Topics in Molecular Modeling I Overview Xiantao Li

Topics in Molecular Modeling: I. Overview Xiantao Li (xiantao. li@gmail. com) Department of Mathematics, Pennsylvania State University

Outline Mathematical models Applications Examples of the interatomic potential Basic computational techniques Various ensembles Statistical interpretation

Atomistic models

Example 1: crack propagation

Confirmation of Macromolecules

Other forms of the equations

Examples of the interatomic potentials

Example: a multi-body interaction

Non-dimensionalization

Discretization in time: Verlet’s scheme

Verlet’s scheme

Force calculation

Force calculation Divide the entire domain into cells Only the atoms in neighboring cells have direct interactions Use a list to identify atoms in each cell.

Periodic boundary conditions Use PBC to mimic a homogeneous system Use basis vectors to represent the shape of the box The relative position is adjusted using the basis vectors

Postprocessing

Radial distribution function (RDF)

Canonical ensemble

Free energy

Gibbs distribution

Pressure

Modeling the canonical ensemble

Realizing canonical ensemble

Dynamics at the virtual scale

Dynamics at the real time scale

Operator splitting

Andersen’s method

Stochastic models (Langevin)

Other ensembles

Linear response

The evolution of a quantity

The evolution of the probability density

Equilibrium Density

Two-point statistics

Time correlation function

Examples

Sampling error

General ODE system

General SDE systems

The Langevin dynamics model

Time correlation function

Example

Linear Response

Linear response (cont’d)

Linear response (cont’d)

Linear response (cont’d)