# Units¶

GALAMOST stores and computes all values in reduced units. The quantities in real units can be converted into the ones in reduced units by defining a set of fundamental units by user himself.

## Fundamental Units¶

The three fundamental units are:

• distance - $$\mathcal{\sigma}$$
• energy - $$\mathcal{\varepsilon}$$
• mass - $$\mathcal{m}$$

## Temperature units (thermal energy)¶

GALAMOST accepts all temperature inputs and provides all temperature output values in units of energy: $$k_{B} T$$, where $$k_{B}$$ is Boltzmann’s constant. In reduced units, one usually reports the value $$T^* = k_{B}T/\mathcal{\varepsilon}$$.

## Charge units¶

The charge used in GALAMOST is also reduced. The units of charge are: $$(4 \pi \epsilon_0 \epsilon_r \mathcal{\sigma} \mathcal{\varepsilon})^{1/2}$$, where $$\epsilon_0$$ is vacuum permittivity and $$\epsilon_r$$ is relative permittivity.

With $$f= 1/4\pi \epsilon_0=138.935\text{ }kJ\text{ }mol^{-1}\text{ }nm\text{ }e^{-2}$$, the units of charge are: $$(\epsilon_r \mathcal{\sigma} \mathcal{\varepsilon}/f)^{1/2}$$. Divide a given charge by this quantity to convert it into an input value for GALAMOST.

## Common derived units¶

Here are some commonly used derived units:

• time - $$\tau = \sqrt{\mathcal{m} \mathcal{\sigma}^2/\mathcal{\varepsilon}}$$
• volume - $$\mathcal{\sigma}^3$$
• velocity - $$\mathcal{\sigma}/\tau$$
• momentum - $$\mathcal{m}\mathcal{\sigma}/\tau$$
• acceleration - $$\mathcal{\sigma}/\tau^2$$
• force - $$\mathcal{\varepsilon}/\mathcal{\sigma}$$
• pressure - $$\mathcal{\varepsilon}/\mathcal{\sigma}^3$$

## Example physical units¶

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

• distance - $$\mathcal{\sigma} = \mathrm{nm}$$
• energy - $$\mathcal{\varepsilon} = \mathrm{kJ/mol}$$
• mass - $$\mathcal{m} = \mathrm{amu}$$

Derived units / values in this system:

• time - picoseconds
• velocity - nm/picosecond
• pressure - 16.3882449645417 atm
• force - 1.66053892103218 pN
• $$k_{B}$$ = 0.00831445986144858 kJ/mol/Kelvin