Bonding molecular orbital

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In theoretical chemistry, the bonding orbital is used in molecular orbital (MO) theory to describe the attractive interactions between the atomic orbitals of two or more atoms in a molecule. In MO theory, electrons are portrayed to move in waves. [1] When more than one of these waves come close together, the in-phase combination of these waves produces an interaction that leads to a species that is greatly stabilized. The result of the waves’ constructive interference causes the density of the electrons to be found within the binding region, creating a stable bond between the two species. [2]


Diatomic molecules

The MO diagram for dihydrogen H2wikibondingmo.png
The MO diagram for dihydrogen

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, 1s, either: merge in phase to get bonding orbitals, where the electron density 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. [3] 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 1s shell of hydrogen come together to fill in the stabilizing bonding orbital. So, hydrogen prefers to exist as a diatomic, and not monatomic, molecule. [4]

The MO diagram for helium He2wikibondingmo.jpg
The MO diagram for helium

When looking at helium, the atom holds two electrons in each valence 1s 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 is 0. This is why helium would prefer to be monatomic over diatomic. [5]

Polyatomic molecules

The MO diagram for a pi bond PibondingMObondingmo.jpg
The MO diagram for a pi bond

Bonding MOs of pi bonds

Pi bonds are created by the “side-on” interactions of the orbitals. [3] 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 electron density 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*. [3]

The MO diagram for butadiene MObutadienebondingmo.jpg
The MO diagram for butadiene

An example of a MO of a simple conjugated π system is butadiene. To create the MO for butadiene, 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): [3] 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. [3]

Localized molecular orbitals

The MO diagram for methane MethaneMObondingmo.jpg
The MO diagram for methane

The spherical 3D shape of s orbitals have no directionality in space and px, py, and pz orbitals are all 90o with respect to each other. Therefore, in order to obtain orbitals corresponding to chemical bonds to describe chemical reactions, Edmiston and Ruedenberg pioneered the development of localization procedures. [6] [7] For example, in CH4, the four electrons from the 1s orbitals of the hydrogen atoms and the valence electrons from the carbon atom (2 in s and 2 in p) occupy the bonding molecular orbitals, σ and π. [6] The delocalized MOs of the carbon atom in the molecule of methane can then be localized to give four sp3 hybrid orbitals.


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; [8] [9] analytical chemists use it in different spectroscopy methods; [10] [11] physical chemists use it in calculations; [8] [12] it is even seen in materials chemistry through band theory—an extension of molecular orbital theory. [13]

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<span class="mw-page-title-main">Chemical bond</span> Lasting attraction between atoms that enables the formation of chemical compounds

A chemical bond is a lasting attraction between atoms, ions or molecules that enables the formation of chemical compounds. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds or through the sharing of electrons as in covalent bonds. The strength of chemical bonds varies considerably; there are "strong bonds" or "primary bonds" such as covalent, ionic and metallic bonds, and "weak bonds" or "secondary bonds" such as dipole–dipole interactions, the London dispersion force and hydrogen bonding.

<span class="mw-page-title-main">Covalent bond</span> Chemical bond that involves the sharing of electron pairs between atoms

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, and 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.

<span class="mw-page-title-main">Molecular orbital</span> Wave-like behavior of an electron in a molecule

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 an electron in any specific region. The terms atomic orbital and molecular orbital were introduced by Robert S. Mulliken in 1932 to mean one-electron orbital wave functions. At an elementary level, they are used to describe the region of space in which a function has a significant amplitude.

<span class="mw-page-title-main">Conjugated system</span> System of connected p orbitals with delocalized electrons increasing molecular stability.

In 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.

<span class="mw-page-title-main">Lone pair</span> Pair of valence electrons which are not shared with another atom in a covalent bond

In chemistry, a lone pair refers to a pair of valence electrons that are not shared with another atom in a covalent bond and is sometimes called an unshared pair or non-bonding pair. Lone pairs are found in the outermost electron shell of atoms. They can be identified by using a Lewis structure. Electron pairs are therefore considered lone pairs if two electrons are paired but are not used in chemical bonding. Thus, the number of electrons in lone pairs plus the number of electrons in bonds equals the number of valence electrons around an atom.

