# What does "force field" mean?

In MD simulations we often hear the term force field. What is it? We know, for example that, Gromacs provides various types of forcefields.

• – Tyberius
Nov 3, 2021 at 3:04
• Three of us have described what "force field means here. If you'd like to ask which force field to use, or how to decide, that might be a good follow-up question (in a new post)! Nov 3, 2021 at 13:50

## What is a force field?

The Wikipedia entry on this is a good resource, but I'll give my own description below.

In the context of molecular dynamics (MD), a force field is one way of describing the interactions between atoms. In classical MD, the motion of atoms is determined by the instantaneous forces acting on the atoms (i.e., we need forces in order to calculate accelerations based Newton's famous $$F=ma$$). Force fields provide a way to calculate those forces.

Force fields are usually contrasted with getting forces from quantum mechanics, e.g., via the Hellmann-Feynman theorem. In general, force fields should be thought of as an approximation to quantum mechanics. For large systems, such as proteins, quantum calculations are too computationally expensive to enable reasonable MD simulations.

Atomistic force fields apply when you're performing simulations using molecular mechanics, which expresses the total force as the sum of physically-motivated force terms. [Aside (pet peeve of mine): many people mix up the terms "classical MD" and "molecular mechanics" -- if you use forces from quantum calculations for Newtonian dynamics, that is still classical MD (not quantum MD), though it is not molecular mechanics.]

Note that a lot of what you'll see described as force fields really applies to the subset of force fields that are widely used in biomolecular simulation. That is, you'll see the forces expressed as the sum of the following physically-motivated terms, divided into bonded and non-bonded terms, typically something like this:

• Bonded terms
• bond between 2 atoms
• angle between 3 atoms
• dihedral angle formed by 4 atoms
• Nonbonded terms
• electrostatic interactions
• van der Walls/dispersion terms (typically Lennard-Jones interactions)

This division of terms is useful as a good example for further discussion, but it's worth keeping in mind that there's no law a that force field must be exclusively expressed in these terms. Molecular mechanics force fields could have 5-atom bonded terms or 3-atom nonbonded terms or more detailed treatment of electronic interactions -- but the choices above represent most common force fields.

In general, each of those terms has a specific functional form, with parameters that depend on the atom types in the system. For example, the potential energy describing a bond is frequently of the functional form

$$V_\text{bond}(r) = k_{AB}(r - r^0_{AB})^2$$

where $$k_{AB}$$ and $$r^0_{AB}$$ are parameters that depend on the atom types (and the force itself is given by the gradient $$F = -\nabla V$$ -- we frequently discuss force terms based on the functional form of the potential energy contribution instead of the functional form of the force itself).

Note that the "atom type" here is usually more specific than just the "element type." For example, it shouldn't be surprising that the angle between three carbons in an sp2 hybridized carbon (e.g., benzene) has different parameters than the angle in sp3 hybridized carbon (e.g., cyclohexane).

Designing what "atom types" a force field recognizes is part of the challenge of making a force field transferable to a wide range of molecules. Overly simple atom types (e.g., just the element) would not accurately account for different chemical environments; overly complex (e.g., having the each atom in each different molecule have a different type) would make it impossible to transfer the model to molecules that haven't been specifically parametrized.

Most biomolecular force fields have limitations in the kind of chemistry they can represent (e.g., they can't capture bond making/breaking if the bonded term is described by a harmonic oscillator as above.) Specialized force fields, such as ReaxFF, are designed to get around those limitations.

## How to choose which force field to use

I'd say there are three answers to this:

1. Take the recommendation of people who know better. For example, the developers of the Amber force field family provide a page with their current recommendations.

2. Keep up with the literature, especially for systems similar to yours. People frequently publish papers comparing different force fields for a given system. Also dig into details of which force fields were used if looking at papers that compare existing computational results (authors should always mention FF when comparing computational results, but don't always). This depends on your specific system -- there are different specialized force fields for lipids, nucleic acids, etc.

3. Use something recent and don't stress too much. If you use a recently-published force field (say, last 5 years) from a group with a good track record of contributing to force field development, your results will probably be a meaningful contribution to science. Barring a major issue specific to your system and that force field, I doubt a paper would be rejected on the basis of a slightly old force field.

The term's origin goes back to vector field which is a function that returns a vector for any given point in space (as in the image below on the left). We can almost "see" that such fields exist, by putting iron filings and a magnet on a sheet of paper (the magnetic field causes the iron filings to move accordingly):

In classical molecular dynamics, we want to calculate how particles (usually forming molecules) move, based on Newton's second law (F=ma). Therefore if you have the initial positions (and masses) of all the particles of interest, and the forces between them, you can use Newton's second law to see where they will go. As the particles in your simulation move), the forces will also change. If two particles in your simulation get further apart from each other, the forces between them may get weaker (for example). Therefore there's different force values depending on the relative positions of the particles, which is why we call it a force field.

Molecular dynamics is based in Molecular Mechanics. Molecular Mechanics do many approximations in order to treat the atomic/molecular system. A good definition can be seen here:

Molecular Mechanics is a computational method that computes the potential energy surface for a particular arrangement of atoms using potential functions that are derived using classical physics. These equations are known as a force-field.
Molecular Mechanics is based on several assumptions:

- It treats the electrons around a nucleus and a the nucleus itself as a perfect sphere.
- The bonds between molecules are treated as springs.
- Potential functions rely on experimental parameters such as force constants and equilibrium values.
- The potential energy function is the sum of individual functions for bond stretching, angle bending, torsional energies, and


non-bonding interactions.

About your second question: how to choose which force field is appropriate for the use of our MD processes? the recommendation is to read the documentation (manual, scientific papers, etc.) about each available force field and look for its applications. As the fore filed used several experimental parameters, some of them are designed/optimized to very specific materials.

On the other hand, you will find the so called universal force fields that have parameters for (almost) all the period table, but their precision is no as good as the specific force fields.