Rotational-vibrational energy levels

Ding, S.-L., and Yi, X-Z. (1990), Algebraic Approach to the Rotation-Vibration Energy Levels for Diatomic Molecules, Chinese J. Atom. Mol. Phys. 7,1861. 

Jensen, P. (1983), The Nonrigid Bender Hamiltonian for Calculating the Rotation-Vibration Energy Levels of a Triatomic Molecule, Comp. Phys. Rep. 1,1. 

Yi, Xi-Zhang, Ding, Shi-liang and Deng, Cong-hao (1988), Lie Algebraic Approach to the Rotation-Vibrational Energy Levels for a Non-Linear Triatomic Molecule X3, Chinese J. Chem. Phys. 1, 255. 

The Raman spectra are quicker and easier to determine than the infrared absorption spectra because ordinary optical equipment can be used, but frequently they are more difficult to interpret. The quantum restrictions in the two phenomena, particularly for symmetrical molecules, are not always the same, because the Raman spectrum involves an intermediate excited state of the molecule. For this reason, it is desirable to have the data of both Raman and infrared absorption spectra in order to determine completely the rotational and rotational-vibrational energy levels in the molecule. The Raman spectrum can be obtained in some solutions where direct absorption measurements are impossible because the solvent is opaque in the infrared. Aqueous solutions offer a good example of such a case. 

Roothaan-Hall equations, 1, 6-8 rotational-vibrational energy levels, 3,159... 

Furtenbacher, T, Csaszar, A.G., Tennyson, J. MARVEL Measured active rotational-vibrational energy levels, J. Mol. Spectry., 2007, submitted. 

Rotational-vibrational energy levels fitted to a quadratic-cum-Lorentzian model potential of cylindrical symmetry about the linear unstable equilibrium configuration. Barrier to inversion in the molecular plane 1.10(13) eV (Gilchrist et al ). 

Among the theories into which the B.O. approximation has been incorporated are the theory of isotope effects on the rotational-vibrational energy levels of a molecule, the theory of isotope effects on chemical equilibria, and various theories of isotope effects on chemical rates. The relative success of these theories in the interpretation of experimental results suggests that the B.O. approximation must be a relatively "good" approximation. 

Let us accept as a starting point that we can, in principle, write down all the rotation-vibration energy levels of the molecule in question. Just... 

D. C. Comeau, I. Shavitt, P. Jensen, and P. R. Bnnker, An ab initio Determination of the Potential Energy Snrfaces and Rotation-Vibration Energy Levels of Methylene in the Lowest Triplet and Singlet States and the Single-Triplet Splitting, J. Chem. Phys. 90, 6491-6500 (1989). 

Whitten GZ, Rabinovitch BS (1964) Approximation for rotation-vibration energy level sums. J Chem Phys 41 1883... 

From a fit of rotational-vibrational energy levels of CH2, CD2 and CH2 to a non-rigid-bender Hamiltonian ([1], with references to the sources of data). 

Starting from the nuclear Hamiltonian defined in Eq. (10.2), the semirigid Watson Hamiltonian [208] gives the rotational-vibrational energy levels of the molecule under consideration and is expressed in dimensionless normal coordinates q as follows ... 

On the other hand, when degenerate bending modes are present, as with linear and symmetric tops, the spectrum in these excited states can be altered markedly. This effect is called Z-type doubling and wiU be discussed for linear molecules after the general expression for the rotation-vibration energy levels is given for a diatomic molecule. 

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