Bonding


Shapes of Molecules

The actual arrangement of the atoms around the central atom in a molecule.

In order to find this we need to consider the number of regions of electron density (electron pairs or unpaired single electrons in some cases) around the central atom. The electrons will repel as far apart as possible as they have the same charge.

The valence shell electron pair repulsion theory (VSEPRT) gives us a means of working out the shapes of molecules and ions.

  1. Draw the Lewis structure to show all of the valence shell electrons.

  2. Then count the number of regions of electron density - this can then be translated into the electronic shape.

  3. Now consider the number of attached atoms and their orientation keeping the lone (non-bonding) pairs as far apart as possible without changing the electronic shape.

  4. The resultant molecular arrangement gives the molecular shape. Note that it may be slightly distorted by repulsions between regions of electron density.


Valence  Shell  Electron  Pair  Repulsion
(VSEPR)

Valence Shell Electron Pair Repulsion theory (VSEPR) is a set of rules whereby the chemist may predict the shape of an isolated molecule. It is based on the premise that groups of electrons surrounding a central atom repel each other, and that to minimize the overall energy of the molecule, these groups of electrons try to get as far apart as possible. Groups of electrons can refer to electrons that participate in a bond (single, double, or triple) to another atom, or to non-bonding electrons (e.g. lone pair electrons).

The ideal electronic symmetry of a molecule consisting of a central atom surrounded by a number of substituents (bonded atoms and non-bonding electrons) is characteristic of the total number of substituents, and is determined solely by geometric considerations -- the substituents are arranged so as to maximize the distances amongst them. VSEPR is useful for predicting the shape of a molecule when there are between 2 and 6 substituents around the central atom (the case of one substituent is not discussed because it is trivial -- the only possible shape for such a molecule is linear). That means that there are only five unique electronic geometries to remember. For each electronic geometry, there may be a number of different molecular geometries (the shape of the molecule when only bonded atoms, not non-bonding electrons are considered). Molecular geometries are really just special cases of the parent electronic geometry -- this will hopefully be evident from the models shown on the pages linked to this one.

Since the molecular geometry is determined by how many bonding and non-bonding electron groups surround the central atom, the first thing one needs to do is count how many of each there are. There is a notation that simplifies this bookkeeping:

 

ABxEy

The A represents the central atom, B represents the electron groups that form bonds to other atoms, and E represents the non-bonding electron groups. The subscripts, x and y, indicate how many of each kind are present.

 

AB4
bonding groups: 4
non-bonding groups: 0
AB3E
bonding groups: 3
non-bonding groups: 1
AB2E2
bonding groups: 2
non-bonding groups: 2

CH4
methane

NH3
ammonia

H2O
water

Note that bonding "electron groups" does not necessarily imply single bonds; it can mean double or triple bonds as well:

 

AB2
bonding groups: 2
non-bonding groups: 0

CO2
Carbon Dioxide

An incidental benefit of using the ABE notation is that it provides a convenient way of remembering the hybridization at the central atom. The total number of substituents (bonding plus non-bonding groups) is equal to the number of atomic orbitals that participate in the hybrid orbital.

 

Molecule ABE representation # of substituents Hybridisation
CH4 AB4 4 sp3
NH3 AB3E 4 sp3
H2O AB2E2 4 sp3
CO2 AB2 2 sp
SF6 AB6 6 sp3d2
I3- ion AB2E3 5 sp3d

 

Displayed in the following table are the five most important electronic symmetries. Each row in the table is linked to a page that shows the different molecular symmetries possible for that electronic symmetry.

 

Class Hybridisation Electronic Symmetry
AB2 sp linear
AB3 sp2 trigonal planar
AB4 sp3 tetrahedral
AB5 sp3d trigonal bipyramidal
AB6 sp3d2 octahedral

 

Molecules in three dimensions

Summary of the possible geometries

No. of electron pairs around the central atom
electronic shape
no of attached atoms
molecular shape
2
linear
2
linear
3
trigonal planar
3
trigonal planar
4
tetrahedral
4
tetrahedral
4
tetrahedral
3
pyramidal
4
tetrahedral
2
angular or bent
5
trigonal bipyramidal
5
trigonal bipyramidal
5
trigonal bipyramidal
4
square pyramid
5
trigonal bipyramidal
3
trigonal planar
5
trigonal bipyramidal
2
angular
6
octahedral
6
octahedral
6
octahedral
5
umbrella
6
octahedral
4
square planar

Shapes of molecules and ions


14.1.1:- State and predict the shape and bond angles using the VSEPR theory for 5- and 6-negative charge centres. The shape of the molecules/ions and bond angles if all pairs of electrons are shared, and the shape of the molecules/ions if one or more lone pairs surround the central atom, should be considered. Examples such as PCl5, SF6 and XeF4 can be used.


