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Units

HOOMD-blue stores and computes all values in a system of generic, fully self-consistent set of units. No conversion factors need to be applied to values at every step. For example, a value with units of force comes from dividing energy by distance.

Fundamental Units

The three fundamental units are:

  • distance - 𝒟
  • energy - ℰ
  • mass - ℳ

All other units that appear in HOOMD-blue are derived from these. Values can be converted into any other system of units by assigning the desired units to 𝒟, ℰ, and ℳ and then multiplying by the appropriate conversion factors.

The standard Lennard-Jones symbols σ and ϵ are intentionally not referred to here. When you assign a value to ϵ in hoomd, for example, you are assigning it in units of energy: ϵ = 5ℰ. ϵ is NOT the unit of energy - it is a value with units of energy.

Temperature (thermal energy)

HOOMD-blue accepts all temperature inputs and provides all temperature output values in units of energy: kT, where k is Boltzmann's constant. When using physical units, the value kB is determined by the choices for distance, energy, and mass. In reduced units, one usually reports the value $T^* = \frac{k T}{\mathcal{E}}$.

Most of the argument inputs in HOOMD take the argument name kT to make it explicit. A few areas of the code may still refer to this as temperature.

Charge

The unit of charge used in HOOMD-blue is also reduced, but is not represented using just the 3 fundamental units -the permittivity of free space ε0 is also present. The units of charge are: (4πε0𝒟ℰ)1/2. Divide a given charge by this quantity to convert it into an input value for HOOMD-blue.

Common derived units

Here are some commonly used derived units:

  • time - $\tau = \sqrt{\frac{\mathcal{M} \mathcal{D}^2}{\mathcal{E}}}$
  • volume - 𝒟3
  • velocity - $\frac{\mathcal{D}}{\tau}$
  • momentum - $\mathcal{M} \frac{\mathcal{D}}{\tau}$
  • acceleration - $\frac{\mathcal{D}}{\tau^2}$
  • force - $\frac{\mathcal{E}}{\mathcal{D}}$
  • pressure - $\frac{\mathcal{E}}{\mathcal{D}^3}$

Example physical units

There are many possible choices of physical units that one can assign. One common choice is:

  • distance - 𝒟 = nm
  • energy - ℰ = kJ/mol
  • mass - ℳ = amu

Derived units / values in this system:

  • time - picoseconds
  • velocity - nm/picosecond
  • k = 0.00831445986144858 kJ/mol/Kelvin