A New Band in the Absorption Spectrum of Methane Gas

The absorption spectrum of methane gas has been examined in the photographic infrared region from 6500A to 9500A in the hope of observing overtones of the known fundamental frequencies. A path length of 10 meters of gas at 70 cm pressure was used. The source of continuous radiation was a tungsten filament and the radiation was analysed with a grating spectrograph having a dispersion of 2.6A per mm at 8000A.One band which may be attributed to methane was observed at about 8900A and may be identified as the third overtone (n=0→4) of the fundamental absorption band at 3.3μ. The fine structure appears to be very complex and irregular, consisting of more than a hundred lines of which about five are very intense.In an attempt to reconcile the apparent irregularity of this structure with the simple and regular fine structure of the fundamental at 3.3μ, the theory of the overtones of a methane type molecule was examined. It is remarked that the higher energy states corresponding to this mode of vibration are in first approximation degenerate and have a weight 1/2(n+1)(n+2). A perturbation representing the anharmonic forces is now introduced and is postulated to have a tetrahedral symmetry. The secular determinant is then constructed and the resulting energy constant is given explicitly for the values $n=0,1,2,3,4$. It is found that for $n=4$ the 15 levels which originally coincided now group themselves into seven neighboring levels having the weights 3,3,3,2,2,1, and 1. These levels may all combine with the vibrationless state $n=0$ and thus it is to be expected that the overtone band under discussion will consist of seven nearly superimposed single bands. These considerations appear to explain the observed degree of complexity although it has not been possible as yet to make a detailed analysis of the positions of the individual lines.