Chemical bond

• 1. Introduction

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  A chemical bond is the association of atoms or ions into molecules, crystals, and other structures, and it is the reason matter holds its shape at all. Pull two hydrogen atoms close and something quietly remarkable happens. Two electrons drift into the narrow space between the nuclei, and the pair settles into an arrangement neither atom could manage alone. The atoms in molecules, crystals, metals, and every other form of matter are held together this way, and these bonds determine the structure and properties of matter itself.

  The attraction has a familiar root. Opposite electric charges attract, so the negatively charged electrons around a nucleus and the positively charged protons inside it pull toward each other. Electrons shared between two nuclei feel the tug of both. Yet the bonded nuclei do not collapse together. They hold an optimal distance, the bond distance, where attractive and repulsive effects balance. Why they sit exactly there, why some bonds shatter like salt while others bend like copper, and how chemists learned to predict any of this are the questions this story will answer.

• 2. A Spectrum Of Attraction

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  A chemical bond is an attraction between atoms, and the behaviors of the outermost valence electrons merge into one another so seamlessly that no clear line can be drawn between the types. Still, it remains useful to distinguish them, because each gives condensed matter different properties. The strong, or primary, bonds are covalent, ionic, and metallic. The weak, or secondary, bonds include dipole-dipole interactions, the London dispersion force, and hydrogen bonds.

  In the simplest view of a covalent bond, one or more electrons are drawn into the space between two atomic nuclei, and energy is released when the bond forms. The surprise is where that energy comes from. It is not a reduction in potential energy, since the attraction of the electrons to the protons is offset by electron-electron and proton-proton repulsions. Instead, stability arises from a drop in kinetic energy. The electrons occupy a more spatially distributed orbital, with a longer de Broglie wavelength, than they would confined close to a single nucleus.

  Covalent bonds exist between two identifiable atoms and have a direction in space, which is why they can be drawn as single lines or modeled as sticks between spheres. They often gather atoms into molecules, and in solids and liquids those molecules cling to one another through forces much weaker than the bonds holding each molecule together. Weak intermolecular bonds give waxes and oils their soft character and low melting points. But when covalent bonds link long chains, as in nylon, or extend through networks like diamond, quartz, and the silicate minerals in rock, the result can be strong, tough, and very high-melting.

• 3. Transfer Versus Sea

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  In a simplified view of an ionic bond, the bonding electron is not shared at all but transferred outright. One atom has a vacancy in its outer orbital that can accept electrons into a lower energy state, effectively closer to more nuclear charge. So one nucleus offers an electron a more tightly bound home than the other, and the transfer leaves one atom positively charged and the other negative. The bond is the electrostatic attraction between those ions, and it can be seen as the extreme case of polarization in a covalent bond.

  Ionic bonds often have no particular orientation, because each ion is pulled equally toward all the ions around it. They are strong, so ionic substances need high temperatures to melt, yet brittle, because the short-range forces between ions do not bridge cracks easily. This is the physics behind crystals of classic mineral salts like table salt. When such crystals melt or dissolve, the non-directional ionic bonds break first.

  Metallic bonding is mentioned less often, but it explains why a metal behaves like a metal. Each atom donates one or more electrons to a sea of electrons residing between many atoms, and by virtue of its wave nature each electron associates with a great many atoms at once. The atoms turn slightly positive while the shared electrons stay attracted to all of them. This bonding can be very strong, giving metals their tensile strength, yet it is collective rather than directional, so metal crystals deform easily and stay malleable. The electron cloud also produces the good electrical and thermal conductivity of metals and the shiny lustre that reflects most frequencies of white light.

• 4. Before The Atom

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  Working in the late 17th century, Robert Boyle developed the concept of a chemical element as a substance different from a compound. Much of what followed arrived before any atomic theory existed at all. Near the end of the 18th century, Antoine Lavoisier showed that compounds consist of elements in constant proportion and redefined an element as a substance that could not be decomposed by experiment. He decomposed water into hydrogen and oxygen, neither of which he could break down further, and he stated the law of conservation of mass, that matter neither appears nor vanishes in a reaction.

  In 1797 the French chemist Joseph Proust established the law of definite proportions, which holds that a compound broken into its elements always yields the same proportions by weight, regardless of quantity or source. This distinguished compounds from mere mixtures. In the early 19th century, Humphry Davy used the newly invented voltaic pile to decompose compounds into elements, which led to speculation that bonding was tied to electricity. In 1812 Jöns Jakob Berzelius published a theory of chemical combination stressing the electronegative and electropositive characters of combining atoms.

  By the mid 19th century, Edward Frankland, F.A. Kekulé, A.S. Couper, Alexander Butlerov, and Hermann Kolbe built the theory of valency, first called combining power, picturing compounds joined by an attraction of positive and negative poles. In 1904, Richard Abegg proposed his rule that the difference between an element's maximum and minimum valencies is often eight, a number that would anchor the bonding models still to come.

