To calculate the vibrational frequency and infrared spectrum of a water molecule H2O using quantum chemistry calculations, we need to follow these steps:1. Choose a suitable quantum chemistry method: There are several quantum chemistry methods available, such as Hartree-Fock HF , Density Functional Theory DFT , and post-Hartree-Fock methods like Mller-Plesset Perturbation Theory MP2 and Coupled Cluster CC . For this problem, we can use DFT, which provides a good balance between accuracy and computational cost.2. Select a basis set: Basis sets are mathematical functions used to describe the molecular orbitals. Common basis sets include STO-3G, 6-31G, and 6-311G. For this problem, we can use the 6-31G basis set, which provides a reasonable level of accuracy.3. Perform geometry optimization: Geometry optimization is the process of finding the minimum energy structure of the molecule. This can be done using a quantum chemistry software package like Gaussian, ORCA, or Psi4. The optimized geometry will provide the equilibrium bond lengths and angles of the water molecule.4. Calculate vibrational frequencies: Once the optimized geometry is obtained, the software can calculate the vibrational frequencies and normal modes of the molecule. This is done by computing the Hessian matrix, which is the second derivative of the energy with respect to atomic displacements. The eigenvalues and eigenvectors of the Hessian matrix correspond to the vibrational frequencies and normal modes, respectively.5. Determine the infrared spectrum: The infrared spectrum can be obtained from the calculated vibrational frequencies and normal modes. The intensity of each vibrational mode in the infrared spectrum is proportional to the square of the transition dipole moment, which can be computed using the software.For a water molecule, there are three vibrational modes: one symmetric stretch, one asymmetric stretch, and one bending mode. The vibrational frequencies for these modes are approximately:- Symmetric stretch: ~3650 cm^-1- Asymmetric stretch: ~3755 cm^-1- Bending mode: ~1595 cm^-1These values can vary slightly depending on the chosen method and basis set. The infrared spectrum of water will show three peaks corresponding to these vibrational frequencies, with the intensities determined by the transition dipole moments.