Hydrogen Bond

One of the most important properties of water is the existence of hydrogen bonds, in which a hydrogen donor and an acceptor form a proper orientation. A water molecule has both donors and acceptors contributing formation of hydrogen bonds. The OH group is a donor: its hydrogen can be shared with an acceptor. Each lone pair of electrons residing on the oxygen of H$_{2}$O can be an acceptor and bind to a donor's hydrogen. The number of hydrogen bonds a water can form with its neighbors ranges from zero to four.

To describe hydrogen bonds in molecular simulations, an explicit 12-10 potential form can be employed in classical force-field MD [7]:

$$U_{HB}(r)=\frac{A}{r^{12}}-\frac{C}{r^{10}}.$$ (1)

Equation (1) is used to model the interaction between the donor hydrogen atom and the acceptor atom. More elaborated hydrogen-bonding terms that take into account deviations from the geometry of the reference hydrogen bond have been devised. For example, the hydrogen-bond energy could incorporate the angle dependence. Equation (1) can be improved, as is done in the YETI force field [29], by taking geometries of molecules into account

$$U_{HB}=\left(\frac{A}{r_{H...Acc}^{12}}-\frac{C}{r_{H...Acc}... ...ht)\cos^{2}\theta_{Don...H...Acc}\cos^{4}\omega_{H...Acc...LP}$$ (2)

where $r_{H...Acc}$ represents the distance from the hydrogen atom of the donor to the oxygen atom of the acceptor, $\theta_{Don...H...Acc}$ is the angle subtended at the hydrogen by the bonds to the donor and the acceptor, and $\omega_{H...Acc...LP}$ represents the deviation of the hydrogen bond from the closest lone-pair direction at the acceptor atom. See Fig. 2.

Figure 2: Definition of hydrogen-bond geometry used in YETI force field.

Another program, GRID [8], mainly used for finding energetically favorable regions in protein binding sites utilizes a direction-dependent 6-4 function to describe hydrogen bonds:

$$U_{HB}=\left(\frac{C}{d^{6}}-\frac{D}{d^{4}}\right)\cos^{m}\theta$$ (3)

where $\theta$ is the angle subtended at the hydrogen atom and $m$ is usually set to 4.

Many classical force-field MD simulation programs do not explicitly include a hydrogen-bond term; instead, its effect is implicitly contained in the electrostatic and van der Waals interaction terms.

In liquid water, most water molecules are in tetrahedral configurations, each having 3-4 hydrogen bonds. The energy of an optimal water-water hydrogen bond in the gas phase is estimated to be about 5.5 kcal/mol. It is the dominant component of the energetics in solid phase. The tetrahedral symmetry of a water molecule defines the structural framework for ice. Crystal structures show that the water molecules in ice $I_{h}$ (the stable form at $273$ K and $1$ atm pressure) have tetrahedral symmetry, which persists in liquid water, as shown in its radial distribution function. The integral of the first peak in the radial distribution function of water is still close to four.

Hydrogen bond weakens with increasing temperature in liquid water. We can measure the number, strength, and angles of hydrogen bonds in liquid water by vibrational spectroscopy. Raman spectroscopy has been used to study the stretching mode of OD bonds when a small amount of deuterated water, D$_{2}$O, is mixed with solvent of H$_{2}$O. The spectral shift from the D$_{2}$O peak at $2500$ cm$^{-1}$ (at 293 K) toward $2650$ cm$^{-1}$ (at 673 K, liquid form at high temperature) indicates that hydrogen bonds bend or break with increasing temperature. Most models predict that not all hydrogen bonds break at the boiling temperature. The special structural property of water gives it many unique properties such as high dielectric constant, in part from polarizable hydrogen bonds.