The Covalent Chemical Bond: A Model

A chemical bond is a force causing atoms to behave as a unit

Chemical bonds result from the tendency of a system to seek its lowest possible energy

Bonds occur when connected atoms have a lower energy (more stable) than the separate atoms.

A mole of fluorine atoms releases 77 kJ of energy forming fluorine molecules

A half mole of fluorine molecules requires 77kJ of energy to break the bonds forming atoms

A mole of fluorine atoms is 77 kJ more stable as a half mole of fluorine molecules

It is useful to assume that the strength of a particular type of bond (i.e. a C-H bond) is independent of its environment. This allows us to assign strengths to types of bonds.


Valence Bond Theory

Valence Bond Theory assumes that the electrons in a molecule occupy atomic orbitals of the individual atoms.

The covalent bond is formed by the overlap (occupying a common space) of atomic orbitals from each atom.

The bond is formed by the attraction of the electrons to the nucleus of the other atom.

The balance between this attraction and the repulsion between the electrons and the repulsion between the nuclei determines the bond length (the distance where the energy is minimum).

The stable bond occurs where the potential energy of the system is at a minimum.

Hybridization of Atomic Orbitals

Atomic orbitals do not provide the geometries that are found in molecules. To account for molecular geometries we use hybrid orbitals.

Hybrid orbitals are atomic orbitals formed, in preparation for bonding, by combining nonequivalent orbitals of the isolated atom.

The number of orbitals that hybridize equals the number of electron domains around the central atom (the number of lone pairs and bonded atoms)

Double and Triple Bonds

In molecules with Double or Triple Bonds, the two or three pairs of electrons do not all occupy the same volume of space.

A single bond consists of a Sigma Bond; a bond formed by orbitals overlapping along the line of the bond with the electron density concentrated between the nuclei of the atoms.

A double bond consists of a Sigma Bond and a Pi Bond; a bond formed by the overlap of orbitals with their electron density concentrated above and below the plane of the nuclei.

A triple bond consists of a Sigma Bond and two Pi bonds oriented 90° apart around the bond

Hybridization with Double and Triple Bonds

Sigma Bonds are generally formed by hybrid orbitals.

Pi bonds are formed by unhybridized p orbitals, two p orbitals on separate atoms oriented in the same direction create an overlap above and below the line of the bond.

A double bond consists of a sigma bond and a pi bond.

A triple bond consists of a sigma bond and two pi bonds.

sp3 Hybridization

Methane has four identical bonds. These four bonds result from the hybridization of the 2s and three 2p orbitals. The four equal hybridized orbitals are called sp3 orbitals (hybrid orbitals). We say the carbon atom is sp3 hybridized or has undergone sp3 hybridization.   The sp3 hybridization has a tetrahedral arrangement with a bond angle of 109.5°.

sp2 Hybridization

Formaldehyde (CH2O) has a trigonal planar arrangement, with a bond angle of 120 degrees. This is the result of sp2 hybridization. The three sp2 hybrid orbitals are centered in a plane. In forming these hybrid orbitals, one p orbital is not used. This is orientated perpendicular to the plane containing the other orbitals. The sp2 orbitals create sigma bonds with the attached atoms, and the perpendicular p orbital forms a pi bond with a similar p orbital on the oxygen atom.

Whenever an atom is surrounded by three areas of electron density, a set of sp2 hybrid orbitals is used.

Sigma (σ) Bond

A sigma bond is a covalent bond with the shared electron pair centered on a line running between the atoms.

pi (π) Bond

A pi bond results from the overlap of p orbitals with the electrons occupying the space above and below a line running between the atoms.

Double Bond

A double bond always consists of one sigma bond and one pi bond.

sp Hybridization

A CO2 molecule has two areas of electron density around the carbon atom, these are located 180 degree apart forming a linear molecule.

The orbitals forming this structure is a sp hybrid orbital (sp hybridization).

Two areas of electron density always require sp hybridization.

Two p orbitals remain, these form two pi bonds. The two p orbitals are perpendicular to each other and the sp hybrid orbitals.

dsp3 Hybridization

In phosphorous pentachloride (PCl5), the phosphorous atom is surrounded by 5 bonding electron pairs and no nonbonding pairs. This results in a trigonal bypyramidal structure. The orbital structure is dsp3 hybridization (dsp3 orbitals).

Five areas of electron density require dsp3 orbitals and a trigonal bipyramidal structure.

d2sp3 Hybridization

In sulfur hexafluoride (SF6) the sulfur has 6 pairs of electrons, this results in an octahedral structure. The orbital structure is d2sp3 hybridization (d2sp3 orbitals).

Six areas of electron density require d2sp3 orbitals and an octahedral structure.

