Lennard-Jones Potential¶
Brief introduction about the Lennard-Jones potential¶
The Lennard-Jones (LJ) potential is given by
\[E_{disp}(r) = 4 \varepsilon \left[ \left( \frac{\sigma}{r}\right)^{12} - \left( \frac{\sigma}{r}\right)^6\right]\]
where \(\varepsilon\) is the well-depth and \(\sigma\) is the distance at witch inter-particle potential is zero, \(E_{disp}=0\). Note that \(\sigma\) is related to the position of the minima of the potential, \(R_{min}\) by \(R_{min} = 2^{1/6}\sigma\).
The Lorentz-Berthelot rule is used to calculated the combined parameter of two interacting atoms \(i\) and \(j\):
\[\varepsilon_{ij} = \sqrt{\varepsilon_i \cdot \varepsilon_j}, \qquad \sigma_{ij} = \frac{\sigma_i \cdot \sigma_j}{2}\]
The potentials can be shifted to zero at the cutoff distance by setting shifted=True when creating the calculator. Tail correction is not yet available in the current version (v0.5).
The file containing the parameters for the Lennard-Jones potential is a simple json file. Below is an example of a json file containing the parameters for the Lennard-Jones potential for TraPPE-Zeo force field [1]:
{
"O": {
"sigma": 3.30,
"epsilon": 53.0000
},
"Si": {
"sigma": 2.30,
"epsilon": 22.0000
},
"C_ch4": {
"sigma": 3.72,
"epsilon": 158.50000
},
"H_ch4": {
"sigma": 3.72,
"epsilon": 0.0
}
}
where the keys are the atom types and the values are the parameters for the Lennard-Jones potential. The units are in Angstroms for \(\sigma\) and Kelvin for \(\varepsilon\).
The same atom types should be assign on the file containing the adsorbate or framework structure. For the adsorbate, it is possible to use a .extxyz file format, with the tag labels to assign the atom types.
For example, the CH 4 molecule can be defined as:
5
Properties=species:S:1:labels:S:1:pos:R:3 pbc="F F F"
C C_ch4 0.00000000 0.00000000 0.00000000
H H_ch4 0.00000000 -0.00000000 1.06937095
H H_ch4 -0.00000000 -1.00821260 -0.35645698
H H_ch4 -0.87313773 0.50410630 -0.35645698
H H_ch4 0.87313773 0.50410630 -0.35645698
ase will automatically read the labels tag and assign the atom types to the atoms in the structure, and the calculator will use the parameters from the json file to calculate the Lennard-Jones potential.
For the framework, it is possible to use a .cif file format, with the tag _atom_site_label to assign the atom types. For example, the MFI zeolite can be defined as:
data_VESTA_phase_1
_chemical_name_common 'MFI'
_cell_length_a 20.021999
_cell_length_b 19.899000
_cell_length_c 13.383000
_cell_angle_alpha 90.000000
_cell_angle_beta 90.000000
_cell_angle_gamma 90.000000
_cell_volume 5332.025146
