Rotational l-type resonance in BeH2, BeD2, and MgH2.

In two previous papers on the infrared emission spectra of gaseous BeH2, BeD2, and MgH2 molecules, we reported rotational analyses of the antisymmetric stretching fundamental band and several hot bands. A customary effective rotational energy level expression, which is a power series in J J+1 with B v , D v , and H v constants, was used for most of the observed vibrational levels. For all the vibrational levels with v2=2, we observed large splittings between the e and f parity components of the states, i.e., 020 g , 021 u , and 02 2 g states. These splittings were attributed to rotational -type resonances between these states and the associated nearby + states, 020 g + , 021 u + , and 022 g + , respectively. Since all the rotational levels of a + state have e parity, they interact only with the e parity component of the nearby state, and thus the f levels are not perturbed. Following Maki and Lide who analyzed rotational -type resonances for HCN, we used a 2 2 Hamiltonian matrix for the e levels, while the rotational energy expression for the f levels was the customary power series in J J+1 . However, only for the BeD2 molecule we could obtain a satisfactory fit to the observed transitions. For BeH2, fitting errors of about 0.08 cm−1 were found for lines of the 021 u →020 g and the 022 g →021 u bands, and were assumed to be due to further perturbations of the 021 u state by the nearby 05 0 u state. Although similar perturbations do not exist in MgH2, a satisfactory -type resonance fit could not be obtained for this molecule, and only lines from the f parity component of the states were fitted. The problems in the -type resonance fits of BeH2 and MgH2 have now been resolved, and the results are reported in this Note. There is an -dependent term in the vibrational energy level expression for symmetric linear triatomic molecules, i.e., g22 2. The theoretical calculations of Martin and Lee for BeH2 had predicted the g22 constant to be +2.46 cm −1, which means that for a vibrational level with v2=2 the vibrational energy of the state =2 is larger than that of the + state =0 by 4g22. In our previous paper on BeH2 and BeD2, 1 the rotational energy had been expressed as a power series in J J+1 , and it was assumed that the rotational levels of the 020 g state lie higher in energy compared with those of the 020 g + state because of the positive g22 value. The common method for assigning any + or state is based on the first observed line in each branch, since J=0 and 1 do not exist in states. However, when spectra are congested because of overlapping bands, it can be difficult to ascertain which lines are missing. We have now realized that our pre+ vious assignments of the e and e components should