Unit conversion done right

We often have to convert units, for example from \(\mathrm{eV}\) to \(\mathrm{Hartree}\), from \(\mathrm{kJ/mol}\) to \(\mathrm{eV/atom}\) perhaps. If you google “unit convertion”, likely there will be online tools though: 1. they may not be right, and 2. you will have to watch some advertisements.

In this post we show various ways to do common unit conversion in atomistic simulations without going to dodgy website or with good old pen and paper (cos I am a bit lazy).

Using ase

The Atomic Simulation Environment has a ase.units module. All variables there are in the atomic unit that ASE uses internally. For example, units.GPa is the value of 1 GPa in the internal unit eV/Å^-3:

from ase import units
pressure_in_ev_A = pressure_in_GPa * units.GPa
energy_per_particle = energy_in_kj_mol * units.kJ / units.mol

It should be kept in mind that the by connecting the value with the unit using * the result is in ase’s internal units. More information can be seen on https://ase-lib.org/ase/units.html:

Electron volts (eV), Ångström (Ang), the atomic mass unit and Kelvin are defined as 1.0. Time is given in units of \(\mathrm{\AA \sqrt{u/eV}}\). Thus, for example, \(1 \mathrm{fs} \approx \mathrm{0.098\AA\sqrt{u / eV}}\) , where \(\mathrm{u}\)is the atomic mass unit.

Using Unitful and UnitfulAtomic

The above approach works well in Python and you probably don’t need to install another package as chances are ase has been installed as needed by your materials science work!

However, what if I want to use other units than eV for energy? Of course, I can convert it to eV and then to others…. Here we introduce a more advanced package for unit conversion (and more) but it is written in Julia (for good reasons).

First, you will need to install Julia, if not already, the best way is to install juliaup which is a julia version manager and installer:

curl -fsSL https://install.julialang.org | sh

On Windows, it can be installed directly from the Windows store here, or use command line.

winget install --name Julia --id 9NJNWW8PVKMN -e -s msstore

Following the instruction to complete the installation, launch a Julia REPL and type:

using Unitful

should prompt you to install the package if not already. Once installed and loaded, we can use a special u"" syntax to mark some number with units:

julia> 1.0u"eV"
1.0 eV

julia> 1.5u"Å"
1.5 Å

julia> 10u"GPa"
10 GPa

PS: In the REPL type \Angstrom then press space to get Å.

Math operations will automatically operate on units as well:

julia> 10.0u"GPa" / 1.0u"Å^3"
10.0 GPa Å^-3

To convert units, one can use the uconvert function with the first arguments being the unit to be converted to:

julia> uconvert(u"eV/Å^3", 10.0u"GPa")
0.06241509074460763 eV Å^-3

A nice thing is that Unitful does dimensionality checks so it unlikely to have unnoticed mistakes:

julia> uconvert(u"eV/Å^2", 10.0u"GPa")
ERROR: DimensionError: eV Å^-2 and GPa are not dimensionally compatible.

We can define units ourselves as well. It can be useful to define a atom unit in order to convert \(\mathrm{kj/mol}\) to \(\mathrm{eV/atom}\). One atom is a 1/\(\mathrm{A_v}\) of a \(\mathrm{mol}\) where \(\mathrm{A_v}\) is the Avogadro’s constant (stored as Unitful.Na):

julia> using Unitful

julia> Unitful.register(@__MODULE__);

julia> @unit atom "atom" atom 1/Unitful.Na true;

julia> uconvert(u"eV/atom", 100u"kJ/mol")
1.0364269656262175 eV atom^-1

The UnitfulAtomic package provides additional atomic units such as u"bohr".