Sigma bond in the context of Electron density

A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between atoms, when they share electrons, is known as covalent bonding. For many molecules, the sharing of electrons allows each atom to attain the equivalent of a full valence shell, corresponding to a stable electronic configuration. In organic chemistry, covalent bonding is much more common than ionic bonding.

Covalent bonding also includes many kinds of interactions, including σ-bonding, π-bonding, metal-to-metal bonding, agostic interactions, bent bonds, three-center two-electron bonds and three-center four-electron bonds. The term "covalence" was introduced by Irving Langmuir in 1919, with Nevil Sidgwick using "co-valent link" in the 1920s. Merriam-Webster dates the specific phrase covalent bond to 1939, recognizing its first known use. The prefix co- (jointly, partnered) indicates that "co-valent" bonds involve shared "valence", as detailed in valence bond theory.

In chemistry, the ball-and-stick model is a molecular model of a chemical substance which displays both the three-dimensional position of the atoms and the bonds between them. The atoms are typically represented by spheres, connected by rods which represent the bonds. Double and triple bonds are usually represented by two or three curved rods, respectively, or alternately by correctly positioned sticks for the sigma and pi bonds. In a good model, the angles between the rods should be the same as the angles between the bonds, and the distances between the centers of the spheres should be proportional to the distances between the corresponding atomic nuclei. The chemical element of each atom is often indicated by the sphere's color.

In a ball-and-stick model, the radius of the spheres is usually much smaller than the rod lengths, in order to provide a clearer view of the atoms and bonds throughout the model. As a consequence, the model does not provide a clear insight about the space occupied by the model. In this aspect, ball-and-stick models are distinct from space-filling (calotte) models, where the sphere radii are proportional to the Van der Waals atomic radii in the same scale as the atom distances, and therefore show the occupied space but not the bonds.

A carbon–carbon bond is a covalent bond between two carbon atoms. The most common form is the single bond: a bond composed of two electrons, one from each of the two atoms. The carbon–carbon single bond is a sigma bond and is formed between one hybridized orbital from each of the carbon atoms. In ethane, the orbitals are sp-hybridized orbitals, but single bonds formed between carbon atoms with other hybridizations do occur (e.g. sp to sp). In fact, the carbon atoms in the single bond need not be of the same hybridization. Carbon atoms can also form double bonds in compounds called alkenes or triple bonds in compounds called alkynes. A double bond is formed with an sp-hybridized orbital and a p-orbital that is not involved in the hybridization. A triple bond is formed with an sp-hybridized orbital and two p-orbitals from each atom. The use of the p-orbitals forms a pi bond.

In chemistry, a ring is an ambiguous term referring either to a simple cycle of atoms and bonds in a molecule or to a connected set of atoms and bonds in which every atom and bond is a member of a cycle (also called a ring system). A ring system that is a simple cycle is called a monocycle or simple ring, and one that is not a simple cycle is called a polycycle or polycyclic ring system. A simple ring contains the same number of sigma bonds as atoms, and a polycyclic ring system contains more sigma bonds than atoms.

A molecule containing one or more rings is called a cyclic compound, and a molecule containing two or more rings (either in the same or different ring systems) is termed a polycyclic compound. A molecule containing no rings is called an acyclic or open-chain compound.

In physical organic chemistry, a conjugated system is a system of connected p-orbitals with delocalized electrons in a molecule, which in general lowers the overall energy of the molecule and increases stability. It is conventionally represented as having alternating single and multiple bonds. Lone pairs, radicals or carbenium ions may be part of the system, which may be cyclic, acyclic, linear or mixed. The term "conjugated" was coined in 1899 by the German chemist Johannes Thiele.

Conjugation is the overlap of one p-orbital with another across an adjacent σ bond. (In transition metals, d-orbitals can be involved.)

In organic chemistry, a bent bond, also known as a banana bond, is a type of covalent chemical bond with a geometry somewhat reminiscent of a banana. The term itself is a general representation of electron density or configuration resembling a similar "bent" structure within small ring molecules, such as cyclopropane (C₃H₆) or as a representation of double or triple bonds within a compound that is an alternative to the sigma and pi bond model.

In chemistry, bond cleavage, or bond fission, is the splitting of chemical bonds. This can be generally referred to as dissociation when a molecule is cleaved into two or more fragments.

In general, there are two classifications for bond cleavage: homolytic and heterolytic, depending on the nature of the process. The triplet and singlet excitation energies of a sigma bond can be used to determine if a bond will follow the homolytic or heterolytic pathway. A metal−metal sigma bond is an exception because the bond's excitation energy is extremely high, thus cannot be used for observation purposes.

In chemistry, a sigma complex or σ-complex usually refers to a family of coordination complexes where one or more ligands interact with the metal using the bonding electrons in a sigma bond. Transition metal silane complexes are often especially stable sigma complexes. A particularly common subset of sigma complexes are those featuring an agostic interaction where a C–H σ-bond on one of its ligands 'leans' towards and interacts with the coordinatively unsaturated metal center to form a chelate. Transition metal alkane complexes (e.g., a methane complex) that bind solely through the C–H bond are also known but structurally characterized examples are rare, as C–H σ-bonds are generally poor electron donors, and, in many cases, the weakened C–H bond cleaves completely (C–H oxidative addition) to form a complex of type M(R)(H). In some cases, even C–C bonds function as sigma ligands.