Hi everybody,
I have a basic question regarding the LAMMPS real unit, i.e., the unit and numeric value of permittivity of free space. By using Coulomb’s law, we get the unit as e^2/ {(kcal/mol)*A} but what about the numerical value? Is there any documentation available regarding this, like what are quantities taken as 1 in the LAMMPS real unit?
Thanks in advance.
All the documentation about units is here:
https://docs.lammps.org/units.html
To be concrete, in units real, two unit charges spaced one unit distance apart will have a force of 330.8 units. It is left as an exercise for the reader to look up what the units of charge, distance, and force are, and to verify that the above number is correct.
Thank you, Dear srtee, for the clarification. However, I would like to ask whether 4pi is there for the equation or not.
Can you send some links where we can gather more knowledge about the LAMMPS real unit? Above written link is not sufficient.
Hi @kunmun,
The above link from @srtee is the reference link for LAMMPS units systems and contains all the information that can be provided on how LAMMPS units work.
What you need to do now is more likely solving the proposed exercise, using a physics textbook if needed, or dive into LAMMPS code itself to get the answer to your question.
The most straightforward way to understand how a unit system works is to calculate some useful quantities in it.
So find a calculator and calculate what the force is when two electrons are held one angstrom apart. You will find that the force comes up to 330 kcal/mol/angstrom.
You can then reverse-engineer any quantity that you used in the equation, checking along the way that you still get the correct answer. For example, one formula for the force is
F = \frac{k q_1 q_2}{r^2}.
What is the value of k in LAMMPS units real? It’s about 330 kcal angstroms/mol/electrons^2.
Another formula for the force is
F = \frac{q_1 q_2}{4 \pi \epsilon_0 r^2}.
What is the value of \epsilon_0 in LAMMPS units real? It’s 4 pi divided by 330, or about 0.036, electrons^2 mol/kcal angstrom. What does that unit even mean? I have no intuitive idea, frankly. But it gets me the correct forces, and that’s what matters.
EDIT: see? I even got the units of k wrong the first time. Working in software you want to get to bare unitless numbers as quickly as possible.
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Thank you srtee and Germain for the clarification.