Carbon dioxide CO2 is a linear molecule with three vibrational modes: symmetric stretching, bending, and asymmetric stretching. The quantum mechanical approach to determine the vibrational frequencies and infrared spectrum involves solving the Schrödinger equation for the vibrational motion of the molecule.Using the quantum mechanical approach, the vibrational frequencies for CO2 are calculated as follows:1. Symmetric stretching v1 : ~1286 cm^-12. Bending v2 : ~667 cm^-13. Asymmetric stretching v3 : ~2349 cm^-1These values are approximate and may vary depending on the specific method used for calculation.The infrared spectrum of CO2 consists of peaks corresponding to the vibrational frequencies. However, due to the selection rules in infrared spectroscopy, only the bending mode v2 and the asymmetric stretching mode v3 are active, meaning they can be observed in the infrared spectrum. The symmetric stretching mode v1 is not active and does not appear in the spectrum.When comparing the calculated vibrational frequencies to experimental data, there is generally good agreement. The experimental values for the vibrational frequencies of CO2 are:1. Symmetric stretching v1 : ~1286 cm^-12. Bending v2 : ~667 cm^-13. Asymmetric stretching v3 : ~2349 cm^-1These values are close to the calculated values, indicating that the quantum mechanical approach provides a reasonably accurate description of the vibrational frequencies and infrared spectrum of CO2. However, more advanced computational methods and inclusion of anharmonic effects can further improve the accuracy of these calculations.