In
chemistry
Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
, orbital hybridisation (or hybridization) is the concept of mixing
atomic orbital
In atomic theory and quantum mechanics, an atomic orbital is a function describing the location and wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in any spe ...
s to form new ''hybrid orbitals'' (with different energies, shapes, etc., than the component atomic orbitals) suitable for the pairing of electrons to form
chemical bond
A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules and crystals. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing of ...
s 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 sp
3 mixtures in a
tetrahedral
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ...
arrangement around the carbon to bond to four different atoms. Hybrid orbitals are useful in the explanation of
molecular geometry
Molecular geometry is the three-dimensional arrangement of the atoms that constitute a molecule. It includes the general shape of the molecule as well as bond lengths, bond angles, torsional angles and any other geometrical parameters that dete ...
and atomic bonding properties and are symmetrically disposed in space. Usually hybrid orbitals are formed by mixing atomic orbitals of comparable energies.
History and uses
Chemist
A chemist (from Greek ''chēm(ía)'' alchemy; replacing ''chymist'' from Medieval Latin ''alchemist'') is a scientist trained in the study of chemistry. Chemists study the composition of matter and its properties. Chemists carefully describe th ...
Linus Pauling first developed the hybridisation theory in 1931 to explain the structure of simple
molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...
s such as
methane
Methane ( , ) is a chemical compound with the chemical formula (one carbon atom bonded to four hydrogen atoms). It is a group-14 hydride, the simplest alkane, and the main constituent of natural gas. The relative abundance of methane on Ea ...
(CH
4) using
atomic orbital
In atomic theory and quantum mechanics, an atomic orbital is a function describing the location and wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in any spe ...
s. Pauling pointed out that a carbon atom forms four bonds by using one s and three p orbitals, so that "it might be inferred" that a carbon atom would form three bonds at right angles (using p orbitals) and a fourth weaker bond using the s orbital in some arbitrary direction. In reality, methane has four C-H bonds of equivalent strength. The angle between any two bonds is the
tetrahedral bond angle of 109°28' (around 109.5°). Pauling supposed that in the presence of four hydrogen atoms, the s and p orbitals form four equivalent combinations which he called ''hybrid'' orbitals. Each hybrid is denoted sp
3 to indicate its composition, and is directed along one of the four C-H bonds. 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
A heuristic (; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediate ...
for rationalizing the structures of
organic compounds
In chemistry, organic compounds are generally any chemical compounds that contain carbon-hydrogen or carbon-carbon bonds. Due to carbon's ability to catenate (form chains with other carbon atoms), millions of organic compounds are known. The s ...
. It gives a simple orbital picture equivalent to
Lewis structures
Lewis structures, also known as Lewis dot formulas, Lewis dot structures, electron dot structures, or Lewis electron dot structures (LEDS), are diagrams that show the bonding between atoms of a molecule, as well as the lone pairs of electrons tha ...
.
Hybridisation theory is an integral part of
organic chemistry
Organic chemistry is a subdiscipline within chemistry involving the scientific study of the structure, properties, and reactions of organic compounds and organic materials, i.e., matter in its various forms that contain carbon atoms.Clayden, J.; ...
, one of the most compelling examples being
Baldwin's rules
Baldwin's rules in organic chemistry are a series of guidelines outlining the relative favorabilities of ring closure reactions in alicyclic compounds. They were first proposed by Jack Baldwin in 1976.
Baldwin's rules discuss the relative rates ...
. For drawing reaction mechanisms sometimes a classical bonding picture is needed with two atoms sharing two electrons. Hybridisation theory explains bonding in alkenes and methane. The amount of p character or s character, which is decided mainly by orbital hybridisation, can be used to reliably predict molecular properties such as acidity or basicity.
Overview
Orbitals are a model representation of the behavior of electrons within molecules. In the case of simple hybridization, this approximation is based on
atomic orbital
In atomic theory and quantum mechanics, an atomic orbital is a function describing the location and wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in any spe ...
s, similar to those obtained for the hydrogen atom, the only neutral atom for which the
Schrödinger equation
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of th ...
can be solved exactly. In heavier atoms, such as carbon, nitrogen, and oxygen, the atomic orbitals used are the 2s and 2p orbitals, similar to excited state orbitals for hydrogen.
