Fractional loop delays in adaptive optics modeling and control.

This paper revisits the problem of optimal (minimum variance) control for adaptive optics (AO) systems when measurement and command applications are asynchronous, resulting in a non-integer servo loop delay. When not properly accounted for, such fractional delays may severely degrade the AO performance, especially in the presence of high-frequency vibrations. We present evidence of this performance degradation thanks to in-lab experimental measurements on the Gran Telescopio Canarias Adaptive Optics (GTCAO) system controlled with standard suboptimal linear quadratic Gaussian (LQG) controllers. A constructive, easy to implement LQG control design is then proposed and validated in a simulation for vibrations affecting the tip-tilt modes. Our methodology is very interesting because it allows a performance assessment for any linear controller in terms of variance, rejection transfer functions, power spectral densities, and stability margins. We also show how the continuous-time disturbance model can be derived from standard discrete-time disturbance data-based modeling.

In vivo stability of 211At-radiopharmaceuticals: on the impact of halogen bond formation.

211At, when coupled to a targeting agent, is one of the most promising radionuclides for therapeutic applications. The main labelling approach consists in the formation of astatoaryl compounds, which often show a lack of in vivo stability. The hypothesis that halogen bond (XB) interactions with protein functional groups initiate a deastatination mechanism is investigated through radiochemical experiments and DFT modelling. Several descriptors agree on the known mechanism of iodoaryl substrates dehalogenation by iodothyronine deiodinases, supporting the higher in vivo dehalogenation of N-succinimidyl 3-[211At]astatobenzoate (SAB) conjugates in comparison with their iodinated counterparts. The guanidinium group in 3-[211At]astato-4-guanidinomethylbenzoate (SAGMB) prevents the formation of At-mediated XBs with the selenocysteine active site in iodothyronine deiodinases. The initial step of At-aryl bond dissociation is inhibited, elucidating the better in vivo stability of SAGMB conjugates compared with those of SAB. The impact of astatine's ability to form XB interactions on radiopharmaceutical degradation may not be limited to the case of aryl radiolabeling.

Pourbaix Diagram of Astatine Revisited: Experimental Investigations.

The Pourbaix diagram of an element displays its stable chemical forms with respect to the redox potential and pH of the solution, whose knowledge is fundamental for understanding and anticipating the chemistry of the element in a specified solution. Unlike most halogens, the Pourbaix diagram in the aqueous phase for astatine (At, Z = 85) is still under construction. In particular, the predominant domains of two astatine species assumed to exist under alkaline conditions, At- and AtO(OH)2-, need to be refined. Through high-performance ion-exchange chromatography, electromobility measurements, and competition experiments, the existence of At- and AtO(OH)2- has been confirmed and the associated standard potential has been determined for the first time (0.86 ± 0.05 V vs the standard hydrogen electrode). On the basis of these results, a revised version of astatine's Pourbaix diagram is proposed, covering the three oxidation states of astatine that exist in the thermodynamic stability range of water: At(-I), At(I), and At(III) (as At-, At+, AtO+, AtO(OH), and AtO(OH)2-).

The pKBHX Hydrogen-Bond Basicity Scale: From Molecules to Anions.

The pKBHX (logarithm of complexation constant K of 4-fluorophenol with bases) hydrogen-bond basicity scale of neutral hydrogen-bond acceptors (HBAs) is extended to anionic HBAs. The scale is constructed for 26 anions through (i) the infrared measurement of K on NBu4+X- ion pairs in CCl4, (ii) the estimation of K from linear free energy relationships between measured K values and literature K values for various phenols in polar solvents, and (iii) the computation of K at the density functional theory level in CCl4. The scale extends on a 9.4 pK unit range from fluoride to tetraphenylborate. Considering a number of anions as organic functions substituted with unipolar substituents, their pKBHX values can be related to the Hammett-Taft substituent constants σ. Unipolar substituents (O- and S-) obey the same pKBHX versus σ relationships as dipolar ionic (N-N+R3) and dipolar (OH, CF3, NR2, or OR) ones for the nitrile, carbonyl, nitroso, nitro, sulfonyl, and phosphoryl functions. Like dipolar substituents, unipolar substituents at carbon and nitrogen operate by field-inductive and resonance effects, whereas substituents at sulfur and phosphorus operate only by the field-inductive effect.

