The concepts of oxidation state and atomic charge are entangled in modern materials science. We distinguish between these quantities and consider their fundamental limitations and utility for understanding material properties. We discuss the nature of bonding between atoms and the techniques that have been developed for partitioning electron density. While formal oxidation states help us count electrons (in ions, bonds, lone pairs), variously defined atomic charges are usefully employed in the description of physical processes including dielectric response and electronic spectroscopies. Such partial charges are introduced as quantitative measures in simple mechanistic models of a more complex reality, and therefore may not be comparable or transferable. In contrast, oxidation states are defined to be universal, with deviations constituting exciting challenges as evidenced in mixed-valence compounds, electrides and highly correlated systems. This Perspective covers how these concepts have evolved in recent years, our current understanding and their significance.

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Oxidation states and ionicity

INTRODUCTION Developing the chemistry of late actinides is hindered by the lack of availability of isotopes, the need for specialized research facilities, and the nuclear instability of the elements. Berkelium represents one of the last elements that can be prepared on a milligram scale in nuclear reactors. However, its only available isotope, 249 Bk, has a half-life of only 320 days, which has greatly curtailed the expansion of its chemistry and fundamental exploration of how large relativistic and spin-orbit coupling effects alter its electronic structure. Furthermore, data gathered from Bk(III) in aqueous media suggest that its coordination may be different from that of earlier actinides. However, a single-crystal structure of a berkelium compound has remained elusive, leaving unanswered whether these structural changes occur in the solid state. RATIONALE This work focuses on characterizing two distinct berkelium compounds on the milligram scale. In particular, the goal was to obtain crystals of these compounds that could be used in structure determinations and physical property measurements. Two compounds were selected: a coordination complex of dipicolinate and a borate. Dipicolinate complexation occurs with most other lanthanides and actinides in the +3 oxidation state, facilitating comparisons across the series to discern periodic trends. In the borate family, the structural frameworks are hypersensitive to the nature of the bonding at the metal center and are rearranged accordingly. Modeling the experimental data using a variety of computational techniques allows us to deconvolute the role of covalent bonding and spin-orbit coupling in determining the electronic properties of berkelium. RESULTS Experiments with milligram quantities of 249 Bk were choreographed for 6 months before the arrival of the isotope because the total quantity used in the studies was 13 mg, which corresponds to a specific activity of 21 Ci. Although this isotope is a low-energy β emitter, it decays to 249 Cf at a rate of about 1.2% per week, and the latter produces hard γ radiation that represents a serious external hazard. In addition, the samples described in this work undergo about 10 12 decays per second. This rapid decomposition necessitated the development of techniques for swiftly preparing and encapsulating samples and for collecting all structural and spectroscopic data within 24 hours of crystal formation. After this preparation, the single-crystal structures of Bk(III)tris(dipicolinate) and Bk(III) borate were determined. The latter compound has the same topology as that of californium(III) (Cf) and contains an eight-coordinate BkO 8 unit. This reduction in coordination number is consistent with previous solution-phase x-ray absorption measurements and indicates that a drop in coordination number in the actinide series from nine to eight begins at berkelium. The magnetic and optical properties of these samples were also measured. The red luminescence from Bk(III) was similar in nature to that of curium(III) and is primarily based on an f - f transition. The ingrowth of the broad green luminescence from Cf(III), which is caused by a ligand-to-metal charge transfer, was shown to be distinct in nature from that originating from Bk(III). Ligand-field, density functional theory, and wave-function calculations were used to understand the spectroscopic features and revealed that the single largest contributor to the unexpected electronic properties of Bk(III) is spin-orbit coupling. This effect mixes the first excited state with the ground state and causes a large deviation from a pure Russell-Saunders state. The reduction in the measured magnetic moment for these samples from that calculated for an f 8 electron configuration is primarily attributable to this multiconfigurational ground state. CONCLUSION The crystallographic data indicate that Bk(III) shares more structural similarities with Cf(III) than with Cm(III). However, ligand-field effects are more similar between Bk(III) and Cm(III). Terbium (Tb), in the lanthanide series, represents the closest analog of Bk because the trivalent cations possess 4 f 8 and 5 f 8 configurations, respectively. Spin-orbit coupling in Bk(III) creates mixing of the first excited state ( 5 G 6 ) with the ground state. In contrast, the ground state of the Tb(III)tris(dipicolinate) contains negligible contributions of this type. An overall conclusion from this study is that spin-orbit coupling plays a large role in determining the ground state of late actinide compounds.

https://science.sciencemag.org/content/sci/353/6302/aaf3762.full.pdf

Characterization of berkelium(III) dipicolinate and borate compounds in solution and the solid state

theory of neutron scattering from condensed matter is available in our digital library an online access to it is set as public so you can download it instantly. Our book servers spans in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the theory of neutron scattering from condensed matter is universally compatible with any devices to read.

Theory Of Neutron Scattering From Condensed Matter

Correlated electron materials display a rich variety of notable properties ranging from unconventional superconductivity to metal-insulator transitions. These properties are of interest from the point of view of applications but are hard to treat theoretically, as they result from multiple competing energy scales. Although possible in more weakly correlated materials, theoretical design and spectroscopy of strongly correlated electron materials have been a difficult challenge for many years. By treating all the relevant energy scales with sufficient accuracy, complementary advances in Green's functions and quantum Monte Carlo methods open a path to first-principles computational property predictions in this class of materials.

https://science.sciencemag.org/content/sci/361/6400/348.full.pdf

Toward a predictive theory of correlated materials.

We present phonon properties of plutonium metal obtained from a combination of density-functional-theory (DFT) electronic structure and the recently developed compressive sensing lattice dynamics (CSLD). The CSLD model is here trained on DFT total energies of several hundreds of quasi-random atomic configurations for best possible accuracy of the phonon properties. The calculated phonon dispersions compare better with experiment than earlier results obtained from dynamical mean-field theory. The density-functional model of the electronic structure consists of disordered magnetic moments with all relativistic effects and explicit orbital-orbital correlations. The magnetic disorder is approximated in two ways: (i) a special quasi-random structure and (ii) the disordered-local-moment method within the coherent potential approximation. Magnetism in plutonium has been debated intensely, but the present magnetic approach for plutonium is validated by the close agreement between the predicted magnetic form factor and that of recent neutron-scattering experiments.

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Phonon and magnetic structure in δ-plutonium from density-functional theory

A central issue in material science is to obtain understanding of the electronic correlations that control complex materials. Such electronic correlations frequently arise because of the competition of localized and itinerant electronic degrees of freedom. Although the respective limits of well-localized or entirely itinerant ground states are well understood, the intermediate regime that controls the functional properties of complex materials continues to challenge theoretical understanding. We have used neutron spectroscopy to investigate plutonium, which is a prototypical material at the brink between bonding and nonbonding configurations. Our study reveals that the ground state of plutonium is governed by valence fluctuations, that is, a quantum mechanical superposition of localized and itinerant electronic configurations as recently predicted by dynamical mean field theory. Our results not only resolve the long-standing controversy between experiment and theory on plutonium’s magnetism but also suggest an improved understanding of the effects of such electronic dichotomy in complex materials.

https://advances.sciencemag.org/content/advances/1/6/e1500188.full.pdf

John M. Lawrence

Papers

The valence-fluctuating ground state of plutonium