Spin–orbit distortion of the hyperfine structure in heavier molecules: Breakdown of the case (aβ) formalism in the B 3Φ–X 3Δ system of gaseous NbN

Abstract

A detailed analysis of the rotational and hyperfine structure of the (0,0) band of the B 3Φ–X 3Δ electronic transition of NbN has been performed from sub-Doppler spectra taken with linewidths of about 50 MHz. The Nb hyperfine structure is impressively wide in both states, but particularly so in X 3Δ where one of the unpaired electrons occupies a σ orbital derived from the metal 5s orbital. The electron spin and hyperfine structures do not follow the expected case (aβ ) coupling because of extensive second order spin-orbit effects. It is shown that the asymmetry in the spin–orbit structure of X 3Δ is explained almost quantitatively by interaction with a 1 Δ state from the same electron configuration (which lies at 5197 cm−1); also cross terms between the spin–orbit and Fermi contact interactions in the matrix element 〈3Δ2‖H‖1Δ〉 produce a large correction to the apparent coefficient of the I⋅L magnetic hyperfine interaction in X 3Δ2. The hyperfine structure in a triplet state turns out to be extremely sensitive to the details of the electron spin coupling, and reversals in the sense of the hyperfine structure in the 3Φ4–3Δ3 and 3Φ2–3Δ1 subbands are shown to be consistent with the3Δ state being a regular spin–orbit multiplet (A>0). Particular care has been taken with the calibration, which has meant that extra terms have needed to be added to the magnetic hyperfine Hamiltonian to account for the spin–orbit distortions: instead of the usual three parameters needed in case (aβ ) coupling, the B 3Φ state has required four parameters and the X 3Δ state has required five. The model explains the data very well, and the standard deviation in the least-squares fit to more than 1000 hyperfine line frequencies was 0.000 58 cm−1 (17 MHz).