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Fixed typos in the UF3 equation

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Ajinkya Hire
2024-03-25 15:17:43 -04:00
committed by GitHub
parent 5c536c8290
commit d55f750dc6
1 changed files with 3 additions and 5 deletions
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doc/src/pair_uf3.rst
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@ -54,11 +54,9 @@ The *uf3* style computes the :ref:`Ultra-Fast Force Fields (UF3) <Xie23>` potent
.. math::
E & = \sum_{i,j} V_2(r_{ij}) + \sum_{i,j,k} V_3 (r_{ij},r_{ik},r_{jk})
V_2(r_{ij}) & = \sum_{n=0}^N c_n B_n(r_{ij})
V_3 (r_{ij},r_{ik},r_{jk}) & = \sum_{l=0}^N_l \sum_{m=0}^N_m \sum_{n=0}^N_n c_{l,m,n} B_l(r_{ij}) B_m(r_{ik}) B_n(r_{jk})
E & = \sum_{i,j} V_2(r_{ij}) + \sum_{i,j,k} V_3 (r_{ij},r_{ik},r_{jk}) \\
V_2(r_{ij}) & = \sum_{n=0}^N c_n B_n(r_{ij}) \\
V_3 (r_{ij},r_{ik},r_{jk}) & = \sum_{l=0}^{N_l} \sum_{m=0}^{N_m} \sum_{n=0}^{N_n} c_{l,m,n} B_l(r_{ij}) B_m(r_{ik}) B_n(r_{jk})
where :math:`V_2(r_{ij})` and :math:`V_3 (r_{ij},r_{ik},r_{jk})` are the two- and three-body interactions, respectively. For the two-body the summation is over all neighbours J and for the three-body the summation is over all neighbors J and K of atom I within a cutoff distance determined from the potential files. :math:`B_n(r_{ij})` are the cubic bspline basis, :math:`c_n` and :math:`c_{l,m,n}` are the machine-learned interaction parameters and :math:`N`, :math:`N_l`, :math:`N_m`, and :math:`N_n` denote the number of basis functions per spline or tensor spline dimension.