Polyvalent s-block elements: A missing link challenges the periodic law of chemistry for the heavy elements.

The Periodic Law of Chemistry is one of the great discoveries in cultural history. Elements behaving chemically similar are empirically merged in groups G of a Periodic Table, each element with G valence electrons per neutral atom, and with upper limit G for the oxidation and valence numbers. Here, we report that among the usually mono- or di-valent s-block elements (G = 1 or 2), the heaviest members (87Fr, 88Ra, 119E, and 120E) with atomic numbers Z = 87, 88, 119, 120 form unusual 5- or 6-valent compounds at ambient conditions. Together with well-reported basic changes of valence at the end of the 6d-series, in the whole 7p-series, and for 5g6f-elements, it indicates that at the bottom of common Periodic Tables, the classic Periodic Law is not as straightforward as commonly expected. Specifically, we predict the feasible experimental synthesis of polyvalent [RaL-n] (n = 4, 6) compounds.

Synthesis and Characterization of U≡C Triple Bonds in Fullerene Compounds.

Despite decades of efforts, the actinide-carbon triple bond has remained an elusive target, defying synthesis in any isolable compound. Herein, we report the successful synthesis of uranium-carbon triple bonds in carbide-bridged bimetallic [U≡C-Ce] units encapsulated inside the fullerene cages of C72 and C78. The molecular structures of UCCe@C2n and the nature of the U≡C triple bond were characterized through X-ray crystallography and various spectroscopic analyses, revealing very short uranium-carbon bonds of 1.921(6) and 1.930(6) Å, with the metals existing in their highest oxidation states of +6 and +4 for uranium and cerium, respectively. Quantum-chemical studies further demonstrate that the C2n cages are crucial for stabilizing the [UVI≡C-CeIV] units through covalent and coordinative interactions. This work offers a new fundamental understanding of the elusive uranium-carbon triple bond and informs the design of complexes with similar bonding motifs, opening up new possibilities for creating distinctive molecular compounds and materials.

On the highest oxidation states of the actinoids in AnO4 molecules (An = Ac - Cm): A DMRG-CASSCF study.

Actinoid tetroxide molecules AnO4 (An = Ac - Cm) are investigated with the ab initio density matrix renormalization group (DMRG) approach. Natural orbital shapes are used to read out the oxidation state (OS) of the f-elements, and the atomic orbital energies and radii are used to explain the trends. The highest OSs reveal a "volcano"-type variation: For An = Ac - Np, the OSs are equal to the number of available valence electrons, that is, AcIII , ThIV , PaV , UVI , and NpVII . Starting with plutonium as the turning point, the highest OSs in the most stable AnO4 isomers then decrease as PuV , AmV , and CmIII , indicating that the 5f-electrons are hard to be fully oxidized off from Pu onward. The variations are related to the actinoid contraction and to the 5f-covalency characteristics. Combined with previous work on OSs, we review their general trends throughout the periodic table, providing fundamental understanding of OS-relevant phenomena.

Cis- and trans-binding influences in [NUO·(N2)n].

Uranium nitride-oxide cations [NUO]+ and their complexes with equatorial N2 ligands, [NUO·(N2)n]+ (n = 1-7), were synthesized in the gas phase. Mass-selected infrared photodissociation spectroscopy and quantum chemical calculations confirm [NUO·(N2)5]+ to be a sterically fully coordinated cation, with electronic singlet ground state of 1A1, linear [NUO]+ core, and C5v structure. The presence of short N-U bond distances and high stretching modes, with slightly elongated U-O bond distances and lowered stretching modes, is rationalized by attributing them to cooperative covalent and dative [ǀN≡U≡Oǀ]+ triple bonds. The mutual trans-interaction through flexible electronic U-5f6d7sp valence shell and the linearly increasing perturbation with increase in the number of equatorial dative N2 ligands has also been explained, highlighting the bonding characteristics and distinct features of uranium chemistry.

Permanganyl Fluoride: A Brief History of the Molecule MnO3 F and of Those Who Cared For It.

Permanganyl fluoride's existence at the stability threshold in the series of oxides and oxide fluorides of the late 3d transition metals is reflected by its experimentally challenging properties and by the difficulties posed in the theoretical description of its bonding characteristics. The history of this molecule is reviewed from early qualitative observations and the growing scattered information on its chemical and physical properties to the accurate determination and interpretation of its molecular structure and spectral features. The still problematic theoretical models for MnO4 - and MnO3 F are briefly presented in the broader context of the chemistry of elements in high oxidation states. Short biographies of the scientists engaged in these studies are offered. Related technetium and rhenium compounds are briefly considered for comparison.

