Short Answer

Bond order according to MO theory tells how strong and stable a bond is by comparing the number of electrons in bonding molecular orbitals and antibonding molecular orbitals. It is calculated using a simple formula that subtracts antibonding electrons from bonding electrons and divides the result by two.

A higher bond order means a stronger and shorter bond, while a bond order of zero means the molecule is not stable. MO theory helps explain bond order in molecules such as H₂, N₂, O₂, and even ions like O₂⁻ and O₂²⁻.

Detailed Explanation :

Bond Order According to MO Theory

Bond order is an important concept in molecular orbital (MO) theory that helps determine the strength, length, and stability of a chemical bond. Instead of thinking about shared electrons between two atoms (as in valence bond theory), MO theory considers how electrons occupy molecular orbitals that extend over the entire molecule. By analyzing the number of electrons present in bonding and antibonding orbitals, we can calculate a bond order value that reflects how strong or weak the bond is.

MO theory gives a clearer and more accurate description of bonding because it includes antibonding orbitals, electron distribution, and magnetic behavior. This theory is especially useful for analyzing molecules that cannot be explained easily by simple Lewis structures, such as O₂ being paramagnetic.

1. Definition of Bond Order in MO Theory

Bond order describes the net bonding effect in a molecule. According to MO theory, electrons in:

• Bonding orbitals stabilize the molecule
• Antibonding orbitals destabilize the molecule

Bond order measures how many bonds effectively exist between atoms.

The formula is:

A positive bond order means the molecule is stable enough to exist.
A bond order of zero means there is no bonding and the molecule cannot exist in stable form.

2. Meaning of Bond Order Values

Bond order indicates:

• Bond strength — higher bond order = stronger bond
• Bond length — higher bond order = shorter bond
• Bond stability — higher bond order = more stable molecule

Examples:

• Bond order 3 → very strong (as in N₂)
• Bond order 2 → strong (O₂)
• Bond order 1 → moderate (H₂)
• Bond order 0 → no stable molecule (He₂)

Bond order also helps predict reactivity and magnetic properties.

3. How Bond Order Is Calculated

To find bond order, follow these steps:

1. Write the molecular orbital configuration.
2. Count electrons in bonding orbitals (σ, π).
3. Count electrons in antibonding orbitals (σ*, π*).
4. Use the formula.

Example: H₂

• Bonding electrons = 2
• Antibonding electrons = 0

Bond order = (2 – 0) / 2 = 1

This means H₂ has a single, stable bond.

4. Examples of Bond Order Using MO Theory

(a) N₂ Molecule

N₂ has a bond order of 3.

This explains:

• Its triple bond
• Very high bond strength
• Very short bond length
• Chemical inertness

(b) O₂ Molecule

O₂ has a bond order of 2, meaning a double bond.
MO theory also shows two unpaired electrons in π* orbitals, explaining paramagnetism.

(c) He₂ Molecule

Bonding electrons = 2, antibonding = 2
Bond order = (2 – 2)/2 = 0

So He₂ is not stable.

(d) O₂⁻ (Superoxide Ion)

One extra electron fills an antibonding orbital.
Bond order drops to 1.5, showing weaker bonding than O₂.

(e) O₂²⁻ (Peroxide Ion)

Two extra electrons go into antibonding orbitals.
Bond order becomes 1, meaning a single bond.

These examples show how MO theory explains variations in bonding.

5. Importance of Bond Order in Chemistry

Bond order helps predict:

• Bond strength
• Bond length
• Chemical reactivity
• Stability of ions and radicals
• Magnetic properties

MO theory gives results that match experimental observations more accurately than simple models.

For instance:

• O₂ is paramagnetic because MO theory shows unpaired electrons in π* orbitals.
• N₂ is very stable because it has a high bond order.
• Peroxide bonds are weaker than oxygen’s double bond because of lower bond order.

6. Bond Order and Molecular Properties

Bond order affects measurable physical properties:

(a) Bond Length

Higher bond order → shorter bond
Example:
N₂ (bond order 3) has one of the shortest known bonds.

(b) Bond Energy

Higher bond order → more energy required to break the bond.

(c) Magnetic Nature

Unpaired electrons in antibonding orbitals cause paramagnetism.
Bond order alone does not determine magnetism, but MO diagrams used to calculate bond order reveal it.

Conclusion

Bond order according to MO theory is a measure of the strength and stability of a chemical bond. It is calculated by comparing the number of electrons in bonding and antibonding orbitals. A higher bond order indicates a stronger and shorter bond, while a bond order of zero means that no stable molecule can form. MO theory provides an accurate explanation of bond properties, magnetic behavior, and stability of molecules and ions, making it an essential tool in modern chemistry.