The vibration-rotation spectrum

Molecules do not have a pure vibrational spectrum because the selection rules require a change in the vibrational state of the molecule to be accompanied by a change in the rotational state as well. As a result, in the infrared region of the spectrum there are vibration-rotation bands each band consists of several closely spaced lines. The appearance of a band can be simply interpreted by supposing that the vibrational and rotational energies of the molecule are additive. For simplicity we consider a diatomic molecule the 

In the transition from the state with energy E to that with energy E, 

The selection rule for vibration is At = 1 since the frequency emitted is v = AE/hc, we have 

The selection rule for the rotational quantum number requires that either J = J + 1 or J = J — 1. Thus we obtain two sets of values for the frequency, designated by and Vp. 

These formulas can be simplified by writing both in the form 

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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 10.7—Representation of the rotational and vibrational energy levels and conversion into the vibrational rotational spectrum (at bottom). The fundamental vibration corresponds to V = +1 and J ll-The vibrational rotational band corresponds to all the allowed quantum leaps. If the scale of the diagram is in cm-1 the arrows correspond to the wavenumbers of absorption. The R branch corresponds to A J = +1 and the P branch to A J = -1. They are located on each side of the Q band, which is absent in the spectrum (AJ = 0 corresponds, here, to a forbidden transition).

A transition with no change in electronic state, and with Ao = 0 gives a line in the pure rotation spectrum of the molecule. Transitions with A0= 1, 2,... give the vibration-rotation spectrum. These two types of transitions will be discussed separately in the next two sections. 

Anharmonic Force Constant Refinements.—The preceding parts of this Section 4 constitute an outline of how the vibration-rotation spectrum of a molecule may be calculated from a knowledge of the force field in some set of geometrically defined internal co-ordinates, denoted V(r) in general in this Report [but denoted V(X) in the special discussion on pp. 126—132], In practice we wish to solve the reverse problem we observe the vibration-rotation spectra, and we wish to deduce the force field. 

Dixon, R. N., and N. Sheppard The Vibration-Rotation Spectrum of Silyl Iodide. J. chem. Physics 23, 215—216 (1955). 

Tennyson J, Sutcliffe BT (1982) The ab initio calculation of the vibrational-rotational spectrum of triatomic systems in the close-coupling approach, with KCN and H2Ne as examples. J Chem Phys 77 4061 1072... 

The primes denote successive derivatives of the operator Oe with respect to R at the equilibrium internuclear separation Re. The values of the coefficients an, as well as Be and < >, are known from analysis of the vibration rotation spectrum [102],... 

Vibrationally excited diatomic molecules will only emit if they are polar, and most of the available results are for reactions which produce diatomic hydrides. Because of their unusually small reduced mass, these molecules have high frequency and very anharmonic vibrations, and their rotational levels are widely spaced. Consequently, their spectra can be resolved more easily than those of nonhydrides, where there are many more individual lines in the vibration-rotation spectrum. Furthermore, the molecular dynamics of these reactions are particularly interesting because of the special kinematic features that arise when an H atom is involved in a reactive collision and because these... 

From a study of the vibration-rotation spectrum of a molecule, the frequency of vibration, the values of the energy levels, the anharmonicity constant and the dissociation energy may be determined. From the rotation spectrum or from the rotational fine structure of the vibration-rotation spectrum the value of I and hence of the interatomic distance may be determined... 

The vibrational-rotational spectrum of BHF2(g) has been studied by Lynds and Bass ( ). The values of Vg, and Vg we... 

An important step toward the identification of this ion in outer space has recently been made by the first report of the vibration-rotation spectrum of the isotope He He by Yu and Wing [44],... 

Each (v, 7) level of the vibration-rotation spectrum is also characterized, in addition to its turning points, by its minimum Rt(J). Recently, Craven, Murrell, and Varandas (Craven et al., 1982) proposed an algorithm for finding Re(J) for Uen(R, 7) with an arbitrary J < Jc, where 7C corresponds to that critical value of 7 above which the given potential Ueff(R, 7) has no minima. They imposed the following assumptions ... 