Electrochemistry-coupled to liquid chromatography-mass spectrometry-density functional theory as a new tool to mimic the environmental degradation of selected phenylurea herbicides.

In vitro and in vivo experimental models, mainly based on cell cultures, animals, healthy humans and clinical trials, are useful approaches for identifying the main metabolic pathways. However, time, cost, and matrix complexity often hinder the success of these methods. In this study, we propose an alternative non-enzymatic method, using electrochemistry (EC) coupled to liquid chromatography (LC) - high resolution mass spectrometry (HRMS) - DFT theoretical calculations (EC/LC-MS/DFT) for the mimicry/simulation of the environmental degradation of phenylurea herbicides, and for the mechanism elucidation of this class of herbicides. Fenuron, monuron, isoproturon, linuron, monolinuron, metoxuron and chlortoluron were selected as relevant model compounds. The intended compounds are oxidized by EC, separated by LC and detected using electrospray ionization HRMS. The main oxidation products were hydroxylated compounds obtained by substitution and addition reactions. Unstable quinone imines/methines, rarely observed by conventional methods, have been identified during the oxidative degradation of phenylurea herbicides for the first time in this study. Some were directly observed and the others were trapped by glutathione GSH. Reactions such as hydrolytic substitutions (-Cl/+OH and -C3H7/+OH and -CH3/+OH and -OCH3/+OH), aromatic hydroxylation, alkyl carbon hydroxylation, dehydrochlorination/dehydromethylation/dehydromethoxylation and conjugation have been successfully mimicked. The obtained results, supported by theoretical calculations, are useful for simulating/understanding and predicting the oxidative degradation pathways of pesticides in the environment.

Advances in the Chemistry of Astatine and Implications for the Development of Radiopharmaceuticals.

ConspectusAstatine (At) is the rarest on Earth of all naturally occurring elements, situated below iodine in the periodic table. While only short-lived isotopes (t1/2 ≤ 8.1 h) are known, 211At is the object of growing attention due to its emission of high-energy alpha particles. Such radiation is highly efficient to eradicate disseminated tumors, provided that the radionuclide is attached to a cancer-targeting molecule. The interest in applications of 211At in nuclear medicine translates into the increasing number of cyclotrons able to produce it. Yet, many challenges related to the minute amounts of available astatine are to be overcome in order to characterize its physical and chemical properties. This point is of paramount importance to develop synthetic strategies and solve the labeling instability in current approaches that limits the use of 211At-labeled radiopharmaceuticals. Despite its discovery in the 1940s, only the past decade has seen a significant rise in the understanding of astatine's basic chemical and radiochemical properties, thanks to the development of new analytical and computational tools.In this Account, we give a concise summary of recent advances in the determination of the physicochemical properties of astatine, putting in perspective the duality of this element which exhibits the characteristics both of a halogen and of a metal. Striking features were evidenced in the recent determination of its Pourbaix diagram such as the identification of stable cationic species, At+ and AtO+, contrasting with other halogens. Like metals, these species were shown to form complexes with anionic ligands and to exhibit a particular affinity for organic species bearing soft donor atoms. On the other hand, astatine shares many characteristics with other halogen elements. For instance, the At- species exists in water, but with the least range of EH-pH stability in the halogen series. Astatine can form molecular interactions through halogen bonding, and it was only recently identified as the strongest halogen-bond donor. This ability is nonetheless affected by relativistic effects, which translate to other peculiarities for this heavy element. For instance, the spin-orbit coupling boosts astatine's propensity to form charge-shift bonds, catching up with the behavior of the lightest halogens (fluorine, chlorine).All these new data have an impact on the development of radiolabeling strategies to turn 211At into radiopharmaceuticals. Inspired by the chemistry of iodine, the chemical approaches have sparsely evolved over the past decades and have long been limited to electrophilic halodemetalation reactions to form astatoaryl compounds. Conversely, recent developments have favored the use of the more stable At- species including the aromatic nucleophilic substitution with diaryliodonium salts or the copper-catalyzed halodeboronation of arylboron precursors. However, it is clear that new bonding modalities are necessary to improve the in vivo stability of 211At-labeled aryl compounds. The tools and data gathered over the past decade will contribute to instigate original strategies for overcoming the challenges offered by this enigmatic element. Alternatives to the C-At bond such as the B-At and the metal-At bonds are typical examples of exciting new axes of research.

