To calculate the wavenumber of the fundamental vibrational mode of carbon dioxide CO2 using Fourier transform infrared spectroscopy, we need to consider the symmetric stretching mode v1 , the bending mode v2 , and the asymmetric stretching mode v3 . However, the symmetric stretching mode v1 is not IR active, so we will focus on the bending mode v2 and the asymmetric stretching mode v3 .The wavenumbers for the bending mode v2 and the asymmetric stretching mode v3 are approximately 667 cm^-1 and 2349 cm^-1, respectively. These values are obtained from experimental data and can vary slightly depending on the sample and instrument used.So, the fundamental vibrational modes of carbon dioxide using Fourier transform infrared spectroscopy are approximately:- Bending mode v2 : 667 cm^-1- Asymmetric stretching mode v3 : 2349 cm^-1