Hybrid orbitals are assumed to be mixtures of atomic orbitals, superimposed on each other in various proportions. For example, in
methane
Methane ( , ) is a chemical compound with the chemical formula (one carbon atom bonded to four hydrogen atoms). It is a group-14 hydride, the simplest alkane, and the main constituent of natural gas. The relative abundance of methane on Ea ...
, the C hybrid orbital which forms each
carbon
Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent
In chemistry, the valence (US spelling) or valency (British spelling) of an element is the measure of its combining capacity with o ...
–
hydrogen
Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, an ...
bond consists of 25% s character and 75% p character and is thus described as sp
3 (read as ''s-p-three'') hybridised.
Quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
describes this hybrid as an sp
3 wavefunction
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements ...
of the form
, where N is a
normalisation constant (here 1/2) and pσ is a p orbital directed along the C-H axis to form a
sigma bond
In chemistry, sigma bonds (σ 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 s ...
. The ratio of coefficients (denoted λ in general) is
in this example. Since the
electron density
In quantum chemistry, 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 va ...
associated with an orbital is proportional to the square of the wavefunction, the ratio of p-character to s-character is λ
2 = 3. The p character or the weight of the p component is N
2λ
2 = 3/4.
Types of hybridisation
sp3
Hybridisation describes the bonding of atoms from an atom's point of view. For a tetrahedrally coordinated carbon (e.g.,
methane
Methane ( , ) is a chemical compound with the chemical formula (one carbon atom bonded to four hydrogen atoms). It is a group-14 hydride, the simplest alkane, and the main constituent of natural gas. The relative abundance of methane on Ea ...
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 1s
2 2s
2 2p
2 or more easily read:
The carbon atom can use its two singly occupied p-type orbitals to form two
covalent bonds with two hydrogen atoms, yielding the singlet
methylene CH
2, the simplest
carbene
In organic chemistry, a carbene is a molecule containing a neutral carbon atom with a valence of two and two unshared valence electrons. The general formula is or where the R represents substituents or hydrogen atoms.
The term "carbene" ma ...
. The carbon atom can also bond to four hydrogen atoms by an excitation (or promotion) of an electron from the doubly occupied 2s orbital to the empty 2p orbital, producing four singly occupied orbitals.
The energy released by the formation of two additional bonds more than compensates for the excitation energy required, energetically favoring the formation of four C-H bonds.
Quantum mechanically, the lowest energy is obtained if the four bonds are equivalent, which requires that they are formed from equivalent orbitals on the carbon. A set of four equivalent orbitals can be obtained that are linear combinations of the valence-shell (core orbitals are almost never involved in bonding) s and p wave functions, which are the four sp
3 hybrids.
In CH
4, four sp
3 hybrid orbitals are overlapped by
hydrogen
Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, an ...
1s orbitals, yielding four
σ (sigma) bonds (that is, four single covalent bonds) of equal length and strength.
translates into
sp2
Other carbon compounds and other molecules may be explained in a similar way. For example,
ethene
Ethylene (IUPAC name: ethene) is a hydrocarbon which has the formula or . It is a colourless, flammable gas with a faint "sweet and musky" odour when pure. It is the simplest alkene (a hydrocarbon with carbon-carbon double bonds).
Ethylene i ...
(C
2H
4) has a double bond between the carbons.
For this molecule, carbon sp
2 hybridises, because one
π (pi) bond is required for the
double bond
In chemistry, a double bond is a covalent bond between two atoms involving four bonding electrons as opposed to two in a single bond. Double bonds occur most commonly between two carbon atoms, for example in alkenes. Many double bonds exist betwee ...
between the carbons and only three σ bonds are formed per carbon atom. In sp
2 hybridisation the 2s orbital is mixed with only two of the three available 2p orbitals, usually denoted 2p
x and 2p
y. The third 2p orbital (2p
z) remains unhybridised.
forming a total of three sp
2 orbitals with one remaining p orbital. In ethylene (
ethene
Ethylene (IUPAC name: ethene) is a hydrocarbon which has the formula or . It is a colourless, flammable gas with a faint "sweet and musky" odour when pure. It is the simplest alkene (a hydrocarbon with carbon-carbon double bonds).
