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In reading Jorgensen's 1983 paper comparing the properties of 6 water models it was mentioned that there is the inclusion of an L-J potential between pairs of oxygen molecules, but no mention of similar terms for other pairwise potentials (O-H or H-H). As far as I'm aware, the continued use and updating of standard water molecules (SPC, TIP3P,...) in classical MD also do not include these extra L-J terms. Is this purely to limit the gross computational excess in performing these pairwise calculations? Thank you.

Paper reference: Jorgensen, William L., et al. "Comparison of simple potential functions for simulating liquid water." The Journal of chemical physics 79.2 (1983): 926-935.

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The original publications may give some reason for omitting HH and OH Lennard-Jones terms -- but my first assumption would certainly be computational simplicity. Having said that, these models are good enough for everyday application.

Molecular dynamics force fields are "models" much more than they are "approximations" -- adding more terms does not guarantee more accurate results. A well-parametrised force field contains a good combination of interactions, even if any of those individual interactions might be poorly motivated on their own.

As an example, because CHARMM36 protein interactions were parametrised with "sTIP3P" water (only OO LJs), their unfolded states are over-stabilised in "mTIP3P" water (both O and H LJ sites -- widely used with CHARMM), according to this paper. More is not always better.

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