In
chemistryChemistry is the science concerned with the composition, behavior, structure, and properties of matter, as well as the changes it undergoes during chemical reactions...
,
hybridisation (or
hybridization) is the concept of mixing
atomic orbitalAn atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons, in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus. These functions...
s within an atom to form new
hybrid orbitals. It is an integral part of the
valence bond theoryIn chemistry, valence bond theory is one of two basic theories, along with molecular orbital theory, that developed to use the methods of quantum mechanics to explain chemical bonding. It focuses on how the atomic orbitals of the dissociated atoms combine on molecular formation to give individual...
.
Hybridisation of orbitals will change the shape of the atom. Hybridised orbitals are also useful in the explanation of the shape of
molecular orbitalIn chemistry, a molecular orbital is a mathematical function that describes 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 use of the term...
s of
moleculeA molecule is defined as an electrically neutral group of at least two atoms in a definite arrangement held together by very strong chemical bonds. Molecules are distinguished from polyatomic ions in this strict sense...
s.
Historical development
The hybridisation theory was promoted by
chemistA chemist is a scientist trained in the science of chemistry. Chemists study the composition of matter and its properties such as density, acidity, size and shape. Chemists carefully describe the properties they study in terms of quantities, with detail on the level of molecules and their component...
Linus PaulingLinus Carl Pauling was an American chemist, peace activist, author, and educator. He was one of the most influential chemists in history and ranks among the most important scientists in any field of the 20th century. Pauling was among the first scientists to work in the fields of quantum...
in order to explain the structure of
moleculeA molecule is defined as an electrically neutral group of at least two atoms in a definite arrangement held together by very strong chemical bonds. Molecules are distinguished from polyatomic ions in this strict sense...
s such as
methaneMethane is a chemical compound with the chemical formula . It is the simplest alkane, and the principal component of natural gas. Methane's bond angles are 109.5 degrees. Burning methane in the presence of oxygen produces carbon dioxide and water. The relative abundance of methane and its clean...
(CH
4). 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.
Hybridisation theory is not as practical for quantitative calculations as
Molecular Orbital TheoryIn chemistry, molecular orbital 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...
. Problems with hybridisation are especially notable when the
d orbitals are involved in bonding, as in coordination compounds. Although hybridisation schemes in transition metal chemistry can be used, they are not generally as accurate.
It is important to note that orbitals are a model representation of the behaviour 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 equationIn physics, specifically quantum mechanics, the Schrödinger equation is an equation that describes how the quantum state of a physical system changes in time...
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
carbonCarbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...
,
nitrogenNitrogen is a chemical element that has the symbol N and atomic number 7 and atomic mass 14.00674 u. Elemental nitrogen is a colorless, odorless, tasteless and mostly inert diatomic gas at standard conditions, constituting 78% by volume of Earth's atmosphere.Many industrially important...
and
oxygenOxygen Oxygen Oxygen (acid, literally "sharp", from the taste of acids) and -γενής (-genēs) (producer, literally begetter) is the element with atomic number 8 and represented by the symbol O...
(and to a lesser extent,
sulfurSulfur or sulphur is the chemical element that has the atomic number 16. It is denoted with the symbol S. It is an abundant, multivalent non-metal. Sulfur, in its native form, is a yellow crystalline solid. In nature, it can be found as the pure element and as sulfide and sulfate minerals...
and
phosphorusPhosphorus is the chemical element that has the symbol P and atomic number 15. A multivalent nonmetal of the nitrogen group, phosphorus is commonly found in inorganic phosphate rocks. Elemental phosphorus exists in two major forms - white phosphorus and red phosphorus...
) the hybridisation theory/model makes the description much easier.
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
methaneMethane is a chemical compound with the chemical formula . It is the simplest alkane, and the principal component of natural gas. Methane's bond angles are 109.5 degrees. Burning methane in the presence of oxygen produces carbon dioxide and water. The relative abundance of methane and its clean...
.
