Four sp³ orbitals.

Three sp² orbitals.

In chemistry, hybridisation or hybridization (see also spelling differences) is the concept of mixing atomic orbitals to form new hybrid orbitals suitable for the qualitative description of atomic bonding properties. Hybridised orbitals are very useful in the explanation of the shape of molecular orbitals for molecules. It is an integral part of valence bond theory. Although sometimes taught together with the valence shell electron-pair repulsion (VSEPR) theory, valence bond and hybridization are in fact not related to the VSEPR model.^[1] Image File history File links Sp3-Orbital. ... Image File history File links Sp3-Orbital. ... Image File history File links Sp2-Orbital. ... Image File history File links Sp2-Orbital. ... For other uses, see Chemistry (disambiguation). ... Spelling differences redirects here. ... In chemistry, an atomic orbital is the region in which an electron may be found around a single atom. ... In chemistry, a molecular orbital is a region in which an electron may be found in a molecule. ... 3D (left and center) and 2D (right) representations of the terpenoid molecule atisane. ... In chemistry, valence bond theory explains the nature of a chemical bond in a molecule in terms of atomic valencies. ... Geometry of the water molecule Molecules have fixed equilibrium geometries--bond lengths and angles--that are dictated by the laws of quantum mechanics. ...

Historical development

The hybridisation theory was promoted by chemist Linus Pauling^[2] in order to explain the structure of molecules such as methane (CH₄). Historically, this concept was developed for such simple chemical systems but the approach was later applied more widely, and today it is considered an effective heuristic for rationalizing the structures of organic compounds. A chemist pours from a round-bottom flask. ... Linus Carl Pauling (February 28, 1901 – August 19, 1994) was an American scientist, peace activist, author and educator of German ancestry. ... 3D (left and center) and 2D (right) representations of the terpenoid molecule atisane. ... Methane is a chemical compound with the molecular formula . ... An organic compound is any of a large class of chemical compounds whose molecules contain carbon, with exception of carbides, carbonates and carbon oxides. ...

Hybridisation theory is not as practical for quantitative calculations as Molecular Orbital Theory. Problems with hybridisation are especially notable when the d orbitals are involved in bonding, as in coordination chemistry and organometallic chemistry. Although hybridisation schemes in transition metal chemistry can be used, they are not generally as accurate. In chemistry, molecular orbital theory (MO theory) is a method for determining molecular structure in which electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule. ... complex In chemistry, a complex is a structure composed of a central metal atom or ion, generally a cation, surrounded by a number of negatively charged ions or neutral molecules possessing lone pairs. ... n-butyllithium, an organometallic compound. ...

It is important to note that orbitals are a model representation of the behavior of electrons within molecules. In the case of simple hybridisation, this approximation is based on the atomic orbitals of hydrogen. Hybridised orbitals are assumed to be mixtures of these atomic orbitals, superimposed on each other in various proportions. Hydrogen orbitals are used as a basis for simple schemes of hybridisation because it is one of the few examples of orbitals for which an exact analytic solution to its Schrödinger equation is known. These orbitals are then assumed to be slightly, but not significantly, distorted in heavier atoms, like carbon, nitrogen, and oxygen. Under these assumptions is the theory of hybridisation most applicable. It must be noted that one does not need hybridisation to describe molecules, but for molecules made up from carbon, nitrogen and oxygen (and to a lesser extent, sulfur and phosphorus) the hybridisation theory/model makes the description much easier. This box:      For a non-technical introduction to the topic, please see Introduction to quantum mechanics. ... For other uses, see Carbon (disambiguation). ... General Name, symbol, number nitrogen, N, 7 Chemical series nonmetals Group, period, block 15, 2, p Appearance colorless gas Standard atomic weight 14. ... This article is about the chemical element and its most stable form, or dioxygen. ... This article is about the chemical element. ... General Name, symbol, number phosphorus, P, 15 Chemical series nonmetals Group, period, block 15, 3, p Appearance waxy white/ red/ black/ colorless Standard atomic weight 30. ...

