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Coordinates are introduced which are irreducible representations of the permutation–inversion group. For triatomic molecules these become essentially hyperspherical coordinates. The system can thus be regarded as a hyperspherical coordinate system for the three identical atoms augmented by coordinates for the remaining atoms symmetry adapted to the environment of the three identical atoms. [ABSTRACT FROM AUTHOR]

Relative coordinates convenient for variational calculations are discussed. The coordinates, for suitable representations of the potential, allow matrix elements to be expressed as sums of products of one-dimensional integrals for product basis functions. A small vibration limit is reviewed in these coordinates. Examples are given for application to the linear triatomic, water, ammonia, acetylene, and finally methane. [ABSTRACT FROM AUTHOR]

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]

The eigenstates of the hydrogen molecule ion have been determined by a variational calculation without resorting to the Born–Oppenheimer or adiabatic approximations. A Slater-type orbital basis in terms of perimetric coordinates was used and the eigenvalues were obtained by diagonalizing a 300×300 matrix. Computational techniques and numerical stability tests are described. Because of the relatively small basis and the large number of bound states, most of the eigenvalues were sensitive to the basis set. With a basis which favored the upper states, 18 bound states were obtained in a single diagonalization vs 20 bound states in the adiabatic approximation. With the best basis for the ground state, the eigenvalues of the six lowest levels were 1 to 3×10-6 a.u. lower than adiabatic calculations and the differences appear to increase with increasing vibrational quantum number. [ABSTRACT FROM AUTHOR]