Hybridisation of 2s and 2p orbitals
When within a carbon atom the 2s orbital is mixed with one or more 2p orbitals there are 3 possibilities:
- 2s orbital + 1 2p orbital → 2 hybridised sp orbitals + 2 remaining 2p orbitals
- 2s orbital + 2 2p orbitals → 3 hybridised sp2 orbitals + 1 remaining 2p orbital
- 2s orbital + 3 2p orbitals → 4 hybridised sp3 orbitals
The hybridised orbitals will be used for
σ bondsIn chemistry, sigma bonds are the strongest type of covalent chemical bond. Sigma bonding is most clearly 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...
with other atoms, whereas the remaining p orbitals will be used for
π bondsIn chemistry, pi bonds are covalent chemical bonds where two lobes of one involved electron orbital overlap two lobes of the other involved electron orbital...
.
sp orbitals will be used for bonding with two other atoms or groups,
sp2 orbitals for bonding with three and
sp3 orbitals give four σ bonds.
- Note: 2 in 2s and 2p refers to electrons in the second electron shell
An electron shell may be thought of as an orbit followed by electrons around an atom nucleus. Because each shell can contain only a fixed number of electrons, each shell is associated with a particular range of electron energy, and thus...
with the corresponding energy level.
Example methane
Hybridisation describes the bonding atoms from an atom's point of view. That is, for a tetrahedrally coordinated carbon like
methaneMethane is a chemical compound with the chemical formula . It is the simplest alkane, and the principal component of natural gas. Methane's bond angles are 109.5 degrees. Burning methane in the presence of oxygen produces carbon dioxide and water. The relative abundance of methane and its clean...
(CH
4), the carbon should have 4 orbitals with the correct symmetry to bond to the 4 hydrogen atoms.
Carbon's ground-state configuration is 1
s2 2
s2 2
px1 2
py1 or more easily read:
The
valence bond theoryIn chemistry, valence bond theory is one of two basic theories, along with molecular orbital theory, that developed to use the methods of quantum mechanics to explain chemical bonding. It focuses on how the atomic orbitals of the dissociated atoms combine on molecular formation to give individual...
would predict, based on the existence of two half-filled
p-type orbitals (the designations
px py or
pz are meaningless at this point, as they do not fill in any particular order), that C forms two
covalent bondA covalent bond is a form of chemical bonding that is characterized by the sharing of pairs of electrons between atoms, or between atoms and other covalent bonds...
s, i.e., CH
2 (
methyleneMethylene is a chemical species in which a carbon atom is bonded to two hydrogen atoms. Three different possibilities present themselves:* the −CH2− group, e.g. dichloromethane...
). However, methylene is a very reactive molecule (see also:
carbeneIn chemistry, a carbene is a organic molecule containing a carbon atom with six valence electrons and having the general formula RR'C:. Carbenes are classified into two varieties, singlets and triplets. Most carbenes are very short lived, although persistent carbenes are known.The prototypical...
) and cannot exist outside of a molecular system. Therefore, this theory alone cannot explain the existence of CH
4.
Furthermore, ground state orbitals cannot be used for bonding in CH
4. While exciting a 2
s electron into a 2
p orbital would, in theory, allow for four bonds according to the valence bond theory, (which has been proved experimentally correct for systems like O
2) this would imply that the various bonds of CH
4 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 CH
4 (and many other molecules) a method by which as many as 12 bonds (for
transition metalThe term transition metal has two possible meanings:*In the past it referred to any element in the d-block of the periodic table, which includes groups 3 to 12 on the periodic table...
s) of equal strength (and therefore equal length) was required.
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 lower-energy 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 2
s orbital (core orbitals are almost never involved in bonding) "mixes" with the three 2
p orbitals to form four sp
3 hybrids (read as s-p-three
). See graphical summary below.
becomes
In CH4, four sp
3 hybridised orbitals are overlapped by hydrogenHydrogen is the chemical element with atomic number 1. It is represented by the symbol H. At standard temperature and pressure, hydrogen is a colorless, odorless, nonmetallic, tasteless, highly flammable diatomic gas with the molecular formula H
2...
's 1s
orbital, yielding four σ (sigma) bondsIn chemistry, sigma bonds are the strongest type of covalent chemical bond. Sigma bonding is most clearly 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...
(that is, four single covalent bonds). The four bonds are of the same length and strength. This theory fits our requirements.
translates into 
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 sp
3-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 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 sp
3 orbitals mix with the 4 hydrogen orbitals.