Electrons are negatively charged and, as such, repel each other. When electrons are in orbitals with the same energy (degenerate) these orbitals then orient themselves to be as far apart as possible so as to minimise repulsion. The orientations that are adopted will depend on the number of regions of electron density (orbitals) surrounding the nucleus.

If there are two regions of electron density attached to a nucleus then they will be on opposite sides of the nucleus i.e. they will be arranged 180 degrees to each other.

The following table summarizes the shapes adopted by the regions of electron density

No of regions
shape adopted
angles between orbitals
2
linear
180
3
trigonal planar
120
4
tetrahedral
109,5
5
trigonal bipyramid
120 and 90
6
octahedral
90 and 180
     

It must be remembered that we are talking about the regions of electron density here and that this may not be reflected in the molecular shape. If the electrons are not being used to bond then they cannot be seen and the molecule must be described as if they were not there.


For example: water

The central oxygen atom has its electron arranged into four pairs in four distinct regions (the orbitals are sp3 hybridized)

These repel one another and adopt a tetrahedral arrangement.

However only two of the electron pairs are used in bonding and the other two pair are 'lone' (ie cannot be seen). The shape of the molecule is therefore 'angular' or 'bent'

Tetrahedral electronically but the molecular shape is angular


The valence shell electron pair repulsion theory now looks at the relative strength of the repulsions between the lone pairs and the bonding pairs. As the lone pairs are not drawn further away from the central atom by another atomic nucleus then they exert a greater repulsion on each other than the bonding pairs do on each other. Intermediate is the repulsion felt between a bonding pair and a one pair.

Order of repulsion strength:

lone pair- lone pair >> lone pair - bonding pair >> bonding pair - bonding pair



This causes the tetrahedral electronic shape to distort and squeezes the bonding pairs together. The bond angle then closes slightly from 109,5 to 104,5


H-O-H bond angle 104,5

Water


Example: PCl5

In this molecule the phosphorus is the central atom and provides 5 electrons.

Each of the bonded chlorines provide one electron making 5 + 5=10 in total around the central atom.

Each bond has two electrons and there are five bonds using up 5 x 2 =10 electrons.

Hence there are no electron pairs left over and the central atom arranges the five regions of electron density into the ideal orientation - a trigonal pyramidal shape.

Phosphorus pentachloride


Example XeF6

Xenon from group 0 has eight electrons in its outer shell and each fluorine provides one for the bond making a total of 8 + 6=14 electrons.

It may be seen from the formula that the Xe-F bonds require a total of 6 x 2=12 electrons therefore there is also a lone pair to make up the 14 electrons.

Electronically the seven orbitals orientate themselves to form a pentagonal bipyramidal shape with two different bond angles 90 and 72. The lone pair will occupy the one of the orbitals at 90 to the plane of the central 5 orbitals but will distort them downwards according to the valence shell electron pair repulsion theory. The final result is a sort of umbrella shape.

 


Example XeF4

Xenon from group 0 has eight electrons in its outer shell and each fluorine provides one for the bond making a total of 8 + 4 = 12 electrons.

It may be seen from the formula that the four Xe-F bonds require a total of 4 x 2 = 8 electrons therefore there are also two lone pairs to make up the 12 electrons.

Electronically the six oribitals orientate themselves to form an octahedral shape with bond angles 90 . The lone pairs will occupy the orbitals as far apart as possible i.e. on opposite sides of the octahedral shape according to the valence shell electron pair repulsion theory.

The final result is a square planar arrangement of Xe-F bonds with lone pairs above and below.


Hybridization

This model explains the tetrahedral geometry of carbon and other atoms.

The electron structure of carbon is 1s2 2s2 2p2 suggesting that it should only be able to form two bonds (using the two singly occupied orbitals). However it is known to make four single bonds in many compounds and indeed never forms just two bonds. This can be explained by hybridization - the mixing of atomic orbitals producing degenerate orbitals used for bonding.