_space_group_name_H-M_alt 'P 1'
_space_group_IT_number 1
loop_
_space_group_symop_operation_xyz
'x, y, z'
loop_
_atom_site_label
_atom_site_occupancy
_atom_site_fract_x
_atom_site_fract_y
_atom_site_fract_z
_atom_site_type_symbol
Si 1.0 0.422380 0.056500 0.664020 Si
Si 1.0 0.577620 0.943500 0.335980 Si
Si 1.0 0.077620 0.943500 0.164020 Si
Si 1.0 0.922380 0.056500 0.835980 Si
Si 1.0 0.577620 0.556500 0.335980 Si
Si 1.0 0.422380 0.443500 0.664020 Si
Si 1.0 0.922380 0.443500 0.835980 Si
Si 1.0 0.077620 0.556500 0.164020 Si
Si 1.0 0.307160 0.027720 0.810700 Si
Si 1.0 0.692840 0.972280 0.189300 Si
Si 1.0 0.192840 0.972280 0.310700 Si
Si 1.0 0.807160 0.027720 0.689300 Si
Si 1.0 0.692840 0.527720 0.189300 Si
Si 1.0 0.307160 0.472280 0.810700 Si
Si 1.0 0.807160 0.472280 0.689300 Si
Si 1.0 0.192840 0.527720 0.310700 Si
Si 1.0 0.279110 0.061270 0.031200 Si
Si 1.0 0.720890 0.938730 0.968800 Si
Si 1.0 0.220890 0.938730 0.531200 Si
Si 1.0 0.779110 0.061270 0.468800 Si
Si 1.0 0.720890 0.561270 0.968800 Si
Si 1.0 0.279110 0.438730 0.031200 Si
Si 1.0 0.779110 0.438730 0.468800 Si
Si 1.0 0.220890 0.561270 0.531200 Si
Si 1.0 0.122150 0.062980 0.026700 Si
Si 1.0 0.877850 0.937020 0.973300 Si
Si 1.0 0.377850 0.937020 0.526700 Si
Si 1.0 0.622150 0.062980 0.473300 Si
Si 1.0 0.877850 0.562980 0.973300 Si
Si 1.0 0.122150 0.437020 0.026700 Si
Si 1.0 0.622150 0.437020 0.473300 Si
Si 1.0 0.377850 0.562980 0.526700 Si
Si 1.0 0.071280 0.027220 0.814490 Si
Si 1.0 0.928720 0.972780 0.185510 Si
Si 1.0 0.428720 0.972780 0.314490 Si
Si 1.0 0.571280 0.027220 0.685510 Si
Si 1.0 0.928720 0.527220 0.185510 Si
Si 1.0 0.071280 0.472780 0.814490 Si
Si 1.0 0.571280 0.472780 0.685510 Si
Si 1.0 0.428720 0.527220 0.314490 Si
Si 1.0 0.186410 0.058960 0.671820 Si
Si 1.0 0.813590 0.941040 0.328180 Si
Si 1.0 0.313590 0.941040 0.171820 Si
Si 1.0 0.686410 0.058960 0.828180 Si
Si 1.0 0.813590 0.558960 0.328180 Si
Si 1.0 0.186410 0.441040 0.671820 Si
Si 1.0 0.686410 0.441040 0.828180 Si
Si 1.0 0.313590 0.558960 0.171820 Si
Si 1.0 0.422650 0.827500 0.672820 Si
Si 1.0 0.577350 0.172500 0.327180 Si
Si 1.0 0.077350 0.172500 0.172820 Si
Si 1.0 0.922650 0.827500 0.827180 Si
Si 1.0 0.577350 0.327500 0.327180 Si
Si 1.0 0.422650 0.672500 0.672820 Si
Si 1.0 0.922650 0.672500 0.827180 Si
Si 1.0 0.077350 0.327500 0.172820 Si
Si 1.0 0.307780 0.869840 0.814520 Si
Si 1.0 0.692220 0.130160 0.185480 Si
Si 1.0 0.192220 0.130160 0.314520 Si
Si 1.0 0.807780 0.869840 0.685480 Si
Si 1.0 0.692220 0.369840 0.185480 Si
Si 1.0 0.307780 0.630160 0.814520 Si
Si 1.0 0.807780 0.630160 0.685480 Si
Si 1.0 0.192220 0.369840 0.314520 Si
Si 1.0 0.275540 0.827210 0.031090 Si