• 5. The Nuclear Picture

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  Ernest Rutherford's 1911 discovery of an atomic nucleus surrounded by electrons made the atom clearer. In his paper Rutherford cited the model of the Japanese physicist Hantaro Nagaoka, who had rejected Thomson's plum pudding model on the grounds that opposite charges are impenetrable. In 1904 Nagaoka had proposed a planetary atom, a positively charged center ringed by revolving electrons, in the manner of Saturn and its rings. His model hypothesized a very massive atomic center, like a massive planet, with electrons revolving around the nucleus bound by electrostatic forces, like rings bound by gravity.

  At the 1911 Solvay Conference, discussing what could regulate energy differences between atoms, Max Planck offered a pointed remark. "The intermediaries could be the electrons." These nuclear models suggested that electrons determine chemical behavior, and Niels Bohr's 1913 model of a nuclear atom with electron orbits came next, carrying that idea forward into the quantum era.

• 6. The Shared Pair

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  In 1916, the chemist Gilbert N. Lewis developed the concept of electron-pair bonds, in which two atoms may share one to six electrons, forming a single-electron bond, a single bond, a double bond, or a triple bond. In his own words, "An electron may form a part of the shell of two different atoms and cannot be said to belong to either one exclusively." That same year Walther Kossel put forward a similar theory, but his assumed complete transfers of electrons, making it a model of ionic bonding. Both men built on Abegg's rule of 1904.

  Niels Bohr proposed his own model of the chemical bond in 1913. For a diatomic molecule, the electrons formed a rotating ring whose plane sat perpendicular to the molecular axis, equidistant from the two nuclei, with equilibrium reached by balancing the nuclei's attraction to the ring against their mutual repulsion. The model accounted for Coulomb repulsion by placing the ring electrons at maximum distance from each other.

  In 1927 the Danish physicist Øyvind Burrau derived the first mathematically complete quantum description of a simple bond, the one produced by a single electron in the hydrogen molecular ion, H2+. It showed the quantum approach could be fundamentally and quantitatively correct, yet the methods could not extend to molecules with more than one electron. In the same year Walter Heitler and Fritz London put forward a more practical approach, and the Heitler-London method became the basis of valence bond theory.

• 7. Calculating The Bond

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  In 1929 Sir John Lennard-Jones introduced the linear combination of atomic orbitals, the LCAO approximation, and suggested ways to derive the electronic structures of the F2 and O2 molecules from basic quantum principles. This molecular orbital theory represented a covalent bond as an orbital built by combining the Schrödinger atomic orbitals of single atoms. The equations for bonding electrons in multi-electron atoms could not be solved analytically, but the approximations still gave many good qualitative predictions.

  In 1933 H. H. James and A. S. Coolidge ran a calculation on the dihydrogen molecule that broke from all earlier work. Previous calculations used only functions of an electron's distance from the nucleus, but theirs explicitly added the distance between the two electrons. With up to 13 adjustable parameters they came very close to the experimental dissociation energy, and later extensions used as many as 54 parameters for excellent agreement. This convinced the scientific community that quantum theory could match experiment, even though the method carried none of the physical pictures of valence bond or molecular orbital theory and was hard to extend to larger molecules.

  Most quantitative work in modern quantum chemistry still starts from valence bond or molecular orbital theory, though a third approach, density functional theory, has grown increasingly popular. The two original frameworks are often viewed as competing but complementary. Valence bond theory is spatially localized and chemically intuitive, focusing attention on the part of a molecule undergoing change. Molecular orbital theory is more natural from a quantum mechanical view, with orbital energies that are physically significant and linked directly to experimental ionization energies from photoelectron spectroscopy.

• 8. Weaker Ties

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  Van der Waals forces are interactions between closed-shell molecules, spanning both Coulombic interactions between partial charges in polar molecules and Pauli repulsions between closed electron shells. Keesom forces act between the permanent dipoles of two polar molecules. London dispersion forces act between the induced dipoles of different molecules, and a permanent dipole in one molecule can also induce a dipole in another.

  Hydrogen bonds take the form A--H...B, arising when A and B are two highly electronegative atoms, usually nitrogen, oxygen, or fluorine. A forms a highly polar bond with H, giving the hydrogen a partial positive charge, and B carries a lone pair drawn to that charge. These bonds are responsible for the high boiling points of water and ammonia compared with their heavier analogues. A similar halogen bond can sometimes form when a halogen atom sits between two electronegative atoms on different molecules.

  The strength of any strong bond traces back to electronegativity, the tendency of an atom to attract shared electrons, where a larger difference gives a bond more polar, more ionic character. There is no precise cutoff, but an electronegativity difference above 1.7 is likely ionic and below 1.7 likely covalent, while non-polar covalent bonds sit between roughly 0 and 0.3. That single continuous scale, running from a shared pair to a transferred electron, is the thread tying together every structure these bonds build, from a grain of table salt to the hydrogen-bonded water that keeps it dissolved.