Variational minimization scheme for the one-particle reduced density matrix functional theory in the ensemble N-representability domain.

The one-particle reduced density-matrix (1-RDM) functional theory is a promising alternative to density-functional theory (DFT) that uses the 1-RDM rather than the electronic density as a basic variable. However, long-standing challenges such as the lack of the Kohn-Sham scheme and the complexity of the pure N-representability conditions are still impeding its wild utilization. Fortunately, ensemble N-representability conditions derived in the natural orbital basis are known and trivial such that almost every functional of the 1-RDM is actually natural orbital functional, which does not perform well for all the correlation regimes. In this work, we propose a variational minimization scheme in the ensemble N-representable domain that is not restricted to the natural orbital representation of the 1-RDM. We show that splitting the minimization into the diagonal and off-diagonal parts of the 1-RDM can open the way toward the development of functionals of the orbital occupations, which remains a challenge for the generalization of site-occupation functional theory in chemistry. Our approach is tested on the uniform Hubbard model using the Müller and the Töws-Pastor functionals, as well as on the dihydrogen molecule using the Müller functional.

Quantum embedding of multi-orbital fragments using the block-Householder transformation.

Recently, some of the authors introduced the use of the Householder transformation as a simple and intuitive method for embedding local molecular fragments [see Sekaran et al., Phys. Rev. B 104, 035121 (2021) and Sekaran et al., Computation 10, 45 (2022)]. In this work, we present an extension of this approach to the more general case of multi-orbital fragments using the block version of the Householder transformation applied to the one-body reduced density matrix, unlocking the applicability to general quantum chemistry/condensed matter physics Hamiltonians. A step-by-step construction of the block Householder transformation is presented. Both physical and numerical areas of interest of the approach are highlighted. The specific mean-field (noninteracting) case is thoroughly detailed as it is shown that the embedding of a given N spin-orbital fragment leads to the generation of two separated sub-systems: (1) a 2N spin-orbitals "fragment+bath" cluster that exactly contains N electrons and (2) a remaining cluster's "environment" described by so-called core electrons. We illustrate the use of this transformation in different cases of embedding scheme for practical applications. We particularly focus on the extension of the previously introduced Local Potential Functional Embedding Theory and Householder-transformed Density Matrix Functional Embedding Theory to the case of multi-orbital fragments. These calculations are realized on different types of systems, such as model Hamiltonians (Hubbard rings) and ab initio molecular systems (hydrogen rings).

Unified picture of anionic redox in Li/Na-ion batteries.

Anionic redox in Li-rich and Na-rich transition metal oxides (A-rich-TMOs) has emerged as a new paradigm to increase the energy density of rechargeable batteries. Ever since, numerous electrodes delivering extra anionic capacity beyond the theoretical cationic capacity have been reported. Unfortunately, most often the anionic capacity achieved in charge is partly irreversible in discharge. A unified picture of anionic redox in A-rich-TMOs is designed here to identify the electronic origin of this irreversibility and to propose new directions to improve the cycling performance of the electrodes. The electron localization function is introduced as a holistic tool to unambiguously locate the oxygen lone pairs in the structure and follow their participation in the redox activity of A-rich-TMOs. The charge-transfer gap of transition metal oxides is proposed as the pertinent observable to quantify the amount of extra capacity achievable in charge and its reversibility in discharge, irrespective of the material chemical composition. From this generalized approach, we conclude that the reversibility of the anionic capacity is limited to a critical number of O holes per oxygen, hO ≤ 1/3.

Author Correction: Unified picture of anionic redox in Li/Na-ion batteries.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Charge Transfer Band Gap as an Indicator of Hysteresis in Li-Disordered Rock Salt Cathodes for Li-Ion Batteries.

Disordered rock salt cathodes showing both anionic and cationic redox are being extensively studied for their very high energy storage capacity. Mn-based disordered rock salt compounds show much higher energy efficiency compared to the Ni-based materials as a result of the different voltage hysteresis, 0.5 and 2 V, respectively. To understand the origin of this difference, we herein report the design of two model compounds, Li1.3Ni0.27Ta0.43O2 and Li1.3Mn0.4Ta0.3O2, and study their charge compensation mechanism through the uptake and removal of Li via an arsenal of analytical techniques. We show that the different voltage hysteresis with Ni or Mn substitution is due to the different reduction potential for anionic redox. We rationalized such a finding by DFT calculations and propose this phenomenon to be nested in the smaller charge transfer band gap of the Ni-based compounds compared to that of the Mn ones. Altogether, these findings provide vital guidelines for designing high-capacity disordered rock salt cathode materials based on anionic redox activity for the next generation of Li ion batteries.

