Rotation–Vibration Motion of Pyramidal XY 3 Molecules Described in the Eckart Frame: The Calculation of Intensities with Application to NH 3 (original) (raw)
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International Journal of Quantum Chemistry, 1991
An exact, within the Born-Oppenheimer approximation, body-fixed Hamiltonian for the nuclear motions of a triatomic system is presented. This Hamiltonian is expressed in terms of two arbitrarily defined internal distances and the angle between them. The body-fixed axis system is related to these coordinates in a general fashion. Problems with singularities and the domain of the Hamiltonian are discussed using specific examples of axis embedding. A number of commonly used coordinate systems including Jacobi, bond-length-bond-angle, and Radau coordinates are special cases of this Hamiltonian. Sample calculations on the HzS molecule are presented using all these and other coordinate systems. The possibility of using this Hamiltonian for reactive scattering calculations is also discussed.
International Reviews in Physical Chemistry
An approximate variational method based in the use of distributed Gaussian functions (DGF) and bond-length coordinates has been applied to study the rotation-vibration spectra of different triatomic molecules. In addition, an approach which employs hyperspherical coordinates (HC) and a basis set of hyperspherical harmonics constitutes a valid benchmark to test its capabilities. This work describes the technical details of both methods to provide the energies and symmetry of the corresponding rovibrational states and reviews their application to three different systems: For Ar 3 and Ne 3 the DGF technique exhibits a particularly good performance, but some limitations are observed for a more demanding scenario such as the H + 3 ion. The possible origin of these deficiencies are also discussed in detail.
A method for using a single Kindependent grid for problems where otherwise a basis of associated Legendre functions or the corresponding K-dependent grids would be employed, specific&y for calculating the rotational-vibrational energy Ievels of a triatomic molecule, has been described and tested. K independence has been achieved by the incorporation of the weight functions of associated Legendre functions into the Hamiltonian. Exact analytical expressions, valid for any DVR basis, of the matrix elements of the ro~tion-bending kinetic energy operator (in terms of scattering coordinates f have been given. Simple numerical tests demonstrate that this new method is a useful ahemative to the methods proposed so far.
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The Journal of Chemical Physics, 1997
A very efficient large-order perturbation theory is formulated for the nuclear motion of a linear triatomic molecule. To demonstrate the method, all of the experimentally observed rotational energies, with values of J almost up to 100, for the ground and first excited vibrational states of CO 2 and for the ground vibrational states of N 2 O and of OCS are calculated. All coupling between vibration and rotation is included. The perturbation expansions reported here are rapidly convergent. The perturbation parameter is D −1/2 , where D is the dimensionality of space. Increasing D is qualitatively similar to increasing the angular momentum quantum number J. Therefore, this approach is especially suited for states with high rotational excitation. The computational cost of the method scales only as JN 5/3 v , where N v is the size of the vibrational basis set.