In chemistry, orbital hybridisation (or hybridization) is the concept of mixing atomic orbitals to form new hybrid orbitals (with different energies, shapes, etc., than the component atomic orbitals) suitable for the pairing of electrons to form chemical bonds in valence bond theory. For example, in a carbon atom which forms four single bonds, the valence-shell s orbital combines with three valence-shell p orbitals to form four equivalent sp3 mixtures in a tetrahedral arrangement around the carbon to bond to four different atoms. Hybrid orbitals are useful in the explanation of molecular geometry and atomic bonding properties and are symmetrically disposed in space. Usually hybrid orbitals are formed by mixing atomic orbitals of comparable energies.
History and uses
Chemist Linus Pauling first developed the hybridisation theory in 1931 to explain the structure of simple molecules such as methane (CH4) using atomic orbitals. 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 sp3 to indicate its composition, and is directed along one of the four C–H bonds.L. Pauling The Nature of the Chemical Bond (3rd ed., Oxford University Press 1960) p.111–120. 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. It gives a simple orbital picture equivalent to Lewis structures.
Hybridisation theory is an integral part of organic chemistry, one of the most compelling examples being Baldwin's rules. For drawing reaction mechanisms sometimes a classical bonding picture is needed with two atoms sharing two electrons. Hybridisation theory explains bonding in alkenesOrganic Chemistry, Third Edition Marye Anne Fox James K. Whitesell 2003 and methane.Organic Chemistry 3rd Ed. 2001 Paula Yurkanis Bruice 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 orbitals, similar to those obtained for the hydrogen atom, the only neutral atom for which the Schrödinger equation 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, the C hybrid orbital which forms each carbon–hydrogen bond consists of 25% s character and 75% p character and is thus described as sp3 (read as s-p-three) hybridised. Quantum mechanics describes this hybrid as an sp3 wavefunction 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. The ratio of coefficients (denoted λ in general) is in this example. Since the electron density associated with an orbital is proportional to the square of the wavefunction, the ratio of p-character to s-character is λ2 = 3. The p character or the weight of the p component is N2λ2 = 3/4.
Types
sp3
Hybridisation describes the bonding of atoms from an atom's point of view. For a tetrahedrally coordinated carbon (e.g., methane CH4), the carbon should have 4 orbitals directed towards the 4 hydrogen atoms.
Carbon's ground state configuration is 1s2 2s2 2p2 or more easily read:
C ↑↓ ↑↓ ↑ ↑
1s 2s 2p 2p 2p
This diagram suggests that the carbon atom could use its two singly occupied p-type orbitals to form two covalent bonds with two hydrogen atoms in a methylene (CH2) molecule, with a hypothetical bond angle of 90° corresponding to the angle between two p orbitals on the same atom. However the true H–C–H angle in singlet methylene is about 102°Isaiah Shavitt (1985), Geometry and singlet-triplet energy gap in methylene: A critical review of experimental and theoretical determinations. Tetrahedron, volume 41, issue 8, page 1531 which implies the presence of some orbital hybridisation.
The carbon atom can also bond to four hydrogen atoms in methane by an excitation (or promotion) of an electron from the doubly occupied 2s orbital to the empty 2p orbital, producing four singly occupied orbitals.
C* ↑↓ ↑ ↑ ↑ ↑ 1s 2s 2p 2p 2p
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.
According to quantum mechanics, 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,McMurray, J. (1995). Chemistry Annotated Instructors Edition (4th ed.). Prentice Hall. p. 272. which are the four sp3 hybrids.
C* ↑↓ ↑ ↑ ↑ ↑ 1s sp3 sp3 sp3 sp3
In CH4, four sp3 hybrid orbitals are overlapped by the four hydrogens' 1s orbitals, yielding four σ (sigma) bonds (that is, four single covalent bonds) of equal length and strength.
The following:
translates into:
sp2
Other carbon compounds and other molecules may be explained in a similar way. For example, ethylene (C2H4) has a double bond between the carbons. For this molecule, carbon sp2 hybridises, because one π (pi) bond is required for the double bond between the carbons and only three σ bonds are formed per carbon atom. In sp2 hybridisation the 2s orbital is mixed with only two of the three available 2p orbitals, usually denoted 2px and 2py. The third 2p orbital (2pz) remains unhybridised.
C* ↑↓ ↑ ↑ ↑ ↑ 1s sp2 sp2 sp2 2p
forming a total of three sp2 orbitals with one remaining p orbital. In ethylene, the two carbon atoms form a σ bond by overlapping one sp2 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–sp2 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 bonds is explained by sp hybridization. In this model, the 2s orbital is mixed with only one of the three p orbitals,
C* ↑↓ ↑ ↑ ↑ ↑ 1s sp sp 2p 2p
resulting in two sp orbitals and two remaining 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 σ s–sp overlap at 180° angles.
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, spx hybridization is used to model the shape of these molecules. Coordination number Shape Hybridisation Examples 2 Linear sp hybridisation (180°) CO2 3 Trigonal planar sp2 hybridisation (120°) BCl3 4 Tetrahedral sp3 hybridisation (109.5°) CCl4 Interorbital angles
spxdy hybridisation As the valence orbitals of transition metals are the five d, one s and three p orbitals with the corresponding 18-electron rule, spxdy 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.
Coordination number Shape Hybridisation Examples 4 Square planar sp2d hybridisation PtCl42− 5 Trigonal bipyramidal sp3d hybridisation Fe(CO)5 Square pyramidal MnCl52− 6 Octahedral sp3d2 hybridisation Mo(CO)6 7 Pentagonal bipyramidal sp3d3 hybridisation ZrF73− Capped octahedral MoF7− Capped trigonal prismatic TaF72− 8 Square antiprismatic sp3d4 hybridisation ReF8− Dodecahedral Mo(CN)84− Bicapped trigonal prismatic ZrF84− 9 Tricapped trigonal prismatic sp3d5 hybridisation ReH92− Capped square antiprismatic
sdx hybridisation In certain transition metal complexes with a low d electron count, the p-orbitals are unoccupied and sdx hybridisation is used to model the shape of these molecules.
Coordination number Shape Hybridisation Examples 3 Trigonal pyramidal sd2 hybridisation (90°) CrO3 4 Tetrahedral sd3 hybridisation (70.5°, 109.5°) TiCl4 5 Square pyramidal sd4 hybridisation (65.9°, 114.1°) Ta(CH3)5 6 C3v Trigonal prismatic sd5 hybridisation (63.4°, 116.6°) W(CH3)6 Interorbital angles
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.
Coordination number Molecular shape Hybridisation Examples 5 Trigonal bipyramidal sp3d hybridisation 6 Octahedral sp3d2 hybridisation 7 Pentagonal bipyramidal sp3d3 hybridisation
In 1990, Eric Alfred Magnusson of the University of New South Wales 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, a better treatment would be to invoke sigma bond resonance in addition to hybridisation, which implies that each resonance structure has its own hybridisation scheme. All resonance structures must obey the octet rule.
Coordination number Resonance structures 5 Trigonal bipyramidal 6 Octahedral 7 Pentagonal bipyramidal
In computational VB theory
While the simple model of orbital hybridisation is commonly used to explain molecular shape, hybridisation is used differently when computed in modern valence bond programs. Specifically, hybridisation is not determined a priori but is instead variationally optimized to find the lowest energy solution and then reported. This means that all artificial constraints, specifically two constraints, on orbital hybridisation are lifted: that hybridisation is restricted to integer values (isovalent hybridisation) that hybrid orbitals are orthogonal to one another (hybridisation defects)