The hybridisation theory finds its use mainly in organic chemistry, and mostly concerns C, N and O (and to a lesser extent P and S). Its explanation starts with the way bonding is organized in methane. Methane is a chemical compound with the molecular formula . ...

sp³ hybrids

Hybridisation describes the bonding atoms from an atom's point of view. That is, for a tetrahedrally coordinated carbon (e.g. methane, CH₄), the carbon should have 4 orbitals with the correct symmetry to bond to the 4 hydrogen atoms. The problem with the existence of methane is now this: Carbon's ground-state configuration is 1s² 2s² 2p_x¹ 2p_y¹ or perhaps more easily read: Methane is a chemical compound with the molecular formula . ... In physics, the ground state of a quantum mechanical system is its lowest-energy state. ...

(Note: The 1s orbital is lower in energy than the 2s orbital, and the 2s orbital is slightly lower in energy than the 2p orbitals)

The valence bond theory would predict, based on the existence of two half-filled p-type orbitals (the designations p_x p_y or p_z are meaningless at this point, as they do not fill in any particular order), that C forms two covalent bonds, i.e. CH₂. However, methylene is a very reactive molecule (see also: carbene) and cannot exist outside of a molecular system. Therefore, this theory alone cannot explain the existence of CH₄. In chemistry, valence bond theory explains the nature of a chemical bond in a molecule in terms of atomic valencies. ... Covalent redirects here. ... In chemistry, methylene is a divalent functional group CH2 derived formally from methane. ... In chemistry a carbene is a short-lived and highly reactive organic molecule with a divalent carbon atom with only six valence electrons and the general formula: R1R2C: . The carbon atom is sp2 hybridised with an empty p-orbital extending above and below a plane containing R1 and R2 and...

Furthermore, ground state orbitals cannot be used for bonding in CH₄. While exciting a 2s electron into a 2p orbital would theoretically allow for four bonds according to the valence bond theory, (which has been proved experimentally correct for systems like O₂) this would imply that the various bonds of CH₄ would have differing energies due to differing levels of orbital overlap. Once again, this has been experimentally disproved: any hydrogen can be removed from a carbon with equal ease.

To summarise, to explain the existence of CH₄ (and many other molecules) a method by which as many as 12 bonds (for transition metals) of equal strength (and therefore equal length) can be created was required. In chemistry, the term transition metal (sometimes also called a transition element) has two possible meanings: It commonly refers to any element in the d-block of the periodic table, including zinc, cadmium and mercury. ...

The first step in hybridisation is the excitation of one (or more) electrons (we consider the carbon atom in methane, for simplicity of the discussion):

The proton that forms the nucleus of a hydrogen atom attracts one of the valence electrons on carbon. This causes an excitation, moving a 2s electron into a 2p orbital. This, however, increases the influence of the carbon nucleus on the valence electrons by increasing the effective core potential (the amount of charge the nucleus exerts on a given electron = Charge of Core − Charge of all electrons closer to the nucleus).

The combination of these forces creates new mathematical functions known as hybridised orbitals. In the case of carbon attempting to bond with four hydrogens, four orbitals are required. Therefore, the 2s orbital (core orbitals are almost never involved in bonding) "mixes" with the three 2p orbitals to form four sp³ hybrids (read as s-p-three). See graphical summary below.

becomes

In CH₄, four sp³ hybridised orbitals are overlapped by hydrogen's 1s orbital, yielding four σ (sigma) bonds. The four bonds are of the same length and strength. This theory fits our requirements. This article is about the chemistry of hydrogen. ... Electron atomic and molecular orbitals, showing among others the sigma bond of two s-orbitals and a sigma bond of two p-orbitals In chemistry, sigma bonds (σ bonds) are a type of covalent chemical bond. ...

translates into Image File history File links This is a lossless scalable vector image. ... My feeble attempt at drawing methane in terms of structure File links The following pages link to this file: Orbital hybridisation Categories: GFDL images ...

