HOMO/LUMO

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Diagram of the HOMO and LUMO of a molecule. Each circle represents an electron in an orbital; when light of a high enough frequency is absorbed by an electron in the HOMO, it jumps to the LUMO. Molecule HOMO-LUMO diagram.svg
Diagram of the HOMO and LUMO of a molecule. Each circle represents an electron in an orbital; when light of a high enough frequency is absorbed by an electron in the HOMO, it jumps to the LUMO.
3D model of the highest occupied molecular orbital in CO2 CO2 HOMO.gif
3D model of the highest occupied molecular orbital in CO2
3D model of the lowest unoccupied molecular orbital in CO2 CO2 LUMO.gif
3D model of the lowest unoccupied molecular orbital in CO2

In chemistry, HOMO and LUMO are types of molecular orbitals. The acronyms stand for highest occupied molecular orbital and lowest unoccupied molecular orbital, respectively.

Molecular orbital energy level in a molecule

In chemistry, a molecular orbital (MO) is a mathematical function describing the 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 term orbital was introduced by Robert S. Mulliken in 1932 as an abbreviation for one-electron orbital wave function. At an elementary level, it is used to describe the region of space in which the function has a significant amplitude. Molecular orbitals are usually constructed by combining atomic orbitals or hybrid orbitals from each atom of the molecule, or other molecular orbitals from groups of atoms. They can be quantitatively calculated using the Hartree–Fock or self-consistent field (SCF) methods.

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HOMO–LUMO gap

The energy difference between the HOMO and LUMO is termed the HOMO–LUMO gap. HOMO and LUMO are sometimes called frontier orbitals in frontier molecular orbital theory. The difference in energy between these two frontier orbitals can be used to predict the strength and stability of transition metal complexes, as well as the colors they produce in solution. [1]

In chemistry, frontier molecular orbital theory is an application of MO theory describing HOMO/LUMO interactions.

In chemistry, the term transition metal has three possible meanings:

Coordination complex molecule or ion containing ligands covalently bonded to a central atom

In chemistry, a coordination complex consists of a central atom or ion, which is usually metallic and is called the coordination centre, and a surrounding array of bound molecules or ions, that are in turn known as ligands or complexing agents. Many metal-containing compounds, especially those of transition metals, are coordination complexes. A coordination complex whose centre is a metal atom is called a metal complex.

Semiconductors

The HOMO level is to organic semiconductors roughly what the valence band maximum is to inorganic semiconductors and quantum dots. The same analogy can be made between the LUMO level and the conduction band minimum. [2]

Quantum dot nano-scale electronic device subject to quantum effects

Quantum dots (QDs) are tiny semiconductor particles a few nanometres in size, having optical and electronic properties that differ from larger LED particles. They are a central theme in nanotechnology. When the quantum dots are illuminated by UV light, some of the electrons receive enough energy to break free from the atoms. This capability allows them to move around the nanoparticle, creating a conductance band in which electrons are free to move through a material and conduct electricity. When these electrons drop back into the outer orbit around the atom, as illustrated in the following figure, they emit light. The color of that light depends on the energy difference between the conductance band and the valence band.

Organometallic chemistry

In organometallic chemistry, the size of the LUMO lobe can help predict where addition to pi ligands will occur.

SOMO

A SOMO is a singly occupied molecular orbital such as half-filled HOMO of a radical. [3] This abbreviation may also be extended to semi occupied molecular orbital.

Radical (chemistry) molecular entity such as ·CH3, ·SnH3, Cl· possessing an unpaired electron (in these formulae the dot,·, symbolizing the unpaired electron, should be placed so as to indicate the atom of highest spin density, if this is possible)

In chemistry, a radical is an atom, molecule, or ion that has an unpaired valence electron. With some exceptions, these unpaired electrons make radicals highly chemically reactive. Many radicals spontaneously dimerize. Most organic radicals have short lifetimes.

