**What is a Force Field?**

- Very briefly, a force fleld is a mathematical function which returns the energy of a system as a function of the conformation of the system. But a better idea may be obtained by considering the situation physically.
- Consider a molecule as a collection of atoms held together by elastic forces. (If you want to get even simpler then one could consider a molecule to be a collection of point masses connected by elastic springs).
- Now the forces can be written in terms of potential energy functions of various structural features such as bond lengths, bond angle, non bonded interactions etc.
- The force fleld is the combination of these potential energy terms. Hence force flelds are also sometimes referred to as potentials.
- Thus the energy, E, of a molecule in a force fleld arises from the deviations from the ideal structural features and so can be written approximately as
- Here E is termed as the steric energy. Es is the energy for bond stretching, Eb is the energy for bond angle bending, E! is the torsional energy due to twisting about bonds and Enb is the energy for non bonded interactions.
- If there are other mechanisms afiecting energy such as electrostatic repulsions or hydrogen bonding then these may be included in E by adding appropriate terms into the above expression.
- It should be kept in mind that E is a measure of the intra-molecular strain relative to a hypothetical situation.
- Thus E on its own has no physical meaning. Many difierent kinds of forceflelds have been developed over the years. Some include additional energy terms that describe other kinds of deformations.
- Some force-flelds account for coupling between bending and stretching in adjacent bonds in order to improve the accuracy of the mechanical model.

**Design of a Force Field**

- The design of force flelds for molecular mechanics is guided by by the following principles:

† Nuclei and electrons are lumped into atom-like particles.

† Atom-like particles are spherical (radii obtained from measurements or theory) and have a net charge (obtained from theory).

† Interactions are based on springs and classical potentials.

† Interactions must be preassigned to speciflc sets of atoms.

† Interactions determine the spatial distribution of atom-like particles and their energies.

Rajarshi Guha and Rajesh Sardar, 2001.

**Types of Interatomic potentials (Force Fields)**

- Transferability: organic force fields (biochemistry)
- AMBER
- CHARMM
- AMOEBA
- COMPASS
- OPLS
- GROMACS
- …

- Reactive: using in solid state materials (physics & materials) [V(∑ρ(r))]
- Tersoff
- EAM
- BOP
- ReaxFF
- GAP ( Gaussian Approximation Potential) in accuracy and speed / Professor Gábor Csányi
- …

- Accuracy: small molecules in gas phase (quantum chemistry)
- Braams & Bowman
- Szalewice
- Paesani
- Thiel
- Misquitta
- …

## Professor Gábor Csányi, Department of Engineering, university of Cambridge, 2019