An alternative view is: View the carbon as the C⁴⁻ anion. In this case all the orbitals on the carbon are filled:

If we now recombine these orbitals with the empty s-orbitals of 4 hydrogens (4 protons, H⁺) and allow maximum separation between the 4 hydrogens (i.e. tetrahedral surrounding of the carbon), we see that at any orientation of the p-orbitals, a single hydrogen has an overlap of 25% with the s-orbital of the C, and a total of 75% of overlap with the 3 p-orbitals (see that the relative percentages are the same as the character of the respective orbital in an sp³-hybridisation model, 25% s- and 75% p-character).

According to the orbital hybridisation theory the valence electrons in methane should be equal in energy but its photoelectron spectrum ^[3] shows two bands, one at 12.7 eV (one electron pair) and one at 23 eV (three electron pairs). This apparent inconsistency can be explained when one considers additional orbital mixing taking place when the sp³ orbitals mix with the 4 hydrogen orbitals. Photoemission Spectroscopy refers to two separate techniques/ X-Ray Photoemission Spectroscopy (XPS, formerly known as ESCA - Electron Spectroscopy for Chemical Analysis) was developed at Uppsala University, Sweden in the 1960s by a group headed by Kai Siegbahn, who in 1981 won the Nobel Prize for Physics for his work in... An electronvolt (symbol: eV) is the amount of energy gained by a single unbound electron when it falls through an electrostatic potential difference of one volt. ...

sp² hybrids

Other carbon based compounds and other molecules may be explained in a similar way as methane. Take, for example, ethylene (C₂H₄). Ethylene has a double bond between the carbons. The Kekule structure looks like this: Ethylene (or IUPAC name ethene) is the chemical compound with the formula C2H4. ...

from rozeta This image is ineligible for copyright and therefore in the public domain, because it consists entirely of information that is common property and contains no original authorship. ...

Carbon will sp² hybridise, because hybrid orbitals will form only σ bonds and one π (pi) bond is required for the double bond between the carbons. The hydrogen-carbon bonds are all of equal strength and length, which agrees with experimental data. Electron atomic and molecular orbitals, showing a Pi-bond at the bottom right of the picture. ... Covalent redirects here. ...

In sp² hybridisation the 2s orbital is mixed with only two of the three available 2p orbitals:

forming a total of 3 sp² orbitals with one p-orbital remaining. In ethylene the two carbon atoms form a σ bond by overlapping two sp² orbitals and each carbon atom forms two covalent bonds with hydrogen by s–sp² overlap all with 120° angles. The π bond between the carbon atoms perpendicular to the molecular plane is formed by 2p–2p overlap (however, the π bond may or may not occur).

The amount of p-character is not restricted to integer values, i.e. hybridisations like sp^2.5 are also readily described. In this case the geometries are somewhat distorted from the ideally hybridised picture. For example, as stated in Bent's rule, a bond tends to have higher p-character when directed toward a more electronegative substituent. Bents rule, which concerns orbital hybridisation of chemical bonds, was stated in 1961 by the American chemist Henry Bent [1]. Originally, it was expressed as follows: Atomic s character concentrates in orbitals directed toward electropositive subsituents In other words, more understandable in terms of p-character of hybridized bonds... Electronegativity is a measure of the ability of an atom or molecule to attract electrons in the context of a chemical bond. ...

sp hybrids

The chemical bonding in compounds such as alkynes with triple bonds is explained by sp hybridization. The structural formula of 2-butyne, a simple alkyne-containing molecule Alkynes are hydrocarbons that have at least one triple bond between two carbon atoms, with the formula CnH2n-2. ...

In this model the 2s orbital mixes with only one of the three p-orbitals resulting in two sp orbitals and two remaining unchanged p orbitals. The chemical bonding in acetylene (ethyne) (C₂H₂) consists of sp–sp overlap between the two carbon atoms forming a σ bond and two additional π bonds formed by p–p overlap. Each carbon also bonds to hydrogen in a sigma s–sp overlap at 180° angles. Acetylene (systematic name: ethyne) is a hydrocarbon belonging to the group of alkynes. ... Electron atomic and molecular orbitals, showing a Pi-bond at the bottom right of the picture. ...