Alkali-Glass Behavior in Honeycomb-Type Layered Li3-xNaxNi2SbO6 Solid Solution.

Layered oxide compositions Li3-xNaxNi2SbO6 have been prepared by solid-state synthesis. A complete solid solution is evidenced and characterized by X-ray and neutron diffraction as well as 7Li and 23Na solid-state nuclear magnetic resonance spectroscopy. The transition-metal layer is characterized by the classic honeycomb Ni2+/Sb5+ ordering, whereas a more uncommon randomly mixed occupancy of lithium and sodium is evidenced within the alkali interslab space. In situ X-ray diffraction and density functional theory calculations show that this alkali disordered feature is entropically driven. Fast cooling then appears as a synthesis root to confine bidimensional alkali glass within crystalline layered oxides.

Electrochemical activity and high ionic conductivity of lithium copper pyroborate Li6CuB4O10.

In the search for new cathode materials for Li-ion batteries, borate (BO3(3-)) based compounds have gained much interest during the last two decades due to the low molecular weight of the borate polyanions which leads to active materials with increased theoretical capacities. In this context we herein report the electrochemical activity versus lithium and the ionic conductivity of a diborate or pyroborate B2O5(4-) based compound, Li6CuB4O10. By combining various electrochemical techniques with in situ X-ray diffraction, we show that this material can reversibly insert/deinsert limited amounts of lithium (∼0.3 Li(+)) in a potential window ranging from 2.5 to 4.5 V vs. Li(+)/Li(0). We demonstrate, via electron paramagnetic resonance (EPR), that such an electrochemical activity centered near 4.25 V vs. Li(+)/Li(0) is associated with the Cu(3+)/Cu(2+) redox couple, confirmed by density functional theory (DFT) calculations. Another specificity of this compound lies in its different electrochemical behavior when cycled down to 1 V vs. Li(+)/Li(0) which leads to the extrusion of elemental copper via a conversion type reaction as deduced by transmission electron microscopy (TEM). Lastly, we probe the ionic conductivity by means of AC and DC impedance measurements as a function of temperature and show that Li6CuB4O10 undergoes a reversible structural transition around 350 °C, leading to a surprisingly high ionic conductivity of ∼1.4 mS cm(-1) at 500 °C.

Chemical Activity of the Peroxide/Oxide Redox Couple: Case Study of Ba5Ru2O11 in Aqueous and Organic Solvents.

The finding that triggering the redox activity of oxygen ions within the lattice of transition metal oxides can boost the performances of materials used in energy storage and conversion devices such as Li-ion batteries or oxygen evolution electrocatalysts has recently spurred intensive and innovative research in the field of energy. While experimental and theoretical efforts have been critical in understanding the role of oxygen nonbonding states in the redox activity of oxygen ions, a clear picture of the redox chemistry of the oxygen species formed upon this oxidation process is still missing. This can be, in part, explained by the complexity in stabilizing and studying these species once electrochemically formed. In this work, we alleviate this difficulty by studying the phase Ba5Ru2O11, which contains peroxide O22- groups, as oxygen evolution reaction electrocatalyst and Li-ion battery material. Combining physical characterization and electrochemical measurements, we demonstrate that peroxide groups can easily be oxidized at relatively low potential, leading to the formation of gaseous dioxygen and to the instability of the oxide. Furthermore, we demonstrate that, owing to the stabilization at high energy of peroxide, the high-lying energy of the empty σ* antibonding O-O states limits the reversibility of the electrochemical reactions when the O22-/O2- redox couple is used as redox center for Li-ion battery materials or as OER redox active sites. Overall, this work suggests that the formation of true peroxide O22- states are detrimental for transition metal oxides used as OER catalysts and Li-ion battery materials. Rather, oxygen species with O-O bond order lower than 1 would be preferred for these applications.

Visualization of O-O peroxo-like dimers in high-capacity layered oxides for Li-ion batteries.

Lithium-ion (Li-ion) batteries that rely on cationic redox reactions are the primary energy source for portable electronics. One pathway toward greater energy density is through the use of Li-rich layered oxides. The capacity of this class of materials (>270 milliampere hours per gram) has been shown to be nested in anionic redox reactions, which are thought to form peroxo-like species. However, the oxygen-oxygen (O-O) bonding pattern has not been observed in previous studies, nor has there been a satisfactory explanation for the irreversible changes that occur during first delithiation. By using Li2IrO3 as a model compound, we visualize the O-O dimers via transmission electron microscopy and neutron diffraction. Our findings establish the fundamental relation between the anionic redox process and the evolution of the O-O bonding in layered oxides.