\(\renewcommand{\AA}{\text{Å}}\)

# pair_style ilp/tmd command

Accelerator Variant: ilp/tmd/opt

## Syntax

    pair_style [hybrid/overlay ...] ilp/tmd cutoff tap_flag

- cutoff = global cutoff (distance units)

- tap_flag = 0/1 to turn off/on the taper function

## Examples

    pair_style  hybrid/overlay ilp/tmd 16.0 1
    pair_coeff  * * ilp/tmd  TMD.ILP Mo S S

    pair_style  hybrid/overlay sw/mod sw/mod ilp/tmd 16.0
    pair_coeff  * * sw/mod 1  tmd.sw.mod Mo S S NULL NULL NULL
    pair_coeff  * * sw/mod 2  tmd.sw.mod NULL NULL NULL W Se Se
    pair_coeff  * * ilp/tmd   TMD.ILP   Mo S S W Se Se

## Description

Added in version 17Feb2022.

The ilp/tmd style computes the registry-dependent interlayer potential (ILP) potential for heterointerfaces of transition metal dichalcogenides (TMD)/TMD, TMD/graphene, and TMD / hexagonal boron nitride (h-BN), as described in (Ouyang7), (Jiang4) and (Jiang5).

\[\begin{split}E = & \frac{1}{2} \sum_i \sum_{j \neq i} V_{ij} \\ V_{ij} = & \mathrm{Tap}(r_{ij})\left \{ e^{-\alpha (r_{ij}/\beta -1)} \left [ \epsilon + f(\rho_{ij}) + f(\rho_{ji})\right ] - \frac{1}{1+e^{-d\left [ \left ( r_{ij}/\left (s_R \cdot r^{eff} \right ) \right )-1 \right ]}} \cdot \frac{C_6}{r^6_{ij}} \right \}\\ \rho_{ij}^2 = & r_{ij}^2 - (\mathbf{r}_{ij} \cdot \mathbf{n}_i)^2 \\ \rho_{ji}^2 = & r_{ij}^2 - (\mathbf{r}_{ij} \cdot \mathbf{n}_j)^2 \\ f(\rho) = & C e^{ -( \rho / \delta )^2 } \\ \mathrm{Tap}(r_{ij}) = & 20\left ( \frac{r_{ij}}{R_{cut}} \right )^7 - 70\left ( \frac{r_{ij}}{R_{cut}} \right )^6 + 84\left ( \frac{r_{ij}}{R_{cut}} \right )^5 - 35\left ( \frac{r_{ij}}{R_{cut}} \right )^4 + 1\end{split}\]

Where \(\mathrm{Tap}(r_{ij})\) is the taper function which provides a continuous cutoff (up to third derivative) for interatomic separations larger than \(r_c\) pair_style ilp_graphene_hbn.

It is important to include all the pairs to build the neighbor list for calculating the normals.

Note

Since each MX2 (M = Mo, W and X = S, Se Te) layer contains two sub-layers of X atoms and one sub-layer of M atoms, the definition of the normal vectors used for graphene and h-BN is no longer valid for TMDs. In (Ouyang7), a new definition is proposed, where for each atom i, its six nearest neighboring atoms belonging to the same sub-layer are chosen to define the normal vector mathbf{n}_i.

The parameter file (e.g. TMD.ILP), is intended for use with metal units, with energies in meV. Two additional parameters, S, and rcut are included in the parameter file. S is designed to facilitate scaling of energies. rcut is designed to build the neighbor list for calculating the normals for each atom pair.

Note

The parameters presented in the parameter file (e.g. TMD.ILP), are fitted with taper function by setting the cutoff equal to 16.0 Angstrom. Using different cutoff or taper function should be careful. These parameters provide a good description in both short- and long-range interaction regimes. This feature is essential for simulations in high pressure regime (i.e., the interlayer distance is smaller than the equilibrium distance). The benchmark tests and comparison of these parameters can be found in (Ouyang7).

This potential must be used in combination with hybrid/overlay. Other interactions can be set to zero using pair_style none.

This pair style tallies a breakdown of the total interlayer potential energy into sub-categories, which can be accessed via the compute pair command as a vector of values of length 2. The 2 values correspond to the following sub-categories:

1. E_vdW = vdW (attractive) energy

2. E_Rep = Repulsive energy

To print these quantities to the log file (with descriptive column headings) the following commands could be included in an input script:

    compute 0 all pair ilp/tmd
    variable Evdw  equal c_0[1]
    variable Erep  equal c_0[2]
    thermo_style custom step temp epair v_Erep v_Evdw

Styles with a gpu, intel, kk, omp, or opt suffix are functionally the same as the corresponding style without the suffix. They have been optimized to run faster, depending on your available hardware, as discussed on the Accelerator packages page. The accelerated styles take the same arguments and should produce the same results, except for round-off and precision issues.

These accelerated styles are part of the GPU, INTEL, KOKKOS, OPENMP, and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Build package page for more info.

You can specify the accelerated styles explicitly in your input script by including their suffix, or you can use the -suffix command-line switch when you invoke LAMMPS, or you can use the suffix command in your input script.

See the Accelerator packages page for more instructions on how to use the accelerated styles effectively.

## Mixing, shift, table, tail correction, restart, rRESPA info

This pair style does not support the pair_modify mix, shift, table, and tail options.

This pair style does not write their information to binary restart files, since it is stored in potential files. Thus, you need to re-specify the pair_style and pair_coeff commands in an input script that reads a restart file.

## Restrictions

This pair style is part of the INTERLAYER package. It is only enabled if LAMMPS was built with that package. See the Build package page for more info.

This pair style requires the newton setting to be on for pair interactions.

The TMD.ILP potential file provided with LAMMPS (see the potentials directory) are parameterized for metal units. You can use this potential with any LAMMPS units, but you would need to create your own custom TMD.ILP potential file with coefficients listed in the appropriate units, if your simulation does not use metal units.

## Related commands

pair_coeff, pair_none, pair_style hybrid/overlay, pair_style drip, pair_style saip_metal, pair_style ilp_graphene_hbn, pair_style pair_kolmogorov_crespi_z, pair_style pair_kolmogorov_crespi_full, pair_style pair_lebedeva_z, pair_style pair_coul_shield.

## Default

tap_flag = 1

(Ouyang7) W. Ouyang, et al., J. Chem. Theory Comput. 17, 7237 (2021).

(Jiang4) W. Jiang, … , W. Ouyang, et al., J. Phys. Chem. A, 127, 46, 9820-9830 (2023).

(Jiang5) W. Jiang, …, W. Ouyang, J. Phys. Chem. C, 129, 2, 1417-1427 (2024).