Sigma bondFrom Wikipedia, the free encyclopedia

σ bond between two atoms : localisation of electronic density.

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 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. By this definition, common

forms of sigma bonds are s+s, pz+pz, s+pz and dz2+dz

2 (where z is defined as the axis of the bond). Quantum

theory also indicates that molecular orbitals (MO) of identical symmetry actually mix. As a practical

consequence of this mixing of diatomic molecules, the wavefunctions s+s and pz+pz molecular

orbitals become blended. The extent of this mixing (or blending) depends on the relative energies of the

like-symmetry MO's.

For homodiatomics, bonding σ orbitals have no nodal planes between the bonded atoms. The

corresponding antibonding, or σ* orbital, is defined by the presence of a nodal plane between these two

bonded atoms.

Sigma bonds are the strongest type of covalent bonds, and the electrons in these bonds are sometimes

referred to as sigma electrons.

The symbol σ is the Greek letter for s. When viewed down the bond axis, a σ MO resembles an s atomic

orbital.

Contents

 [hide]

1 Sigma bonds in polyatomic compounds

2 Sigma bonds in multiply bonded species

3 Sigma bonds in organic molecules

4 See also

5 External links

[edit]Sigma bonds in polyatomic compounds

They are obtained by head on overlap of atomic orbitals. The concept of sigma bonding is extended, albeit

loosely, to describe bonding interactions involving overlap of a single lobe of one orbital with a single lobe of

another. For example,propane is described as consisting of ten sigma bonds, one each for the two C-C

bonds and one each for the eight C-H bonds. The σ bonding in such a polyatomic molecule is highly

delocalized, which conflicts with the two-orbital, one-bond concept. Despite this complication, the concept of

σ bonding is extremely powerful and therefore pervasive.

[edit]Sigma bonds in multiply bonded species

Compounds that feature multiple bonds, such as ethylene and chromium(II) acetate, have sigma bonds

between the multiply bonded atoms. These sigma bonds are supplemented by π-bonds, e.g. in the case of

ethylene, and even δ-bonds, e.g. in the case of chromium(II) acetate.

[edit]Sigma bonds in organic molecules

Organic molecules are often made up of one cyclic compound or more, such as benzene, and are often

made up of many sigma bonds along with pi bonds. According to the sigma bond rule, the number of

sigma bonds in a molecule is equivalent to the number of atoms plus the number of rings minus one.

Nb σ = Nb atoms + Nb rings - 1

This can easily be concluded by realizing that the creation of bonds between atoms that are not

connected in a ring requires the same number of atoms minus one (such as in hydrogen gas, H2,

where there is only one sigma bond, or ammonia, NH3, where there are only 3 sigma bonds), and that

rings do not obey this rule (such as benzene rings, which have 6 sigma bonds within the ring for 6

carbon atoms).

Pi bondFrom Wikipedia, the free encyclopedia

Electron atomic and molecular orbitals, showing a pi bond at the bottom right of the picture.

In chemistry, pi bonds (π bonds) are covalent chemical bonds where two lobes of one involved

electron orbital overlap two lobes of the other involved electron orbital. Only one of the orbital's nodal

planes passes through both of the involvednuclei.

Two p-orbitals forming a π-bond.

The Greek letter π in their name refers to p orbitals, since the orbital symmetry of the pi bond is the same

as that of the p orbital when seen down the bond axis. P orbitals usually engage in this sort of bonding. D

orbitals are also assumed to engage in pi bonding but this is not necessarily the case in reality, although the

concept of bonding d orbitals still accounts well forhypervalence.

Pi bonds are usually weaker than sigma bonds. From the perspective ofquantum mechanics, this bond's

weakness is explained by significantly less overlap between the component p-orbitals due to their parallel

orientation.

Pi bonds result from overlap of atomic orbitals that are in contact through two areas of overlap. Pi-bonds are

more diffuse bonds than the sigma bonds. Electrons in pi bonds are sometimes referred to as pi electrons.

Molecular fragments joined by a pi bond cannot rotate about that bond without breaking the pi bond,

because rotation involves destroying the parallel orientation of the constituent p orbitals.

Contents

 [hide]

1 Multiple bonds

2 Effect of bond rotation

3 Special cases

4 See also

5 References

[edit]Multiple bonds

Atoms connected via a double bond or triple bond have, in addition to one sigma bond, one or two pi bonds,

respectively.

Although the pi bond by itself is weaker than a sigma bond, pi bonds are often components of multiple

bonds, together with sigma bonds. The combination of pi and sigma bond is stronger than either bond by

itself. The enhanced strength of a multiple bond versus a single (sigma bond) is indicated in many ways, but

most obviously by a contraction in bond lengths. For example in organic chemistry, carbon-carbon bond

lengths are in ethane (154 pm), in ethylene (134 pm) and in acetylene (120 pm). More bonds make the total

bond shorter and stronger.

ethane ethylene acetylene

[edit]Effect of bond rotation

Top: two parallel p-orbitals. Bottom: pi

bond formed by overlap. Pink and gray

represent a ball and stick model of the

molecular fragment that contains the pi

bond.

Pi bond breaking when bond rotates

because parallel orientation is lost. Pink

and gray represent a ball and stick model

of the molecular fragment that contains the

pi bond.

Two s-orbitals continue to overlap when

bond rotates because orientation is along

axis. Circles represent s orbitals. Ellipses

represent merged sigma bond. Pink and

gray represent a ball and stick model of the

molecular fragment that contains the sigma

bond.

[edit]Special cases

Pi bonds do not necessarily connect a pair of atoms that are also sigma-bonded.

