A hydrogen bond results from a dipole-dipole force between an electronegative atom and a hydrogen atom bonded to nitrogen, oxygen or fluorine (thus the name "hydrogen bond", which must not be confused with a covalent bond to hydrogen). The energy of a hydrogen bond (typically 5 to 30 kJ/mole) is comparable to that of weak covalent bonds (155 kJ/mol), and a typical covalent bond is only 20 times stronger than an intermolecular hydrogen bond. These bonds can occur between molecules (intermolecularly), or within different parts of a single molecule (intramolecularly). The hydrogen bond is a very strong fixed dipole-dipole van der Waals-Keesom force, but weaker than covalent, ionic and metallic bonds. The hydrogen bond is somewhere between a covalent bond and an electrostatic intermolecular attraction. This type of bond occurs in both inorganic molecules (water) and organic molecules (DNA).
Intermolecular hydrogen bonding is responsible for the high boiling point of water (100 °C). This is because of the strong hydrogen bond, as opposed to other group 16 hydrides. Intramolecular hydrogen bonding is partly responsible for the secondary, tertiary, and quaternary structures of proteins and nucleic acids.
Carbon can also participate in hydrogen bonding, especially when the carbon atom is bound to several electronegative atoms, as is the case in chloroform, CHCl3. The electronegative atom attracts the electron cloud from around the hydrogen nucleus and, by decentralizing the cloud, leaves the atom with a positive partial charge. Because of the small size of hydrogen relative to other atoms and molecules, the resulting charge, though only partial, nevertheless represents a large charge density. A hydrogen bond results when this strong positive charge density attracts a lone pair of electrons on another heteroatom, which becomes the hydrogen-bond acceptor.
The hydrogen bond is often described as an electrostatic dipole-dipole interaction. However, it also has some features of covalent bonding: it is directional, strong, produces interatomic distances shorter than sum of van der Waals radii, and usually involves a limited number of interaction partners, which can be interpreted as a kind of valence. These covalent features are more significant when acceptors bind hydrogens from more electronegative donors.
The partially covalent nature of a hydrogen bond raises the questions: "To which molecule or atom does the hydrogen nucleus belong?" and "Which should be labeled 'donor' and which 'acceptor'?" Usually, this is easy to determine simply based on interatomic distances in the X-H...Y system: X-H distance is typically ~1.1 Å, whereas H...Y distance is ~ 1.6 to 2.0 Å. Liquids that display hydrogen bonding are called associated liquids.
Hydrogen bonds can vary in strength from very weak (1-2 kJ mol−1) to extremely strong (>155 kJ mol−1), as in the ion HF2−. Typical values include:
The length of hydrogen bonds depends on bond strength, temperature, and pressure. The bond strength itself is dependent on temperature, pressure, bond angle, and environment (usually characterized by local dielectric constant). The typical length of a hydrogen bond in water is 1.97 Å (197 pm). The ideal bond angle depends on the nature of the hydrogen bond donor. Experimental results of hydrofluoric acid donor with various receptors shows the following angles:
|Acceptor···Donor||VSEPR Symmetry||Angle (°)|
|H2CO ··· HF||trigonal planar||110|
|H2O ··· HF||pyramidal||46|
|H2S ··· HF||pyramidal||89|
|SO2 ··· HF||trigonal planar||145|
The most ubiquitous, and perhaps simplest, example of a hydrogen bond is found between water molecules. In a discrete water molecule, water has two hydrogen atoms and one oxygen atom. Two molecules of water can form a hydrogen bond between them; the simplest case, when only two molecules are present, is called the water dimer and is often used as a model system. When more molecules are present, as is the case in liquid water, more bonds are possible because the oxygen of one water molecule has two lone pairs of electrons, each of which can form a hydrogen bond with hydrogens on two other water molecules. This can repeat so that every water molecule is H-bonded with up to four other molecules, as shown in the figure (two through its two lone pairs, and two through its two hydrogen atoms.)
