Changing the mass of the atoms in a molecule affects its vibrational frequencies and infrared spectra because the vibrational frequencies are directly related to the masses of the atoms and the force constants of the bonds between them. According to Hooke's law, the vibrational frequency of a diatomic molecule can be expressed as: = 1/2 * k/ where k is the force constant of the bond and is the reduced mass of the two atoms, which is given by: = m1 * m2 / m1 + m2 where m1 and m2 are the masses of the two atoms.As the mass of the atoms in a molecule changes, the reduced mass will also change, which in turn affects the vibrational frequencies. This change in vibrational frequencies will be reflected in the infrared spectra, as the positions of the absorption bands will shift.Quantum chemistry calculations can be used to predict these changes in vibrational frequencies and infrared spectra. One common approach is to use computational methods based on quantum mechanics, such as density functional theory DFT or ab initio methods like Hartree-Fock or post-Hartree-Fock methods e.g., MP2, CCSD T . These methods allow for the calculation of the potential energy surface of a molecule, which can then be used to determine the vibrational frequencies and infrared spectra.In these calculations, the molecular geometry is optimized, and the Hessian matrix second derivatives of the potential energy with respect to atomic coordinates is computed. Diagonalization of the Hessian matrix yields the vibrational frequencies and normal modes of the molecule. The intensities of the infrared absorption bands can also be calculated using the dipole moment derivatives with respect to the normal modes.By performing these quantum chemistry calculations for different isotopologues molecules with different isotopes of the same element or isotopomers molecules with isotopes in different positions , one can predict how the vibrational frequencies and infrared spectra will chas a fution of the mass of the atoms in the molecule. This information can be useful for interpreting experimental infrared spectra and for understanding the effects of isotopic substitution on molecular properties.