Electronic Structure and Spectroscopic Properties of Group-7 Tri-Oxo-Halides MO3X (M = Mn-Bh, X = F-Ts).

The 24 trioxide halide molecules MO3X of the manganese group (M = Mn-Bh; X = F-Ts), which are iso-valence-electronic with the famous MnO4- ion, have been quantum-chemically investigated by quasi-relativistic density-functional and ab initio correlated approaches. Geometric and electronic structures, valence and oxidation numbers, vibrational and electronic spectral properties, energetic stabilities of the monomers in the gas phase, and the decay mode of MnO3F have been investigated. The light Mn-3d species are most strongly electron-correlated, indicating that the concept of a closed-shell Lewis-type single-configurational structure [Mn+7(d0) O-2(p6)3 F-(p6)] reaches its limits. The concept of real-valued spin orbitals φ(r)·α and φ(r)·ß breaks down for the heavy Bh-6d, At-6p and Ts-7p elements because of the dominating spin-orbit coupling. The vigorous decomposition of MnO3F at ambient conditions starts by the autocatalyzed release of n O2 and the formation of MnmO3m-2nFm clusters, triggered by the electron-depleted "oxylic" character of the oxide ligands in MnO3X.

Metal Oxo-Fluoride Molecules OnMF2 (M = Mn and Fe; n = 1-4) and O2MnF: Matrix Infrared Spectra and Quantum Chemistry.

On reacting laser-ablated manganese or iron difluorides with O2 or O3 during codeposition in solid neon or argon, infrared absorptions of several new metal oxo-fluoride molecules, including OMF2, (η1-O2)MF2, (η2-O3)MF2, (η1-O2)2MF2 (M = Mn and Fe), and O2MnF, have been observed. Quantum chemical density functional and multiconfiguration wavefunction calculations have been applied to characterize these new products by their geometric and electronic structures, vibrations, charges, and bonding. The assignment of the main vibrational absorptions as dominant symmetric or antisymmetric M-F or M-O stretching modes is confirmed by oxygen isotopic shifts and quantum chemical calculations of frequencies and thermal stabilities. The tendency of Fe to form polyoxygen complexes in lower oxidation states than the preceding element Mn is affirmed experimentally and supported theoretically. The M-F stretching frequencies of the isolated metal oxo-fluorides may provide a scale for the local charge on the MF2 sites in active energy conversion systems. The study of these species provides insights for understanding the trend of oxidation state changes across the transition-metal series.

Understanding the Uniqueness of 2p Elements in Periodic Tables.

The Periodic Table, and the unique chemical behavior of the first element in a column (group), were discovered simultaneously one and a half centuries ago. Half a century ago, this unique chemistry of the light homologs was correlated to the then available atomic orbital (AO) radii. The radially nodeless 1s, 2p, 3d, 4f valence AOs are particularly compact. The similarity of r(2s)≈r(2p) leads to pronounced sp-hybrid bonding of the light p-block elements, whereas the heavier p elements with n≥3 exhibit r(ns) ≪ r(np) of approximately -20 to -30 %. Herein, a comprehensive physical explanation is presented in terms of kinetic radial and angular, as well as potential nuclear-attraction and electron-screening effects. For hydrogen-like atoms and all inner shells of the heavy atoms, r(2s) ≫ r(2p) by +20 to +30 %, whereas r(3s)≳r(3p)≳r(3d), since in Coulomb potentials radial motion is more radial orbital expanding than angular motion. However, the screening of nuclear attraction by inner core shells is more efficient for s than for p valence shells. The uniqueness of the 2p AO is explained by this differential shielding. Thereby, the present work paves the way for future physical explanations of the 3d, 4f, and 5g cases.

Nine questions on energy decomposition analysis.

