Density Functional Study of Tetra-Atomic Clusters and Complexes of the Group 16 Elements: Trends in Structure and Bonding

A DFT study of Se n Te n clusters

First principles calculations have been performed to study the characteristic properties of Se _n Te _n (n = 5-10) clusters. The present study reveals that the properties of these small clusters are consistent with the properties of Se-Te glassy systems. Several hundred equilibrium structures obtained from a genetic algorithm based USPEX code are relaxed to their minimum energy using the VASP code. Most of the lowest energy buckled ring-like structures are formed from Se-Te heteropolar bonds. Detailed structural analysis and distance energy plots unveil that many equilibrium structures are close in energy to their global minimum. The computed Raman and IR spectra show the dominance of Se-Te heteropolar bonds, consistent with earlier simulation and experimental findings in Se_1-x Te _x glass materials. Low frequency vibrational modes observed in small clusters are characteristic features of amorphous materials. Non-bonding orbitals (lone pair) are observed in the HOMO, whereas the LUMO is formed from purely antibonding orbitals. The dielectric functions corroborate the bonding mechanism and slightly polar nature of Se _n Te _n clusters. The energy loss and absorption coefficient indicate the presence of π-plasmons in the UV-visible region. Furthermore, it is ascertained that the use of a hybrid functional (B3LYP) does not affect the properties of small clusters appreciably, except causing a blue shift in the optical spectra. Hence, we find that the small clusters have bearing on the formation of glassy Se-Te systems.

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.

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

The rotational spectrum of S4 has been observed for the first time in an electrical discharge through sulfur vapor. Two techniques have been used: Fourier transform microwave spectroscopy and long-path millimeter-wave absorption spectroscopy. Small, but systematic shifts of the measured transition frequencies of the normal isotopic species indicate that S4 has C2v symmetry but with a low-lying transition state of D2h symmetry, yielding interchange tunneling at 14.1(2) kHz in its ground vibrational state. From the rotational constants of the normal and the single 34S isotopic species, an experimental (r0) structure has been derived: S4 is a singlet planar trapezoid with a terminal bond length of 1.899(7) A, a central bond of 2.173(32) A, and an S-S-S angle of 103.9(8) degrees. Like thiozone (S3), S4 is a candidate for detection in the atmosphere of the Jovian moon Io and in other astronomical sources.

Evidence for the Blue 10π S62+ Dication in Solutions of S8(AsF6)2: A Computational Study Including Solvation Energies

The energetics of dissociation reactions of S(8)(2+) into stoichiometric mixtures of S(n)(+), n = 2-7, and S(m)(2+), m = 3, 4, 6, 10, were investigated by the B3PW91 method [6-311+G(3df)//6-311+G] in the gas phase and in solution, with solvation energies calculated using the SCIPCM model and in some cases also the COSMO model [B3PW91/6-311+G*, dielectric constants 2-30, 83, 110]. UV-vis spectra of all species were calculated at the CIS/6-311G(2df) level and for S(4)(2+) and S(6)(2+) also at the TD-DFT level (BP86/SV(P)). Standard enthalpies of formation at 298 K were derived for S(3)(2+) (2538 kJ/mol), S(6)(2+) (2238 kJ/mol), and S(10)(2+) (2146 kJ/mol). A comparison of the observed and calculated UV-vis spectra based on our calculated thermochemical data in solution suggests that, in the absence of traces of facilitating agent (such as dibromine Br(2)), S(8)(2+) dissociates in dilute SO(2) solution giving an equilibrium mixture of ca. 0.5S(6)(2+) and S(5)(+) (K approximately 8.0) while in the more polar HSO(3)F some S(8)(2+) remains (K approximately 0.4). According to our calculations, the blue color of this solution is likely due to the pi-pi transition of the previously unknown 10 pi S(6)(2+) dication, and the previously assigned S(5)(+) is a less important contributor. Although not strictly planar, S(6)(2+) may be viewed as a 10 pi electron Hückel-aromatic ring containing a thermodynamically stable 3p(pi)-3p(pi) bond [d(S-S) = 2.028 A; tau(S-S-S-S) = 47.6 degrees ]. The computations imply that the new radical cation S(4)(+) may be present in sulfur dioxide solutions given on reaction of sulfur oxidized by AsF(5) in the presence of a facilitating agent. The standard enthalpy of formation of S(6)(AsF(6))(2)(s) was estimated as -3103 kJ/mol, and the disproportionation enthalpy of 2S(6)(AsF(6))(2)(s) to S(8)(AsF(6))(2)(s) and S(4)(AsF(6))(2)(s) as exothermic by 6-17 kJ/mol. The final preference of the observed disproportionation products is due to the inclusion of solvent molecules, e.g., AsF(3), that additionally favors the disproportionation of 2S(6)(AsF(6))(2)(s) into S(8)(AsF(6))(2)(s) and S(4)(AsF(6))(2)(AsF(3))(s) by 144 kJ/mol.