Example ethene
In sp2 hybridisation the 2
s orbital is mixed with only two of the three available 2
p orbitals:
forming a total of 3
sp2 orbitals with one p-orbital remaining.
Other carbon based compounds and other molecules may be explained in a similar way as methane. Take, for example, ethene (C
2H
4). Ethene has a double bond between the carbons. The Kekule structure looks like this:
Carbon will
sp2 hybridise, because hybrid orbitals will form only σ bonds and one
π (pi) bondIn chemistry, pi bonds are covalent chemical bonds where two lobes of one involved electron orbital overlap two lobes of the other involved electron orbital...
is required for the
double bondA covalent bond is a form of chemical bonding that is characterized by the sharing of pairs of electrons between atoms, or between atoms and other covalent bonds...
between the carbons. The hydrogen-carbon bonds are all of equal strength and length, which agrees with experimental data.
In ethylene (ethene) 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 2
p–2
p 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
sp2.5 are also readily described. In this case the geometries are somewhat distorted from the ideally hybridised picture. For example, as stated in
Bent's ruleBent's rule, which concerns orbital hybridisation of chemical bonds, was stated in 1961 by the American chemist Henry Bent. Originally, it was expressed as follows:* Atomic s character concentrates in orbitals directed toward electropositive substituents...
, a bond tends to have higher
p-character when directed toward a more
electronegativeElectronegativity, symbol χ, is a chemical property that describes the ability of an atom to attract electrons towards itself in a covalent bond. An atom's electronegativity is affected by both its atomic weight and the distance that its valence electrons reside from the charged nucleus...
substituent.
Example ethyne
The chemical bonding in compounds such as
alkyneAlkynes are hydrocarbons that have a triple bond between two carbon atoms, with the formula CnH2n-2. Alkynes are traditionally known as acetylenes, although the name acetylene also refers specifically to C2H2, known formally as ethyne using IUPAC...
s with triple bonds is explained by sp
hybridization.
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 acetyleneAcetylene is the chemical compound with the formula HC
2H. It is a hydrocarbon and the simplest alkyne. This colourless gas is widely used as a fuel and a chemical building block...
(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.
Hybridisation and molecule shape
Hybridisation, along with the VSEPR theoryValence shell electron pair repulsion theory is a model in chemistry used to predict the shape of individual molecules based upon the extent of electron-pair electrostatic repulsion. It is also named Gillespie-Nyholm theory after its two main developers...
, helps to explain molecule shape:
- AX1 (e.g., LiH): no hybridisation; trivially linear shape
- AX2 (e.g., BeCl2):
sp
hybridisation; linearIn Euclidean geometry, a line is a straight curve. When geometry is used to model the real world, lines are used to represent straight objects with negligible width and height. Lines are an idealisation of such objects and have no width or height at all and are usually considered to be infinitely...
or diagonal shape; bond angles are cos−1(−1) = 180°
- AX2E (e.g., GeF2): bent/V shape, < 120°
AX3 (e.g., BCl3): sp
2 hybridisation; trigonal planarIn chemistry, trigonal planar is a molecular geometry with one atom at the center and three atoms at the corners of a triangle all in one plane. In an ideal trigonal planar species, all three ligands are identical and all bond angles are 120°. Such species belong to the point group D3h...
shape; bond angles are cos−1(−1/2) = 120°
- AX3E (e.g.,NH3): trigonal pyramidal, 107°
AX4 (e.g., CCl4): sp
3 hybridisation; tetrahedralIn a Tetrahedral molecular geometry a central atom is located at the center with four substituents that are located at the corners of a tetrahedron. The bond angles are cos−1 ≈ 109.5° when all four substituents are the same, as in CH4...
shape; bond angles are cos−1(−1/3) ≈ 109.5°
AX5 (e.g., PCl5): sp
3d
hybridisation; trigonal bipyramidalIn chemistry a trigonal bipyramid formation is a molecular geometry with one atom at the center and 5 more atoms at the corners of a triangular dipyramid...
shape
AX6 (e.g., SF6): sp
3d
2 hybridisation; octahedralIn chemistry, octahedral molecular geometry describes the shape of compounds where in six atoms or groups of atoms or ligands are symmetrically arranged around a central atom, defining the vertices of an octahedron...