See also

In organic chemistry, the Diels–Alder reaction is a chemical reaction between a conjugated diene and a substituted alkene, commonly termed the dienophile, to form a substituted cyclohexene derivative. It is the prototypical example of a pericyclic reaction with a concerted mechanism. More specifically, it is classified as a thermally-allowed [4+2] cycloaddition with Woodward–Hoffmann symbol [π4s + π2s]. It was first described by Otto Diels and Kurt Alder in 1928. For the discovery of this reaction, they were awarded the Nobel Prize in Chemistry in 1950. Through the simultaneous construction of two new carbon–carbon bonds, the Diels–Alder reaction provides a reliable way to form six-membered rings with good control over the regio- and stereochemical outcomes. Consequently, it has served as a powerful and widely applied tool for the introduction of chemical complexity in the synthesis of natural products and new materials. The underlying concept has also been applied to π-systems involving heteroatoms, such as carbonyls and imines, which furnish the corresponding heterocycles; this variant is known as the hetero-Diels–Alder reaction. The reaction has also been generalized to other ring sizes, although none of these generalizations have matched the formation of six-membered rings in terms of scope or versatility. Because of the negative values of ΔH° and ΔS° for a typical Diels–Alder reaction, the microscopic reverse of a Diels–Alder reactions becomes favorable at high temperatures, although this is of synthetic importance for only a limited range of Diels-Alder adducts, generally with some special structural features; this reverse reaction is known as the retro-Diels–Alder reaction.

Electron configuration property of an atom

In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule in atomic or molecular orbitals. For example, the electron configuration of the neon atom is 1s2 2s2 2p6, using the notation explained below.

In the theory of chemical reactivity, the Klopman-Salem equation describes the energetic change that occurs when two species approach each other in the course of a reaction and begin to interact, as their associated molecular orbitals begin to overlap with each other and atoms bearing partial charges begin to experience attractive or repulsive electrostatic forces. First described independently by Gilles Klopman and Lionel Salem in 1968, this relationship provides a mathematical basis for the key assumptions of frontier molecular orbital theory and hard soft acid base (HSAB) theory. Conceptually, it highlights the importance of considering both electrostatic interactions and orbital interactions when rationalizing the selectivity or reactivity of a chemical process.

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Ligand molecule or functional group that binds or can bind to the central atom in a coordination complex

In coordination chemistry, a ligand is an ion or molecule that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's electron pairs. The nature of metal–ligand bonding can range from covalent to ionic. Furthermore, the metal–ligand bond order can range from one to three. Ligands are viewed as Lewis bases, although rare cases are known to involve Lewis acidic "ligands".

Excimer

An excimer is a short-lived dimeric or heterodimeric molecule formed from two species, at least one of which has completely filled valence shell by electrons. In this case, formation of molecules is possible only if such atom is in an electronic excited state. Heteronuclear molecules and molecules that have more than two species are also called exciplex molecules. Excimers are often diatomic and are composed of two atoms or molecules that would not bond if both were in the ground state. The lifetime of an excimer is very short, on the order of nanoseconds. Binding of a larger number of excited atoms form Rydberg matter clusters, the lifetime of which can exceed many seconds.

The color of chemicals is a physical property of chemicals that in most cases comes from the excitation of electrons due to an absorption of energy performed by the chemical. What is seen by the eye is not the color absorbed, but the complementary color from the removal of the absorbed wavelengths. This spectral perspective was first noted in atomic spectroscopy.

In chemistry, Molecular orbital (MO) theory is a method for describing the electronic structure of molecules using quantum mechanics. Electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule. The spatial and energetic properties of electrons are described by quantum mechanics as molecular orbitals surround two or more atoms in a molecule and contain valence electrons between atoms. Molecular orbital theory, which was proposed in the early twentieth century, revolutionized the study of bonding by approximating the states of bonded electrons—the molecular orbitals—as linear combinations of atomic orbitals (LCAO). These approximations are now made by applying the density functional theory (DFT) or Hartree–Fock (HF) models to the Schrödinger equation.

Kenichi Fukui Japanese chemist

Kenichi Fukui was a Japanese chemist, known as the first Asian scientist to receive a chemistry Nobel Prize.

Crystal Field Theory (CFT) is a model that describes the breaking of degeneracies of electron orbital states, usually d or f orbitals, due to a static electric field produced by a surrounding charge distribution. This theory has been used to describe various spectroscopies of transition metal coordination complexes, in particular optical spectra (colors). CFT successfully accounts for some magnetic properties, colors, hydration enthalpies, and spinel structures of transition metal complexes, but it does not attempt to describe bonding. CFT was developed by physicists Hans Bethe and John Hasbrouck van Vleck in the 1930s. CFT was subsequently combined with molecular orbital theory to form the more realistic and complex ligand field theory (LFT), which delivers insight into the process of chemical bonding in transition metal complexes.

