Ro-vibrational spectra

Sutcliffe BT, Tennyson J (1986) Ageneralized approach to the calculation of ro-vibrational spectra of triatomic molecules. Mol Phys 58 1053-1066... 

Let us consido the most common electronic-vibrational-rotational behavior of a given molecule. For those systems where the ro-vibrational spectra corresponds to a well-defined electronic state, the nuclear states 9 ) are defined relative to a given electronic state, say k). This latter is invariant to the instantaneous positions of the nuclei. Actually, to speak of instantaneous positions for the nuclei is strongly model dependent. The quantum nuclear states are defined relative to particular electronic... 

ABSTRACT. Developments in the use of supercomputers for the generation of first principles, synthetic, ro-vibrational spectra for triatomic molecules are discussed. Refinements to a previously published two-step procedure for calculating rotationally excited states are given. 

Mullay JJ (1987) Estimation of Atomic and Group Electronegativities. 66 1-25 Muller A, Baran E), Carter RO (1976) Vibrational Spectra of Oxo-, Thio-, and Selenometallates of Transition Elements in the Solid State. 26 81-139 Muller A, Diemann E, Jorgensen CK (1973) Electronic Spectra of Tetrahedral Oxo, Thio and Seleno Complexes. Formed by Elements of the Beginning of the Transition Groups. 14 23-47... 

As the molecule vibrates it can also rotate and each vibrational level has associated rotational levels, each of which can be populated. A well-resolved ro - vibrational spectrum can show transitions between the lower ro-vibrational to the upper vibrational level in the laboratory and this can be performed for small molecules astronomically. The problem occurs as the size of the molecule increases and the increasing moment of inertia allows more and more levels to be present within each vibrational band, 3N — 6 vibrational bands in a nonlinear molecule rapidly becomes a big number for even reasonable size molecules and the vibrational bands become only unresolved profiles. Consider the water molecule where N = 3 so that there are three modes of vibration a rather modest number and superficially a tractable problem. Glycine, however, has 10 atoms and so 24 vibrational modes an altogether more challenging problem. Analysis of vibrational spectra is then reduced to identifying functional groups associated... 

Figure 9.20 Calculated (a) time-dependent ro-vibrational states probabilities with initially pop-Jh = 0 small inset for other transiently pop spectra for different rotational states. Taken from Ref. [43].

It must be emphasized that in fact a very similar situation characterizes experimental investigations, since very different experimental techniques are employed, and different questions are asked, when investigating simple diatomics on the one hand and complex systems, such as chlorophyl, proteins, fullerenes, etc. on the other. Even if one could resolve and measure, for instance, all the individual ro-vibrational lines in the electronic spectra of large systems involving, say, more than 50 carbon atoms, the usefulness of such information is debatable. Likewise, our theoretical inquiries call for different models, approximations and techniques when handling different types of problems. 

Durig J (ed) (1972) Vibrational Spectra and Structure, A Series of Advances. Elsevier, Amsterdam Durig JR, Carter RO, Carreira LA (1974) J Chem Phys 60 3098 Durig JR, Little TS (1981) J Chem Phys 75 3360... 

Flaud, J.-M., Camy-Peyret, C., Maillard, J.P Higher ro-vibrational levels of H2O deduced from high resolution oxygen-hydrogen flame spectra between 2800-6200 cm . Mol. Phys. 1976, 32, 499-521. 

Figure 8.7 Raman spectra (pure rotational -Sqo(S) and ro-vibrational Soi(Q) branches), for ambient air and for a cell filled with a 1 1 mixtureofDjand H2, atatmospheric pressure...

The spectra for the H2 D2 mixture exhibit both pure rotational and ro-vibrational Raman features, i.e. Soo(5)- and Soi(G)-branches (the Soi(<9)- and Soi(5)-branches are too weak to be seen above the detector noise. Because of the huge isotope effect the pure rotational Raman lines are well resolved, even at... 

Figure 23.17 The D atom kinetic energy spectra (labora-toryframe)producedinthereactionH + D2(v =0, J = 0) HD(v, J ) + D,atacollisionenergyofl.28eV.Theresolution of the experiment is such (Af /E 0.4 per cent) that the D atom kinetic energy distribution mirrors the fully resolved ro-vibrational distribution of the HD counterpart. Adapted from Schnieder eto/. Science, 1995,269 207, with permission of AAAS...

---