Molecular Orbital Theory

Molecular orbital theory (MO theory) explains chemical bonding that accounts for the paramagnetism of the oxygen molecule. It also explains the bonding in several other molecules, such as violations of the octet rule and more molecules with more complicated bonding that are difficult to describe with Lewis structures. Additionally, it provides a model for describing the energies of electrons in a molecule and the probable location of these electrons.

The table given below explains the major differences between the valence bond theory and molecular orbital theory.

Molecular orbital theory describes the distribution of electrons in molecules in much the same way that the distribution of electrons in atoms is described using atomic orbitals. Using quantum mechanics, the behavior of an electron in a molecule is still described by a wave function, Ψ, analogous to the behavior in an atom. Just like electrons around isolated atoms, electrons around atoms in molecules are limited to discrete (quantized) energies. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital (Ψ²). Like an atomic orbital, a molecular orbital is full when it contains two electrons with opposite spin.

We will consider the molecular orbitals in molecules composed of two identical atoms (H₂ or Cl₂, for example). Such molecules are called homonuclear diatomic molecules. In these diatomic molecules, several types of molecular orbitals occur.

The mathematical process of combining atomic orbitals to generate molecular orbitals is called the linear combination of atomic orbitals (LCAO). The wave function describes the wavelike properties of an electron. Molecular orbitals are combinations of atomic orbital wave functions. Combining waves can lead to constructive interference, in which peaks line up with peaks, or destructive interference, in which peaks line up with troughs as shown in the figure below. In orbitals, the waves are three-dimensional, and they combine with in-phase waves producing regions with a higher probability of electron density and out-of-phase waves producing nodes, or regions of no electron density.

(a) When in-phase waves combine, constructive interference produces a wave with greater amplitude. (b) When out-of-phase waves combine, destructive interference produces a wave with less (or no) amplitude.

Recommended topic video on (Molecular orbital theory)

Some Solved Examples

Example 1: During the formation of a molecular orbital from atomic orbital, the electron density is :

1)Minimum in the nodal place

2)Maximum in the nodal place

3) Zero in the nodal place

4)Zero on the surface of the lobe

Solution

Nodal planes are regions around atomic nuclei where the probability of finding an electron is zero.

For example, see in the p-orbitals

Hence, option C is correct.

Example 2: The stability of molecular orbital is:

1)Less than atomic orbitals

2) More than atomic orbitals

3)Can’t be predicted

4)None of these.

Solution

The number of molecular orbitals formed is equal to the number of combining atomic orbitals. When two atomic orbitals combine, two molecular orbitals are formed. One is known as a bonding molecular orbital while the other is called an antibonding molecular orbital.
Hence, the answer is the option (1).

Example 3: The number of molecular orbitals is:

1) Equal to the number of combining atomic orbitals.

2)Not equal to the number of combining atomic orbitals.

3)Equal to twice the number of combining atomic orbitals.

4)None of these.

Solution

The number of molecular orbitals formed is equal to the number of combining atomic orbitals. When two atomic orbitals combine, two molecular orbitals are formed. One is known as a bonding molecular orbital while the other is called an antibonding molecular orbital.
Hence, the answer is the option (1).

Example 4: Of the species $\mathrm{NO}, \mathrm{NO}^{+}, \mathrm{NO}^{2+}$ NO,NO+,NO2+ and $\mathrm{NO}^{-}$NO− the one with the minimum bond strength is

1)NO⁺NO+
2) NO
3)NO²⁺NO2+
4)NO^-NO−

Solution

Bond order of NO²⁺ = 2.5
Bond order of NO⁺ = 3
Bond order of NO = 2.5
Bond order of NO^- = 2

Bond order $\propto$ ∝ bond strength

Thus, NO^- has the minimum bond strength.

Hence, the answer is the option (4).

Summary

The molecular geometry is a three-dimensional arrangement of atoms in a molecule. It is decided by the spatial distribution of electron pairs around the central atom. The VSEPR theory predicts this geometry by minimizing electron pair repulsion. The key factors are bonding pairs, lone pairs, and bond types. The common shapes are linear, bent, trigonal planar, tetrahedral, trigonal bipyramidal, and octahedral. For example, CO₂ is linear, while NH₃ has a trigonal pyramidal geometry due to a lone pair at nitrogen.