Rotational spectrum of SO3 and theoretical evidence for the formation of sixfold rotational energy-level clusters in its vibrational ground state

Abstract

The structure of the purely rotational spectrum of sulphur trioxide (32)S(16)O3 is investigated using a new synthetic line list. The list combines line positions from an empirical model with line intensities determined, in the form of Einstein coefficients, from variationally computed ro-vibrational wavefunctions in conjunction with an ab initio dipole moment surface. The empirical model providing the line positions involves an effective, Watsonian-type rotational Hamiltonian with literature parameter values resulting from least-squares fittings to observed transition frequencies. The formation of so-called 6-fold rotational energy clusters at high rotational excitation are investigated. The SO3 molecule is planar at equilibrium and exhibits a unique type of rotational-energy clustering associated with unusual stabilization axes perpendicular to the S-O bonds. This behaviour is characterized theoretically in the J range from 100-250. The wavefunctions for these cluster states are analysed, and the results are compared to those of a classical analysis in terms of the rotational-energy-surface formalism.

The ExoMol project: Software for computing large molecular line lists

“…Apart from computing energies and spectra for a series of polyatomic molecules, the program TROVE has being applied to study some of their properties, for example, the so‐called rotational energy clustering or the temperature‐averaged nuclear spin–spin matrix elements and isotropic hyperfine coupling constant …”

“…TROVE has been used to study the effect of the rotational energy clustering for the XY 3 type molecules SbH 3 , BiH 3 , PH 3 , AsH 3 , and SO 3 . To analyze the associated localization rotations, the following modules were implemented: (i) construction of classical rotational energy surfaces, (ii) construction of rotational probability density, and (iii) determination of axes characterized by stable localized rotations.…”

Perspective: Computing (ro-)vibrational spectra of molecules with more than four atoms

“…The basis functions are products of vibrational wavefunctions (which are contracted basis functions) and Wigner functions. 2,65,88,89,91 All SF/D calculations are limited by the size of the Hamiltonian matrix. Using commonly accessible computers it is not possible to use a direct diagonalization algorithm for matrices whose size is larger than 100'000.…”

Perspective: Accurate ro-vibrational calculations on small molecules

“…24,25 Even without the need for refining the PES, variational nuclear motion calculations have been used to predict 26 and assign 27,28 spectra. They have also been used to probe the fundamental behaviour of molecules revealing the clustering of energy levels at high rotational angular momentum, 29,30 the rearrangement of the levels around the monodromy point which occurs when a bent molecule becomes linear, 31 and the quantal behavior of classically chaotic systems. 32 More recently such calculations are playing a role in guiding observations of processes important for fundamental physics such as a possible change with time in the proton-to-electron mass ratio.…”