RESUMEN
The question of the non-magnetic (NM) vs. antiferromagnetic (AF) nature of the ε phase of solid oxygen is a matter of great interest and continuing debate. In particular, it has been proposed that the ε phase is actually composed of two phases, a low-pressure AF ε1 phase and a higher pressure NM ε0 phase [Crespo et al., Proc. Natl. Acad. Sci. U. S. A., 2014, 111, 10427]. We address this problem through periodic spin-restricted and spin-polarized Kohn-Sham density functional theory calculations at pressures from 10 to 50 GPa using calibrated GGA and hybrid exchange-correlation functionals with Gaussian atomic basis sets. The two possible configurations for the antiferromagnetic (AF1 and AF2) coupling of the 0 ≤ S ≤ 1 O2 molecules in the (O2)4 unit cell were studied. Full enthalpy-driven geometry optimizations of the (O2)4 unit cells were done to study the pressure evolution of the enthalpy difference between the non-magnetic and both antiferromagnetic structures. We also address the evolution of structural parameters and the spin-per-molecule vs. pressure. We find that the spin-less solution becomes more stable than both AF structures above 50 GPa and, crucially, the spin-less solution yields lattice parameters in much better agreement with experimental data at all pressures than the AF structures. The optimized AF2 broken-symmetry structures lead to large errors of the a and b lattice parameters when compared with experiments. The results for the NM model are in much better agreement with the experimental data than those found for both AF models and are consistent with a completely non-magnetic (O2)4 unit cell for the low-pressure regime of the ε phase.
RESUMEN
The experimentally characterized ε and ζ phases of solid oxygen are studied by periodic Hartree-Fock (HF) and Density Functional Theory calculations at pressures from 10 to 160 GPa using different types of exchange-correlation functionals with Gaussian atomic basis sets. Full geometry optimizations of the monoclinic C2/m (O2)4 unit cell were done to study the evolution of the structural and electronic properties with pressure. Vibrational calculations were performed at each pressure. While periodic HF does not predict the ε-ζ phase transition in the considered range, Local Density approximation and Generalized Gradient approximation methods predict too low transition pressures. The performance of hybrid functional methods is dependent on the amount of non-local HF exchange. PBE0, M06, B3PW91, and B3LYP approaches correctly predict the structural and electronic changes associated with the phase transition. GGA and hybrid functionals predict a pressure range where both phases coexist, but only the latter type of methods yield results in agreement with experiment. Using the optimized (O2)4 unit cell at each pressure we show, through CASSCF(8,8) calculations, that the greater accuracy of the optimized geometrical parameters with increasing pressure is due to a decreasing multireference character of the unit cell wave function. The mechanism of the transition from the non-conducting to the conducting ζ phase is explained through the Electron Pair Localization Function, which clearly reveals chemical bonding between O2 molecules in the ab crystal planes belonging to different unit cells due to much shorter intercell O2-O2 distances.
RESUMEN
We report high level ab initio supermolecular calculations for the cuboid structure of the disulfur tetramer, (S2)4. Accurate geometries and interaction energies with respect to 4S2 ((3)Σg (-)) were obtained using four different methods, Möller-Plesset perturbation theory (MP2), complete-active-space SCF (CASSCF) + complete active space second-order perturbation (CASPT2), RCCSD(T), and a hybrid CASPT2(singlet-nonet)∕RCCSD(T)-nonet approach with systematic sequences of augmented correlation-consistent basis sets extrapolated to the complete basis set limit. Unlike the van der Waals-like (O2)4 cluster, (S2)4 is found to be much more chemically bound. Our best estimate of the dissociation energy to four S2 molecules is 65 kcal∕mol including the counterpoise correction and an intermolecular distance of 2.74 Å. The singlet ground state of (S2)4 is much less multiconfigurational than that of (O2)4 van der Waals complex, which allows a reliable CCSD(T) description of the singlet potential energy surface of the supermolecule around its equilibrium geometry. The electron pair localization function clearly reveals electron pairing between the S2 units in the complex at the ROHF and the CASSCF∕aug-cc-pVTZ levels. Vibrational analysis at the MP2∕cc-pV(D,T,Q)Z,aug-cc-pVTZ levels yield stable cuboid structures; however, at the CCSD∕aug-cc-pV(D,T)Z levels this analysis reveals a transition state with one imaginary frequency. Thus, further multireference-based studies with large basis sets are required to reliably settle the stability issue for this supermolecular sulfur species.