A charge-transfer complex or electron-donor-acceptor complex is an association of two or more molecules, or of different parts of one large molecule, in which a fraction of electronic charge is transferred between the molecular entities. The resulting electrostatic attraction provides a stabilizing force for the molecular complex. The source molecule from which the charge is transferred is called the electron donor and the receiving species is called the electron acceptor.

Ligand field theory (LFT) describes the bonding, orbital arrangement, and other characteristics of coordination complexes. It represents an application of molecular orbital theory to transition metal complexes. A transition metal ion has nine valence atomic orbitals - consisting of five nd, three (n+1)p, and one (n+1)s orbitals. These orbitals are of appropriate energy to form bonding interaction with ligands. The LFT analysis is highly dependent on the geometry of the complex, but most explanations begin by describing octahedral complexes, where six ligands coordinate to the metal. Other complexes can be described by reference to crystal field theory.

Isolobal principle

The isolobal principle is a strategy used in organometallic chemistry to relate the structure of organic and inorganic molecular fragments in order to predict bonding properties of organometallic compounds. Roald Hoffmann described molecular fragments as isolobal "if the number, symmetry properties, approximate energy and shape of the frontier orbitals and the number of electrons in them are similar – not identical, but similar." One can predict the bonding and reactivity of a lesser-known species from that of a better-known species if the two molecular fragments have similar frontier orbitals, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Isolobal compounds are analogues to isoelectronic compounds that share the same number of valence electrons and structure. A graphic representation of isolobal structures, with the isolobal pairs connected through a double-headed arrow with half an orbital below, is found in Figure 1.

The 1,3-dipolar cycloaddition is a chemical reaction between a 1,3-dipole and a dipolarophile to form a five-membered ring. The earliest 1,3-dipolar cycloadditions were described in the late 19th century to the early 20th century, following the discovery of 1,3-dipoles. Mechanistic investigation and synthetic application were established in the 1960s, primarily through the work of Rolf Huisgen. Hence, the reaction is sometimes referred to as the Huisgen cycloaddition. 1,3-dipolar cycloaddition is an important route to the regio- and stereoselective synthesis of five-membered heterocycles and their ring-opened acyclic derivatives.

An electrocyclic reaction can either be classified as conrotatory or disrotatory based on the rotation at each end of the molecule. In conrotatory mode, both atomic orbitals of the end groups turn in the same direction. In disrotatory mode, the atomic orbitals of the end groups turn in opposite directions. The cis/trans geometry of the final product is directly decided by the difference between conrotation and disrotation.

Koopmans' theorem states that in closed-shell Hartree–Fock theory (HF), the first ionization energy of a molecular system is equal to the negative of the orbital energy of the highest occupied molecular orbital (HOMO). This theorem is named after Tjalling Koopmans, who published this result in 1934.

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.

Walsh diagram

Walsh diagrams, often called angular coordinate diagrams or correlation diagrams, are representations of calculated orbital binding energies of a molecule versus a distortion coordinate, used for making quick predictions about the geometries of small molecules. By plotting the change in molecular orbital levels of a molecule as a function of geometrical change, Walsh diagrams explain why molecules are more stable in certain spatial configurations.

The Inverse electron demand Diels–Alder reaction, or DAINV or IEDDA is an organic chemical reaction, in which two new chemical bonds and a six-membered ring are formed. It is related to the Diels–Alder reaction, but unlike the Diels–Alder reaction, the DAINV is a cycloaddition between an electron-rich dienophile and an electron-poor diene. During a DAINV reaction, three pi-bonds are broken, and two sigma bonds and one new pi-bond are formed. A prototypical DAINV reaction is shown on the right.

In computational chemistry, the Fukui function or frontier function is a function that describes the electron density in a frontier orbital, as a result of a small change in the total number of electrons. The condensed Fukui function or condensed reactivity indicator is the same idea, but applied to an atom within a molecule, rather than a point in three-dimensional space.

A metal-centered cycloaddition is a subtype of the more general class of cycloaddition reactions. In such reactions "two or more unsaturated molecules unite directly to form a ring", incorporating a metal bonded to one or more of the molecules. Cycloadditions involving metal centers are a staple of organic and organometallic chemistry, and are involved in many industrially-valuable synthetic processes.

References

  1. Griffith, J.S. and L.E. Orgel. "Ligand Field Theory". Q. Rev. Chem. Soc. 1957, 11, 381-383
  2. Bredas, J,-L. "Mind the gap!". Mater. Horiz. 2014,1, 17-19
  3. IUPAC , Compendium of Chemical Terminology , 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006) " SOMO ".