Anomalous hyperfine structure of NSF3in the degenerate vibrational statev5=1: Lifting of the parity degeneracy by the

Abstract

For the principal isotopologue 14 N 32 S 19 F 3 of thiazyl trifluoride in the degenerate fundamental state (v 5 = 1), the hyperfine structure has been investigated in the Q-branch spectrum between 8 and 26.5 GHz using microwave Fourier transform waveguide spectrometers with a resolution limit of ≈30 kHz. In addition to l-type doubling spectra and l-type resonance transitions with ( k = l = ±2), perturbation-allowed spectra were measured with (k − l) = ±3, ±6. The range in J was from 13 to 61; for the lower states, kl = −3, −2, −1, 0, +1. For all the transitions, the hyperfine patterns observed are predicted to be doublets when only the nitrogen quadrupole Hamiltonian H N Q is taken into account. Doublets were indeed measured for transitions with RV = A 1 ↔ A 2 , where RV is the rovibrational symmetry. However, when RV = E ↔ E, triplets and quartets were observed in addition to doublets. These anomalous hyperfine patterns are shown to be due to the ( k = ±1) and ( k = ±2) matrix elements of the fluorine spin-rotation Hamiltonian H F SR characterized by the fluorine spin-rotation constants c(1) = 1 2 (c xz + c * zx ) and c(2) = 1 2 (c xx − c yy ), respectively. These terms in H F SR lift the parity degeneracy for RV = E. The rovibrational Hamiltonian H RV was adopted from an earlier partner study [S. Macholl et al., J. Phys. Chem. A 113, 668 (2009)]. A good fit to the hyperfine data was obtained with a standard deviation of 3.1 kHz. In the fitting process, 12 rovibrational parameters were varied, while the remaining constants in H RV were left at the values of Macholl et al. In addition, six hyperfine parameters were determined: four in H N Q , and two in H F SR . It was found that |c(1)| = 7.48(24) kHz and |c(2)| = 2.423 (22) kHz. This determination of c(1) is the first to be reported based on frequency measurements. In all the previous detections of parity doubling where the splittings were accounted for quantitatively, the levels involved had K = |k| = 1 in studies of the ground vibrational state or G ≡ |k − l| = 1 in investigations of degenerate vibrational states. In the current work, several different values of G were involved, thus demonstrating experimentally for the first time that this splitting process is a general phenomenon. The key to the observation of the parity doubling lies in the regional resonances discovered by Macholl et al. The clustering of rovibrational levels at low K leads to severe mixing. For each eigenstate involved in a regional resonance, the eigenstate consists of a linear superposition of basis vectors with several different values of kl having sizable expansion coefficients. As a result, the ( k = ±1, ±2) matrix elements of H F SR that typically connect levels widely separated in energy occur here effectively on the diagonal, thereby greatly enhancing the effects of c(1) and c(2). These spin-rotation matrix elements are derived here for RV = E in the low-field representation.

Simulating quantum magnets with symmetric top molecules

“…In contrast, when K = 3N ± 1 the rovibrational wave function has E symmetry, and so the nuclear spin wave function must also have E symmetry, para-CH 3 F, in order that the complete wave function transforms properly. The actual rovibrational and spin wavefunctions corresponding to these representations have been given in the literature [37,104,106,107], and the methods of group theory can be applied to simplify evaluation of matrix elements, just as for the case of SU(2) [108].…”

“…in the molecule-fixed frame. The tensor cH (1) is not a priori symmetric when computed in a specific reference frame, and so the spin-rotation Hamiltonian of the first Hydrogen nucleus must be made manifestly Hermitian [107] as Ĥs−r;H (1) →…”