The quadratic force field method is a computational approach used to determine the vibrational frequencies and infrared spectrum of a molecule. In the case of the water molecule H2O , we can use this method to calculate the vibrational frequencies and predict the infrared spectrum.To do this, we first need to determine the force constants for the water molecule. The force constants can be obtained from experimental data or quantum mechanical calculations. For simplicity, we will use the following force constants for the water molecule:k_OH = 1050 N/m O-H stretching k_HOH = 75 N/m H-O-H bending Next, we need to calculate the reduced masses for the O-H stretching and H-O-H bending vibrations. The reduced mass can be calculated using the formula: = m1 * m2 / m1 + m2 where m1 and m2 are the masses of the two atoms involved in the vibration. For the O-H stretching, m1 = m_O = 16 amu and m2 = m_H = 1 amu. For the H-O-H bending, m1 = m_O = 16 amu and m2 = m_H = 1 amu._OH = 16 * 1 / 16 + 1 = 0.941 amu_HOH = 16 * 1 / 16 + 1 = 0.941 amuNow, we can calculate the vibrational frequencies using the formula: = 1 / 2 * * k / For the O-H stretching:_OH = 1 / 2 * * 1050 N/m / 0.941 amu = 165.5 THzFor the H-O-H bending:_HOH = 1 / 2 * * 75 N/m / 0.941 amu = 44.3 THzFinally, to obtain the infrared spectrum, we can plot the vibrational frequencies against the infrared absorption intensities. The intensities can be calculated using the transition dipole moment and the change in the dipole moment during the vibration. The infrared spectrum of the water molecule will show two main peaks corresponding to the O-H stretching and H-O-H bending vibrations at 165.5 THz and 44.3 THz, respectively.