Ethylene i ...
) the two carbon atoms form a σ bond by overlapping one sp
2 orbital from each carbon atom. The π bond between the carbon atoms perpendicular to the molecular plane is formed by 2p–2p overlap. Each carbon atom forms covalent C–H bonds with two hydrogens by s–sp
2 overlap, all with 120° bond angles. The hydrogen–carbon bonds are all of equal strength and length, in agreement with experimental data.
sp
The chemical bonding in compounds such as
alkynes with
triple bond
A triple bond in chemistry is a chemical bond between two atoms involving six bonding electrons instead of the usual two in a covalent single bond. Triple bonds are stronger than the equivalent single bonds or double bonds, with a bond order o ...
s is explained by sp hybridization. In this model, the 2s orbital is mixed with only one of the three p orbitals,
resulting in two sp orbitals and two remaining p orbitals. The chemical bonding in
acetylene (ethyne) (C
2H
2) 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 σ s–sp overlap at 180° angles.
Hybridisation and molecule shape
Hybridisation helps to explain
molecule shape, since the angles between bonds are approximately equal to the angles between hybrid orbitals. This is in contrast to
valence shell electron-pair repulsion (VSEPR) theory, which can be used to predict molecular geometry based on empirical rules rather than on valence-bond or orbital theories.
spx hybridisation
As the valence orbitals of
main group elements are the one s and three p orbitals with the corresponding
octet rule
The octet rule is a chemical rule of thumb that reflects the theory that main-group elements tend to bond in such a way that each atom has eight electrons in its valence shell, giving it the same electronic configuration as a noble gas. The rul ...
, sp
x hybridization is used to model the shape of these molecules.
spxdy hybridisation
As the valence orbitals of
transition metal
In chemistry, a transition metal (or transition element) is a chemical element in the d-block of the periodic table (groups 3 to 12), though the elements of group 12 (and less often group 3) are sometimes excluded. They are the elements that ca ...
s are the five d, one s and three p orbitals with the corresponding
18-electron rule, sp
xd
y hybridisation is used to model the shape of these molecules. These molecules tend to have multiple shapes corresponding to the same hybridization due to the different d-orbitals involved. A square planar complex has one unoccupied p-orbital and hence has 16 valence electrons.
sdx hybridisation
In certain
transition metal
In chemistry, a transition metal (or transition element) is a chemical element in the d-block of the periodic table (groups 3 to 12), though the elements of group 12 (and less often group 3) are sometimes excluded. They are the elements that ca ...
complexes with a low
d electron count
The d electron count is a chemistry formalism used to describe the electron configuration of the valence electrons of a transition metal center in a coordination complex. The d electron count is an effective way to understand the geometry and rea ...
, the p-orbitals are unoccupied and sd
x hybridisation is used to model the shape of these molecules.
Hybridisation of hypervalent molecules
Octet expansion
In some general chemistry textbooks, hybridization is presented for main group coordination number 5 and above using an "expanded octet" scheme with d-orbitals first proposed by Pauling. However, such a scheme is now considered to be incorrect in light of computational chemistry calculations.
In 1990, Eric Alfred Magnusson of the
University of New South Wales
The University of New South Wales (UNSW), also known as UNSW Sydney, is a public research university based in Sydney, New South Wales, Australia. It is one of the founding members of Group of Eight, a coalition of Australian research-intensiv ...
published a paper definitively excluding the role of d-orbital hybridisation in bonding in hypervalent compounds of second-row (
period 3) elements, ending a point of contention and confusion. Part of the confusion originates from the fact that d-functions are essential in the basis sets used to describe these compounds (or else unreasonably high energies and distorted geometries result). Also, the contribution of the d-function to the molecular wavefunction is large. These facts were incorrectly interpreted to mean that d-orbitals must be involved in bonding.