  • sp3 hybridization occurs when the 2s and 2p orbitals merge to become sp3 orbitals (all of equal energy, length etc.).

  • sp2 is the same except only two of the p orbitals are hybridized, leaving one p orbital unchanged

  • sp is the same except only one of the p orbitals is hybridized and two p orbitals are left unchanged

hybridisation
geometry
example
carbon in
sp3
tetrahedral methane
CH4
sp2
trigonal planar ethene
CH2=CH2
sp
linear ethyne
CH=CH
       

Delocalisation of electrons

When a particular molecule can be represented as several different Lewis structures is is generally not actually any of these, but a hybrid (mixture) of all of them. This can be represented either by using delocalised electrons, or through resonance (where each possible structure is drawn and the actual state 'resonates' between them. The delocalisation of these pi electrons (which is effectively what happens) makes the molecule more stable (as evidenced by lower energy) and gives the bonds a shorter length than would be expected.

Examples:

benzene    O3     SO42-

Hybridization

14.2.1: Describe s and p bonds. Treatment should be restricted to:

  • sigma bonds electron distribution has axial symmetry around the axis joining the two nuclei
  • pi bonds resulting from the combination of parallel 'p' orbitals
  • double bonds formed by a sigma and a pi bond
  • triple bonds formed by a sigma and two pi bonds.

An orbital is a region of space in which there is a 99% probability of finding an electron with a specific quantity of energy. The shape plotted out by this probability is accepted to be the region of space where the electron is, as this makes discussions of electrons and their movements much easier to understand.

For example electrons with the lowest energy are 99% likely to be within a region of spherical shape around the nucleus of an atom. It is convenient for us to describe this region of space as the orbital in which a maximum of two electrons may be housed. We call it an 's' orbital. If it is the lowest energy level, then it is designated 1s.


Sigma bonds

When two s orbitals overlap, the electrostatic forces of attraction for the nucleus of one atom will attract the electrons of the other atom and vice versa. This produces an overall force that holds the two nuclei together. We call this a chemical bond.

If two s orbitals directly overlap then the bond formed is linear between the two nuclear centres and is called a sigma bond.

Sigma bonds are produced by any direct orbital overlap along the axis joining the two nuclear centres together.

Although it is convenient to show this overlap using two 1s orbitals, in fact this is the exception rather than the rule. Direct orbital overlap usually happens by overlap of a hybridised orbital with a 1s orbital (in hydrogen) or between two hybridised orbitals.


p 'pi' bonds

When a sigma bond is formed by direct orbital overlap and this brings two parallel 'p' orbitals into close proximity then these can overlap sideways (laterally) to form a region of electron density that is not directly between the two nuclear centres but which nevertheless contributes to bonding. This is called a pi bond.

It should be emphasized that a pi bond can only form after a sigma bond has already formed. It is always part of a double or triple bond.


Double and triple bonds

As stated above a pi bond can only form after a sigma bond. Consequently the pi bond must be part of a double (or triple) bond system. Whenever there is a double bond it is made up of one sigma (direct orbital overlap) bond and one pi (lateral orbital overlap) bond.

Triple bonds have two pi bonds arranged at 90 to one another brought about by the lateral overlap of one pair of py orbitals and one pair of pz orbitals.

Summary:

  • Double bonds - 1 sigma and 1 pi bond
  • Triple bonds - 1 sigma and 2 pi bonds

14.2.2 State and explain the meaning of the term hybridization. Hybridization should be explained in terms of the mixing of atomic orbitals to form new orbitals for bonding. Students should consider sp, sp2 and sp3 hybridization, and the shapes and orientation of these orbitals.


Hybridization

Hybridization means making something new from an amalgamation or combination of other parts. A hybrid plant is one made from two different plants blended together. The hybrid shows the characteristics of both plants.

In terms of chemistry we refer to the hybridization of atomic orbitals to explain the change that seems to happen between the atomic orbitals in an uncombined atom and the orbitals used by the same atom when bonding.

We are familiar with the orbitals in an atom and their different shapes. The 's' orbital is spherical about the nucleus and the 'p' orbitals are like double headed balloons arranged along the axis of (imaginary) three dimensional coordinates.

