Vibrational spectra inertia

Vibrational spectra are accompanied by rotational transitions. Rgure 1-4 shows the rotational fine structure observed for the gaseous ammonia molecule. In most polyatomic molecules, however, such a rotational fine structure is not observed because the rotational levels are closely spaced as a result of relatively large moments of inertia. Vibrational spectra obtained in solution do not exhibit rotational fine structure, since molecular collisions occur before a rotation is completed and the levels of the individual molecules are perturbed differently. Since Raman spectra are often obtained in liquid state, they do not exhibit rotational fine structure. 

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... 

This experiment is concerned with the rotational fine structure of the infrared vibrational spectrum of a linear molecule such as HCI. From an interpretation of the details of this spectrum, it is possible to obtain the moment of inertia of the molecule and thus the intemuclear separation. In addition the pure vibrational frequency determines a force constant that is a measure of the bond strength. By a study of DCI also, the isotope effect can be observed. 

Infrared spectroscopy has broad appHcations for sensitive molecular speciation. Infrared frequencies depend on the masses of the atoms involved in the various vibrational motions, and on the force constants and geometry of the bonds connecting them band shapes are determined by the rotational stmcture and hence by the molecular symmetry and moments of inertia. The rovibrational spectmm of a gas thus provides direct molecular stmctural information, resulting in very high specificity. The vibrational spectrum of any molecule is unique, except for those of optical isomers. Every molecule, except homonudear diatomics such as O2, N2, and the halogens, has at least one vibrational absorption in the infrared. Several texts treat infrared instrumentation and techniques (22,36—38) and their appHcations (39—42). 

There are several ways in which information about molecular structure can be obtained from infrared and Raman spectra. Probably the most important is the determination of moments of inertia from the spacing of the rotational lines. This remains one of the most reliable methods known for the determination of molecular sizes of simple molecules although with present experimental techniques it cannot be used for any but very light molecules. In recent years this method has been enormously extended by the development of techniques for the use of the millimeter and centimeter wavelength regions, i.e., the regions of micro-wave spectroscopy. The vibrational spectrum can also be used to provide clues as to the structure of a molecule, especially with regard to its symmetry. 

The chemistry of all of these molecules is fascinating but, concentrating on the origins of life, a detailed look at the organic species is appropriate to see what molecules are present and how they might have been formed. The only alkane detected directly in the ISM is methane but this is due to the problem of detection. All alkanes are non-polar and so do not have a pure rotation spectrum. However, there is one allowed vibration of methane that is infrared active and with the low moment of inertia of methane the vibration-rotation spectrum can be observed and a rotational progression identifies the molecule with confidence. 

Figure 10.6—Vibrational-rotational bands of carbon monoxide (P = 1000 Pa). The various lines illustrate the principle of the selection rules (see Fig. 10.7). In this case, AV = +1 and AJ = 1. Branch R can be seen on the left-hand side of the spectrum while branch P is on the right. The distance between the rotational bands allows the moment of inertia I of the molecule to be calculated. I is not constant due to the anharmonicity factor.

The infrared absorption spectrum of NOBr(g) has been examined from 400 to 5303 cm" by Burns and Bernstein (6). The authors observed the first two fundamental vibrational frequencies and obtained the third from combination and overtones. These assignments are adopted. The principal moments of inertia are I. = 0.9405 x lO", I ... 

The selected vibrational frequencies were obtained from infrared and Raman spectrum measurements by Ryason and Wilson (6). However, the assignment of the fundamental frequencies has been revised by Dodd et al. (7) and Morino and Tanaka (8). Morino and Tanaka s assignment was adopted. The principal moments of inertia are I. = 6.3641 x 10 I- = 16.3632 x 10 and I-, 22.7272... 

While the tg structure represents the most well-defined molecular geometry, it is not, unfortunately, one that exists in nature. Real molecules exist in the quantum states of the 3N-6 (or 5) vibrational states with quantum numbers (vj, V2.-..V3N-6 (or 5)). Vj = 0, 1, 2,. Even in the lowest (ground) (0,0...0) vibrational state, the N atoms of the molecule undergo their zero point vibrational motions, oscillating about the equilibrium positions defined by the B-O potential energy surface. It is necessary then to speak of some type of average or effective structures, and to account for the vibrational motions, which vary with vibrational state and isotopic composition. In spectroscopy, a molecule s structural information is carried most straightforwardly by its molecular moments of inertia (or their inverses, the rotational constants), which are determined hy analysis of the pure rotational spectrum or fire resolved rotational structure of vibration-rotation bonds. Thus, the spectroscopic determination of molecular structure boils down to how one uses the rotational constants of a molecule... 

The vibration-rotation band for a molecule such as HCl is shown in Fig. 25.1. There is no absorption at the fundamental frequency Vo The spacing between the lines Av = V J +1 — V J = 2B. Since B contains the moment of inertia, measurement of the spacing yields a value of I immediately. The spacing between the lines is the same, 2B, in both the vibration-rotation band and in the pure rotational spectrum. The first line in the rotational spectrum is at the position 2B. The location of the vibration-rotation band is determined by the vibrational frequency. 

The electronic spectrum of a nonlinear polyatomic molecule is very complicated. In addition to three modes of rotation with distinct moments of inertia, there are 3N — 6 modes of vibration. While some of these may be forbidden in the infrared or Raman spectrum on the basis of symmetry, there is no rule to forbid their appearance in the electronic spectrum, which is extraordinarily complex as a consequence. For our purposes here, we mention only a few fundamental points and present one example. 

We may now consider the various mechanisms and predict, in a general way, the relaxation frequency for each one. Electrons with their extremely small mass have little inertia and can follow alterations of the electric field up to very high frequencies. Relaxation of electronic polarization is thus not observed until about 10 Hz (ultraviolet region). Atoms or ions vibrate with thermal energy, and the frequencies of these vibrations correspond to the infrared frequencies of the electromagnetic spectrum. The relaxation frequencies for ionic polarization are thus in the infrared range. 

Fig. 6.6. What can we learn about the HCl molecule from its IR spectrum (al The IR spectrum (each doublet results from two chlorine isotopes Cl and Cl present in the specimen), (b) The central position in the spectrum (between R and P brandies) seems to be missing because the transition u = 0, 7 = 0- u = l, T = Ois forbidden by the selection rules (as described in the text), and its hypothetical position can be determined with high precision as the mean value of the two transitions shown J = 0 - J = I and / = 1 -> 7 = 0. This allows us to compute the force constant of the HCl bond. The energy difference rf the same two quanta allows us to estimate the moment of inertia, and therefore the H... Cl distance. Note that the rotational levels corresponding to the vibrational state r = 1 are closer to each other than those for v = 0. This is due to the wider and wider well and longer and longer equilibrium distance corresponding to the rotationally corrected potential for the motion of the nuclei.

For the molecule carbonyl sulphide, OCS, the experimental data are not very complete. A study of the infra-red absorption spectrum has been made by Bailey and Cassie(23,45), of the Raman spectrum by Dadieu and Kohlrausch(53). Very likely this molecule is rectilinear in analogy with COg and CSg, but whether it is OCS or COS cannot at present be decided, chemical notions, however, pleading for the first. Only the possibility CSO must be excluded since the moment of inertia /g= 230.10 g.cm estimated from the separation of the intensity maxima in the P- and P-branches of the vibration bands is so large that it could only be obtained by having the S-atom at an end position. 

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