Introduction:

Pyridine is a heterocyclic aromatic compound composed of a pyridine ring, which consists of six carbon atoms and one nitrogen atom. It is known for its basicity and aromaticity. In order to determine the number of OR (out-of-plane) active vibrational modes of pyridine, we need to consider its molecular structure and symmetry.

Pyridine Structure:

Pyridine has a planar structure due to the sp2 hybridization of the carbon and nitrogen atoms. The nitrogen atom donates a lone pair of electrons into the π system, making it a basic heteroatom. The pyridine ring possesses symmetry elements, such as a C6 rotation axis perpendicular to the plane of the ring and a σh plane that bisects the molecule.

Symmetry Considerations:

The number of OR active vibrational modes can be determined by considering the symmetry of the molecule. In the case of pyridine, we need to analyze its irreducible representations (IRs) under the symmetry operations.

Application of Group Theory:

Group theory is a mathematical tool used to analyze the symmetry properties of molecules. By applying group theory, we can determine the IRs of different vibrational modes and their activity under various symmetry operations.

Steps to Determine OR Active Vibrational Modes:

1. Identify the point group: The point group of pyridine is C6h, which has the following symmetry elements: identity (E), six C6 rotation axes (C6), six C2 rotation axes perpendicular to the C6 axes (C2), six σh planes, and a σv plane.

2. Construct the character table: The character table provides information about the IRs and their transformations under different symmetry operations. By analyzing the character table for the C6h point group, we can determine the IRs of the vibrational modes.

3. Determine the IRs of the vibrational modes: The vibrational modes of pyridine can be classified into different IRs based on their symmetry properties. In the case of OR active modes, the IRs must contain the irreducible representation ΓOR.

4. Determine the number of OR active vibrational modes: Count the number of vibrational modes corresponding to the irreducible representation ΓOR. This will give us the total number of OR active modes.

Conclusion:

In conclusion, the number of OR active vibrational modes of pyridine can be determined by applying group theory and considering the symmetry properties of the molecule. By analyzing the character table for the C6h point group, we can identify the IRs of the vibrational modes and count the number of OR active modes. The exact number will depend on the specific character table used and the calculations performed.