RESUMO
We present a detailed theoretical study of the molecular oxygen trimer where the potential energy surfaces of the seven multiplet states have been calculated by means of a pair approximation with very accurate dimer ab initio potentials. In order to obtain all the states a matrix representation of the potential using the uncoupled spin representation has been applied. The S = 0 ${S = 0}$ and S = 1 ${S = 1}$ states are nearly degenerate and low-lying isomers appear for most multiplicities. A crucial point in deciding the relative stabilities is the zero-point energy which represents a sizable fraction of the electronic well-depth. Therefore, we have performed accurate diffusion Monte Carlo studies of the lowest state in each multiplicity. Analysis of the wavefunction allows a deeper interpretation of the cluster structures, finding that they are significantly floppy in most cases.
RESUMO
Oxygen in its elemental form shows a variety of magnetic properties in its condensed phases; in particular, the epsilon solid phase loses its magnetism. These phenomena reflect the nature of the intermolecular forces present in the solid and the changes that arise with variations in pressure and temperature. In this study, we use intermolecular potentials obtained with unrestricted ab initio methods to model the singlet state of the oxygen tetramer [(O2)4], which is the unit cell, consistent with the non-magnetic character of this phase. To do this, we perform an analysis of the coupled-uncoupled representations of the spin operator together with a pairwise approximation and the Heisenberg Hamiltonian. We start from unrestricted potentials for the dimer calculated at a high level as well as different density functional theory (DFT) functionals and then apply a finite model to predict the properties of the epsilon phase. The results obtained in this way reproduce well the experimental data in the entire pressure range below 60 GPa. Additionally, we show the importance of calculating the singlet state of the tetramer as opposed to previous DFT periodic calculations, where the unrestricted description leads to a mixture of spin states and a poor comparison with the experiment. This point is crucial in the recent discussion about the coexistence of two epsilon phases: one where the identity of each O2 with spin S = 1 is retained within the tetramer unit vs another at higher pressures where the tetramer behaves as a single unit with a closed-shell character.
RESUMO
The properties of molecular oxygen including its condensed phases continue to be of great relevance for the scientific community. The richness and complexity of its associated properties stem from the fact that it is a very stable diradical. Its open-shell nature leads to low-lying multiplets with total electronic spin S = 0, 1, 2 in the case of the dimer, (O2)2, and the accurate calculation of the intermolecular potentials represents a challenge to ab initio electronic structure methods. In this work, we present intermolecular potentials calculated at a very high level, thus competing with the most accurate restricted potentials obtained to date. This is accomplished by drawing on an analogy between the coupled and uncoupled representations of angular momentum and restricted vs unrestricted methodologies. The S = 2 state can be well represented by unrestricted calculations in which the spins of the unpaired electrons are aligned in parallel; however, for the state where they are aligned in antiparallel fashion, it would seem that the total spin is not well defined, i.e., the well-known spin contamination problem. We show that its energy corresponds to that of the S = 1 state and perform unrestricted coupled cluster calculations for these two states. Then, we obtain the S = 0 state through the Heisenberg Hamiltonian and show that this is very reliable in the well region of the potentials. We make extensive comparisons with the best restricted potentials [Bartolomei et al., Phys. Chem. Chem. Phys. 10(35), 5374-5380 (2008)] and with reliable experimental determinations, and a very good agreement is globally found.