An unrestricted approach for the accurate calculation of the interaction potentials of open-shell monomers: The case of O2–O2

Abstract

The properties of molecular oxygen including its condensed phases continue to be of great relevance for the scientific community. The richness and complexity of their 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, (𝑶 𝟐 ) 𝟐 , and the accurate calculation of their 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 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, 1-7, 2008) and with reliable experimental determinations, a very good agreement is globally found.

Molecular Oxygen Trimer: Multiplet Structures and Stability

“…In the more recent study where dimer, trimer and tetramer were analyzed they found a small deflection consistent with singlet states; however, the authors point out that the deflection is larger than the experimental error suggesting non‐zero spin states could be present. In the older study the authors conclude that the dimer is paramagnetic in contradiction with the more recent study and many other experimental and theoretical studies [4,6,8,9,11,13,15] …”

“…These matrices are diagonal, and their elements are the interaction potentials obtained previously by our group [12,25] and then, by means of a similarity transformation, change the basis to the uncoupled representation, where block-diagonal matrices are obtained when selecting the uncoupled basis set in a decreasing order of the spin projection operator, S z . [13] Once we obtained the interaction potential matrix of the dimer in the uncoupled representation, we use its matrix elements to construct the trimer matrix. We use Eq.…”

“…To do so, we construct the potential matrices of the oxygen dimer in the coupled representation. These matrices are diagonal, and their elements are the interaction potentials obtained previously by our group [12,25] and then, by means of a similarity transformation, change the basis to the uncoupled representation, where block‐diagonal matrices are obtained when selecting the uncoupled basis set in a decreasing order of the spin projection operator, S z [13] …”

“…Furthermore, most of the detailed studies on neutral trimers have relied on the infrared activity of the monomers. [2,3] In this sense it is worth noticing that most of the studies on neutral molecular oxygen clusters so far have concentrated on the dimer, [4][5][6][7][8][9][10][11][12][13][14][15] the only exceptions we know about are a theoretical study of large clusters [16] and Stern-Gerlach studies [17,18] where only the total spin of the system is determined. In the more recent study where dimer, trimer and tetramer were analyzed they found a small deflection consistent with singlet states; however, the authors point out that the deflection is larger than the experimental error suggesting nonzero spin states could be present.…”

“…In the older study the authors conclude that the dimer is paramagnetic in contradiction with the more recent study and many other experimental and theoretical studies. [4,6,8,9,11,13,15] It is of interest to mention that molecular oxygen tetramer units characterize the high pressure solid epsilon phase. [19,20] This phase has several unique properties such as a magnetic and volumetric collapse with increasing pressure.…”