Terahertz rotational spectra of NH 2 OH in the ground and some low excited vibrational states

Centrifugal Distortion Analysis of a Near-Spherical Top, SO2F2: The First Determination of All Six Quartic Centrifugal Distortion Constants for an Asymmetric Top

“…[13], [16], the contributions of the transformation [2] to the quartic distortion constants represented by Eqs. [3]- [8] are small and these constants according to the classification on p. 135 of Ref. (20) are only marginally affected by the transformation.…”

“…[3]- [8] that there is an infinite number of sets of the six distortion constants T , one for each value of the free parameter s 111 , that all reproduce the energies equally well and this is the cause of the well-known problem of indeterminacies (2,4,5,6,20) in fitting the quartic distortion constants of an asymmetric rotor. The problem is solved by constraining one of the fitted quartic parameters to a predetermined value, usually to zero value, and such a constraint assigns a definite value to the free parameter s 111 .…”

“…Inspection of Eqs. [3]- [8] show that in such a case the alternative constraint is T 022 ϭ 0, [14] called S Reduction (4,6,7), which should be preferred for quasisymmetric asymmetric tops. However, both A and S reductions blow up for an accidental spherical top, where [15] and in addition to the relation [13] we have also:…”

“…[2] that besides its principal contributions to the quartic distortion constants represented by Eqs. [3]- [8], this parameter contributes also to the higher order terms, contributions to the sextic parameters being described by Eqs. [17]- [26].…”

“…The solution of the problem, the reduction of the rotational Hamiltonian for the nondegenerate isolated states, has become by now part of the textbooks on the subject (2)(3)(4). Specific cases requiring modifications of the Watson's standard A Reduction for an asymmetric rotor (5,6), when two rotational constants have nearly equal values, an asymmetric rotor becomes accidentally quasisymmetric top and the S Reduction (6, 7) must be applied, as is the case for molecules like D 2 S 2 (7) and NH 2 OH (8), are now well understood and documented in the literature. Similarly, when the two different rotational constants of a symmetric rotor have very close values, the B Reduction (9, 10) appropriate for quasispheric molecules must be applied.…”