The most significant development in the first half of the 20th century is the human's ability to understand the structure of atoms and molecules. Computation has made mathematical concepts visible to the extent that we now can see the atomic and molecular orbitals. On the other hand, Using everyday encountered materials or toys can also generate beautiful illustrations of hybrid atomic orbitals.
The valence bond (VB) approach is different from the molecular orbital (MO) theory. Despite their differences, most of their results are the same, and they are interesting.
The overlapping AOs can be of different types, for example, a sigma bond may be formed by the overlapping the following AOs.
|Chemical bonds formed due to overlap of atomic orbitals|
However, the atomic orbitals for bonding may not be "pure" atomic orbitals directly from the solution of the Schrodinger Equation. Often, the bonding atomic orbitals have a character of several possible types of orbitals. The methods to get an AO with the proper character for the bonding is called hybridization. The resulting atomic orbitals are called hybridized atomic orbitals or simply hybrid orbitals.
We shall look at the shapes of some hybrid orbitals first, because these shapes determine the shapes of the molecules.
The solution to the Schrodinger Equation provides the wavefunctions for the following atomic orbitals:
Quantum mechanical approaches by combining the wave functions to give new wavefunctions are called hybridization of atomic orbitals. Hybridization has a sound mathematical fundation, but it is a little too complicated to show the details here. Leaving out the jargons, we can say that an imaginary mixing process converts a set of atomic orbitals to a new set of hybrid atomic orbitals or hybrid orbitals.
At this level, we consider the following hybrid orbitals:
H sp1 Be sp2 H
The ground state electronic configuration of Be is 1s22s2, and one may think of the electronic configuration "before" bonding as 1s2sp2. The two electrons in the sp hybrid orbitals have the same energy.
In general, when two and only two atoms bond to a third atom and the third atom makes use of the sp hybridized orbitals, the three atoms are on a straight line. For example, sp hybrid orbitals are used in the central atoms in the molecules shown on the right.
When the central atom makes use of sp2 hybridized orbitals, the compound so formed has a trigonal shape. BF3 is such a molecule:
|Molecules with sp2 Hybrid orbitals|
| . . -2|
Not all three sp2 hybridized orbitals have to be used in bonding. One of the orbitals may be occupied by a pair or a single electron. If we do not count the unshared electrons, these molecules are bent, rather than linear. The three molecules shown together with the BF3 molecule are such molecules.
Carbon atoms also makes use of the sp2 hybrid orbitals in the compound H2C=CH2. In this molecule, the remaining p orbital from each of the carbon overlap to form the additional pi, p, bond.
|Planar molecules with sp2 Hybrid orbitals|
C = C
C = O
N = O
Other ions such as CO32-, and NO3-, can also be explained in the same way.
When sp3 hybrid orbitals are used for the central atom in the formation of molecule, the molecule is said to have the shape of a tetrahedron.
The typical molecule is CH4, in which the 1s orbital of a H atom overlap with one of the sp3 hybrid orbitals to form a C-H bond. Four H atoms form four such bonds, and they are all equivalent. The CH4 molecule is the most cited molecule to have a tetrahedral shape. Other molecules and ions having tetrahedral shapes are SiO44-, SO42-,
As are the cases with sp2, hybrid orbitals, one or two of the sp3 hybrid orbitals may be occupied by non-bonding electrons. Water and ammonia are such molecules.
|Tetrahedral arrangements of |
CH4, NH3E and OH2E2
The VSEPR number is equal to the number of bonds plus the number of lone pair electrons. Does not matter what is the order of the bond, any bonded pair is considered on bond. Thus, the VSEPR number is 4 for all of CH4, :NH3, ::OH2.
According the the VSEPR theory, the lone electron pairs require more space, and the H-O-H angle is 105 deegrees, less than the ideal tetrahedral angle of 109.5 degrees.
Some of the dsp3 hybrid orbitals may be occupied by electron pairs. The shapes of these molecules are interesting. In TeCl4, only one of the hybrid dsp3 orbitals is occupied by a lone pair. This structure may be represented by TeCl4E, where E represents a lone pair of electrons. Two lone pairs occupy two such orbitals in the molecule BrF3, or BrF3E2. These structures are given in a VSEPR table of 5 and 6 coordinations.
The compound SF4 is another AX4E type, and many interhalogen compounds ClF3 and IF3 are AX3E2 type. The ion I3- is of the type AX2E3.
