Carbon dioxide CO2 is a linear molecule with a central carbon atom double-bonded to two oxygen atoms. It has a total of 4 vibrational modes, but only 3 of them are unique due to its linear geometry. These 3 unique vibrational modes are called normal modes of vibration and are characterized by their frequencies and the type of motion involved. They are as follows:1. Symmetric Stretch 1 : This mode has a frequency of approximately 1330 cm. In this mode, both oxygen atoms move symmetrically towards and away from the central carbon atom along the molecular axis. Since the motion is symmetrical, there is no change in the dipole moment of the molecule, and this mode is considered to be infrared inactive.2. Bending 2 : This mode has a frequency of approximately 667 cm. In this mode, the molecule bends in a plane, with the carbon atom remaining stationary while the two oxygen atoms move in and out of the plane. This motion changes the dipole moment of the molecule, making it infrared active.3. Asymmetric Stretch 3 : This mode has a frequency of approximately 2349 cm. In this mode, one oxygen atom moves towards the central carbon atom while the other moves away from it, causing an asymmetric stretching motion. This motion also changes the dipole moment of the molecule, making it infrared active.In summary, the vibrational frequencies of carbon dioxide are related to its molecular geometry through the types of motion involved in each mode. The symmetric stretch is a result of the linear arrangement of atoms, while the bending and asymmetric stretch modes are due to the presence of two oxygen atoms bonded to the central carbon atom. The infrared activity of these modes is determined by whether the motion causes a change in the dipole moment of the molecule.