Resonance
In light of
computational chemistry
Computational chemistry is a branch of chemistry that uses computer simulation to assist in solving chemical problems. It uses methods of theoretical chemistry, incorporated into computer programs, to calculate the structures and properties of m ...
, a better treatment would be to invoke
sigma bond
In chemistry, sigma bonds (σ 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 s ...
resonance
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied Periodic function, periodic force (or a Fourier analysis, Fourier component of it) is equal or close to a natural frequency of the system ...
in addition to hybridisation, which implies that each resonance structure has its own hybridisation scheme. All resonance structures must obey the
octet rule
The octet rule is a chemical rule of thumb that reflects the theory that main-group elements tend to bond in such a way that each atom has eight electrons in its valence shell, giving it the same electronic configuration as a noble gas. The rul ...
.
Isovalent hybridisation
Although ideal hybrid orbitals can be useful, in reality, most bonds require orbitals of intermediate character. This requires an extension to include flexible weightings of atomic orbitals of each type (s, p, d) and allows for a quantitative depiction of the bond formation when the molecular geometry deviates from ideal bond angles. The amount of p-character is not restricted to integer values; i.e., hybridizations like sp
2.5 are also readily described.
The hybridization of bond orbitals is determined by
Bent's rule
In chemistry, Bent's rule describes and explains the relationship between the orbital hybridization of central atoms in molecules and the electronegativities of substituents. The rule was stated by Henry A. Bent as follows:
The chemical struct ...
: "Atomic character concentrates in orbitals directed towards electropositive substituents".
Molecules with lone pairs
For molecules with lone pairs, the bonding orbitals are isovalent sp
x hybrids. For example, the two bond-forming hybrid orbitals of oxygen in water can be described as sp
4.0 to give the interorbital angle of 104.5°. This means that they have 20% s character and 80% p character and does ''not'' imply that a hybrid orbital is formed from one s and four p orbitals on oxygen since the 2p subshell of oxygen only contains three p orbitals. The shapes of molecules with lone pairs are:
*
Trigonal pyramidal
In chemistry, a trigonal pyramid is a molecular geometry with one atom at the apex and three atoms at the corners of a trigonal base, resembling a tetrahedron (not to be confused with the tetrahedral geometry). When all three atoms at the corner ...
** Three isovalent bond hybrids (>90°)
** E.g., NH
3
*
Bent
** Two isovalent bond hybrids (>90°)
** E.g., SO
2, H
2O
In such cases, there are two mathematically equivalent ways of representing lone pairs. They can be represented by orbitals of sigma and pi symmetry similar to molecular orbital theory or by equivalent orbitals similar to VSEPR theory.
Hypervalent molecules
For hypervalent molecules with lone pairs, the bonding scheme can be split into a hypervalent component and a component consisting of isovalent sp
x bond hybrids. The hypervalent component consists of resonant bonds using p orbitals. The table below shows how each shape is related to the two components and their respective descriptions.
Hybridisation defects
Hybridisation of s and p orbitals to form effective sp
x hybrids requires that they have comparable radial extent. While 2p orbitals are on average less than 10% larger than 2s, in part attributable to the lack of a radial node in 2p orbitals, 3p orbitals which have one radial node, exceed the 3s orbitals by 20–33%.
The difference in extent of s and p orbitals increases further down a group. The hybridisation of atoms in chemical bonds can be analysed by considering localised molecular orbitals, for example using natural localised molecular orbitals in a
natural bond orbital (NBO) scheme. In
methane
Methane ( , ) is a chemical compound with the chemical formula (one carbon atom bonded to four hydrogen atoms). It is a group-14 hydride, the simplest alkane, and the main constituent of natural gas. The relative abundance of methane on Ea ...
, CH
4, the calculated p/s ratio is approximately 3 consistent with "ideal" sp
3 hybridisation, whereas for
silane
Silane is an inorganic compound with chemical formula, . It is a colourless, pyrophoric, toxic gas with a sharp, repulsive smell, somewhat similar to that of acetic acid. Silane is of practical interest as a precursor to elemental silicon. Sila ...
, SiH
4, the p/s ratio is closer to 2. A similar trend is seen for the other 2p elements. Substitution of fluorine for hydrogen further decreases the p/s ratio.