<span class="mw-page-title-main">Pi bond</span> Type of chemical bond

In chemistry, pi 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 orbitals has an electron density of zero at a shared nodal plane that passes through the two bonded nuclei. This plane also is a nodal plane for the molecular orbital of the pi bond. Pi bonds can form in double and triple bonds but do not form in single bonds in most cases.

In chemistry, molecular orbital theory is a method for describing the electronic structure of molecules using quantum mechanics. It was proposed early in the 20th century.

In chemistry, valence bond (VB) theory is one of the two basic theories, along with molecular orbital (MO) theory, that were developed to use the methods of quantum mechanics to explain chemical bonding. It focuses on how the atomic orbitals of the dissociated atoms combine to give individual chemical bonds when a molecule is formed. In contrast, molecular orbital theory has orbitals that cover the whole molecule.

<span class="mw-page-title-main">Sigma bond</span> Covalent chemical bond

In chemistry, sigma bonds are the strongest type of covalent chemical bond. They are formed by head-on overlapping between atomic orbitals. Sigma bonding is most simply defined for diatomic molecules using the language and tools of symmetry groups. In this formal approach, a σ-bond is symmetrical with respect to rotation about the bond axis. By this definition, common forms of sigma bonds are s+s, pz+pz, s+pz and dz2+dz2 . Quantum theory also indicates that molecular orbitals (MO) of identical symmetry actually mix or hybridize. As a practical consequence of this mixing of diatomic molecules, the wavefunctions s+s and pz+pz molecular orbitals become blended. The extent of this mixing depends on the relative energies of the MOs of like symmetry.

In chemistry, orbital hybridisation is the concept of mixing atomic orbitals to form new hybrid orbitals suitable for the pairing of electrons to form chemical bonds in valence bond theory. For example, in a carbon atom which forms four single bonds the valence-shell s orbital combines with three valence-shell p orbitals to form four equivalent sp3 mixtures in a tetrahedral arrangement around the carbon to bond to four different atoms. Hybrid orbitals are useful in the explanation of molecular geometry and atomic bonding properties and are symmetrically disposed in space. Usually hybrid orbitals are formed by mixing atomic orbitals of comparable energies.

In chemistry, bond order, as introduced by Linus Pauling, is defined as the difference between the number of bonds and anti-bonds.

<span class="mw-page-title-main">Hyperconjugation</span> Concept in organic chemistry

In organic chemistry, hyperconjugation refers to the delocalization of electrons with the participation of bonds of primarily σ-character. Usually, hyperconjugation involves the interaction of the electrons in a sigma (σ) orbital with an adjacent unpopulated non-bonding p or antibonding σ* or π* orbitals to give a pair of extended molecular orbitals. However, sometimes, low-lying antibonding σ* orbitals may also interact with filled orbitals of lone pair character (n) in what is termed negative hyperconjugation. Increased electron delocalization associated with hyperconjugation increases the stability of the system. In particular, the new orbital with bonding character is stabilized, resulting in an overall stabilization of the molecule. Only electrons in bonds that are in the β position can have this sort of direct stabilizing effect — donating from a sigma bond on an atom to an orbital in another atom directly attached to it. However, extended versions of hyperconjugation can be important as well. The Baker–Nathan effect, sometimes used synonymously for hyperconjugation, is a specific application of it to certain chemical reactions or types of structures.

The 3-center 4-electron (3c–4e) bond is a model used to explain bonding in certain hypervalent molecules such as tetratomic and hexatomic interhalogen compounds, sulfur tetrafluoride, the xenon fluorides, and the bifluoride ion. It is also known as the Pimentel–Rundle three-center model after the work published by George C. Pimentel in 1951, which built on concepts developed earlier by Robert E. Rundle for electron-deficient bonding. An extended version of this model is used to describe the whole class of hypervalent molecules such as phosphorus pentafluoride and sulfur hexafluoride as well as multi-center π-bonding such as ozone and sulfur trioxide.

