theoretical chemistry Theoretical chemistry is the branch of chemistry which develops theoretical generalizations that are part of the theoretical arsenal of modern chemistry: for example, the concepts of chemical bonding, chemical reaction, valence, the surface ...

, the bonding orbital is used in

molecular orbital In chemistry, a molecular orbital is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding ...

(MO) theory to describe the attractive interactions between the

atomic orbital In quantum mechanics, an atomic orbital () is a Function (mathematics), function describing the location and Matter wave, wave-like behavior of an electron in an atom. This function describes an electron's Charge density, charge distribution a ...

s of two or more

atom Atoms are the basic particles of the chemical elements. An atom consists of a atomic nucleus, nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished fr ...

s in a

molecule A molecule is a group of two or more atoms that are held together by Force, attractive forces known as chemical bonds; depending on context, the term may or may not include ions that satisfy this criterion. In quantum physics, organic chemi ...

. In MO theory,

electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...

s are portrayed to move in

wave In physics, mathematics, engineering, and related fields, a wave is a propagating dynamic disturbance (change from List of types of equilibrium, equilibrium) of one or more quantities. ''Periodic waves'' oscillate repeatedly about an equilibrium ...

s. When more than one of these waves come close together, the

in-phase In physics and mathematics, the phase (symbol φ or ϕ) of a wave or other periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is expressed in such a s ...

combination of these waves produces an interaction that leads to a species that is greatly stabilized. The result of the waves’

constructive interference In physics, interference is a phenomenon in which two coherence (physics), coherent waves are combined by adding their intensities or displacements with due consideration for their phase (waves), phase difference. The resultant wave may have ...

causes the density of the electrons to be found within the binding region, creating a stable bond between the two species.

Diatomic molecules

In the classic example of the H₂ MO, the two separate H atoms have identical atomic orbitals. When creating the molecule dihydrogen, the individual valence orbitals, 1''s'', either: merge in phase to get bonding orbitals, where the

electron density Electron density or electronic density is the measure of the probability of an electron being present at an infinitesimal element of space surrounding any given point. It is a scalar quantity depending upon three spatial variables and is typical ...

is in between the nuclei of the atoms; or, merge out of phase to get antibonding orbitals, where the electron density is everywhere around the atom except for the space between the nuclei of the two atoms. Bonding orbitals lead to a more stable species than when the two hydrogens are monatomic. Antibonding orbitals are less stable because, with very little to no electron density in the middle, the two nuclei (holding the same charge) repulse each other. Therefore, it would require more energy to hold the two atoms together through the antibonding orbital. Each electron in the valence 1''s'' shell of hydrogen come together to fill in the stabilizing bonding orbital. So, hydrogen prefers to exist as a diatomic, and not monatomic, molecule. He2wikibondingmo

When looking at helium, the atom holds two electrons in each valence 1''s'' shell. When the two atomic orbitals come together, they first fill in the bonding orbital with two electrons, but unlike hydrogen, it has two electrons left, which must then go to the antibonding orbital. The instability of the antibonding orbital cancels out the stabilizing effect provided by the bonding orbital; therefore, dihelium's

bond order In chemistry, bond order is a formal measure of the multiplicity of a covalent bond between two atoms. As introduced by Gerhard Herzberg, building off of work by R. S. Mulliken and Friedrich Hund, bond order is defined as the difference between t ...

is 0. This is why helium would prefer to be monatomic over diatomic.

Polyatomic molecules

Bonding MOs of pi bonds

Pi bond In chemistry, pi bonds (π bonds) are covalent chemical bonds, in each of which two lobes of an orbital on one atom overlap with two lobes of an orbital on another atom, and in which this overlap occurs laterally. Each of these atomic orbital ...

s are created by the “side-on” interactions of the orbitals. Once again, in molecular orbitals, bonding pi (π) electrons occur when the interaction of the two π atomic orbitals are in-phase. In this case, the

of the π orbitals needs to be symmetric along the mirror plane in order to create the bonding interaction. Asymmetry along the mirror plane will lead to a node in that plane and is described in the antibonding orbital, π*. MObutadienebondingmo

An example of a MO of a simple conjugated π system is butadiene. To create the MO for

butadiene 1,3-Butadiene () is the organic compound with the formula CH2=CH-CH=CH2. It is a colorless gas that is easily condensed to a liquid. It is important industrially as a precursor to synthetic rubber. The molecule can be viewed as the union of two ...

, the resulting π and π* orbitals of the previously described system will interact with each other. This mixing will result in the creation of 4 group orbitals (which can also be used to describe the π MO of any diene): π₁ contains no vertical nodes, π₂ contains one and both are considered bonding orbitals; π₃ contains 2 vertical nodes, π₄ contains 3 and are both considered antibonding orbitals.

Localized molecular orbitals

The spherical 3D shape of ''s'' orbitals have no directionality in space and ''p_x'', ''p_y'', and ''p_z'' orbitals are all 90^o with respect to each other. Therefore, in order to obtain orbitals corresponding to

chemical bond A chemical bond is the association of atoms or ions to form molecules, crystals, and other structures. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds or through the sharing of electrons a ...

s to describe chemical reactions, Edmiston and Ruedenberg pioneered the development of localization procedures. For example, in CH₄, the four electrons from the 1''s'' orbitals of the hydrogen atoms and the

valence electron In chemistry and physics, valence electrons are electrons in the outermost shell of an atom, and that can participate in the formation of a chemical bond if the outermost shell is not closed. In a single covalent bond, a shared pair forms with b ...

s from the carbon atom (2 in ''s'' and 2 in ''p'') occupy the bonding molecular orbitals, σ and π. The delocalized MOs of the carbon atom in the molecule of methane can then be localized to give four ''sp''³ hybrid orbitals.

Applications

Molecular orbitals and, more specifically, the bonding orbital is a theory that is taught in all different areas of chemistry, from organic to physical and even analytical, because it is widely applicable. Organic chemists use molecular orbital theory in their thought rationale for reactions; analytical chemists use it in different spectroscopy methods; physical chemists use it in calculations; it is even seen in materials chemistry through band theory—an extension of molecular orbital theory.

References

{{Chemical bonding theory Chemical bonding