The 2p elements exhibit near ideal hybridisation with orthogonal hybrid orbitals. For heavier p block elements this assumption of orthogonality cannot be justified. These deviations from the ideal hybridisation were termed hybridisation defects by
Kutzelnigg.
Photoelectron spectra
One misconception concerning orbital hybridization is that it incorrectly predicts the
ultraviolet photoelectron spectra of many molecules. While this is true if
Koopmans' theorem
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 aft ...
is applied to localized hybrids, quantum mechanics requires that the (in this case ionized) wavefunction obey the symmetry of the molecule which implies
resonance
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied Periodic function, periodic force (or a Fourier analysis, Fourier component of it) is equal or close to a natural frequency of the system ...
in valence bond theory. For example, in methane, the ionised states (CH
4+) can be constructed out of four resonance structures attributing the ejected electron to each of the four sp
3 orbitals. A linear combination of these four structures, conserving the number of structures, leads to a triply degenerate T
2 state and an A
1 state. The difference in energy between each ionized state and the ground state would be
ionization energy, which yields two values in agreement with experimental results.
Localized vs canonical molecular orbitals
Bonding orbitals formed from hybrid atomic orbitals may be considered as localized molecular orbitals, which can be formed from the delocalized orbitals of molecular orbital theory by an appropriate mathematical transformation. For molecules in the ground state, this transformation of the orbitals leaves the total many-electron wave function unchanged. The hybrid orbital description of the ground state is, therefore ''equivalent'' to the delocalized orbital description for ground state total energy and electron density, as well as the molecular geometry that corresponds to the minimum total energy value.
Two localized representations
Molecules with multiple bonds or multiple lone pairs can have orbitals represented in terms of sigma and pi symmetry or equivalent orbitals. Different valence bond methods use either of the two representations, which have mathematically equivalent total many-electron
wave function
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements ...
s and are related by a
unitary transformation
In mathematics, a unitary transformation is a transformation that preserves the inner product: the inner product of two vectors before the transformation is equal to their inner product after the transformation.
Formal definition
More precisely, ...
of the set of occupied molecular orbitals.
For multiple bonds, the sigma-pi representation is the predominant one compared to the equivalent orbital (
bent bond
In organic chemistry, a bent bond, also known as a banana bond, is a type of covalent chemical bond with a geometry somewhat reminiscent of a banana. The term itself is a general representation of electron density or configuration resembling a ...
) representation. In contrast, for multiple lone pairs, most textbooks use the equivalent orbital representation. However, the sigma-pi representation is also used, such as by Weinhold and Landis within the context of
natural bond orbitals, a localized orbital theory containing modernized analogs of classical (valence bond/Lewis structure) bonding pairs and lone pairs.
For the hydrogen fluoride molecule, for example, two F lone pairs are essentially unhybridized p orbitals, while the other is an sp''
x'' hybrid orbital. An analogous consideration applies to water (one O lone pair is in a pure p orbital, another is in an sp''
x'' hybrid orbital).
See also
*
Crystal field theory Crystal field theory (CFT) 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 (anion neighbors). This theory has been used ...
*
Isovalent hybridisation
*
Ligand field theory
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 valen ...
*
Linear combination of atomic orbitals
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 wavefun ...
*
MO diagram
Mo or MO may refer to:
Arts and entertainment Fictional characters
* Mo, a girl in the ''Horrible Histories'' TV series
* Mo, also known as Mortimer, in the novel ''Inkheart'' by Cornelia Funke
* Mo, in the webcomic '' Jesus and Mo''
* Mo, the ...
s
*
VALBOND In molecular mechanics, VALBOND is a method for computing the angle bending energy that is based on valence bond theory. It is based on ''orbital strength functions'', which are maximized when the hybrid orbitals on the atom are orthogonal. The hy ...
References
External links
Covalent Bonds and Molecular StructureHybridisation flash movieHybrid orbital 3D preview program in OpenGLUnderstanding Concepts: Molecular Orbitals
General Chemistry tutorial on orbital hybridization
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Chemical bonding
Molecular geometry
Stereochemistry
Quantum chemistry