======================= Lennard-Jones Potential ======================= Brief introduction about the Lennard-Jones potential ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The Lennard-Jones (LJ) potential is given by .. math:: E_{disp}(r) = 4 \varepsilon \left[ \left( \frac{\sigma}{r}\right)^{12} - \left( \frac{\sigma}{r}\right)^6\right] where :math:`\varepsilon` is the well-depth and :math:`\sigma` is the distance at witch inter-particle potential is zero, :math:`E_{disp}=0`. Note that :math:`\sigma` is related to the position of the minima of the potential, :math:`R_{min}` by :math:`R_{min} = 2^{1/6}\sigma`. The Lorentz-Berthelot rule is used to calculated the combined parameter of two interacting atoms :math:`i` and :math:`j`: .. math:: \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]_: .. code:: json { "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 :math:`\sigma` and Kelvin for :math:`\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 :sub:`4` molecule can be defined as: .. code:: none 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: .. code:: none 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 References ~~~~~~~~~~ .. [1] Bai, P., Tsapatsis, M. and Siepmann, J.I., 2013. TraPPE-zeo: Transferable potentials for phase equilibria force field for all-silica zeolites. The Journal of Physical Chemistry C, 117(46), pp.24375-24387.