There are also cases that some of the d2sp3 hybrid orbitals are occupied by lone pair electrons leading to the structures of the following types:
No known compounds of AX3E3 and AX2E4 are known or recognized, because they are predicted to have a T shape and linear shape respectively when the lone pairs of electrons are ignored.
A summary in the form of a table is given here to account for the concepts of hybrid orbitals, valence bond theory, VSEPR, resonance structures, and octet rule. In this table, the geometric shapes of the molecules are described by linear, trigonal planar, tetrahedral, trigonal bypyramidal, and octahedral. The hybrid orbitals use are sp, sp2, sp3, dsp3, and d2sp3.
The VSEPR number is the same for all molecules of each group. Instead of using NH3E, and OH2E2, we use :NH3, ::OH2 to emphasize the unshared (or lone) electron pairs.
|A summary of hybrid orbitals, valence bond theory, VSEPR,
resonance structures, and octet rule.
| a lone odd electron : a lone electron pair|
Only Be and C atoms are involved in linear molecules. In gas phase, BeH2 and BeF2 are stable, and these molecules do not satisfy the octet rule. The element C makes use of sp hybridized orbitals and it has the ability to form double and triple bonds in these linear molecules.
Carbon compounds are present in trigonal planar and tetrahedral molecules, using different hybrid orbitals. The extra electron in nitrogen for its compounds in these groups appear as lone unpaired electron or lone electron pairs. More electrons in O and S lead to compounds with lone electron pairs. The five-atom anions are tetrahedral, and many resonance structures can be written for them.
Trigonal bipyramidal and octahedral molecules have 5 and 6 VSEPR pairs. When the central atoms contain more than 5 or 6 electrons, the extra electrons form lone pairs. The number of lone pairs can easily be derived using Lewis dot structures for the valence electrons.
In describing the shapes of these molecules, we often ignore the lone pairs. Thus, NO2, N3-, :OO2 (O3), and :SO2 are bent molecules whereas :NH3, :PF3, and :SOF2 are pyramidal. You already know that ::OH2 (water) and ::SF2 are bent molecules.
The lone electron pair takes up the equatorial location in :SF4, which has the same structure as :TeF4 described earlier. If you lay a model of this molecule on the side, it looks like a butterfly. By the same reason, ::ClF3 and ::BrF3 have a T shape, and :::XeF2, :::I3-, and :::ICl2- are linear.
Similarly, :BrF5 and :IF5 are square pyramidal whereas ::XeF4 is square planar.
Which atom in the formula is usually the center atom?
Usually, the atom in the center is more electropositive than the terminal atoms. However, the H and halogen atoms are usually at the terminal positions because they form only one bond.
Take a look at the chemical formulas in the table, and see if the above statement is true.
However, the application of VSEPR theory can be expanded to complicated
molecules such as
H H H O | | | // H-C-C=C=C-C=C-C-C | | \ H N O-H / \ H H
Molecular orbital theory considers the energy states of the molecule.
Number of orbitals does not change in hybridization of atomic orbitals.
Since the lone electron pair in :SO2 and lone electron in NO2 takes up more space, we expect the structure to distort leaving a smaller angle than 120 between the bonds.
The 4 H atoms form a tetrahedron, and methane has a tetrahedral shape.
The structure of this ion is very similar to that of CH4.
Sigma (s) bonds are due to sp hybrid orbitals, and 2 p orbitals are used for pi (p) bonds. The two sigma bonds for each C are due to overlap of sp hybrid orbitals of each C atom.
H O=C< HThis is a trigonal planar molecule. It is called formaldehyde, a solvent for preserving biological samples. The compound has an unpleasant smell.
The C atom has 3 sigma (s) bonds by using three sp2) hybrid orbitals and a pi (p) bond, due to one 2p orbital.
Since the S atom uses d2sp3 hybrid orbitals, you expect the shape to be octahedral. The F atoms form an octahedron around the sulfur.
A total of 5 atomic orbitals are used in the hybridization: one 3d, one 3s and three 3p orbitals. The dsp3 hybrid orbitals of P give rise to a trigonalbipyramidal coordination around the P atom.
The energy of d orbitals in N is not compatible with 2s and 2p orbitals for hybridization. Thus, you seldom encounter a compound with formula NX5 with N as the central atom.