Infra‐Red Spectra of Axially Symmetric XY3Z Molecules I. Vibration‐Rotation Energies

1942 ◽  
Vol 10 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Wave Henry Shaffer

The technique described in part I has been used to obtain constants of interest in molecular spectroscopy. The vibration-rotation interaction factor, F for HCl has been evaluated from the infra-red emission spectrum. The critical parameter in F is θ = M 0 / M 1 r e , where M 0 and M 1 are the first two coefficients in the electric dipole moment expansion about the equilibrium internuclear distance r e . A value of θ = + 1.12 ± 0.18 has been obtained. It is shown that for molecules with θ = +1 the total band intensity in emission is independent of the rotational distribution in the vibrational state from which the emission occurs. This has been made use of in evaluating radiative transition probabilities. For the HCl v (3-1) transition a value for | R 3 1 | 2 (= 1.60 x 10 -4 debye 2 ) was obtained for the first time. The same method yields a value of | R 2 1 | 2 / | R 2 0 | 2 = 204, in good agreement with an earlier estimate from absorption data.


Although the infra-red bands of carbon monoxide have been known for years, they have not yet been resolved. In 1913 Burmeister found, among the many doublets which he measured, one due to CO with its centre at 4·66 μ, and from the Rayleigh-Bjerrum separation an approximation to the moment of inertia was made. The harmonic at 2·35 μ was observed by Brinsmade and Kemble in 1917 ; Schaefer and Thomas added a second harmonic, at 1·2 μ, to the known bands ; E. F. Lowry in 1924 tried to analyse Burmeister's doublet into the rotational fine structure which it must be supposed to have, but had no success. There has been some theoretical speculation based upon the scanty data of the vibration bands. Hettner* in 1920 showed the frequency relationships of the bands found by Burmeister and by Brinsraade and Kemble could be explained by the assumption that the 2·35 μ. band was an overtone of the 4·66 μ band (in the paper published later in the same year which is the foundation of our theoretical knowledge of vibration-rotation spectra. Kratzer did not include these frequencies as an example of the anharmony which lie was able to prove for other molecules). Dennison compared the observed intensity ratios with a ratio calculated from a very rough approximation. The molecule has generally been assumed HCl-like, but for confirmation theory had to wait upon experiment.


The infra-red absorption of nitrous oxide gas near 4·5 μ has been re-investigated using high resolving power. The rotational fine structure has been split up and shown to involve two vibrational transitions, one due to absorption of a fundamental from the ground state, and the other to a π → π transition from an excited vibrational level. The transitions have been analyzed theoretically and rotational constants obtained. The results serve to emphasize the importance of using more precise wave-length standards for infra-red measurements than have been used hitherto, if the rotational constants are to be obtained with accuracy com­parable to that achieved by microwave measurements. Excellent agreement with the latter has now been found.


There have been few attempts at the resolution of the vibration-rotation bands of a diatomic molecule. In 1919 Imes was successful with the bands of three of the hydrogen halides, work which was later extended by Colby and Meyer; Czerny proved the existence of a doublet due to HI, but the weakness of the absorption prevented more detailed study; E. F. Lowry in 1924 failed to analyse the structureless doublets of carbon monoxide, although his apparatus was similar to that used by Imes. It does not seem possible that the fine-structure would reveal itself if a lower pressure of the gas were used (E. F. Lowry worked at one atmosphere pressure). The molecule of CO, like those of the hydrogen halides, has a permanent electric moment, and its bands must be similar in kind. Apart from HF, HCI, HBr, HI and CO, NO is the only other diatomic molecule with a permanent electric moment, and its choice as the subject of this research was natural. It is more definitely homopolar than the hydrogen halides, although the distinction is almost certainly one of degree; there was the interest of establishing the self-evident proposition that there is no fundamental difference in the bands of No and the bands HCI. There was also the advantage of knowledge of the electronic band spectrum of the molecule acquired by Guillery, Jenkins, Barton and Mulliken, and summarised by Mulliken. The thoroughness of this work makes NO one of the best-known of molecules to the spectroscopist. It has been mentioned in the introduction to Part I that throughout this series of papers there will be maintained the deal of correlation between infra-red and electronic band spectra. Accordingly, it became our aim to compare the constants of the molecule in the normal state as derived from electronic band spectra and as obtained from the direct measurements of the infra-red. The unexcited electronic state of the molecule measurements of the infra-red. The unexcited electronic state of the molecule is, of course, the only one with which infra-red observations are concerned.


The vibration-rotation bands of methyl fluoride between 2⋅5 and 5 μ have been measured with higher resolution than previously. Three parallel bands have been analyzed, providing three independent values for B ", the rotational constant in the ground state. Each of these values is close to that obtained from the microwave spectrum (0⋅8518 cm -1 ), and some earlier values deduced from infra-red bands are shown to be incorrect. A value of 2⋅28 x 10 -6 cm -1 has also been obtained for D J , the centrifugal stretching constant, which is shown to be more satisfactory than that previously deduced from the microwave spectrum. A perpendicular type band has been resolved fairly completely, and it has been possible to measure the P and R lines of the sub-bands in addition to the strong Q branches. An analysis has been made which accounts satisfactorily for most of the lines in the entire band, and this provides the first example of such a complete analysis of a perpendicular band of a symmetrical top molecule.


The purpose of the first papers of this series was the development of a machinery for the determination of the structure of simple polyatomic molecules. Studies of diatomic molecules were the means by which experience was to be gained for the more ambitious work. So much is now known of the diatomic molecule from the analysis of electronic band spectra that most infrared investigations can only hope to fill in details where, for many examples, the details are already known to a far greater accuracy; and now that confirmation of the essentials of electronic band spectra analysis has been given by the more direct but less precise method of the infra-red and Raman effect, it is clear that further work upon these lines would be redundant. The position is far different for even the simplest of polyatomic molecules. It would be unreasonable to expect from the analysis of their band spectra the same degree of theoretical completeness which has been obtained for the diatomic molecule, but there is a necessity that the analyses should at least not conflict with evidence from slightly different but connected spectroscopic fields. Judged by this last criterion, there have been very few satisfactory analyses of the electronic band spectra of polyatomic molecules. On the other hand, as Mecke has urged more than once, there is a real need for the knowledge which the spectroscopy of these molecules alone can give, particularly if physical ideas of molecular structure are to be introduced into chemistry without a long delay. It is this need which is the first justification of the study of the vibration-rotation spectra of polyatomic molecules. At the worst, such work must give data which will make the analysis of electronic band spectra easier and more certain than it is at the moment. For most molecules, as will be seen later, information should follow from the independent analysis of the vibration-rotation bands, apart from the use as a clue to the electronic bands on the one hand, or the mere assignment of a geometrical arrangement to the nuclei on the other.


The infra-red absorption spectrum of methane 12 CH 4 in the region of 3 μ has been re-investigated with higher resolving power than has been used previously. A very complex system of overlapping vibration bands has been revealed. The rotational fine structure of these bands has been partially analyzed, particularly having regard to the Coriolis interactions which occur in this case. The corresponding absorption bands of 13 CH 4 have also been examined.


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