# Units

HOOMD-blue does not adopt a particular system of units, nor does it offer a variety of systems to choose from. Instead, it follows a self-consistent system of units where all derived units (e.g. force) are defined in terms of base units (e.g. energy / length). To adopt a system of units for your simulations, choose a set of base units (e.g. meters versus centimeters for length), and then determine what the derived units are.

## Base Units

The base units are:

• $$[\mathrm{energy}]$$

• $$[\mathrm{length}]$$

• $$[\mathrm{mass}]$$

## Unit Conversion

Example unit conversions between derived units and base units:

Derived units

Relation to base units

$$[\mathrm{area}]$$

$$[\mathrm{length}]^2$$

$$[\mathrm{volume}]$$

$$[\mathrm{length}]^3$$

$$[\mathrm{time}]$$

$$[\mathrm{energy}]^{-1/2} \cdot [\mathrm{length}] \cdot [\mathrm{mass}]^{1/2}$$

$$[\mathrm{velocity}]$$

$$[\mathrm{energy}]^{1/2} \cdot [\mathrm{mass}]^{-1/2}$$

$$[\mathrm{force}]$$

$$[\mathrm{energy}] \cdot [\mathrm{length}]^{-1}$$

$$[\mathrm{pressure}]$$

$$[\mathrm{energy}] \cdot [\mathrm{length}]^{-3}$$

$$[\mathrm{charge}]$$

$$\left(4 \pi \epsilon_{0} \cdot [\mathrm{energy}] \cdot [\mathrm{length}] \right)^{1/2}$$ - where $$\epsilon_{0}$$ is permittivity of free space

Note

In HPMC, the primary unit is that of length. Mass is factored out of the partition function and does not enter into the simulation. In addition, the energy scale is irrelevant in athermal HPMC systems where overlapping energies are infinite and valid configurations have zero potential energy. However, energy does appear implicitly in derived units like $$[\mathrm{pressure}] = [\mathrm{energy}] \cdot [\mathrm{length}]^{-3}$$. In HPMC, $$kT$$ is set to 1 $$\mathrm{energy}$$.

## Common unit systems

Example base and derived units for common MD unit systems.

Note

All conversion factors given here are computed with Wolfram Alpha using the provided links.

Unit

AKMA

MD

$$[\mathrm{energy}]$$

kcal/mol

kJ/mol

$$[\mathrm{length}]$$

Å

nm

$$[\mathrm{mass}]$$

atomic mass unit

atomic mass unit

$$[\mathrm{area}]$$

$$\mathrm{Å}^2$$

$$\mathrm{nm}^2$$

$$[\mathrm{volume}]$$

$$\mathrm{Å}^3$$

$$\mathrm{nm}^3$$

$$[\mathrm{time}]$$

48.8882129 fs

1 ps

$$[\mathrm{velocity}]$$

0.02045482828 Å/fs

1 nm/ps

$$[\mathrm{force}]$$

kcal/mol/Å

kJ/mol/nm

$$[\mathrm{pressure}]$$

68568.4230 atm

16.3882464 atm

$$[\mathrm{charge}]$$

0.05487686461 e

0.0848385920 e

$$k$$ (Boltzmann’s constant)

0.00198720426 kcal/mol/K

0.00831446262 kJ/mol/K