Topic: Concept of Molecular orbital theory, symmetry elements and their correlation

 

Topic: "Concept of Molecular orbital theory, symmetry elements and their correlation"

Introduction:

Molecular orbital theory (MOT) is a fundamental concept in chemistry that helps in understanding the electronic structure and bonding of molecules. Symmetry elements and symmetry operations are integral to the theory of molecular symmetry, which plays a critical role in determining the molecular properties. This article explores the relationship between molecular orbital theory and symmetry elements and symmetry operations.

Bonding and Anti-Bonding Molecular Orbitals:

Molecular orbitals are formed by the combination of atomic orbitals of individual atoms in a molecule. The formation of molecular orbitals can lead to the creation of bonding and anti-bonding molecular orbitals. Bonding molecular orbitals are formed by the constructive overlap of atomic orbitals, whereas anti-bonding molecular orbitals result from the destructive overlap of atomic orbitals. The relative energies of these molecular orbitals play a crucial role in determining the stability and reactivity of a molecule.

Aufbau Principle:

Aufbau principle states that electrons fill the lowest energy molecular orbitals first, following a specific order of energy levels.

Hund's Rule:

Hund's rule states that electrons prefer to occupy separate orbitals of the same energy level, with their spins parallel.

Pauli Exclusion Principle:

The Pauli exclusion principle states that no two electrons in a molecule can have the same set of four quantum numbers.

Here are some keypoints for MOT;

• The atomic orbitals combine (overlap) to form a new orbital known as molecular orbital.
• An M.O gives electron probability distribution around a group of nuclei.
• Only those A.Os are combined to form M.Os which have comparable energy, and orientations
• The no. of M.Os formed are equal to the no. of A.Os combined.
• When two A.Os combine, they form two M.Os known as bonding molecular orbital (B.M.O) and antibonding molecular orbital (A.M.O).
• The, B.M.O has lower energy and hence greater stability than the corresponding A.M.O.
• The shapes of molecular orbitals depends upon the type of combining atomic orbitals.
• The filling of M.Os takes place by same rule as for atomic orbitals. Like they follow, Aufbau, Pauli exclusion, and Hund'e rule.

 Origin of MOT-Symmetry correlation:

·         Évariste Galois (1811-1832) is the founder of group theory.

·         Woodward and Hoffmann discussed the nature of the highest occupied molecular orbitals (HOMO).

·   Longuet-Higgins and Abrahamson fromalised the concepts of Galois & Woodward together into orbital correlation diagram.

·         Group theoretical symmetries of the reactant and product orbitals matched exactly. 

·         Set basis for concepts of transition state aromaticity and frontier orbitals approach.

Symmetry Elements and Symmetry Operations:

Symmetry elements are the specific features of a molecule that can be used to identify its symmetry. The various symmetry elements include identity (E), axis of rotation (C_n), reflection (σ), inversion (i), plane of symmetry (σ_h), center of symmetry (i), improper axis of rotation (S_n), and proper symmetry (C_n).

Symmetry operations are the transformations that leave the molecule unchanged. These include rotation, reflection, inversion, and combinations of these operations.

N-fold axis:

If rotation through an angle of 360°/n about an axis of symmetry leaves the molecule in an indistinguishable condition, it is said to have an n-fold axis.

NH₃: Rotation by 120^o in a clockwise or counterclockwise direction provide two different orientations of the molecule.

b) Plane of Symmetry

A plane of symmetry is an imaginary plane that bisects a molecule into halves that are mirror images of each other.

The reflection of the water molecule in either of its two mirror planes results in a molecule that looks unchanged. e.g H₂O

c) Center of symmetry/Inversion of Symmetry

We proceed to identify centre of symmetry as following

1. Choose a centre within the molecule.
2. Draw lines in the direction where the atoms are located.
3. If the same atom in equal and opposite direction is seen, true for every situation, than the molecule possesses a centre of symmetry or inversion of symmetry.

The inversion operation projects each atom through the center of inversion, and across to the other side of the molecule.

d) Improper axis of rotation

An improper rotation is rotation, followed by reflection in the plane perpendicular to the axis of rotation. 

                        S_n = C_n * i = i * C_n

Thus, both independent symmetry operations commute. Essentially C_n is perpendicular to σ.

Principal axis:

A molecular orbital may contain several axes like C₃¹, C₃², 3C₂. Among them, highest order axis is known as principal axis. Here is the example of BF3

The identity E and rotations C_n are symmetry operations that could actually be carried out on a molecule. For this reason they are called proper symmetry operations. While reflections, inversions and improper rotations can only be imagined (it is not actually possible to turn a molecule into its mirror image or to invert it without some fairly drastic rearrangement of chemical bonds) and as such, are termed improper symmetry operations.

 

Relationship between MOT and Symmetry Elements:

Symmetry elements and operations play a crucial role in the formation of molecular orbitals. In symmetric molecules, the molecular orbitals formed by the combination of atomic orbitals exhibit symmetry, which can be described by the symmetry elements of the molecule. The symmetry of the molecular orbitals determines their degeneracy, i.e., whether they have the same energy or not. In symmetric molecules, the bonding and anti-bonding molecular orbitals may have different energies, leading to an increase or decrease in the stability of the molecule.

Conclusion:

Molecular orbital theory and symmetry elements and operations are intertwined concepts that help in understanding the electronic structure and bonding of molecules. The bonding and anti-bonding molecular orbitals, along with the Aufbau principle, Hund's rule, and Pauli Exclusion Principle, play a crucial role in determining the stability and reactivity of a molecule. The symmetry elements and operations of a molecule determine the symmetry of the molecular orbitals, which, in turn, affects the stability of the molecule. Therefore, the understanding of these concepts is essential for predicting the properties of molecules and designing new compounds.