Liquid water's high boiling point is due to the high number of hydrogen bonds each molecule can have relative to its low molecular mass, not to mention the great strength of these hydrogen bonds. Realistically the water molecule has a very high boiling point, melting point and viscosity compared to other similar substances not conjoined by hydrogen bonds. The reasoning for these attributes is the inability to, or the difficulty in, breaking these bonds. Water is unique because its oxygen atom has two lone pairs and two hydrogen atoms, meaning that the total number of bonds of a water molecule is up to four. For example, hydrogen fluoride—which has three lone pairs on the F atom but only one H atom—can have a total of only two bonds (ammonia has the opposite problem: three hydrogen atoms but only one lone pair).
The exact number of hydrogen bonds in which a molecule in liquid water participates, fluctuates with time and depends on the temperature. From TIP4P liquid water simulations at 25 °C, it was estimated that each water molecule participates in an average of 3.59 hydrogen bonds. At 100 °C, this number decreases to 3.24 due to the increased molecular motion and decreased density, while at 0 °C, the average number of hydrogen bonds increases to 3.69. A more recent study found a much smaller number of hydrogen bonds: 2.357 at 25 °C. The differences may be due to the use of a different method for defining and counting the hydrogen bonds.
Where the bond strengths are more equivalent, one might instead find the atoms of two interacting water molecules partitioned into two polyatomic ions of opposite charge, specifically hydroxide (OH−) and hydronium (H3O+). (Hydronium ions are also known as 'hydroxonium' ions.)
Indeed, in pure water under conditions of standard temperature and pressure, this latter formulation is applicable only rarely; on average about one in every 5.5 × 108 molecules gives up a proton to another water molecule, in accordance with the value of the dissociation constant for water under such conditions. It is a crucial part of the uniqueness of water.
Hydrogen bonding also plays an important role in determining the three-dimensional structures adopted by proteins and nucleic bases. In these macromolecules, bonding between parts of the same macromolecule cause it to fold into a specific shape, which helps determine the molecule's physiological or biochemical role. The double helical structure of DNA, for example, is due largely to hydrogen bonding between the base pairs, which link one complementary strand to the other and enable replication.
In proteins, hydrogen bonds form between the backbone oxygens and amide hydrogens. When the spacing of the amino acid residues participating in a hydrogen bond occurs regularly between positions i and i + 4, an alpha helix is formed. When the spacing is less, between positions i and i + 3, then a 310 helix is formed. When two strands are joined by hydrogen bonds involving alternating residues on each participating strand, a beta sheet is formed. Hydrogen bonds also play a part in forming the tertiary structure of protein through interaction of R-groups.(See also protein folding).
Symmetric hydrogen bonds have been observed recently spectroscopically in formic acid at high pressure (>GPa). Each hydrogen atom forms a partial covalent bond with two atoms rather than one. Symmetric hydrogen bonds have been postulated in ice at high pressure (Ice X). Low-barrier hydrogen bonds form when the distance between two heteroatoms is very small.
Most generally, the hydrogen bond can be viewed as a metric-dependent electrostatic scalar field between two or more intermolecular bonds. This is slightly different from the intramolecular bound states of, for example, covalent or ionic bonds; however, hydrogen bonding is generally still a bound state phenomenon, since the interaction energy has a net negative sum. The initial theory of hydrogen bonding proposed by Linus Pauling suggested that the hydrogen bonds had a partial covalent nature. This remained a controversial conclusion until the late 1990's when NMR techniques were employed by F. Cordier et al. to transfer information between hydrogen-bonded nuclei, a feat that would only be possible if the hydrogen bond contained some covalent character. While a lot of experimental data has been recovered for hydrogen bonds in water, for example, that provide good resolution on the scale of intermolecular distances and molecular thermodynamics, the kinetic and dynamical properties of the hydrogen bond in dynamic systems remains unchanged.