Si 1.0 0.724460 0.172790 0.968910 Si
Si 1.0 0.224460 0.172790 0.531090 Si
Si 1.0 0.775540 0.827210 0.468910 Si
Si 1.0 0.724460 0.327210 0.968910 Si
Si 1.0 0.275540 0.672790 0.031090 Si
Si 1.0 0.775540 0.672790 0.468910 Si
Si 1.0 0.224460 0.327210 0.531090 Si
Si 1.0 0.120580 0.826900 0.029790 Si
Si 1.0 0.879420 0.173100 0.970210 Si
Si 1.0 0.379420 0.173100 0.529790 Si
Si 1.0 0.620580 0.826900 0.470210 Si
Si 1.0 0.879420 0.326900 0.970210 Si
Si 1.0 0.120580 0.673100 0.029790 Si
Si 1.0 0.620580 0.673100 0.470210 Si
Si 1.0 0.379420 0.326900 0.529790 Si
Si 1.0 0.070440 0.869630 0.818000 Si
Si 1.0 0.929560 0.130370 0.182000 Si
Si 1.0 0.429560 0.130370 0.318000 Si
Si 1.0 0.570440 0.869630 0.682000 Si
Si 1.0 0.929560 0.369630 0.182000 Si
Si 1.0 0.070440 0.630370 0.818000 Si
Si 1.0 0.570440 0.630370 0.682000 Si
Si 1.0 0.429560 0.369630 0.318000 Si
Si 1.0 0.187060 0.826730 0.680670 Si
Si 1.0 0.812940 0.173270 0.319330 Si
Si 1.0 0.312940 0.173270 0.180670 Si
Si 1.0 0.687060 0.826730 0.819330 Si
Si 1.0 0.812940 0.326730 0.319330 Si
Si 1.0 0.187060 0.673270 0.680670 Si
Si 1.0 0.687060 0.673270 0.819330 Si
Si 1.0 0.312940 0.326730 0.180670 Si
O 1.0 0.372600 0.053400 0.755800 O
O 1.0 0.627400 0.946600 0.244200 O
O 1.0 0.127400 0.946600 0.255800 O
O 1.0 0.872600 0.053400 0.744200 O
O 1.0 0.627400 0.553400 0.244200 O
O 1.0 0.372600 0.446600 0.755800 O
O 1.0 0.872600 0.446600 0.744200 O
O 1.0 0.127400 0.553400 0.255800 O
O 1.0 0.308400 0.058700 0.921100 O
O 1.0 0.691600 0.941300 0.078900 O
O 1.0 0.191600 0.941300 0.421100 O
O 1.0 0.808400 0.058700 0.578900 O
O 1.0 0.691600 0.558700 0.078900 O
O 1.0 0.308400 0.441300 0.921100 O
O 1.0 0.808400 0.441300 0.578900 O
O 1.0 0.191600 0.558700 0.421100 O
O 1.0 0.200700 0.059200 0.028900 O
O 1.0 0.799300 0.940800 0.971100 O
O 1.0 0.299300 0.940800 0.528900 O
O 1.0 0.700700 0.059200 0.471100 O
O 1.0 0.799300 0.559200 0.971100 O
O 1.0 0.200700 0.440800 0.028900 O
O 1.0 0.700700 0.440800 0.471100 O
O 1.0 0.299300 0.559200 0.528900 O
O 1.0 0.096900 0.061100 0.914400 O
O 1.0 0.903100 0.938900 0.085600 O
O 1.0 0.403100 0.938900 0.414400 O
O 1.0 0.596900 0.061100 0.585600 O
O 1.0 0.903100 0.561100 0.085600 O
O 1.0 0.096900 0.438900 0.914400 O
O 1.0 0.596900 0.438900 0.585600 O
O 1.0 0.403100 0.561100 0.414400 O
O 1.0 0.114900 0.054100 0.723700 O
O 1.0 0.885100 0.945900 0.276300 O
O 1.0 0.385100 0.945900 0.223700 O
O 1.0 0.614900 0.054100 0.776300 O
O 1.0 0.885100 0.554100 0.276300 O
O 1.0 0.114900 0.445900 0.723700 O
O 1.0 0.614900 0.445900 0.776300 O
O 1.0 0.385100 0.554100 0.223700 O
O 1.0 0.243500 0.055300 0.754000 O
O 1.0 0.756500 0.944700 0.246000 O
