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
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)
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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