A self-consistent field optimization of the vibrational coordinates for nonlinear triatomic molecules is presented. The optimal coordinates are obtained by making a three-dimensional rotational transformation of the normal modes and determining the rotation angles as those for which the SCF energy is stationary. The utility of the optimized coordinates in full variational calculations of vibrational energies is studied for the molecules of H20, 0 3 , HzD', HzT', and DzT'. For HzO and 0 3 , the optimization procedure leads to the local mode representation. It is shown that the use of the optimal coordinates in variational calculations allows a large reduction of the dimension of the Hamiltonian matrix to be diagonalized in order to reach convergence.
Several recursion relations connecting Kratzer oscillator matrix elements of different operators are derived using the hypervirial theorem. These relations can be easily used to calculate such matrix elements, either numerically or by developing analytical expressions. In particular, analytical expressions for the matrix elements of the xα and xαd/dx operators, where x is an internuclear separation coordinate, are obtained.
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