Units

Meters and kilograms are not meant to measure molecules. Using these units would imply the clumsy manipulation of small numbers. We want to choose units of mass, energy, and length such that the values of the quantities are always of the order $1$. For instance, in the case of the Lennard-Jones potential is wise to use $\sigma$ as a unit of length, $\epsilon$ as a unit of energy, and $m_{0}=1AMU$ as the unit of mass. Re-scaling by these quantities, the potentia would be

$$V^{*}(r)=4\left[ u^{-12}-u^{-6}\right] ,$$

where $V^{*}=V/\epsilon$ and $u=r/\sigma$. The advantages are that the Lennard-Jones parameters never show in the formulas, and that we are spared of many computationally expensive calculations. With this choice of units, we find that time is measured in units of $t_{0}=\sqrt{m_{0}\sigma ^{2}/\epsilon }$. For the electrical charge, the natural unit is the charge of the electron $e$, and for temperature, $\epsilon /k$. After finishing the simulation, we transform the results back to the original units to be compared with the experimental data.