Number of effective Pairs

Shape

Hybrid orbitals

Bond Angles

2

Linear

sp

180°

3

Trigonal Planar

sp2

120°

4

Tetrahedral

sp3

109.5°

5

Trigonal bipyramidal

dsp3

90° and 120°

6

Octahedral

d2sp3

90°

Delocalized pi bonding

In molecules with resonance structures consisting of double bonds, such as benzene or sulfur trioxide; these molecules have pi bonds consisting of unhybridized p-orbitals oriented in the same direction.

We can draw these structures with pi bonds between certain atoms, and other structures with the pi bond between different atoms. The molecule "resonates" between these structures. Or we can say that the pi bond is delocalized over the available p-orbitals, where the electrons can move between any of the p-orbitals.

Delocalized pi bonds confer additional stability upon molecules.


Valence Bond Theory Summary

·        Every pair of bonded atoms shares one or more pairs of electrons. In every bond, one pair of electrons is localized in the space between the atoms in a sigma bond.

·        Hybrid orbitals form the sigma bonds. Sigma bonds are located between two bonded atoms and do not make a significant contribution to the bonding of any other atoms.

·        When bonds contain more than one pair of electrons, one pair forms the sigma bond, and other pairs form pi bonds. The centers of charge density in pi bonds lie above and below the bond axis.

·        Molecules with resonance structures can have pi bonds that extend over two or more bonds (delocalized).

Valence Bond Theory Conclusions

·        Valence Bond Theory qualitatively accounts for the stability of the covalent bond in terms of overlapping orbitals.

·        With Hybridization, it explains the molecular geometries predicted by the VSEPR theory.

·        It does not satisfactorily explain all observed properties of molecules, such as diamagnetism and paramagnetism.


Molecular Orbital Theory

Molecular Orbital Theory explains Magnetic and some other properties better than Valence Bond Theory.

In Molecular Orbital Theory, the electrons occupy molecular orbitals which result from the interaction of the atomic orbitals of the bonding atoms and are associated with the molecule as a whole.

Molecular Orbitals (MO)

The overlap of two atomic orbitals results in the formation of two molecular orbitals, one bonding molecular orbital, and one antibonding molecular orbital.

A bonding molecular orbital has lower energy and greater stability than the atomic orbitals from which it was formed. The electron density is concentrated between the nuclei of the atoms.

A antibonding molecular orbital has higher energy and less stability than the atomic orbitals from which it was formed. The electron density decreases to zero between the nuclei.

In general, the number of atomic orbitals used is equal to the number of molecular orbitals formed.

The overlap of two s atomic orbitals produce one sigma bonding (s) molecular orbital and one sigma antibonding (s*) molecular orbital.

The overlap the the three p orbitals from two atoms results one sigma bonding molecular orbital and one sigma antibonding molecular orbital; and two pi bonding (p) molecular orbitals and two pi antibonding (p*) molecular orbitals.

Molecular Orbital Diagram (Energy Level Diagram)

This is a diagram that shows the relative energy levels of molecular orbitals and the atomic orbitals from which they are formed.

Two s-atomic orbitals from separate atoms will form one sigma bonding and one sigma anti-bonding orbitals.

Three p-orbitals from two atoms (6 orbitals total) will combine to form one sigma bonding orbital, one sigma antibonding orbital, two pi bonding orbitals (degenerate, same energy), and two pi anti-bonding orbitals (degenerate). The normal order of increasing energy is:
sigma-s bonding < sigma-s antibonding < sigma-p bonding < pi-p bonding < pi-p antibonding < sigma-p antibonding.

However, for diatomic molecules of B, C, and N the pi-p bonding drops to a lower energy than the sigma-p bonding.

Bond Order

In Molecular orbital theory, the stability of a covalent bond is related to its bond order.

Bond Order = (1/2)(# bonding electrons - # antibonding electrons)

Bond order       Meaning
0                      no bond
1                      single bond
2                      double bond
3                      triple bond

Fractional (1/2; 3/2; 5/2) bond orders are possible.

Delocalized Molecular Orbitals

The properties of a molecule cannot always be explained accurately by a single structure. This has been previously explained by Resonance.

We can now explain this using delocalized molecular orbitals which are not confined between two adjacent bonding atoms, but actually extend over three or more atoms.

Molecules with delocalized molecular orbitals are generally more stable than those containing molecular orbitals extending over only two atoms.

Molecular properties

Molecular orbital theory correctly explains paramagnetism and diamagnetism of molecules along with the bond order.

Paramagnetism is the attractive magnetic force resulting from unpaired electrons in molecules.

Diamagnetism is a weak magnetic repulsion when only paired electrons are present.