the stretching of bonds, the opening and closing of angles, rotations about bonds, etc. – Transferability: the ability to apply a given form for a force field to many materials by tweaking parameters (e.g. polystyrene vs. polyethylene) taken from Dr. S. C. Glotzer’s lectures on Computational Nanoscience of Soft Materials, University of Michigan http://www.engin.umich.edu/dept/cheme/people/glotzertch.html
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NC STATE Classes of Force Field Models There are essentially three “classes” of force field models, each one corresponding to a different level of detail: Explicit atom (all atoms represented explicitly) - Used to model a specific system United atom (coarse-grained) - Treat a group of atoms (e.g. -CH 3 , -OH, -NH 2 ) as a spherical interaction site. Used to model a specific system
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This note was uploaded on 08/01/2008 for the course CHEM 596M taught by Professor Franzen during the Spring '08 term at N.C. State.

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lec11 - CHE596M Multi-Scale Modeling of Matter Instructor...

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