In a paper in 1979, Carl Ballhausen [1] expressed the belief that today we realize that the whole of chemistry is one huge manifestation of quantum phenomena, but he was perfectly well aware of the care that had to be taken to express the relevant quantum theory appropriately. So in an earlier review [2] that he had undertaken with Aage Hansen, he scorned the usual habit of chemists in naming an experimental observation as if it was caused by the theory that was used to account for it. Thus in the review they remark that a particular phenomenon observed in molecular vibration spectra is presently refered to as the Duchinsky effect. The effect is, of course, just as fictitious as the Jahn-Teller effect. Their aim in the review was to make a start towards rationalization of the nomenclature and to specify the form of the molecular Hamiltonian implicit in any nomenclature. In an article that Jonathan Tennyson and I published in the festschrift to celebrate his sixtieth birthday in 1987 [3], we tried to present a clear account of a molecular Hamiltonian suitable for treating the vibration rotation spectrum of a triatomic molecule. In an article that I wrote that appeared in 1990 [4], I discussed the difficulty of deciding just how far the basic chemical idea of molecular structure could really be fitted into quantum mechanics. 

Not until 1985, did Owrutsky et al. [1, 4] have any success in the experimental determination of bond length and stretching fundamental, viz. 96.43 pm and 3555.6 cm- respectively, by measuring the vibration-rotation spectrum of free OH- ions. The corresponding data of OD- ions were reported by Rehfuss et al. [8] (96.42 pm and 2625.3 cm-1). These values were confirmed slightly later by matrix isolation studies, viz. 3554.0 and 2622.5 cm-1 for OH- and OD- in... 

Watson, J.K.G. The vibration-rotation spectrum and anharmonic potential of H3+, Chem. Phys. 1995,190,291-300. 

After a great amount of preliminary work by other authors Meoke and his collaborators (37,68,124) have succedeed in giving a satisfactory analysis of the vibration-rotation spectrum of H2O. Their success depended essentially upon the fact that by means of sensitised plates they could photograph the combination bands in the near infra-red, thus obtaining a much higher resolution than was possible formerly. Eig. 47 shows one of these combination bands. 

The molecule hydrogen sulphide, HgS, is of the same type as HgO. The vibration-rotation spectrum of HgS has recently been reinvestigated by Nielsen and Barker (i3i), by Mischke(i25) and by Cross (Si). Bands of the same character as in H2O are found, leading to... 

X-nucleus moves along the axis of symmetry while the F-atoms are displaced symmetrically in planes through it so that the electric moment oscillates parallel to the axis of symmetry (parallel type of vibrations). The two others, v(cr), 8 (o-), which are doubly degenerate (see section 32), yield an oscillating electric moment perpendicular to the axis of symmetry (perpendicular type of vibrations). All four normal vibrations are active, appearing in the vibration-rotation spectrum as well as in the Raman effect. Since two of the moments of inertia and oi the molecule are equal while the third Iq will in general be different, the rotation of the molecule should be that of a symmetrical top. The rotational energy is then obtained from equation (34-3). 

In the vibration-rotation spectrum the parallel type of vibration bands has a particularly simple rotational structure since for it K may not change at aU while J, as always, may... 

One class of molecules that conforms to this simple first-order pattern comprises linear molecules in or states. For example, mid-IR LMR has been used to record the vibration rotation spectrum of SO, which species was generated by the reaction of OCS with a large excess of discharged O2 (Yamada et. al, 1978). 

The vibrational overtone spectrum of OH-Ar complexes shown in Fig. 6 has been obtained by fixing the ultraviolet probe laser on an OH-Ar excitation feature associated with the OH A(v =l) - X(v"=2) transition, while the infrared pump laser was scanned. The ultraviolet laser was fixed on the Qi bandhead, probing the N=1 to 4 levels of the vibrationally excited complex OH-Ar (vqh=2). The infrared spectrum exhibits a distinctive P, Q, R branch structure, centered at 6970.4 0.2 cm", characteristic of the vibration-rotation spectrum of a molecule with electronic angular momentum (A > 0) in its ground electronic state. A linear OH-Ar complex will have the same ground state symmetry label as OH, namely IT. 

The vibration-rotation spectrum can be understood on the basis of a partial energy level diagram for the lowest vibrational and rotational levels (Fig. 3.9). The upper and lower level quantum numbers are denoted by (v J ) and (v"J ), respectively. Transitions for which AJ— -h 1, AJ = — 1, and A J = 0 (the latter occurring only in states with nonzero orbital angular momentum along the molecular axis) are called R-, P-, and Q-branch transitions. The transition frequencies are derived from... 

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