I have seen that many MD simulations compute the torques due to dipole-dipole interactions and other interactions. I understand that there is a torque on a dipole in an electric field. I don't understand why this effect is not just captured by the forces? How do I actually incorporate the computed torques into an MD simulation? That is, we are usually integrating Newton's equations of motion, which are related to the forces by acceleration. Torques are related to forces, but in a way where it is not obvious to me how to transform the torques into forces in general.

Put another way, normally when implementing a force field, the measure of consistency between energies and forces is whether or not the those forces can be computed as a finite difference derivative of the energy. From my own experience, this criterion is satisfied without the inclusion of torques. Why do we need to evaluate torques then?

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    $\begingroup$ A simple example of needing torque is rigid body molecular dynamics where it is actually rigid, not constrained like using SHAKE or SETTLE or LINCS etc. If you want the rigid body to rotate, you need to solve angular acceleration as well, not just translational. I would say that hardly anyone does rigid body MD simulations, but thought I would mention it... $\endgroup$
    – B. Kelly
    Mar 30, 2023 at 3:52

1 Answer 1


There is a wide variety of molecular dynamics force fields; many incorporate (per-particle) torques, as you have noted, but many do not. For example, I am not familiar with any atomistic protein force fields which use torques. From my experience, the difference will boil down to the force field fitting methodology: "bottom-up" force fields naturally don't need torques (as you have noted) while "top-down" force fields often do.

"Bottom-up" force fields are those which are fitted to "ground truths" of atomistic position or energy data. In materials science, these are parameterised from density functional theory or other quantum chemistry techniques; in protein science, these are parameterised from experimental structure resolution such as through X-ray crystallography or cryo-electron microscopy. And yes, absolutely, if you are dealing with atoms, atoms typically aren't represented as extended particles or fixed dipoles or anything quite so fancy, so there are no torques to talk about!

But "top-down" force fields frequently make good use of torques. For example, consider the oxDNA model family:

Depiction of particles in oxDNA coarse-grained model

oxDNA is a "top down" model because it is fitted to thermodynamic and kinetic "ground truths", such as energies and rates of base pair dissociation and polymeric persistence lengths of the targeted double-stranded DNA. This makes sense since oxDNA aims explicitly to capture DNA structure on scales where the exact atomic positions are irrelevant. Thus, a nucleobase can be represented with seven* numbers (three for position and four* for an orientation quaternion) instead of the thirty or so needed for a fully atomistic description, and simulations are correspondingly much cheaper.

oxDNA models DNA as sites with FENE bonds, and a key ingredient of its success is representing nucleobase stacking interactions as an energetic alignment between the orientations of neighbouring nucleotide sites (the blue "pancakes" like to "lie flat" near each other). The energy depends on angles and thus the model dynamics naturally include torques (which are the angular derivatives of energy) which go into evolving the site orientations over time.

I hope this demonstrates the general principle: when a force field is fitted to an atomistic energy surface or structure, the energy is naturally described purely by atomic Cartesian coordinates and only atomistic forces are needed for dynamics; but when a force field is being fitted to some more general ground truth, there is great freedom for the force field developers to choose appropriate internal representations, and where these representations are primarily angular (such as the orientations of idealized dipoles or extended bodies) then torques naturally arise as the angular derivatives of energy. (Indeed, while bond-angle and dihedral interactions are typically implemented as forces, conceptually they are torques too!)

*these could be six and three respectively; I don't remember how the code internally represents quaternions.


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