Rotation-vibration band spectra

The oldest of the spectroscopic radiation sources, a flame, has a low temperature (see Section 4.3.1) but therefore good spatial and temporal stability. It easily takes up wet aerosols produced by pneumatic nebulization. Flame atomic emission spectrometry [265] is still a most sensitive technique for the determination of the alkali elements, as eg. is applied for serum analysis. With the aid of hot flames such as the nitrous oxide-acetylene flame, a number of elements can be determined, however, not down to low concentrations [349]. Moreover, interferences arising from the formation of stable compounds are high. Further spectral interferences can also occur. They are due to the emission of intense rotation-vibration band spectra, including the OH (310-330 nm), NH (around 340 nm), N2 bands (around 390 nm), C2 bands (Swan bands around 450 nm, etc.) [20], Also analyte bands may occur. The S2 bands and the CS bands around 390 nm [350] can even be used for the determination of these elements while performing element-specific detection in gas chromatography. However, SiO and other bands may hamper analyses considerably. 

Part of the high-resolution rotational-vibrational FTIR spectrum of CO(g), showing the P(<2140cm 1) and R (>2140 cm-1) bands, and the contributions from the C13 isotope [9],... 

As an example of the rotation-vibration band of a diatomic molecule, the nitrogen-broadened spectrum of C 0 is shown in Fig. 4.3-2. An additional band appears, less intense, but shifted, which is attributed to the isotope. Fig. 4.3-3 displays an... 

Fig. 31. Two superimposed spectra of the rotation-vibration band of CO2 at about 6500 cm t obtained from Venus by means of Fourier transform spectroscopy (ledt) and corresponding portion of the spectrum obtained by means of conventional spectroscopy (right). For comparison, a spectrum is shown which was obtained by conventional spectroscopy in a laboratory. Data taken from Ref.

Figure 10.5 Rotation/vibration levels of carbon monoxide. V and J are the quantum numbers of vibration and rotation. The fundamental vibration corresponds to V = +l and 7 = +1. (a) A rotation-vibration band corresponds to all of the allowed quantum transitions. If the scale of the diagram is in cm , the arrows correspond to the wavenumbers of the absorptions (b) branch R corresponds to A7 = +1 and the band P to A7 = — 1. They are situated either side of band Q, absent from the spectrum (here it can be supposed that A7 = 0 corresponding to a forbidden transition) (c) below, vibration-rotation absorption band of carbon monoxide (pressure of 1000 Pa). The various lines illustrate the principle of the selection rules. The difference (wavenumbers) between successive rotational peaks are not constant due to anharmonicity factors.

Microwave spectroscopy of gaseous mixtures of HF with MeCN " or has confirmed that hydrogen-bonded species are generated this technique promises to yield useful structural information for such complexes. Thus the N— F distance in MeCN-HF has been estimated to be 2.741 and the O—F distance in H2O-HF is 2.68 A. The i.r. spectrum of the latter complex in the vapour phase has been reported for the first time. The enthalpy of association was estimated to be -26kJmor at 315 K. The i.r. spectra of mixtures of HCl and DCl or DBr cooled to 166 K have been shown to give additional lines in the HCl rotation—vibration band attributable to HC1,DC1 and HCl,DBr molecules. ... 

An example of a typical rotation-vibration band, measured with a high-resolution FT-IR spectrometer, is shown in Figure 11. It is the bending band V2 of CO2 near 667 cm . This spectrum was recorded by the Oulu spectrometer with an instrumental resolution of 0.002 cm The relative errors of the wavenumber compared to model equations are of the order of 10 . The vibration energy levels of different normal modes are sometimes very close to each other. In this case these normal modes can be coupled so that the energy levels are shifted apart. Now the observed wavenumber cannot be expressed in a closed form and the rotational lines of the spectrum are shifted. With the proper quantum... 

