Lennard-Jones potential

The Lennard-Jones (LJ) potential is one of the simplest two-body potentials used in MD simulations. The pair potential between particles \(i\) and \(j\) is

\[U_{ij} = 4 \epsilon_{ij} \left( \frac{ \sigma_{ij}^{12} }{ r_{ij}^{12} } - \frac{\sigma_{ij}^{6} }{ r_{ij}^{6} } \right).\]

For the implementation in GPUMD the potential has neither been shifted nor damped. This is important to keep in mind when using this model as it implies that both energy and force change discontinuously at the cutoff.

The implementation in GPUMD supports up to 10 atom types.

There are two parameters, which respectively control the depth (\(\epsilon\)) and the position (\(\sigma\)) of the potential well. They are given in units of eV and Å, respectively.

File format

If there is only one atom type, the potential file for this potential model reads:

lj 1 element
epsilon sigma cutoff

Here, cutoff is the cutoff distance and element is the chemical symbol of the element.

If there are two atom types, the potential file reads:

lj 2 <list of the 2 elements>
epsilon_00 sigma_00 cutoff_00
epsilon_01 sigma_01 cutoff_01
epsilon_10 sigma_10 cutoff_10
epsilon_11 sigma_11 cutoff_11

If there are three atom types, the potential file reads:

lj 3 <list of the 3 elements>
epsilon_00 sigma_00 cutoff_00
epsilon_01 sigma_01 cutoff_01
epsilon_02 sigma_02 cutoff_02
epsilon_10 sigma_10 cutoff_10
epsilon_11 sigma_11 cutoff_11
epsilon_12 sigma_12 cutoff_12
epsilon_20 sigma_20 cutoff_20
epsilon_21 sigma_21 cutoff_21
epsilon_22 sigma_22 cutoff_22

The extension to more than three atom types should be apparent from the examples above.