Model calculations of the vibrations of bonded water molecules

Model calculations have been made of the vibrational frequencies and normal modes of a water molecule vibrating in a combined internal and external field. A constant internal force field has been used together with an external central force field from four or three nearest-neighbour atoms to the water molecule. These neighbour atoms have been arranged either tetrahedrally or trigonally around the water molecule. The external force field has been further restricted by the use of five possible site symmetries for the water molecule, C_2v, C₂, C_s(σ_xz, C_s(σ_yz) and C₁. A series of calculations have been made where the external force constants have been varied within the range 1—80 Nm^?1.The nine calculated normal modes can be divided into three groups: intra-molecular, rotational and translational vibrations. Among the rotational vibrations it is found that, in the tetrahedral environment, the rocking mode occurs at lower frequencies than the twisting and wagging modes, whereas the opposite occurs for the trigonal environment. Frequency ratios have been calculated using the isotopic species H₂O, D₂O, HDO and H,¹⁸O. The twisting and wagging modes have the vH₂O/vD₂O ratio in the range 1.35-3-1.41 and the rocking mode in the range 1.26—1.41.