Vibrational excitations in H2O in the framework of a local model

The vibrational description of H2 16 O in terms of Morse local oscillators for both bending and stretching degrees of freedom is presented. Expansions of the kinetic and potential energies of the vibrational Hamiltonian are considered up to quartic terms. The local Morse coordinates yi as well as the momenta pi are thereafter expanded in terms of creation and annihilation operators of the Morse functions keeping terms up to order 1= ffiffiffi p (up to quadratic terms in the operators), where j is a parameter related with the depth of the potential. Only terms conserving the polyad are considered. The resulting Hamiltonian includes the known Darling– Dennison and Fermi-like interactions, but unlike the description in terms of a harmonic basis, all the force constants up to quartic order are involved. A tensorial formalism is developed to expand the Hamiltonian in powers of 1= ffiffiffi p in terms of symmetry adapted operators. An energy fit is carried out for 72 experimental energies up to 23 000 cm � 1 , obtaining an rms deviation of 5.00 cm � 1 . The force constants are determined and predictions for the isotopes H2 17 O, H2 18 O, D2 16 O, and T2 16 O are presented.