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How do computer simulations of liquid hydrogen-bonding systems incorporate hydrogen bonding? Since I think hydrogen bonding has mixed covalent and electrostatic character, wouldn't you need something beyond a classical force field? Yet, for example, simulations of water using a simple classical model like spc/e reproduce the structure, including the tetrahedral coordination.

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  • $\begingroup$ People have tried adding special hydrogen bonding contributions to FF's. They don't catch on, possibly because hydrogen bonding is over-rated. Hydrogens are elements with electrons, just like the other elements. You can parameter fit them just the same as the others and unsurprisingly, get as reasonable of results as the others. Hydrogen bonding makes for a good catch phrase though. $\endgroup$
    – Wesley
    Oct 28 at 15:05
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The short answer is that, while hydrogen bonds do have some covalent character, you can mimic that covalent character by increasing the electrostatic term. For example you can specify point charges to the oxygen and hydrogen atoms that are larger than they would otherwise be, and the overestimated electrostatic attraction will compensate for the neglect of covalent character. Water models are usually fitted against experimentally observable quantities, such as heat of vaporization, radial correlation function, dimerization energy, and so on, rather than against the ab initio electrostatic, polarization, Pauli repulsion, dispersion and covalent contributions to the energy, so if the model neglects a term, the other terms must be absorbing the resulting error.

Besides, the tetrahedral coordination structure of water (or more accurately speaking, ice) does not require the description of the covalent part of the hydrogen bond. Even with a purely electrostatic description of water molecules, the oxygen atoms will still be tetrahedral (just with somewhat inaccurate hydrogen bond lengths), due to angular repulsion effects.

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The current biomolecular force fields that I'm familiar with don't include any special energy terms for hydrogen bonds. Typically, hydrogen atoms that are capable of hydrogen bonding have very small Lennard-Jones radii and significant positive charges, which allow for very strong electrostatic interactions. For example, in the CHARMM force field, the alcohol hydrogen of serine has a 12-6 potential Rmin of 0.449 Å and a charge of 0.43, while a terminal methyl hydrogen of leucine has an Rmin of 2.68 Å and a charge of 0.09. So, the alcohol hydrogen can donate strong hydrogen bonds, while the methyl hydrogen does not. In the Amber force field, the situation is similar, although less pronounced: the alcohol hydrogen of serine has an Rmin of 1.2 Å and a charge of 0.4275, while the leucine methyl has an Rmin of 2.974 Å and a charge 0.1.

Very old versions of the CHARMM force field used to have a special 12-10 potential term for hydrogen bonds, but that has been long deprecated.

Now, maybe, in principle, the bonded terms involving the hydrogen should change upon formation of the hydrogen bond. I would imagine that an alcohol hydrogen interacts differently with its parent oxygen depending on whether it participates in a hydrogen bond with something else. But force fields such as CHARMM and Amber ignore any such effects: the bond, angle, and dihedral terms don't change depending on whether a hydrogen bond has formed or not. These force fields have been very successful in reproducing many experimental results with proteins, lipids, DNA and carbohydrates in water, so, at least for some purposes, the approximation is valid.

Covalent character does not necessarily mean you can't represent a interaction by a classical force field. With a sufficiently complex force field, you can represent a lot of chemistry (for example, ReaxFF). I should also mention that ReaxFF has a special term for hydrogen bonds: $$E_\mathrm{Hbond} = p_\mathrm{hb1} \left[ 1 - \exp(p_\mathrm{hb2} \mathsf{BO}_\mathrm{XH}) \right] \exp \left[ p_\mathrm{hb3} \left( \frac{r^\circ_\mathrm{hb}}{r_\mathrm{HZ}} + \frac{r_\mathrm{HZ}}{r^\circ_\mathrm{hb}} - 2 \right) \right] \sin^8 \left( \frac{\Theta_\mathrm{XHZ}}{2} \right),$$ where $\mathsf{BO}_\mathrm{XH}$ is the bond order between the donor atom and the hydrogen atom (calculated as detailed in the supporting information of the paper), $r_\mathrm{HZ}$ is the distance between hydrogen atom and the acceptor atom, $\Theta_\mathrm{XHZ}$ is the donor-hydrogen-acceptor angle, and all other variables are free parameters defined in the force field.

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