Hybridisation and molecule shape

Hybridisation, along with the VSEPR theory, helps to explain molecule shape: Valence shell electron pair repulsion theory (VSEPR) (1957) is a model in chemistry that aims to generally represent the shapes of individual molecules [1] . To achieve this, it is necessary to construct a valid Lewis structure that shows all of the bonds within the molecule and the locations of lone...

• AX₁ (e.g., LiH): no hybridisation; trivially linear shape
• AX₂ (e.g., BeCl₂): sp hybridisation; linear or diagonal shape; bond angles are cos⁻¹(−1) = 180°
  • AX₂E (e.g., GeF₂): bent/V shape, < 120°
• AX₃ (e.g., BCl₃): sp² hybridisation; trigonal planar shape; bond angles are cos⁻¹(−1/2) = 120°
  • AX₃E (e.g.,NH₃): trigonal pyramidal, 107°
• AX₄ (e.g., CCl₄): sp³ hybridisation; tetrahedral shape; bond angles are cos⁻¹(−1/3) ≈ 109.5°
• AX₅ (e.g., PCl₅): sp³d hybridisation; trigonal bipyramidal shape
• AX₆ (e.g., SF₆): sp³d² hybridisation; octahedral (or square bipyramidal) shape

This holds if there are no lone electron pairs on the central atom. If there are, they should be counted in the X_i number, but bond angles become smaller due to increased repulsion. For example, in water (H₂O), the oxygen atom has two bonds with H and two lone electron pairs (as can be seen with the valence bond theory as well from the electronic configuration of oxygen), which means there are four such 'elements' on O. The model molecule is, then, AX₄: sp³ hybridisation is utilized, and the electron arrangement of H₂O is tetrahedral. This agrees with the experimentally-determined shape for water, a non-linear, bent structure, with a bond angle of 104.5 degrees (the two lone-pairs are not visible). Line redirects here. ... ǃǁɚɵ A generic trigonal planar molecule showing ideal bond angle. ... In a tetrahedral molecular geometry a central atom is located at the center with four substituents located at the corners of a tetrahedron. ... In chemistry a trigonal bipyramid is a molecular geometry with one atom at the center and 5 more at the corners of a Triangular dipyramid. ... A generic octahedral molecule. ... An octahedron (plural: octahedra) is a polyhedron with eight faces. ... Impact from a water drop causes an upward rebound jet surrounded by circular capillary waves. ... This article is about the chemical element and its most stable form, or dioxygen. ...

In general, for an atom with s and p orbitals forming hybrids h_i and h_j with included angle θ, the following holds: 1 + λ_iλ_j cos(θ) = 0. The p-to-s ratio for hybrid i is λ_i², and for hybrid j it is λ_j². In the special case of equivalent hybrids on the same atom, again with included angle θ, the equation reduces to just 1 + λ² cos(θ) = 0. For example, BH₃ has a trigonal planar geometry, three 120^o bond angles, three equivalent hybrids about the boron atom, and thus 1 + λ² cos(θ) = 0 becomes 1 + λ² cos(120^o) = 0, giving λ² = 2 for the p-to-s ratio. In other words, sp² hybrids, just as expected from the list above.

Controversy regarding d-orbital participation

Hybridisation theory has failed in a few aspects, notably in explaining the energy considerations for the involvement of d-orbitals in chemical bonding (See above for sp³d and sp³d² hybridisation). This can be well-explained by means of an example. Consider, for instance, how the theory in question accounts for the bonding in phosphorus pentachloride (PCl₅). d-orbitals are large, comparatively distant from the nucleus and high in energy. Radial distances of orbitals from the nucleus seem to reveal that d-orbitals are far too high in energy to 'mix' with s- and p-orbitals. 3s - 0.47 , 3p - 0.55, 3d - 2.4 (in angstroms). Thus, at first sight, it seems improbable for sp³d hybridisation to occur. Phosphorus pentachloride is the chemical compound with the formula PCl5. ... An angstrom, angström, or Ã¥ngström (symbol Ã…) is a unit of length. ...