<span class="mw-page-title-main">Antibonding molecular orbital</span> Type of molecular orbital which weakens the chemical bond between two atoms

In chemical bonding theory, an antibonding orbital is a type of molecular orbital that weakens the chemical bond between two atoms and helps to raise the energy of the molecule relative to the separated atoms. Such an orbital has one or more nodes in the bonding region between the nuclei. The density of the electrons in the orbital is concentrated outside the bonding region and acts to pull one nucleus away from the other and tends to cause mutual repulsion between the two atoms. This is in contrast to a bonding molecular orbital, which has a lower energy than that of the separate atoms, and is responsible for chemical bonds.

<span class="mw-page-title-main">Quadruple bond</span> Chemical bond involving eight electrons; has one sigma, two pi, and one delta bond

A quadruple bond is a type of chemical bond between two atoms involving eight electrons. This bond is an extension of the more familiar types double bonds and triple bonds. Stable quadruple bonds are most common among the transition metals in the middle of the d-block, such as rhenium, tungsten, technetium, molybdenum and chromium. Typically the ligands that support quadruple bonds are π-donors, not π-acceptors.

A molecular orbital diagram, or MO diagram, is a qualitative descriptive tool explaining chemical bonding in molecules in terms of molecular orbital theory in general and the linear combination of atomic orbitals (LCAO) method in particular. A fundamental principle of these theories is that as atoms bond to form molecules, a certain number of atomic orbitals combine to form the same number of molecular orbitals, although the electrons involved may be redistributed among the orbitals. This tool is very well suited for simple diatomic molecules such as dihydrogen, dioxygen, and carbon monoxide but becomes more complex when discussing even comparatively simple polyatomic molecules, such as methane. MO diagrams can explain why some molecules exist and others do not. They can also predict bond strength, as well as the electronic transitions that can take place.

Localized molecular orbitals are molecular orbitals which are concentrated in a limited spatial region of a molecule, such as a specific bond or lone pair on a specific atom. They can be used to relate molecular orbital calculations to simple bonding theories, and also to speed up post-Hartree–Fock electronic structure calculations by taking advantage of the local nature of electron correlation. Localized orbitals in systems with periodic boundary conditions are known as Wannier functions.

Physical organic chemistry, a term coined by Louis Hammett in 1940, refers to a discipline of organic chemistry that focuses on the relationship between chemical structures and reactivity, in particular, applying experimental tools of physical chemistry to the study of organic molecules. Specific focal points of study include the rates of organic reactions, the relative chemical stabilities of the starting materials, reactive intermediates, transition states, and products of chemical reactions, and non-covalent aspects of solvation and molecular interactions that influence chemical reactivity. Such studies provide theoretical and practical frameworks to understand how changes in structure in solution or solid-state contexts impact reaction mechanism and rate for each organic reaction of interest.

A non-bonding orbital, also known as non-bonding molecular orbital (NBMO), is a molecular orbital whose occupation by electrons neither increases nor decreases the bond order between the involved atoms. Non-bonding orbitals are often designated by the letter n in molecular orbital diagrams and electron transition notations. Non-bonding orbitals are the equivalent in molecular orbital theory of the lone pairs in Lewis structures. The energy level of a non-bonding orbital is typically in between the lower energy of a valence shell bonding orbital and the higher energy of a corresponding antibonding orbital. As such, a non-bonding orbital with electrons would commonly be a HOMO.

<span class="mw-page-title-main">Chemical bonding of water</span>

Water is a simple triatomic bent molecule with C2v molecular symmetry and bond angle of 104.5° between the central oxygen atom and the hydrogen atoms. Despite being one of the simplest triatomic molecules, its chemical bonding scheme is nonetheless complex as many of its bonding properties such as bond angle, ionization energy, and electronic state energy cannot be explained by one unified bonding model. Instead, several traditional and advanced bonding models such as simple Lewis and VSEPR structure, valence bond theory, molecular orbital theory, isovalent hybridization, and Bent's rule are discussed below to provide a comprehensive bonding model for H
, explaining and rationalizing the various electronic and physical properties and features manifested by its peculiar bonding arrangements.


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