The paper collects the answers of the authors to the following questions: Is the lack of precision in the definition of many chemical concepts one of the reasons for the coexistence of many partition schemes? Does the adoption of a given partition scheme imply a set of more precise definitions of the underlying chemical concepts? How can one use the results of a partition scheme to improve the clarity of definitions of concepts? Are partition schemes subject to scientific Darwinism? If so, what is the influence of a community's sociological pressure in the "natural selection" process? To what extent does/can/should investigated systems influence the choice of a particular partition scheme? Do we need more focused chemical validation of Energy Decomposition Analysis (EDA) methodology and descriptors/terms in general? Is there any interest in developing common benchmarks and test sets for cross-validation of methods? Is it possible to contemplate a unified partition scheme (let us call it the "standard model" of partitioning), that is proper for all applications in chemistry, in the foreseeable future or even in principle? In the end, science is about experiments and the real world. Can one, therefore, use any experiment or experimental data be used to favor one partition scheme over another? © 2019 Wiley Periodicals, Inc.

Correspondence on "Core Electron Topologies in Chemical Compounds: Case Study of Carbon versus Silicon".

The conclusions of a recent Communication of Yoshida, Raebiger, Shudo, and Ohno published in this journal, that varying core orbital topologies with minuscule negative tails upon bond formation determine the different chemistries of carbon and silicon and affect ionization energies, excitation energies and bond properties of molecules, are now shown to be based on computational artifacts and oversimplified models. The all-electron wave function uniquely determines the observables, while its representation by one-electron orbital products depends on the details of the chosen approximation and therefore need to be considered with great care.

On the Upper Limits of Oxidation States in Chemistry.

The concept of oxidation state (OS) is based on the concept of Lewis electron pairs, in which the bonding electrons are assigned to the more electronegative element. This approach is useful for keeping track of the electrons, predicting chemical trends, and guiding syntheses. Experimental and quantum-chemical results reveal a limit near +8 for the highest OS in stable neutral chemical substances under ambient conditions. OS=+9 was observed for the isolated [IrO4 ]+ cation in vacuum. The prediction of OS=+10 for isolated [PtO4 ]2+ cations is confirmed computationally for low temperatures only, but hasn't yet been experimentally verified. For high OS species, oxidation of the ligands, for example, of O-2 with formation of . O-1 and O-O bonds, and partial reduction of the metal center may be favorable, possibly leading to non-Lewis type structures.

Diversity of Chemical Bonding and Oxidation States in MS4 Molecules of Group†8 Elements.

The geometric and electronic ground-state structures of 30 isomers of six MS4 molecules (M=Group 8 metals Fe, Ru, Os, Hs, Sm, and Pu) have been studied by using quantum-chemical density functional theory and correlated wavefunction approaches. The MS4 species were compared to analogous MO4 species recently investigated (W. Huang, W.-H. Xu, W. H. E. Schwarz, J. Li, Inorg. Chem. 2016, 55, 4616). A metal oxidation state (MOS) with a high value of eight appeared in the low-spin singlet Td geometric species (Os,Hs)S4 and (Ru,Os,Hs)O4 , whereas a low MOS of two appeared in the high-spin septet D2d species Fe(S2 )2 and (slightly excited) metastable Fe(O2 )2 . The ground states of all other molecules had intermediate MOS values, with S2- , S22- , S21- (and O2- , O1- , O22- , O21- ) ligands bonded by ionic, covalent, and correlative contributions. The known tendencies toward lower MOS on going from oxides to sulfides, from Hs to Os to Ru, and from Pu to Sm, and the specific behavior of Fe, were found to arise from the different atomic orbital energies and radii of the (n-1)p core and (n-1)d and (n-2)f valence shells of the metal atoms in row n of the periodic table. The comparative results of the electronic and geometric structures of the MO4 and MS4 species provides insight into the periodicity of oxidation states and bonding.

Probing the Electronic Structure and Chemical Bonding of Mono-Uranium Oxides with Different Oxidation States: UOx(-) and UOx (x = 3-5).

Uranium oxide clusters UOx(-) (x = 3-5) were produced by laser vaporization and characterized by photoelectron spectroscopy and quantum theory. Photoelectron spectra were obtained for UOx(-) at various photon energies with well-resolved detachment transitions and vibrational resolution for x = 3 and 4. The electron affinities of UOx were measured as 1.12, 3.60, and 4.02 eV for x = 3, 4, and 5, respectively. The geometric and electronic structures of both the anions and the corresponding neutrals were investigated by quasi-relativistic electron-correlation quantum theory to interpret the photoelectron spectra and to provide insight into their chemical bonding. For UOx clusters with x ≤ 3, the O atoms appear as divalent closed-shell anions around the U atom, which is in various oxidation states from U(II)(fds)(4) in UO to U(VI)(fds)(0) in UO3. For x > 3, there are no longer sufficient valence electrons from the U atom to fill the O(2p) shell, resulting in fractionally charged and multicenter delocalized valence states for the O ligands as well as η(1)- or η(2)-bonded O2 units, with unusual spin couplings and complicated electron correlations in the unfilled poly oxo shell. The present work expands our understanding of both the bonding capacities of actinide elements with extended spdf valence shells as well as the multitude of oxygen's charge and bonding states.