However, a deeper look into the factors that affect orbital size (and energy) reveals more. Formal charge on the central atom is one such factor, and it's obvious that the P atom in PCl₅ has quite a large partial positive charge on itself. Thus the 3d orbital contracts in size to enough of an extent so that hybridisation may occur with s and p orbitals. Further, note the cases in which d-orbital participation was proposed in hybridisation: SF₆(sulfur hexafluoride), IF₇, XeF₆; in all these molecules, the central atom is surrounded by the highly electronegative fluorine atom, thus making hybridisation probable among s, p and d orbitals. A further study reveals that orbital size also depends on the number of electrons occupying it. And even further, coupling of d orbital electrons also results in contraction, albeit to a smaller extent. In chemistry, a formal charge (FC) on an atom in a molecule is defined as: FC = number of valence electrons of the atom - number of Lone pair electrons on this atom - half the total number of electrons participating in covalent bonds with this atom. ... Sulfur hexafluoride is an inorganic compound with the formula . ... It has been suggested that this article or section be merged with electronegativity. ... Distinguished from fluorene and fluorone. ...

The molecular orbital theory, however, offers a clearer insight into the bonding in these molecules. In chemistry, molecular orbital theory (MO theory) is a method for determining molecular structure in which electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule. ...

Hybridisation theory vs. MO theory

Hybridisation theory is an integral part of organic chemistry and in general discussed together with molecular orbital theory in advanced organic chemistry textbooks although for different reasons. One textbook notes that for drawing reaction mechanisms sometimes a classical bonding picture is needed with 2 atoms sharing two electrons ^[4]. It also comments that predicting bond angles in methane with MO theory is not straightforward. Another textbook treats hybridisation theory when explaining bonding in alkenes ^[5] and a third ^[6] uses MO theory to explain bonding in hydrogen but hybridisation theory for methane. Organic chemistry is a specific discipline within chemistry which involves the scientific study of the structure, properties, composition, reactions, and preparation (by synthesis or by other means) of chemical compounds consisting primarily of carbon and hydrogen, which may contain any number of other elements, including nitrogen, oxygen, the halogens as... In chemistry, molecular orbital theory (MO theory) is a method for determining molecular structure in which electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule. ...

Although the language and pictures arising from Hybridisation Theory, more widely known as Valence Bond Theory, remain widespread in synthetic organic chemistry, this qualitative analysis of bonding has been largely superseded by molecular orbital theory in other branches of chemistry. For example, inorganic chemistry texts have all but abandoned instruction of hybridisation, except as a historical footnote.^[7][8] One specific problem with hybridisation is that it incorrectly predicts the photoelectron spectra of many molecules, including such fundamental species such as methane and water. From a pedagogical perspective, hybridisation approach tends to over-emphasize localisation of bonding electrons and does not effectively embrace molecular symmetry as does MO Theory. In chemistry, valence bond theory explains the nature of a chemical bond in a molecule in terms of atomic valencies. ... Organic synthesis is the construction of organic molecules via chemical processes. ... Molecular symmetry in chemistry describes symmetry in molecules and the classification of molecules in groups based on symmetry. ...

References

The Journal of the American Chemical Society (usually abbreviated as , or JACS), is a peer-reviewed scientific journal, published since 1879 by the American Chemical Society. ...

See also

• Linear combination of atomic orbitals molecular orbital method
• MO diagrams

This article may be too technical for most readers to understand. ... A molecular orbital diagram or MO diagram for short is a simple qualitative descriptive tool explaining chemical bonding in molecules in terms of molecular orbital theory in general and the Linear combination of atomic orbitals molecular orbital method (LCAO method) in particular [1] [2] [3]. This tool is very well...

External links

• Covalent Bonds and Molecular Structure
• Hybridisation flash movie
• Hybridised orbital 3D preview progam in OpenGL
• Understanding Concepts: Molecular Orbitals