Valence bond theory accounts, at least qualitatively, for the stability of the covalent bond in terms of overlapping atomic orbitals.

Using the concept of hybridization, valence bond theory can explain molecular geometries predicted by the VSEPR model.

However, the assumption that electrons in a molecule occupy atomic orbitals of the individual atoms can only be an approximation, since each bonding electron in a molecule must be in an orbital that is characteristic of the molecule as a whole.

But experiments have shown that the oxygen molecule is paramagnetic, with two unpaired electrons.

According to VB description, all the electrons in O2 are paired and the molecule should therefore be diamagnetic.

Molecular Orbital Theory

Molecular orbital theory describes covalent bonds in terms of molecular orbitals, which result from interaction of the atomic orbitals of the bonding atoms and are associated with the entire molecule.

The difference between a molecular orbital and an atomic orbital is that an atomic orbital is associated with only one atom.

Linear combination of atomic orbitals (LCAO) approximation. A ‘linear combination’ is a sum with various weighting coefficients.

In simple terms, we combine the atomic orbitals of contributing atoms to give molecular orbitals that extend over the entire molecule.

Only the valence shell atomic orbitals are used to form molecular orbitals.

Thus, the molecular orbitals of H2 are approximated by using two hydrogen 1s orbitals, one from each atom:

A basis set of orbitals is composed of those which are available for orbital interactions.

In this case the basis set, the atomic orbitals from which the molecular orbital is built, consists of two H1s orbitals, one on atom A and the other on atom B.

The coefficients c in the linear combination show the extent to which each atomic orbital contributes to the molecular orbital:

Because H2 is a homonuclear diatomic molecule (cA2 = cB

2)

cA =+cB or cA =− cB

The two molecular orbitals are

The orbital + is an example of a bonding orbital: the energy of the molecule is lowered relative to that of the separated atoms if this orbital is occupied by electrons.

The orbital − is an example of an antibonding orbital. It is so-called because, if it is occupied, the energy of the molecule is higher than for the two separated atoms.

molecular orbital energy level diagram, a diagram depicting the relative energies of molecular orbitals.

Each MO arises from interactions between orbitals of atomic centres in the molecule, and such interactions are:

efficient if the region of overlap between the two atomic orbitals is significant;

allowed if the symmetries of the atomic orbitals are compatible with one another;

efficient if the atomic orbitals are relatively close in energy.

Homonuclear diatomic molecules

Absorption spectroscopy are used to study diatomic molecules.

Ultraviolet photoelectron spectroscopy (UPS) in which electrons are ejected from the orbitals they occupy in molecules and their energies determined.

(a) The orbitals

We are concerned predominantly with outer-shell valence orbitals, rather than core orbitals.

Minimal basis set, the smallest set of atomic orbitals from which useful molecular orbitals can be built.

A orbital can be formed in several ways, including s,s overlap, s,p overlap, and p,p overlap, with the p orbitals directed along the internuclear axis.

Two p orbitals can overlap to form a orbital. The orbital has a nodal plane passing through the internuclear axis, shown here from the side.

This pattern of overlap gives rise to the two pairs of doubly degenerate energy levels (two energy levels of the same energy)

The operation of inversion consists of starting at an arbitrary point in the molecule, travelling in a straight line to the centre of the molecule, and then continuing an equal distance out on the other side of the centre.

And u (for ungerade, odd) if it changes sign.

The orbital is designated g (for gerade, even) if it is identical under inversion

(a) Bonding and (b) antibonding interactions with the arrow indicating the inversion.

(a) Bonding and (b) antibonding interactions with the arrow indicating the inversions.

The molecular orbital energy level diagram for the later Period 2 homonuclear diatomic molecules. This diagram should be used for O2 and F2.

To establish the actual location of the energy levels, it is necessary to use electronic absorption spectroscopy, photoelectron spectroscopy, or detailed computation.

The molecular orbital energy level diagram for Period 2 homonuclear diatomic molecules from Li2 to N2.

The reversal of order can be traced to the increasing separation of the 2s and 2p orbitals that occurs on going to the right across Period 2.

When the s,p energy separation is small, each molecular orbital is a mixture of s and p character on each atom.

A general principle of quantum mechanics is that the mixing of wavefunctions is strongest if their energies are similar

mixing is not important if their energies differ by more than about 1 eV.

As the s and p energy separation increases, the molecular orbitals become more purely s-like and p-like

The bond order indicates the strength of a bond.

