PYGAMD 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.
The three fundamental units are:
- distance - \mathcal{\sigma}
- energy - \mathcal{\varepsilon}
- mass - \mathcal{m}
PYGAMD 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}.
The charge used in PYGAMD 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 PYGAMD.
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
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