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Molecular Orbital Theory

>> Parts of this equation/concept include:

A -	Molecular Orbital Diagrams >> Magnetism >> Bond Order

Molecular orbital theory is a different way of looking at bonding. It combines atomic orbitals into molecular orbitals. This chapter only looks at the molecular orbitals of homonuclear (same-atom) diatomic (two-atom) molecules of main group elements. With these molecules only atomic orbitals of the same type combine. That is, s orbitals with s orbitals and the p orbitals with p orbitals of the same orientation.

The atomic orbitals can combine in two ways. If the orbitals overlap on the bonding axis (head on), it will form a bond. If the orbitals meet on either side of the bonding axis (side-to-side), it will form a bond. The s orbitals and the p orbitals oriented along the z-axis will form bonds. The other two p orbitals will form bonds. See Figure 6.16.

It is traditional to graph the energy of the molecular orbitals in comparison to the atomic orbitals. When the two atomic orbitals are combined, they create two molecular orbitals. One of those molecular orbitals will be lower in energy than the atomic orbitals (bonding orbital) One will be higher in energy than the atomic orbitals (antibonding orbital). For all of the main group, homonuclear diatomic molecules, the molecular orbital diagram is show in Figure 6.19.

The number of valence electrons is determined as usual. The electrons will go into the lowest available orbital. If there are two degenerate orbitals, the electrons will go into each orbital before any electrons pair up.

>> Magnetism

If there are unpaired electrons in the molecular orbital diagram, the molecule is paramagnetic. If all electrons are paired, the molecule is diamagnetic.

>> Bond Order

The molecular orbital diagram can also be used to calculate bond order. (This is similar in idea to single, double, or triple bonds.)

Bond order = (bonding electrons – antibonding electrons)/2

Molecules with a higher bond order have shorter, stronger bonds and are more stable than molecules with a lower bond order.

>> Example 1

What is the molecular orbital diagram for O₂? Is it paramagnetic or diamagnetic? What is its bond order?

Solution:

Oxygen has six valence electrons. Therefore O₂ has 12 valence electrons. This is sufficient electrons to fill the _s (2 e), _s*( 2 e), _z (2 e), both (4 e) and one in each * (2 e) orbital.

The unpaired electrons in the * orbitals make the molecule paramagnetic. Bond order = (8 – 4)/2 = 2

>> Example 2

What is the molecular orbital diagram for C₂⁺? Is it paramagnetic or diamagnetic? What is its bond order?

Solution:

Carbon has four valence electrons. The C₂⁺ molecule has 4 + 4 – 1 = 7 electrons. This is sufficient to fill the _s (2 e), _s* (2 e), _z (2 e) and one electron in one orbital.

The unpaired electron in the orbital makes the molecule paramagnetic. Bond order = (5 – 2)/2 = 1.5

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