's' orbitals
 
'p' orbitals


However, it is apparent that the shapes of these orbitals are inadequate to explain the orientation of the bonds produced in molecules. The 'p' orbitals are oriented at 90 to one another and yet there are few molecules that show a bond angle of 90 (in fact the bond angle 90 does appear in some of the larger molecules but that is due to different reasons).

The classic molecule to consider is methane CH4. In this molecule the bond angles indicate that the shape of the molecule is a perfect tetrahedron with bond angles of 109 28' (approximately 109,5)

It seems that the orbitals used for bonding are arranged as far apart as possible suggesting that they have the same energy (degenerate). We know that the orbitals on the carbon atom do not have the same energy - the 2s orbital is of lower energy that the three 2p orbitals. Hybridization is a model that allows us to combine the atomic orbitals and then produce four degenerate orbitals to be used for bonding. In order for the electrons to be ready for this process one of them must be promoted from the 2s orbital to the 2pz orbital as in the diagram.

The 2s electron is promoted to the 2pz orbital and the four orbitals then undergo hybridization to form four degenerate orbitals. As these new orbital have emerged from one s and three p orbitals they are called 'sp3' orbitals.

 

It should be emphasized at this point that this is the norm rather than the exception. It seems that all elements undergo this hybridization process (or a similar one) when bonding. Logically, the 2s orbital is in no position to overlap directly with another orbital from another atom without interfering with the p orbitals. This hybridization process allows the 2s electrons to be involved in bonding.

If we study the shape of the water molecule we accept that the four electron pairs around the oxygen are tetrahedrally arranged. They have hybridized and the sp3 orbitals so formed overlap directly with the 1s orbitals of the two hydrogens. The two lone pairs on the oxygen remain in the sp3 orbitals that are not used in bonding.

Other types of hybridization

Carbon can also bond to three other atoms instead of four (as in methane) and it seems that it hybridised its orbitals using only the 2s and two of the 2p orbitals to do this.

As can be seen this leaves an unaffected p orbital that is then used for lateral overlap pi bonding

This is the formation of a double bond in molecules such as ethene. The three sp2 hybrid orbitals are degenerate (same energy) and consequently arrange as far apart as possible in space i.e. at 120 to each other. This creates a trigonal shape that is planar leaving the remaining 2pz orbital to orientate itself above and below the plane of the other orbitals. This 2p orbital can then laterally overlap with adjacent singly occupied 'p' orbitals on adjacent atoms.

In sp hybridisation, carbon bonds to two other atoms by hybridising the 2s and only one of the 2p orbitals to produce two sp orbitals arranged at 180 to one another. The remaining two 2p prbitals can overlap with suitable orbitals on adjacent atoms to produce pi systems. Examples include ethyne, the nitrogen molecule, hydrogen cyanide, and any other triple bond systems.

Other forms of hybridisation

Although not specifically required for the IB diploma, it should be mentioned that this hybridisation process can be extended to allow atoms to bond with more than four other atoms (octet expansion). In this case the hybridization invariably involves one or more of the 'd' orbitals. Sulphur hexafluoride forms six attachments to the six fluorines and consequently needs six available orbitals. It gets these by promoting one electron from the 3s and 3px orbitals into two of the 3d orbitals. It can then hybridise the 3s, 3px, 3py, 3pz, and 3dxy, 3dxz orbitals into an octagonal arrangement each with one electron.

Summary

Atoms rearrange their atomic orbitals when bonding to produce orbitals with shapes more suitable for the bonding process. This is called hybridisation. It is performed by almost all atoms when bonding although carbon provided the easiest examples to show. It is easy to recognize the hybridization used by simply observing the double or triple bonds.

Only single bonds = sp3 hybridisation

1 double bond = sp2 hybridisation

1 triple bond =sp hybridisation


14.2.3: Discuss the relationships between Lewis structures, molecular shapes and types of hybridization (sp, sp2 and sp3). Using examples from inorganic as well as organic chemistry, students should write the Lewis structure, deduce the shape of the molecule and recognize the type of hybridization.


Lewis structures

These are diagrams (dot - cross drawings) that show all of the valence electrons around the atoms in a molecule. Although the "rules " for drawing these structures are not hard and fast, they do provide a useful guideline for arriving at the 'correct ' structure.

