To determine the vibrational frequencies and corresponding infrared spectra for a water molecule H2O using quantum chemistry calculations, we will follow these steps:1. Choose a suitable quantum chemistry method and basis set.2. Perform the geometry optimization of the water molecule.3. Calculate the vibrational frequencies and normal modes.4. Analyze the results and explain the observed peaks in the IR spectra in terms of the vibrational modes of the molecule.Step 1: Choose a suitable quantum chemistry method and basis setFor this problem, we will use the Density Functional Theory DFT method with the B3LYP functional, which is a popular choice for calculating molecular properties. For the basis set, we will use the 6-31G d basis set, which provides a good balance between accuracy and computational cost.Step 2: Perform the geometry optimization of the water moleculeUsing the chosen method and basis set, we will perform a geometry optimization of the water molecule to find its minimum energy structure. The optimized geometry will have an O-H bond length of approximately 0.96 and an H-O-H bond angle of approximately 104.5.Step 3: Calculate the vibrational frequencies and normal modesWith the optimized geometry, we can now calculate the vibrational frequencies and normal modes of the water molecule. The calculation will yield three vibrational frequencies, as a non-linear molecule with N atoms has 3N-6 vibrational modes 3*3-6 = 3 modes for water .Step 4: Analyze the results and explain the observed peaks in the IR spectra in terms of the vibrational modes of the moleculeThe calculated vibrational frequencies for the water molecule are approximately:1. 1 3650 cm symmetric O-H stretching 2. 2 1595 cm bending or scissoring 3. 3 3755 cm asymmetric O-H stretching The symmetric O-H stretching mode 1 is IR inactive due to its lack of change in the molecular dipole moment during the vibration. Therefore, it will not show a peak in the IR spectrum.The bending mode 2 involves the in-plane bending of the H-O-H angle and results in a change in the molecular dipole moment. This mode is IR active and will show a peak in the IR spectrum at around 1595 cm.The asymmetric O-H stretching mode 3 also results in a change in the molecular dipole moment and is IR active. It will show a peak in the IR spectrum at around 3755 cm.In summary, the observed peaks in the IR spectra of the water molecule can be explained by the bending mode 2 at around 1595 cm and the asymmetric O-H stretching mode 3 at around 3755 cm. The symmetric O-H stretching mode 1 does not show a peak in the IR spectrum due to its IR inactivity.