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A different approach for calculating the zero angular momentum, vibrational energy levels of polyatomic molecules was implemented for H2O. The special features of this approach are that, even for arbitrarily large amplitudes of vibration, all operators in the Hamiltonian are easily evaluated analytically, there are no pathological singularities, angular momentum is rigorously decoupled, and the variables are a mixture of two curvilinear and 3N-8 Cartesian coordinates. As a demonstration of the approach, a full variational calculation was done and the results are compared with a prior result based on the Watson Hamiltonian. Although the two Hamiltonians appear to be very different and although two different computational methods were employed, the results of the two independent calculations were virtually identical for the lowest 14 vibrational states of H2O. Compared to the conventional normal coordinate formalism, the kinetic energy operator contains products of anti-Hermitian operators and these ‘‘extra’’ terms are found to change the vibrational frequencies by tens of wave numbers. [ABSTRACT FROM AUTHOR]