Predict the order of stability of H2+, H2, He2

+, and He2

The variation of orbital energies for Period 2 homonuclear diatomic molecules from Li2 to F2

(b) The building-up principle for molecules

Molecular orbital configurations

For example, the electron configuration of N2, with 10 valence electrons, is

The highest occupied molecular orbital (HOMO) is the molecular orbital that, according to the building-up principle, is occupied last.

The lowest unoccupied molecular orbital (LUMO) is the next higher molecular orbital.

Frontier orbitals, the LUMO and the HOMO

The term SOMO, denoting a singly occupied molecular orbital

2.9 Heteronuclear diatomic molecules

In heteronuclear diatomic molecules, the more electronegative element makes the larger contribution to bonding orbitals and

The less electronegative element makes the greater contribution to the antibonding orbitals.

(a) Heteronuclear molecular orbitals

(b) Hydrogen fluoride

In hydrogen fluoride the bonding orbital is more concentrated on the F atom and the antibonding orbital is more concentrated on the H atom.

The molecular orbital energy level diagram for HF. The relative positions of the atomic orbitals reflect the ionization energies of the atoms.

It is possible to generate a molecular orbital that has the same energy as the initial atomic orbitals. In this case, occupation of this orbital neither stabilizes nor destabilizes the molecule and so it is described as a nonbonding orbital.

No centre of inversion in a heteronuclear diatomic molecule

Nonbonding orbital is a molecular orbital that consists of a single orbital on one atom, perhaps because there is no atomic orbital of the correct symmetry for it to overlap on a neighbouring atom.

(c) Carbon monoxide

Both atoms have 2s and 2p orbitals that can participate in the formation of and orbitals.

The ground-state configuration is

The 1 orbital is localized mostly on the O atom and essentially nonbonding.

The 2 orbital is bonding

A schematic illustration of the molecular orbitals of CO, with the size of the atomic orbital indicating the magnitude of its contribution to the molecular orbital.

The HOMO in CO is 3, which is predominantly C2pz in character, largely nonbonding, and located on the C atom.

The LUMO is the doubly degenerate pair of antibonding orbitals, with mainly C2p orbital character

2.10 Bond properties

(a) Bond order

The bond order assesses the net number of bonds between two atoms in the molecular orbital formalism; the greater the bond order between a given pair of atoms, the greater the bond strength.

Isoelectronic molecules and ions have the same bond order, so F2 and O2 2− both have bond order 1. The bond order of the CO molecule, like that of the isoelectronic molecule N2, is 3

(b) Bond correlations

Bond enthalpy increases as bond order increases.

Bond length decreases as bond order increases.

Bond enthalpy increases as bond length decreases.

Structure and bond properties

The equilibrium bond length in a molecule is the separation of the centres of the two bonded atoms; covalent radii vary through the periodic table in much the same way as metallic and ionic radii.

It obtained by X-ray diffraction on solids.

Equilibrium bond lengths of molecules in the gas phase are usually determined by infrared or microwave spectroscopy, or more directly by electron diffraction.

Equilibrium bond lengths, Re /pm

The contribution of an atom to a covalent bond is called the covalent radius of the element

Covalent radii, rcov /pm*

A covalent radius expresses the closeness of approach of bonded atoms

The van der Waals radius of the element, which is the internuclear separation when the valence shells of the two atoms are in nonbonding contact

A convenient thermodynamic measure of the strength of an AB bond is the bond dissociation enthalpy, Ho(A-B), the standard reaction enthalpy for the process

The mean bond enthalpy, B, is the average bond dissociation enthalpy taken over a series of A−B bonds in different molecules

2.14 Bond strength

Mean bond enthalpies, B/(kJ mol−1)*

2.15 Electronegativity and bond enthalpy

Linus Pauling’s original formulation of electronegativity drew on concepts relating to the energetics of bond formation. For example, in the formation of AB from the diatomic A2 and B2 molecules,

He argued that the excess energy, ΔE, of the A-B bond over the average energy of A-A and B-B bonds can be attributed to the presence of ionic contributions to the covalent bonding.

He defined the difference in electronegativity as

Thus, if the A-B bond enthalpy is significantly greater than the average of the nonpolar A-A and B-B bonds, then it is presumed that there is a substantial ionic contribution to the wavefunction and hence a large difference in electronegativity between the two atoms.

2.16 Oxidation states

The oxidation number, Nox, is a parameter obtained by exaggerating the ionic character of a bond.

The oxidation state is the physical state of the element corresponding to its oxidation number.

Thus, an atom may be assigned an oxidation number and be in the corresponding oxidation state.