Ionic bonding of lanthanides, as influenced by d- and f-atomic orbitals, by core-shells and by relativity.

Lanthanide trihalide molecules LnX3 (X = F, Cl, Br, I) were quantum chemically investigated, in particular detail for Ln = Lu (lutetium). We applied density functional theory (DFT) at the nonrelativistic and scalar and SO-coupled relativistic levels, and also the ab initio coupled cluster approach. The chemically active electron shells of the lanthanide atoms comprise the 5d and 6s (and 6p) valence atomic orbitals (AO) and also the filled inner 4f semivalence and outer 5p semicore shells. Four different frozen-core approximations for Lu were compared: the (1s(2) -4d(10) ) [Pd] medium core, the [Pd+5s(2) 5p(6) = Xe] and [Pd+4f(14) ] large cores, and the [Pd+4f(14) +5s(2) 5p(6) ] very large core. The errors of LuX bonding are more serious on freezing the 5p(6) shell than the 4f(14) shell, more serious upon core-freezing than on the effective-core-potential approximation. The LnX distances correlate linearly with the AO radii of the ionic outer shells, Ln(3+) -5p(6) and X(-) -np(6) , characteristic for dominantly ionic Ln(3+) -X(-) binding. The heavier halogen atoms also bind covalently with the Ln-5d shell. Scalar relativistic effects contract and destabilize the LuX bonds, spin orbit coupling hardly affects the geometries but the bond energies, owing to SO effects in the free atoms. The relativistic changes of bond energy BE, bond length Re , bond force k, and bond stretching frequency vs do not follow the simple rules of Badger and Gordy (Re ∼BE∼k∼vs ). The so-called degeneracy-driven covalence, meaning strong mixing of accidentally near-degenerate, nearly nonoverlapping AOs without BE contribution is critically discussed.

An 18-electron system containing a superheavy element: theoretical studies of sg@au12.

M@Au12 cage molecules (M = transition element from group 6) are interesting clusters with high-symmetric structure and significant stability. As the heavier homologue of W is (106)Sg, it is interesting to pinpoint whether the Sg@Au12 cluster is also stable. Geometric and electronic structures and bonding of various Sg@Au12 isomers were investigated with density functional theory (PW91, PBE, B3LYP) and wave function theory (MP2, CCSD(T)) approaches. The lowest-energy isomer of Sg@Au12 has icosahedral symmetry with significant Sg(6d)-Au(6s) covalent-metallic interaction and is comparable to the lighter homologues (M = Mo, W), with similar binding energy, although Sg follows (as a rare case) the textbook rule "ns below (n - 1)d". The 12 6s valence electrons from Au12 and the six 7s6d ones from Sg can be viewed as an 18e system below and above the interacting Au 5d band, forming nine delocalized multicenter bond pairs with a high stability of ∼0.8 eV of bond energy per each of the 12 Sg-Au contacts. Different prescriptions (orbital, multipole-deformation, charge-partition, and X-ray-spectroscopy based ones) assign ambiguous atomic charges to the centric and peripheral atoms; atomic core-level energy shifts correspond to some negative charge shift to the gold periphery, more so for Cr@Au12 than for Sg@Au12 or Au@Au12.

Theoretical Studies on Hexanuclear Oxometalates [M6L19](q-) (M = Cr, Mo, W, Sg, Nd, U). Electronic Structures, Oxidation States, Aromaticity, and Stability.

