Chemical bond
In 1927, Øyvind Burrau derived the first mathematically complete quantum description of a simple chemical bond. This work focused on one electron in the hydrogen molecular ion H2+. The calculation showed that quantum theory could be fundamentally and quantitatively correct for describing how atoms stick together. Before this moment, chemists relied on empirical rules without knowing the underlying physics. Burrau's equations proved that electrons behave as waves when they move between atomic nuclei. Constructive quantum mechanical wavefunction interference stabilizes paired nuclei at an optimal distance. This balance explains why bonded nuclei maintain a specific separation rather than collapsing into each other or flying apart.
The simplest view of a covalent bond involves two electrons drawn into the space between two atomic nuclei. Energy releases during bond formation not because potential energy drops, but because kinetic energy reduces. Electrons occupy a more spatially distributed orbital with a longer de Broglie wavelength compared to being confined closer to their respective nucleus. This reduction in kinetic energy creates stability. Such bonds exist between two particular identifiable atoms and have a direction in space. Chemists show them as single connecting lines between atoms in drawings or model them as sticks between spheres.
Ionic bonding operates differently by transferring electrons completely instead of sharing them. In 1904, Richard Abegg proposed his rule stating the difference between maximum and minimum valencies is often eight. This early insight helped later scientists understand how one atom might transfer an electron to another. The outer atomic orbital of one atom has a vacancy allowing addition of one or more electrons. These newly added electrons potentially occupy a lower energy state effectively closer to more nuclear charge. One nucleus offers a more tightly bound position to an electron than does another nucleus. Thus one atom may transfer an electron to the other causing it to assume a net positive charge while the other assumes a net negative charge. The bond then results from electrostatic attraction between these oppositely charged ions.
Working in the late 17th century Robert Boyle developed the concept of a chemical element as substance different from a compound. Near the end of the 18th century Antoine Lavoisier showed that compounds consist of elements in constant proportion. He redefined an element as a substance which scientists could not decompose into simpler substances by experimentation. This brought an end to the ancient idea of the elements of matter being fire earth air and water. Lavoisier demonstrated that water can be decomposed into hydrogen and oxygen which he could not decompose further thereby proving these are elements.
In 1797 Joseph Proust established the law of definite proportions stating masses of constituents always have same proportions by weight regardless of quantity or source. This definition distinguished compounds from mixtures. In the early years of the 17th century Humphry Davy experimented on decomposing compounds using the newly invented voltaic pile. His work led to speculation that chemical bonding was related to electricity. In 1812 Jöns Jakob Berzelius published a theory stressing 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 developed the theory of valency originally called combining power. They built on radical theories showing compounds joined owing to attraction of positive and negative poles. The nature of the atom became clearer with Ernest Rutherford's 1911 discovery of an atomic nucleus surrounded by electrons. At the 1911 Solvay Conference Max Planck stated intermediaries could be electrons suggesting nuclear models where electrons determine chemical behavior.
In 1916 Gilbert N. Lewis developed the concept of electron-pair bonds allowing two atoms to share one to six electrons forming single double or triple bonds. Lewis wrote An electron may form part of shell of two different atoms and cannot be said to belong to either one exclusively. Also in 1916 Walther Kossel put forward a similar model assuming complete transfers of electrons between atoms creating a model of ionic bonding. Both scientists structured their bonding models on Abegg's rule from 1904. Niels Bohr proposed a model of chemical bond in 1913 describing electrons forming rotating ring perpendicular to molecular axis.
Walter Heitler and Fritz London put forward a practical approach in 1927 known as the Heitler, London method. This forms basis of what is now called valence bond theory. In 1929 Sir John Lennard-Jones introduced linear combination of atomic orbitals molecular orbital method approximation. This represented covalent bond as orbital formed combining quantum mechanical Schrödinger atomic orbitals hypothesized for electrons in single atoms. Equations for bonding electrons in multi-electron atoms could not solve analytically but approximations gave many good qualitative predictions. Most quantitative calculations use either valence bond or molecular orbital theory as starting point though density functional theory has become increasingly popular recently.
In 1933 H.H. James and A.S. Coolidge carried out calculation on dihydrogen molecule using functions adding distance between two electrons explicitly. With up to 13 adjustable parameters they obtained result very close to experimental dissociation energy. Later extensions used up to 54 parameters giving excellent agreement with experiments. This convinced scientific community that quantum theory could match experiment despite lacking physical pictures of other theories.
