Theoretical background
Units of measurement
Scymol does not have a predetermined system of fundamental units and does not deal with unit conversions in any way. The user is responsible for keeping track of the units used when creating, importing, and configuring particle simulations. In the following section, we give a brief insight on units and base quantities, and present 3 examples to show you how to choose and establish a unit system in Scymol.
There are two kinds of units: fundamental and derived. Fundamental units are those that measure base quantities such as length, mass, time, or temperature. There are 7 base quantities which are listed in Table 1. Derived units are those used to measure quantities that can be obtained by a mathematical combination of fundamental quantities, such as what is used to measure velocity, force, power, or energy.
Table 1. List of fundamental units used to measure base quantities. Derived quantities such as velocity, force, energy, or diffusivity are derived using a mathematical combination of base quantities (and thereby fundamental units).
| Base quantity | Symbol for quantity | SI unit symbol |
|---|---|---|
| Length | \(l\) | \(m\) |
| Mass | \(m\) | \(Kg\) |
| Time | \(t\) | \(s\) |
| Electric current | \(I\) |
\(A\) |
| Thermodynamic temperature | \(T\) | \(K\) |
| Amount of substance | \(n\) |
\(mol\) |
| Luminous intensity | \(I_v\) | \(cd\) |
We present three examples to show how to establish a unit system in Scymol. Example 1 shows how International System (SI) of units are used in a simple physics problem. Example 2 shows how to establish a custom unit system in a Molecular Dynamics (MD) simulation of a simple Lennard-Jones fluid. Example 3 shows how to establish a custom unit system for a charged surface simulation of particles whose interactions are governed by a Coulomb potential.
Table 2 shows how to convert some quantities from units commonly used in MD simulations (\(Å-Da-ps-K-C\)) to SI units.
| Physical quantity | (Da-A-ps) | SI (Kg-m-s) |
|---|---|---|
| Distance | \(1 Å\) | \(1×10^{-10} m\) |
| Mass |
\(1 Da\) | \(1.661×10^{-27} Kg\) |
| Time |
\(1 ps\) | \(1×10^{-12} s\) |
| Energy | \(1 Da-Å^2/{ps^2}\) | \(1.661×10^{-23} Kg-m^2/{s^2}\) |
| Force | \(1 Da-Å/{ps^2}\) | \(1.661×10^{-15} Kg-m/{s^2}\) |
| Pressure | \(1 Da/{Å-ps^2}\) | \(1.661×10^{7} Kg/{m-s^2}\) |
| Diffusivity | \(1 Å^2/{ps}\) | \(1×10^{-8} m^2/{s}\) |
| Viscosity | \(1 Da/{Å-ps}\) | \(1.661×10^{-5} Kg/{m-s}\) |
| Velocity | \(1 Å/{ps}\) | \(1×10^{2} m/s\) |
| Kb (Boltzmann constant) |
\(0.831036\) \(Å^2-Da/{ps^2-K}\) |
\(1.38064852\) \(m^2-Kg/{s^2-K}\) |
| \(ε_0\) (Vacuum permittivity) |
\(5.7289×10^{-7}\) \(ps^2-e^2/{Å^3-Da}\) |
\(8.854×10^{-12}\) \(ps^2-C^2/{m^3-Kg}\) |