Hydrogen can only share one pair of electrons (1 covalent bond)

Oxygen usually forms two covalent bonds, however it may share two pairs evenly OR accept a lone pair to form a dative coordinate bond (the same as a covalent bond except that both the electrons are provided by one atom)

The method for arriving at the Lewis structure is:

1. Count the number of valence electrons on the central atom (e.g. Phosphorus =5 from group 5)

2. Add one electron from each attached atom for each bond.

3. Count up the total number of electrons

4. Subtract the electrons used in forming the bonds

5. The number remaining will be the 'extra' electrons on the central atom



Phosphorus Trichloride

Lewis structure

The central atom is phosphorus therefore it has 5 valence electrons

There are three chlorine atoms each providing one electron to bond = 3 electrons

Total number of electrons = 8

Number of electrons used in bonding three chlorines = 3 x 2 = 6

This leaves 2 electrons unused (1 pair) that must go onto the phosphorus.

Shape

The central phosphorus then has four regions of electron density (three bonds and one lone pair)

Electronically these four regions adopt a tetrahedral orientation but only three pairs are used for the bonding.

The molecule is therefore pyramidal (with one invisible lone pair forming the apex of the electronic tetrahedron)


Lewis structures become difficult when the central atoms donates electron pairs. The only useful advice here is that when oxygen is attached to the central atom it can accept lone pairs from the central atom to make up its own octet (set of eight outer electrons) and that you should look out for this.

Examples are the oxides of phosphorus, sulphur and chlorine as well as their oxy-ions (phosphate, sulphate, sulphite, chlorate etc.)


 

Sulphur dioxide SO2

The central sulphur provides 6 electrons

Each oxygen can accept one pair of donated electrons from the sulphur making four electrons used

However this gives the sulphur only six electrons in total in the outer shell. It is therefore appropriate to share another pair from one of the oxygens making an effective double bond and giving sulphur a complete octet.

This picture suggests that the bonding between the sulphur and each of the oxygens is different.

Bond measurements show us that this is not the case - this can be explained by the concept of resonance.

This leaves the central sulphur with a lone pair

It then has three regions of electron density and is electronically trigonal

Only two of the regions are used in bonding therefore the molecule is angular (bent)

It should be clear from the two examples above that the hybridisation is determined by the number of molecular orbitals attached to the central atom. In the case to the PCl3 it can clearly be seen that there are four regions of electron density and so the hybridisation adopted is sp3 (tetrahedral)

In the case of the SO2 there are only three regions of electron density and therefore sp2 hybridisation is adopted. This also leaves the remaining p orbital able to form a pi system with either of the oxygens and can then resonate between pi bonding with one oxygen and the other.

Summary

The relationship between the Lewis arrangement of electrons, the hybridisation, the resonance and the molecular shape supports the theories of bonding by linear combination of atomic orbitals and molecular orbital theory.

  • The Lewis structure allows us to map out a probable arrangement of electrons around the atoms in the molecule.
  • This in turn shows us the number of regions of electron density around the central atom which can be used to ascertain the hybridisation.
  • From the hybridisation and the valence shell electron pair repulsion theory, we can predict the molecular shape (and the electronic shape from which it derives).
  • The different valid Lewis structures that can be drawn give an idea about the possible resonances within the molecule.

Molecules and ions that should be studied in depth

Molecule
formula
shape
Nitrogen dioxide
NO2
Sulphur dioxide
SO2
Sulphur trioxide
SO3
Phosphorus trichloride
PCl3
Phosphine
PH3
Ammonia
NH3
Sulphur oxychloride
SOCl2
Water
H2O
Carbon monoxide
CO
Carbon dioxide
CO2
Xenon tetrafluoride
XeF4
Phosphorus pentafluoride
PF5
Xenon hexafluoride
XeF6
Sulphur hexafluoride
SF6
Hydrogen sulphide
H2S
Methane
CH4
Ethane
C2H4
Ethyne
C2H2
Hydrogen cyanide
HCN
Ion
formula
shape
Nitrate
NO3-
Nitrite
NO2-
Carbonate
CO32-
Phosphate
PO43-
Sulphate
SO42-
Sulphite
SO32-
Chlorate
ClO3-
Perchlorate
ClO4-
Chlorite
ClO2-
Cyanide
CN-