Tetrasulfur, S4: Rotational spectrum, interchange tunneling, and geometrical structure

High-resolution CH stretch spectroscopy of jet-cooled cyclopentyl radical: First insights into equilibrium structure, out-of-plane puckering, and IVR dynamics

First, high-resolution sub-Doppler infrared spectroscopic results for cyclopentyl radical (C5H9) are reported on the α-CH stretch fundamental with suppression of spectral congestion achieved by adiabatic cooling to Trot ≈ 19(4) K in a slit jet expansion. Surprisingly, cyclopentyl radical exhibits a rotationally assignable infrared spectrum, despite 3N − 6 = 36 vibrational modes and an upper vibrational state density (ρ ≈ 40–90 #/cm−1) in the critical regime (ρ ≈ 100 #/cm−1) necessary for onset of intramolecular vibrational relaxation (IVR) dynamics. Such high-resolution data for cyclopentyl radical permit detailed fits to a rigid-rotor asymmetric top Hamiltonian, initial structural information for ground and vibrationally excited states, and opportunities for detailed comparison with theoretical predictions. Specifically, high level ab initio calculations at the coupled-cluster singles, doubles, and perturbative triples (CCSD(T))/ANO0, 1 level are used to calculate an out-of-plane bending potential, which reveals a C2 symmetry double minimum 1D energy surface over a C2v transition state. The inversion barrier [Vbarrier ≈ 3.7(1) kcal/mol] is much larger than the effective moment of inertia for out-of-plane bending, resulting in localization of the cyclopentyl wavefunction near its C2 symmetry equilibrium geometry and tunneling splittings for the ground state too small (<1 MHz) to be resolved under sub-Doppler slit jet conditions. The persistence of fully resolved high-resolution infrared spectroscopy for such large cyclic polyatomic radicals at high vibrational state densities suggests a “deceleration” of IVR for a cycloalkane ring topology, much as low frequency torsion/methyl rotation degrees of freedom have demonstrated a corresponding “acceleration” of IVR processes in linear hydrocarbons.

Ab initio molecular dynamics studies of tetrasulfur. Dynamics coupling the C2v open and D2h closed forms of S4

Ab initio molecular dynamics (AIMD) simulations were performed on the closed D(2h) and open C(2v) isomers of tetrasulfur. After a careful calibration of the electronic structure method, the calculations were done using the BPW91/aug-cc-pVTZ method. This combination of method/basis set adequately reproduces the relative benchmark CCSD(T) energy difference [Matus, M.; Dixon, D.; Peterson, K. A.; Harkless, J. A. W.; Francisco, J. S. J. Chem. Phys. 2007, 127, 174305] between these two isomers and, crucially, the fact that the D(2h) structure is a transition state linking two equivalent (mirror images) C(2v) isomers. The trajectories show that the symmetric open C(2v) isomers interconvert when passing through the D(2h) closed transition state structure and that, unlike tetraoxygen, no three-dimensional structures arise. The dynamic vibrational analysis yields peaks in good agreement with the static CCSD(T) harmonic frequencies and explains higher peaks as overtones, thus showing that unlike previous AIMD DFT-based approaches, carefully calibrated exchange-correlation functionals can produce reliable molecular dynamics results for complex PESs as the one corresponding to the lowest singlet of S(4).

On the Electronic States of S4+ and S4- Isomers

For three energetically most stable structures of tetrasulfur, S4, S4+ and S4- (cis-chain, rectangular, and trans-chain forms), equilibrium geometries, harmonic wavenumbers, ionization energies, electron affinities, electronic vertical and adiabatic excitation energies, and electronic transition moments were calculated by ab initio methods. It was found that similarly to the ground state of S4, the S4+ cis-isomer could interconvert, perturbed, however, by vibronic coupling with a very close-lying excited state and large-amplitude vibrations. Moreover, the cis- and rectangular minima are calculated to be energetically degenerated. The ω values in all three species agree reasonably well with existing experimental and theoretical data. The calculated patterns of harmonic modes suggest the existence of very complex low-lying anharmonic polyads in all three species. The calculated ionization energies reported previously are compared with the present more accurate data. Also the electronic transition moments and the energy positions of the electronic states with higher spin multiplicities are given.

Pseudo-Jahn-Teller origin of geometry and pseudorotations in second row tetra-atomic clusters X4 (X=Na,Mg,Al,Si,P,S)

Experimentally determined or ab initio calculated molecular geometries carry no information about their origin. Employing the Jahn-Teller (JT) vibronic coupling effects as the only source of instability and consequent distortions of high-symmetry molecular configurations, we have worked out a procedure that allows us to trace the origin of particular geometries and determine the detailed electronic mechanism of their formation. This procedure is illustrated by considering a series of X(4) clusters with X=Na, Mg, Al, Si, P, and S. It shows explicitly why Na(4), Si(4), and Al(4) have a rhombic geometry in the ground state, while Mg(4) and P(4) are tetrahedral, whereas S(4) is a trapezium. Even when the minimum-energy geometries are the same (as in the case of rhombic Na(4), Si(4), and Al(4)), the electronic mechanism of their formation is quite different. In particular, in Na(4) and Si(4) the rhombic minima are produced by a strong pseudo JT coupling between two excited states in the square-planar configuration (different in the two cases) that stabilizes one of them and makes it the ground state by rhombic distortions. The rhombic configuration of Al(4) is due to the pseudo JT effect in its ground-state square-planar configuration, and the trapezium in S(4) is formed by two pseudo JT couplings essentially involving excited states. In several cases this analysis shows also the tunneling paths between equivalent configurations.

Rotational spectroscopy and equilibrium structures of S3 and S4

The sulfur molecules thiozone S3 and tetrasulfur S4 have been observed in a supersonic molecular beam in the centimeter-wave band by Fourier transform microwave spectroscopy, and in the millimeter- and submillimeter-wave bands in a low-pressure glow discharge. For S3 over 150 rotational transitions between 10 and 458 GHz were measured, and for S4 a comparable number between 6 and 271 GHz. The spectrum of S3 is reproduced to within the measurement uncertainties by an asymmetric top Hamiltonian with three rotational and 12 centrifugal distortion constants; ten distortion constants, but an additional term to account for very small level shifts caused by interchange tunneling, are required to reproduce to comparable accuracy the spectrum of S4. Empirical equilibrium (r(e)(emp)) structures of S3 and S4 were derived from experimental rotational constants of the normal and sulfur-34 species and vibrational corrections from coupled-cluster theory calculations. Quantum chemical calculations show that interchange tunneling occurs because S4 automerizes through a transition state with D2h symmetry which lies about 500 cm(-1) above the two equivalent C2upsilon minima on the potential energy surface.

Structures of the trisulfur oxides S3O and S3O˙+: branched rings, not open chains

Higher-level ab initio calculations showed that the global energy minimum for both S3O and S3O.+ is a branched, three-membered ring, not an open chain form.