Bond lengths can be converted to angstroms by division by 100 where one angstrom equals 100 picometers. The hydrogen-hydrogen bond measures 74 picometers with energy of 436 kilojoules per mole. Carbon-carbon bonds vary from 154 picometers in single bonds to 120 picometers in triple bonds carrying 839 kilojoules per mole. Electronegativity serves as simple way to quantitatively estimate bond energy characterizing continuous scale from covalent to ionic bonding. Large difference in electronegativity leads to more polar ionic character while small differences typically create non-polar covalent bonds ranging 0 to 0.3.
Ionic crystals form when species arrange so no ion specifically paired with any single other ion in directional bond. Each species surrounded by ions opposite charge with spacing same for all surrounding atoms of same type. X-ray diffraction shows sodium chloride crystals contain electrostatic forces between sodium cations and chloride anions. When such crystals melt into liquids ionic bonds break first because they are non-directional allowing charged species move freely. Similarly salts dissolve into water breaking ionic bonds while covalent bonds continue holding molecules together like cyanide ions moving independently through solution.
Metallic bonding delocalizes electrons over lattice creating free movement leading to luster electrical conductivity ductility and high tensile strength. The cloud of electrons causes shiny lustre reflecting most frequencies white light. Metallic bonds allow metal crystals deform easily since composed of atoms attracted without particularly oriented ways resulting malleability. Covalent polymers extending networks through solids like diamond or quartz produce structures both strong and tough at least direction oriented correctly with network.
Van der Waals forces include Coulombic interactions between partial charges in polar molecules and Pauli repulsions between closed electron shells. Keesom forces act between permanent dipoles of two polar molecules while London dispersion forces operate between induced dipoles different molecules. Hydrogen bonds form when A and B are highly electronegative atoms usually nitrogen oxygen or fluorine. Such bonds occur when A forms highly polar covalent bond with hydrogen giving it partial positive charge attracting lone pair electrons on B forming hydrogen bond.
Hydrogen bonds responsible for high boiling points water and ammonia relative heavier analogues. In some cases similar halogen bond formed by halogen atom located between two electronegative atoms on different molecules. At short distances repulsive forces between atoms become important influencing physical characteristics such as melting point substance. Weak intermolecular bonds give organic molecular substances waxes oils soft bulk character low melting points liquids must cease most structured oriented contact each other.
Molecules formed primarily from non-polar covalent bonds often immiscible water other polar solvents much more soluble non-polar solvents hexane. Dipole-dipole interactions arise from significant ionic character where shared electrons closer one atom creating imbalance charge. Electronegativity difference between atoms these bonds ranges 0.3 to 1.7 allowing moderate polarity.
Common questions
When did Øyvind Burrau derive the first mathematically complete quantum description of a chemical bond?
Øyvind Burrau derived the first mathematically complete quantum description of a simple chemical bond in 1927. This work focused on one electron in the hydrogen molecular ion H2+ and proved that electrons behave as waves when they move between atomic nuclei.
What is the difference between covalent bonds and ionic bonding according to Richard Abegg's rule from 1904?
Covalent bonds involve two electrons drawn into the space between two atomic nuclei while ionic bonding operates by transferring electrons completely instead of sharing them. Richard Abegg proposed his rule stating the difference between maximum and minimum valencies is often eight which helped scientists understand how one atom might transfer an electron to another.
Who developed the concept of a chemical element as substance different from a compound in the late 17th century?
Robert Boyle developed the concept of a chemical element as substance different from a compound working in the late 17th century. Antoine Lavoisier later redefined an element as a substance which scientists could not decompose into simpler substances by experimentation near the end of the 18th century.
How did Gilbert N. Lewis and Walther Kossel structure their bonding models based on Abegg's rule from 1904?
Gilbert N. Lewis developed the concept of electron-pair bonds allowing two atoms to share one to six electrons forming single double or triple bonds in 1916. Walther Kossel put forward a similar model assuming complete transfers of electrons between atoms creating a model of ionic bonding also in 1916.
What are the bond lengths and energies for hydrogen-hydrogen and carbon-carbon bonds mentioned in the text?
The hydrogen-hydrogen bond measures 74 picometers with energy of 436 kilojoules per mole while carbon-carbon bonds vary from 154 picometers in single bonds to 120 picometers in triple bonds carrying 839 kilojoules per mole.