How to develope a new potential function.

It's a very hard question to answer. You can easily become famous
and popular for deveoping a new, accurate, transferrable, and
easy-to-use force field.

Well,
first, it depends on what kind of materials you are interested in:
metals, polymers, glasses, ceramics, molecular materials - they all
have different function forms. Then do literature search to find
relevant papers and start from there.

You may start from a generic force field and adjust some parameters to fit better for your purpose.

Again, it's not easy but definitely a very important topic in MD simulations.

You can use Quantom mechanics to find your suitable potential function. your question is too general. you can use even open source softwares in this regard. QM/MM is more accurate but harder answer.

Developing a potential, to put it simply (real simply), is a two-step process.

First, you require a potential form.  This refer to the general potential expression, usually containing potential parameters and interatomic separation/bond angle housed in mathematical expressions.  The form depends on the type of atomic bond that you are looking at.  The form therefore describes the characteristic of the atomic bond, based upon first-principles approximation like the Born-Oppenheimer or tight-binding method.  This is the most difficult part for potential formulation and you need background in atomic chemistry to achieve this.

Second, when you have the form, you shall fit the parameters to physical properties.  It is usually not possible to fit a potential to all physical properties, as the number of potential parameters will usually be less than the total number of independent physical properties related to that material.  We usually perform specific fit to a limited number of crucial properties like lattice parameter, phonon dispersion, bond energy, bulk modulus etc.  Then be very careful in analyzing the output from the simulation, by avoiding the computation of properties that we did not perform parameter fitting on.  This is a relatively simpler process and you require experitise in mathematical manipulation and some knowledge on thermodynamics and mechanics of materials.

You may try reading some literatures on potential formulation like the EAM for metals, Stillinger-Weber for Si and the more sophisticated ZnO potential formulation.

This process will take a long time, but the returns are usually good if your potential describes a large group of atomic systems.  Good luck.

Adrian KSJ

This process will take a long time, but the returns are usually good if
your potential describes a large group of atomic systems.

Another way to go is to use density functional theory and then coarse grain upwards in space and time.  An interesting "orbital-free" approach for calculating the electronic properties of materials has been proposed in a recent paper :

"Introducing PROFESS: a new program for orbital-free density functional theory calculations"

by

Gregory S. Hoa, Vincent L. Lignèresa and Emily A. Carter

Computer Physics Communications, doi:10.1016/j.cpc.2008.07.002 .

For an example of how to move from a DFT calculation to a potential, see

"Combined Density Functional Theory and Interatomic Potential Study of the Bulk and Surface Structures and Properties of the Iron Sulfide Mackinawite (FeS)"

by

A. J. Devey,* R. Grau-Crespo, and N. H. de Leeuw ,

J. Phys. Chem. C, 112 (29), 10960–10967, 2008. doi:10.1021/jp8001959.

-- Biswajit