The emission spectrum observed by high resolution spectroscopy for the A - X vibrational bands [4] has been very well reproduced theoretically for several low-lying vibrational quantum numbers and the spectrum for the A - A n vibrational bands has been theoretically derived for low vibrational quantum numbers to be subjected to further experimental analysis [8]. Related Franck-Condon factors for the latter and former transition bands [8] have also been derived and compared favourably with semi-empirical calculations [25] performed for the former transition bands. Pure rotational, vibrationm and rovibrational transitions appear to be the largest for the X ground state followed by those... 

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... 

The number of fundamental vibrational modes of a molecule is equal to the number of degrees of vibrational freedom. For a nonlinear molecule of N atoms, 3N - 6 degrees of vibrational freedom exist. Hence, 3N - 6 fundamental vibrational modes. Six degrees of freedom are subtracted from a nonlinear molecule since (1) three coordinates are required to locate the molecule in space, and (2) an additional three coordinates are required to describe the orientation of the molecule based upon the three coordinates defining the position of the molecule in space. For a linear molecule, 3N - 5 fundamental vibrational modes are possible since only two degrees of rotational freedom exist. Thus, in a total vibrational analysis of a molecule by complementary IR and Raman techniques, 31V - 6 or 3N - 5 vibrational frequencies should be observed. It must be kept in mind that the fundamental modes of vibration of a molecule are described as transitions from one vibration state (energy level) to another (n = 1 in Eq. (2), Fig. 2). Sometimes, additional vibrational frequencies are detected in an IR and/or Raman spectrum. These additional absorption bands are due to forbidden transitions that occur and are described in the section on near-IR theory. Additionally, not all vibrational bands may be observed since some fundamental vibrations may be too weak to observe or give rise to overtone and/or combination bands (discussed later in the chapter). 

Here a third selection rule applies for linear molecules, transitions corresponding to vibrations along the main axis are allowed if Aj = 1. The A/=0 transition is only allowed for vibrations perpendicular to the main axis. Note that because of this selection rule the purely vibrational transition (called Q branch) appears in the gas phase spectrum of C(X but is absent in that of CO. In both cases, two branches of rotational side bands appear (called P and R branch) (see Fig. 8.3 for gas phase CO). 

As in the infrared spectrum, overtone bands with Ac > 1 are possible, but have much weaker intensity and are usually not observed.) The A/= -2, 0, and +2 branches of a vibration-rotation Raman band are called O, Q, and S branches, respectively, in an extension of the P, Q, R notation used in infrared spectra. 

Figure 2. Overview SEP spectrum for DCO(X) as measured by Stock et al. [16]. The energy is measured with respect to the vibrational ground state (0,0,0). Each vibrational band consists of four different rotational lines. For a detailed discussion of the assignment the reader is referred to the theoretical analysis of Keller et al. [17], (Reprinted with permission of the American Institute of Physics, from Ref. 16).

It is well known that the v, band of liquid acetonitrile is significantly asymmetric due to an overlap of hot band transitions in the low frequency side. A study of gas phase rotation-vibration spectrum [19] showed that the hot band transition from the first exited state of the degenerated C-C = N bending v8 mode, v hl = v + v8 - vs, has its center at 4.944 cm 1 lower than that of the fundamental transition, v,. Also the presence of v,h2 = v, + 2v8 - 2v8 transition is expected. The careful study on the v band of liquid acetonitrile by Hashimoto et al [20] provided the reorientational and vibrational relaxation times of liquid acetonitrile molecule. They corrected the contribution by the hot band transition using the Boltzmann population law and approximated the v , v,hl, 2h2, and v, + v4 bands by Lorentzian curves. 

The 1400 to 1700 A Region (B-X System). The spectrum in this region consists of a progression of out-of-plane vibrational bands. Rotational structure is diffuse but it can be resolved. The upper electronic state is planar 1E" in D, (318). 

Excitation of ClNO(Ti) in any one of the three vibrational bands yields exclusively NO products in vibrational state n — n (Qian et al. 1990). The left-hand side of Figure 9.12 depicts the results of a three-dimensional wavepacket calculation including all three degrees of freedom and using an ab initio PES (Solter et al. 1992). This calculation reproduces the absorption spectrum and the final vibrational and rotational distributions of NO in good agreement with experiment. 

---