We here report a systematic theoretical study on geometries, electronic structures, and energetic stabilities of six hexanuclear polyoxometalates [M6O19](2-) of the six-valence-electron metals including the d-elements M = Cr, Mo, W, Sg from group 6 and the f-elements M = Nd, U. Scalar relativistic density functional theory was applied to these clusters in vacuum and in solution. It is shown that the Oh Lindqvist structure of the isolated [M6O19](2-) units with hexavalent M elements (M(+6)) is only stable for the three heavy transition metals M = Mo, W, and Sg. The rare Th symmetry is predicted for M = U both in vacuum and in solution, owing to pseudo-Jahn-Teller distortion of these closed-shell systems. The Oh and Th structures correspond to cyclic "aromatic" U-̇O-̇U and alternating U=O-U bonding of cross-linked U4O4 rings, respectively. The reduced [U6O19](8-) cluster with pentavalent U(+5) also shows Th symmetry in vacuum, but Oh symmetry in a dielectric environment. The occurrence of different structures for varying fractional oxidation states in different environments is rationalized. Theoretical investigation of the recently synthesized U(+5) complex [U6O13L6](0) (L6 = tetracyclopentadienyl dibipyridine) shows a distorted Th-type symmetry, too. The stabilities of these complexes of different metal oxidation states are consistent with the general periodic trends of oxidation states.

Structures and stability of AnO4 isomers, An = Pu, Am, and Cm: a relativistic density functional study.

Equilibrium structures and energetics of various isomers of molecules with stoichiometry An·4O (An = Pu, Am, and Cm) are studied through electronic structure calculations at the relativistic density functional theory level in the frame of an accurate small-core pseudopotential model. In all cases, the global minima of the An·4O potential energy surfaces correspond to dioxo-superoxido-like species, [AnO2](O2). The stability of the "true" oxides AnO4 decreases from Pu to Cm, whereas the isomers with two O2 groups become relatively more stable. Correlation between the formal oxidation states and the Bader net charges of actinide atoms is discussed. Structural parameters, vibrational frequencies and charge and spin magnetization density distributions are analyzed in order to characterize the different isomers in chemical terms. Decrease of the An oxidation states along the An series is evident.

On two different objectives of the concepts of ionic radii.

Experimentally and theoretically derived interatomic distances (D) and ionic radii (R) of more than a hundred monomeric (AX), dimeric (A2X2, ABXY), and crystalline ([AX]) alkali halide species (A=Li, Na, K, Rb, Cs, Fr; X=H, F, Cl, Br, I, At) have been analyzed. Chemists use the word "atomic radius" for two antithetic concepts. Let D(CiEE'jj') be the "billion" of distances i between two adjacent atoms in the millions of known compounds C from a hundred different elements E in bonding states j. The common chemical aim is partitioning D approximately into increments R(Ej) +R(E'j'). This can be achieved with a few (say

On structure and bonding of lanthanoid trifluorides LnF3 (Ln = La to Lu).

The trends in the series of lanthanoid (lanthanide) trifluoride molecules LnF3 (Ln = La to Lu) are governed by the valence-active Ln(4f,5d,5p,6s) shells. The series is investigated by quasi-relativistic density functional theory at both the scalar and spin-orbit-coupled levels. Integrating many of the previous experimental and theoretical deductions, we obtain the following comprehensive picture: (1) The comparatively small Ln-F bond length contraction of 14 pm from La to Lu is rather smooth but weakly modulated by spin-orbit coupling. (2) From La to Lu the floppy structure becomes more quasi-planar. (3) The heterolytic LnF bond energies (⅓LnF3→⅓Ln(3+) + F(-)) at the spin-orbit averaged level increase smoothly from 15.3 to 16.3 eV for La to Lu, only the 'divalent' lanthanoids Eu and Yb are outliers with 0.2 eV higher bond energies. (4) The homolytic LnF bond energies (⅓LnF3→⅓Ln + F) however show an overall W-shaped double-periodicity with maxima for LaF3, GdF3 and LuF3, decreasing from La to Eu and from Gd to Yb, the large individual variations being caused by different spin-orbit coupling and Coulomb interaction effects in Ln(0) and LnF3. (5) The Ln-F interaction is basically ionic (increasing with decreasing ionic radii) with some dative Ln(3+)← F(-) bonding. (6) The latter is of the Ln(5d)-F(2p) type with a rather constant bond order from La to Lu, with small Ln(5p) and very small Ln(4f) semi-core contributions decreasing from La to Lu. All these trends are rationalized.

100th anniversary of Bohr's model of the atom.

In the fall of 1913 Niels Bohr formulated his atomic models at the age of 27. This Essay traces Bohr's fundamental reasoning regarding atomic structure and spectra, the periodic table of the elements, and chemical bonding. His enduring insights and superseded suppositions are also discussed.