(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 Xi
number, but bond angles become smaller due to increased repulsion. For example, in waterWater is an ubiquitous chemical substance that is composed of hydrogen and oxygen and is essential for all known forms of life.In typical usage, water refers only to its liquid form or state, but the substance also has a solid state, ice, and a gaseous state, water vapor or steam. Water covers 71%...
(H2O), the oxygenOxygen Oxygen Oxygen (acid, literally "sharp", from the taste of acids) and -γενής (-genēs) (producer, literally begetter) is the element with atomic number 8 and represented by the symbol O...
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: sp
3 hybridisation is utilized, and the electron arrangement of H
2O 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).
In general, for an atom with s and p orbitals forming hybrids h
i and h
j with included angle , the following holds: 1 +
ij cos = 0. The p-to-s ratio for hybrid i is
i2, and for hybrid j it is
j2. In the special case of equivalent hybrids on the same atom, again with included angle , the equation reduces to just 1 +
2 cos = 0. For example, BH
3 has a trigonal planar geometry, three 120
o bond angles, three equivalent hybrids about the boron atom, and thus 1 +
2 cos = 0 becomes 1 +
2 cos(120
o) = 0, giving
2 = 2 for the p-to-s ratio. In other words, sp
2 hybrids, just as expected from the list above.
- Note: 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.
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 sp
3d and sp
3d
2 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 (PCl
5). The 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
angstromThe ångström or angstrom is an internationally recognized unit of length equal to 0.1 nanometre or 1 metres. It is named after Anders Jonas Ångström...
s). Thus, at first sight, it seems improbable for sp
3d hybridisation to occur.
However, a deeper look into the factors that affect orbital size (and energy) reveals more.
Formal chargeIn chemistry, a formal charge is the charge assigned to an atom in a molecule, assuming that electrons in a chemical bond are shared equally between atoms, regardless of relative electronegativity....
on the central atom is one such factor, and it is obvious that the P atom in PCl
5 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: SF
6(
sulfur hexafluorideSulfur hexafluoride is an inorganic, colorless, odorless, non-toxic and non-flammable gas . has an octahedral geometry, consisting of six fluorine atoms attached to a central sulfur atom. It is a hypervalent molecule. Typical for a nonpolar gas, it is poorly soluble in water but soluble in...
), IF
7, XeF
6; in all these molecules, the central atom is surrounded by the highly electronegative
fluorineFluorine is the chemical element with atomic number 9, represented by the symbol F. Fluorine forms a single bond with itself in elemental form, resulting in the diatomic F
2 molecule. F
2 is a supremely reactive, poisonous, pale, yellowish brown gas. Elemental fluorine is the...
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.
The
molecular orbital theoryIn chemistry, molecular orbital 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...
, however, offers a clearer insight into the bonding in these molecules.
Hybridisation theory vs. MO theory
Hybridisation theory, more widely known as
Valence Bond TheoryIn chemistry, valence bond theory is one of two basic theories, along with molecular orbital theory, that developed to use the methods of quantum mechanics to explain chemical bonding. It focuses on how the atomic orbitals of the dissociated atoms combine on molecular formation to give individual...
, is an integral part of
organic chemistryOrganic chemistry is a discipline within chemistry which involves the scientific study of the structure, properties, composition, reactions, and preparation of chemical compounds that contain carbon...
. Although the language and pictures arising from Hybridisation Theory remain widespread in
synthetic organic chemistryOrganic synthesis is a special branch of chemical synthesis and is concerned with the construction of organic compounds via organic reactions. Organic molecules can often contain a higher level of complexity compared to purely inorganic compounds, so the synthesis of organic compounds has...
, this qualitative analysis of bonding has been largely superseded by molecular orbital theory in other branches of chemistry. 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.
See also
- Linear combination of atomic orbitals molecular orbital method
A linear combination of atomic orbitals or LCAO is a quantum superposition of atomic orbitals and a technique for calculating molecular orbitals in quantum chemistry. In quantum mechanics, electron configurations of atoms are described as wavefunctions...
- MO diagram
A molecular orbital diagram or MO diagram for short 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 molecular orbital method in particular...
s
External links