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Table 1 The OPLS force field potential energy terms and corresponding embedding basis

From: Force field-inspired molecular representation learning for property prediction

OPLS potential energy terms

Embedding basis

\({E}_{\mathrm{bond}}={\sum }_{\mathrm{bonds}}{K}_{r}{\left(r-{r}_{\mathrm{eq}}\right)}^{2}\)

\(\{r, {r}^{2}\}\)

\({E}_{\mathrm{angle}}={\sum }_{\mathrm{angles}}{K}_{\theta }{\left(\theta -{\theta }_{\mathrm{eq}}\right)}^{2}\)

\(\{\theta , {\theta }^{2}\}\)

\({E}_{\mathrm{torsion}}={\sum }_{\mathrm{dihedrals}}\frac{{V}_{\phi ,1}}{2}\left[1+\mathrm{cos}\left(\phi +{f}_{\phi ,1}\right)\right]+\frac{{V}_{\phi ,2}}{2}\left[1-\mathrm{cos}\left(2\phi +{f}_{\phi ,2}\right)\right]+\frac{{V}_{\phi ,3}}{2}\left[1+\mathrm{cos}\left(3\phi +{f}_{\phi ,3}\right)\right]\)

\(\{\mathrm{cos}\phi ,\mathrm{ cos}2\phi ,\mathrm{cos}3\phi ,\mathrm{sin}\phi ,\mathrm{sin}2\phi ,\mathrm{sin}3\phi \}\)

\({E}_{\mathrm{nonbonded}}={\sum }_{i}{\sum }_{j}\left[\frac{{q}_{i}{q}_{j}}{{r}_{ij}}+4{\epsilon }_{ij}\left(\frac{{\sigma }_{ij}^{12}}{{r}_{ij}^{12}}-\frac{{\sigma }_{ij}^{6}}{{r}_{ij}^{6}}\right)\right]{f}_{ij}\)

\(\{{r}^{-1},{r}^{-12}, {r}^{-6}\}\)

  1. \(r\) is bond length, \(\theta\) is valence angle, and \(\phi\) is the dihedral angle; other variables are parameters of the force field (specific definitions can be found in Reference [27])