Vibration-rotation interactions in infrared active overtone levels of spherical top molecules; 2[nu]3 and 2[nu]4 of CH4, 2[nu]3 of CD4

Abstract

The theory of the vibration-rotation lines of the first overtones of the infrared active fundamentals of tetrahedral molecules has been re-examined. Theory predicts an overtone spectrum consisting of five P, Q, and R branches of roughly comparable intensities provided that the vibrational angular momentum quantum number l is approximately a good quantum number for the complete vibration-rotation Hamiltonian. In this case the separation of the E and F2 vibrational substates of the l = 2 vibrational state must be small compared with the splittings which arise from the 2B[zeta] (P[middle dot]1) term. The band 2[nu]4 of CH4 is shown to be consistent with this approximation. If however the separation between the E and F2 vibrational substates is very large theory predicts an overtone spectrum consisting of single strong P, Q, and R branches with P and R branch spacings of approximately 2B(1 + [zeta]). These P, Q, and R lines are associated with the F2 vibrational substate, and have relative intensities much larger than the lines of the E vibrational substate. The bands 2[nu]3 of both CH4 and CD4 are shown to be accounted for by this limit.The detailed calculations exploit the spherical tensor formalism. In the first case a conventional angular momentum coupled representation, an extension of Hecht's work on the fundamental [nu]3, is used in the calculations. In the second case a new representation is introduced which formally has many of the mathematical properties of the conventional representation for an l = 1 vibrational state.The tetrahedral splittings in the vibration-rotation levels of 2[nu]3 of CD4 are appreciable, and are accounted for very well by the following constants which give the splittings throughout the spectrum: Dt = 1.1 x 10-6cm-1, F3t = -1.4 x 10-4cm-1, . The following linear combinations of effective rotational constants are obtained from the spectrum: From the P and R branches, B + B0 + 2(B[zeta]3) = 6.00 +/- 0.02 cm-1, B - B0 = -0.050 +/- 0.004 cm-1. From the Q branch, B - B0 = -0.062 +/- 0.002 cm-1. In 2[nu]3 of CH4 the tetrahedral splittings are quite small, making a quantitative fit more difficult. However, the best fit is obtained with Dt = 4.5 x 10-6cm-1, F3t = -1.25 x 10-4cm-1, and [gamma]3t = -5.0 x 10-4cm-1. Also, from the P and R branches, B + B0 + 2(B[zeta]3) = 10.76 +/- 0.02 cm-1, B - B0 = -0.063 +/- 0.004 cm-1; from the Q branch, B - B0 = -0.058 +/- 0.002 cm-1. The spectrum of 2[nu]4 of CH4 is extremely complex as a result of the tetrahedral splittings and the overlapping of the five P, Q, and R branches. It is not possible to make definite assignments for the observed lines at this time.