Modulated patchy Lennard-Jones model

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The modulated patchy Lennard-Jones model is given by [1] (Eqs. 4.3 and 4.4)

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \Phi _{\mathrm {patchy} }({\mathbf {r} }_{ij},{\mathbf {\Omega } }_{i},{\mathbf {\Omega } }_{j})=\left\{{\begin{array}{lll}\Phi _{\mathrm {LJ} }(r_{ij})&;&r_{ij}<\sigma _{\mathrm {LJ} }\\\Phi _{\mathrm {LJ} }(r_{ij})\exp \left(-{\frac {\theta _{k_{min},ij}^{2}}{2\sigma ^{2}}}\right)\exp \left(-{\frac {\theta _{l_{min},ji}^{2}}{2\sigma ^{2}}}\right)&;&r_{ij}\geq \sigma _{\mathrm {LJ} }\end{array}}\right.}

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi_{\mathrm {LJ}}(r_{ij})} is the Lennard-Jones potential and

References