O 1.0 0.256500 0.944700 0.254000 O
O 1.0 0.743500 0.055300 0.746000 O
O 1.0 0.756500 0.555300 0.246000 O
O 1.0 0.243500 0.444700 0.754000 O
O 1.0 0.743500 0.444700 0.746000 O
O 1.0 0.256500 0.555300 0.254000 O
O 1.0 0.374200 0.843900 0.762800 O
O 1.0 0.625800 0.156100 0.237200 O
O 1.0 0.125800 0.156100 0.262800 O
O 1.0 0.874200 0.843900 0.737200 O
O 1.0 0.625800 0.343900 0.237200 O
O 1.0 0.374200 0.656100 0.762800 O
O 1.0 0.874200 0.656100 0.737200 O
O 1.0 0.125800 0.343900 0.262800 O
O 1.0 0.308500 0.844800 0.927200 O
O 1.0 0.691500 0.155200 0.072800 O
O 1.0 0.191500 0.155200 0.427200 O
O 1.0 0.808500 0.844800 0.572800 O
O 1.0 0.691500 0.344800 0.072800 O
O 1.0 0.308500 0.655200 0.927200 O
O 1.0 0.808500 0.655200 0.572800 O
O 1.0 0.191500 0.344800 0.427200 O
O 1.0 0.198000 0.844600 0.028800 O
O 1.0 0.802000 0.155400 0.971200 O
O 1.0 0.302000 0.155400 0.528800 O
O 1.0 0.698000 0.844600 0.471200 O
O 1.0 0.802000 0.344600 0.971200 O
O 1.0 0.198000 0.655400 0.028800 O
O 1.0 0.698000 0.655400 0.471200 O
O 1.0 0.302000 0.344600 0.528800 O
O 1.0 0.091000 0.838600 0.922300 O
O 1.0 0.909000 0.161400 0.077700 O
O 1.0 0.409000 0.161400 0.422300 O
O 1.0 0.591000 0.838600 0.577700 O
O 1.0 0.909000 0.338600 0.077700 O
O 1.0 0.091000 0.661400 0.922300 O
O 1.0 0.591000 0.661400 0.577700 O
O 1.0 0.409000 0.338600 0.422300 O
O 1.0 0.116900 0.842200 0.730600 O
O 1.0 0.883100 0.157800 0.269400 O
O 1.0 0.383100 0.157800 0.230600 O
O 1.0 0.616900 0.842200 0.769400 O
O 1.0 0.883100 0.342200 0.269400 O
O 1.0 0.116900 0.657800 0.730600 O
O 1.0 0.616900 0.657800 0.769400 O
O 1.0 0.383100 0.342200 0.230600 O
O 1.0 0.244800 0.840600 0.757800 O
O 1.0 0.755200 0.159400 0.242200 O
O 1.0 0.255200 0.159400 0.257800 O
O 1.0 0.744800 0.840600 0.742200 O
O 1.0 0.755200 0.340600 0.242200 O
O 1.0 0.244800 0.659400 0.757800 O
O 1.0 0.744800 0.659400 0.742200 O
O 1.0 0.255200 0.340600 0.257800 O
O 1.0 0.304700 0.949000 0.813400 O
O 1.0 0.695300 0.051000 0.186600 O
O 1.0 0.195300 0.051000 0.313400 O
O 1.0 0.804700 0.949000 0.686600 O
O 1.0 0.695300 0.449000 0.186600 O
O 1.0 0.304700 0.551000 0.813400 O
O 1.0 0.804700 0.551000 0.686600 O
O 1.0 0.195300 0.449000 0.313400 O
O 1.0 0.076800 0.948100 0.823100 O
O 1.0 0.923200 0.051900 0.176900 O
O 1.0 0.423200 0.051900 0.323100 O
O 1.0 0.576800 0.948100 0.676900 O
O 1.0 0.923200 0.448100 0.176900 O
O 1.0 0.076800 0.551900 0.823100 O
O 1.0 0.576800 0.551900 0.676900 O
O 1.0 0.423200 0.448100 0.323100 O
O 1.0 0.416100 0.127600 0.610400 O
O 1.0 0.583900 0.872400 0.389600 O
O 1.0 0.083900 0.872400 0.110400 O
O 1.0 0.916100 0.127600 0.889600 O
O 1.0 0.583900 0.627600 0.389600 O