In certain metal complexes, pi interactions between a metal atom and alkyne and alkene pi antibonding

orbitals form pi-bonds.

In some cases of multiple bonds between two atoms, there is no sigma bond at all, only pi bonds. Examples

include diiron hexacarbonyl (Fe2(CO)6), dicarbon (C2) and the borane B2H2. In these compounds the central

bond consists only of pi bonding, and in order to achieve maximum orbital overlap the bond distances are

much shorter than expected.[1]

Sigma Bonds

This particular kind of covalent bond in which electrons are shared between atoms is called a sigma bond. 

Also, this particular kind of bonding orbital is called a sigma orbital. Sometimes the term molecular orbital is used rather than bonding orbital. That term emphasizes that this represents the space taken up by the electrons in a molecule. The distinguishing feature of a sigma bond (or sigma bonding orbital) is that theoverlap region lies directly between the two nuclei.

In this diagram, there are quite a few examples of sigma bonds. Notice that it does not matter what shapes the orbitals have or what types they are. They can be s orbitals or p orbitals or hybrid orbitals. What makes each of these a sigma bond is that the orbital overlap occurs directly between the nuclei of the atoms. Those nuclei are represented by dots in this diagram.

Sigma Bonding in Alkane Molecules

As you know, a carbon atom can form a single sigma bond to other carbon atoms, as well as to hydrogen atoms when alkane molecules are formed.

Let's look at the orbitals in some of those molecules. This diagram shows the sigma bond formed by the overlap of hybrid orbitals from two carbon atoms. Notice that in this drawing of the hybrid orbitals the smaller lobes have been left off. As usual, only the large lobes (where the electrons spend most of their time) are shown. Each atom has four such orbitals and can form four bonds. In this diagram, only one such bond is indicated so each carbon atom can form three more bonds.

If all of those bonds are to hydrogen atoms, the result would be a molecule like the one diagrammed here. The C's and H's show the location of the centers of the atoms and the shaded areas represent the bonding orbitals. The lines emphasize the tetrahedral shapes. They do not represent bonds or anything like that.

Pi Bonds

Pi bonds involve the electrons in the leftover p orbital for each carbon atom. Those p orbitals are the electron clouds or orbitals that are shown going up above and below each carbon atom.

In the sketch at the top here, the sp2 hybrid orbitals of one atom are shown as sticks so that you can concentrate on the unhybridized, or leftover, p orbital. The bottom sketch shows you how the hybrid orbitals of two carbon atoms can come together, overlap, and form a regular sigma bond (shown as a stick). Notice that this also brings the leftover p orbitals so close that they can also overlap and form what we call a pi bond. Notice that the overlapping occurs in two places, above and below the sigma bond. The pi bond does not overlap in the region directly between the two carbon atoms where the sigma bond is formed.

The distinction between a sigma bond and a pi bond is diagrammed here. The sigma bond has orbital overlap directly between the two nuclei. The pi bond has orbital overlap off to the sides of the line joining the two nuclei.

The combination of a sigma and a pi bond between the same two carbon atoms is a double bond. A double bond consists of a sigma bond (using hybrid orbitals) and a pi bond (using p orbitals).

Another way of showing how two carbon atoms can form a double bond is indicated in the bottom (part c) of this diagram. Here we have two carbon atoms with sp2hybridization, and each of those carbon atoms is bonded to two hydrogen atoms and also to the other carbon atom. Notice that this diagram shows how the carbon atoms and the hydrogen atoms are all in a flat plane. This is drawn in perspective. Notice that there is a sigma bond between the carbon atoms and each of the hydrogen atoms. Notice also a sigma bond between the two carbon atoms. The sigma bonds (or sigma orbitals) are shown as the dark shaded areas in this drawing. Each one of those sigma bonds uses one of the hybrid orbitals. Remember that with sp2 hybridization, there are three hybrid orbitals, and those are the ones used to form the sigma bonds between all the atoms.

Remember also that we have a leftover p orbital for each carbon atom. Those p orbitals are the electron clouds or orbitals that are shown going

up above and below each carbon atom. In this particular diagram, the shading between those p orbitals shows that the p orbitals overlap one another and allow the electrons in those p orbitals to be shared. This kind of bond is called a pi bond. The pi bond results when p orbitals overlap one another in this side-to-side fashion.

This diagram tries to represent all of the sigma and pi bonds in ethene (C2H4). This is perhaps the best way to represent that a double bond consists of a sigma bond and a pi bond. It may possibly look like three bonds to you, but it is not. There is a sigma bond in the center and a pi bond above and below that. Altogether that represents a double bond.

Let me point out some important structural consequences of a double bond.

The double bonded carbon atoms and the atoms bonded to them all lie in a flat plane.

The pi bond sticks out above and below that plane.

There is no rotation around a double bond. You could not twist and turn those two carbon atoms without breaking the pi bond. The pi part of a double bond does not allow for rotation.

Models

Model kits are generally inadequate for showing this sigma-pi nature of a bouble bond. In the model kits available to you, the double bonds are represented using either springs or curved pieces of plastic.

These models might lead you to think that double bonds are formed by some kind of process, in which normal single bonds are bent around to form a curved bond, but that is just not true at all. It is just the simplest way to indicate a double bond using models like this. So keep that in mind when you use models that include double bonds.

The models are not all bad, however. When you make a model of this molecule as part of your lab work, you will note that it does show that all six atoms lie in a flat plane and that you cannot twist or turn or rotate this model like you could the alkanes that you made earlier, which had only single bonds.