Transition rotational-vibrational

The vibrational and rotational motions of the chemically bound constituents of matter have frequencies in the IR region. Industrial IR spectroscopy is concerned primarily with molecular vibrations, as transitions between individual rotational states can be measured only in IR spectra of small molecules in the gas phase. Rotational - vibrational transitions are analysed by quantum mechanics. To a first approximation, the vibrational frequency of a bond in the mid-IR can be treated as a simple harmonic oscillator by the following equation ... 

As detailed in Section 2, we have derived and programmed the expression for line strengths of individual rotation-vibration transitions of XY3 molecules the line strengths depend on the vibronic transition moments entering into equation (70). With the theory of Section 2, we can simulate rotation-vibration absorption spectra of XY3 molecules. In computing the transition wavenumbers, line strengths, and intensities we use rovibronic wavefunctions generated as described in Ref. [1]. 

While the 3.39 m He-Ne laser line excites a C-H vibration, the argon laser line = 2.7 /im, for instance, causes rotation-vibration transitions associated with 0-H vibrations... 

If a molecule loses A E via molecular collision, it is called a radiationless transition. Pure rotational and rotational-vibrational transitions are also observed in IR and Raman spectra. Many excellent textbooks are available on these and other subjects (see general references given at the end of this chapter). 

P, Hennig, W. P, Kraemer and 6. H. F. Oierckseni A Compilation of Theoretical Spectroscopic Constants and Rotational-Vibrational Transition Frequencies for the Isoelectronic Series of Linear Triatomic Molecules HCN, HNC, HCO , HOC", HNN Obtained from Ab Initio Calculated Energy Hypersurface, Max-Plenck-Insti-tut fur Physik und Astrophysik, Munich 1977. 

Coefficients of the energy-level polynomials are calculated from the theoretical values of Hg ( ) using rho = 0.866117 in isotopic equations. These polynomials are confirmed by six rotation-vibration transitions (v 3, N 2) observed between 1642 and 1869 cm" by an Infrared laser-resonance method (8). Our polynomials predict these transitions within 0.1 cm. We give the polynomial coefficients, especially higher order ones, to many more digits than are justified by their accuracy. The equations are very approximate near but, judging by Hg (1 ), this should have little effect on the thermodynamic... 

Rotational-vibrational transitions of PH and PD (generated by reacting phosphorus vapor with H or D atoms) in the fundamental band region were observed in the IR absorption [4] and emission [5] spectra and by mid-IR LMR [6] ... 

The selection rules are less restrictive for rotation-vibration transitions. Thus while AVC c> still holds for totally symmetric vibrational fundamentals, = transitions are possible for... 

Fig. 2.21 Hyperfine and super-hyperfine structures of a rotational-vibrational transition in SP6, showing the molecular transitions and cross-over signals (a) experimental spectrum (b) calculated spectrum [223]...

Optical-microwave double resonance (OMDR) can considerably improve the situation and extends the advantages of microwave spectroscopy to excited vibrational or electronic states, because selected levels in these states can be populated by optical pumping. Generally dye lasers or tunable diode lasers are used for optical pumping. However, even fixed frequency lasers can often be used. Many lines of intense infrared lasers (for example, CO2, N2O, CO, HF, and DF lasers) coincide with rotational-vibrational transitions of polyatomic molecules. Even for lines that are only close to molecular transitions the molecular lines may be tuned into resonance by external magnetic or electric fields (Sect. 1.6). The advantages of this OMDR may be summarized as follows ... 

For transitions with small natural linewidths the Ramsey resonances can be extremely narrow. For instance, the nonlinear Ramsey technique applied to the resolution of rotational-vibrational transitions in CH4 in a methane cell at 2 mbar pressure yielded a resonance width of 35 kHz for the separation L = 7 mm of the laser beams. With the distance L = 3.5 cm the resonance width decreased to 2.5 kHz, and the Ramsey resonances of the well-resolved hyperflne components of the CH4 transition at k = 3.39 pm could be measured [1263]. 

The small signal width of the OODR signal /s becomes essential if the levels 3) are high-lying rotation-vibration levels of heavy molecules just below the dissociation limit, where the level density may become very high. As an example, Eig. 9.84 shows such an OODR signal of a rotation-vibration transition D Eu(v = 50, J = 48) X Ug v" = 125, J" = 49) in the Cs2 molecule. A comparison with... 

The rotational structure in the region of the Fermi diad v, 2V2 (900 to 955 cm" ) was partly resolved. The comparison with a calculated curve led to the band origins [4]. Seven rotational -vibrational transitions in this range were observed and classified by IR-microwave double resonance using five CO2 and two N2O laser lines [14]. 

For frequency standards the rotational-vibrational transition of CH4 at A = 3.39 p.m is used (Vol. 2, Sect. 2.3). In order to reduce the transit-time broadening for CH4 molecules with F = 7xl0 cm/s below their natural linewidth of 8v = 10 kHz, the laser-beam diameter must be enlarged to 2w > 6 cm. 

The molecular beam method devised originally for the study of chemical reactions is used at present for the study of energy transfer in molecular collisions [136, 480]. An energy of neutral molecules up to several eV can be obtained by means of supersonic beams. Measurements of the change in the kinetic energy of colliding partners is accomplished either by direct selection of velocity or by the time-of-flight technique. Most detailed information on the unreactive collision dynamics have thus been obtained for some molecules, namely the differential cross sections of particular rotation-vibrational transitions. 

While AJ = 0 is forbidden in a pure rotational-vibrational transition, this type of transition is allowed in connection with electronic transitions (still not for E- E transitions). The new selection rule gives rise to a 0 branch, in addition to the R and P branches. 

Mercury is a further gas which can have a geophysical origin apart from anthropogenic ones. It is the only pollutant which is present in the atmosphere in atomic form. Compared to molecules with a multitude of rotational-vibrational transitions, mercury in contrast exhibits only a single... 

Polyansky OL, Caszar AG, Shririn SV, Zobob NF, Barletta P, Tennyson J, Schenke DW, Knowles PJ (2003) High-accuracy ab initio rotation-vibration transitions for water. Science... 

In the gaseous or vapor phase, molecules can rotate freely, which leads to a modification of their vibrational spectra by some significant rotational structure. The study of rotation-vibration transitions for the determination of molecular structure can be carried out using infrared and Raman spectroscopy. The pure rotational spectra in the vibrational ground state and, to a lesser extent due to reduced intensities, in excited vibrational states can be observed in the microwave and in the far-infrared region for molecules with a permanent dipole moment. For symmetric molecules without a dipole moment, but with polarizability allowing for anisotropic scattering, the pure rotational Raman spectra are an equivalent... 

The coherent Raman processes are generated when two laser beams, one of which has a tunable frequency, are brought to a common focus in a sample (see Fig. 7), As soon as the frequency difference coi — co 2 of the two lasers corresponds to the frequency (Oj of a Raman-allowed rotation-vibrational transition, a nonlinear interaction with the molecules occurs via the third-order nonlinear susceptibility the corresponding state is... 

---