O 1.0 0.416100 0.372400 0.610400 O
O 1.0 0.916100 0.372400 0.889600 O
O 1.0 0.083900 0.627600 0.110400 O
O 1.0 0.408600 0.998300 0.586400 O
O 1.0 0.591400 0.001700 0.413600 O
O 1.0 0.091400 0.001700 0.086400 O
O 1.0 0.908600 0.998300 0.913600 O
O 1.0 0.591400 0.498300 0.413600 O
O 1.0 0.408600 0.501700 0.586400 O
O 1.0 0.908600 0.501700 0.913600 O
O 1.0 0.091400 0.498300 0.086400 O
O 1.0 0.402000 0.868600 0.576100 O
O 1.0 0.598000 0.131400 0.423900 O
O 1.0 0.098000 0.131400 0.076100 O
O 1.0 0.902000 0.868600 0.923900 O
O 1.0 0.598000 0.368600 0.423900 O
O 1.0 0.402000 0.631400 0.576100 O
O 1.0 0.902000 0.631400 0.923900 O
O 1.0 0.098000 0.368600 0.076100 O
O 1.0 0.188600 0.129800 0.616400 O
O 1.0 0.811400 0.870200 0.383600 O
O 1.0 0.311400 0.870200 0.116400 O
O 1.0 0.688600 0.129800 0.883600 O
O 1.0 0.811400 0.629800 0.383600 O
O 1.0 0.188600 0.370200 0.616400 O
O 1.0 0.688600 0.370200 0.883600 O
O 1.0 0.311400 0.629800 0.116400 O
O 1.0 0.194000 0.000700 0.591800 O
O 1.0 0.806000 0.999300 0.408200 O
O 1.0 0.306000 0.999300 0.091800 O
O 1.0 0.694000 0.000700 0.908200 O
O 1.0 0.806000 0.500700 0.408200 O
O 1.0 0.194000 0.499300 0.591800 O
O 1.0 0.694000 0.499300 0.908200 O
O 1.0 0.306000 0.500700 0.091800 O
O 1.0 0.195100 0.870900 0.581000 O
O 1.0 0.804900 0.129100 0.419000 O
O 1.0 0.304900 0.129100 0.081000 O
O 1.0 0.695100 0.870900 0.919000 O
O 1.0 0.804900 0.370900 0.419000 O
O 1.0 0.195100 0.629100 0.581000 O
O 1.0 0.695100 0.629100 0.919000 O
O 1.0 0.304900 0.370900 0.081000 O
O 1.0 0.996300 0.050200 0.792000 O
O 1.0 0.003700 0.949800 0.208000 O
O 1.0 0.503700 0.949800 0.292000 O
O 1.0 0.496300 0.050200 0.708000 O
O 1.0 0.003700 0.550200 0.208000 O
O 1.0 0.996300 0.449800 0.792000 O
O 1.0 0.496300 0.449800 0.708000 O
O 1.0 0.503700 0.550200 0.292000 O
O 1.0 0.996000 0.847200 0.792200 O
O 1.0 0.004000 0.152800 0.207800 O
O 1.0 0.504000 0.152800 0.292200 O
O 1.0 0.496000 0.847200 0.707800 O
O 1.0 0.004000 0.347200 0.207800 O
O 1.0 0.996000 0.652800 0.792200 O
O 1.0 0.496000 0.652800 0.707800 O
O 1.0 0.504000 0.347200 0.292200 O
O 1.0 0.419200 0.750000 0.646000 O
O 1.0 0.580800 0.250000 0.354000 O
O 1.0 0.080800 0.250000 0.146000 O
O 1.0 0.919200 0.750000 0.854000 O
O 1.0 0.188400 0.750000 0.646200 O
O 1.0 0.811600 0.250000 0.353800 O
O 1.0 0.311600 0.250000 0.146200 O
O 1.0 0.688400 0.750000 0.853800 O
O 1.0 0.288300 0.750000 0.057900 O
O 1.0 0.711700 0.250000 0.942100 O
O 1.0 0.211700 0.250000 0.557900 O
O 1.0 0.788300 0.750000 0.442100 O
O 1.0 0.108500 0.750000 0.061100 O
O 1.0 0.891500 0.250000 0.938900 O
O 1.0 0.391500 0.250000 0.561100 O
O 1.0 0.608500 0.750000 0.438900 O