Astatine Facing Janus: Halogen Bonding vs. Charge-Shift Bonding.

The nature of halogen-bond interactions was scrutinized from the perspective of astatine, potentially the strongest halogen-bond donor atom. In addition to its remarkable electronic properties (e.g., its higher aromaticity compared to benzene), C6At6 can be involved as a halogen-bond donor and acceptor. Two-component relativistic calculations and quantum chemical topology analyses were performed on C6At6 and its complexes as well as on their iodinated analogues for comparative purposes. The relativistic spin-orbit interaction was used as a tool to disclose the bonding patterns and the mechanisms that contribute to halogen-bond interactions. Despite the stronger polarizability of astatine, halogen bonds formed by C6At6 can be comparable or weaker than those of C6I6. This unexpected finding comes from the charge-shift bonding character of the C-At bonds. Because charge-shift bonding is connected to the Pauli repulsion between the bonding σ electrons and the σ lone-pair of astatine, it weakens the astatine electrophilicity at its σ-hole (reducing the charge transfer contribution to halogen bonding). These two antinomic characters, charge-shift bonding and halogen bonding, can result in weaker At-mediated interactions than their iodinated counterparts.

An expanded halogen bonding scale using astatine.

As a non-covalent interaction, halogen bonding is now acknowledged to be useful in all fields where the control of intermolecular recognition plays a pivotal role. Halogen-bond basicity scales allow quantification of the halogen bonding of referential donors with organic functional groups from a thermodynamic point of view. Herein we present the pK BAtI basicity scale to provide the community an overview of halogen-bond acceptor strength towards astatine, the most potent halogen-bond donor element. This experimental scale is erected on the basis of complexation constants measured between astatine monoiodide (AtI) and sixteen selected Lewis bases. It spans over 6 log units and culminates with a value of 5.69 ± 0.32 for N,N,N',N'-tetramethylthiourea. On this scale, the carbon π-bases are the weakest acceptors, the oxygen derivatives cover almost two-thirds of the scale, and sulphur bases exhibit the highest AtI basicity. Regarding the applications of 211At in targeted radionuclide therapy, stronger labelling of carrier agents could be envisaged on the basis of the pK BAtI scale.

Delocalized relativistic effects, from the viewpoint of halogen bonding.

The ability of organic and inorganic compounds bearing both iodine and astatine atoms to form halogen-bond interactions is theoretically investigated. Upon inclusion of the relativistic spin-orbit interaction, the I-mediated halogen bonds are more affected than the At-mediated ones in many cases. This unusual outcome is disconnected from the behavior of iodine's electrons. The significant decrease of astatine electronegativity with the spin-orbit coupling triggers a redistribution of the electron density, which propagates relativistic effects toward the distant iodine atom. This mechanism can be controlled by introducing suitable substituents and, in particular, strengthened by taking advantage of electron-withdrawing inductive and mesomeric effects. Noticeable relativistic effects can actually be transferred to light atoms properties, e.g., the halogen-bond basicity of bridgehead carbon atoms doubled in propellane derivatives.

Using electrochemistry coupled to high resolution mass spectrometry for the simulation of the environmental degradation of the recalcitrant fungicide carbendazim.

Currently, there is a growing interest in the study of environmental degradation pathways of organic contaminants such as pesticides, with the objective to better understand their potential risk for environmental systems and living organisms. In this context, DFT (conceptual density functional theory) and predictive methods may systematically be used to simplify and accelerate the elucidation of environmental degradation. We report herein the electrochemical behavior/degradation of the carbendazim (CBZ) fungicide widely used to treat cereal and fruit crops. Oxidative degradation of CBZ was studied using an electrochemical flow-through cell directly coupled to a mass spectrometer for rapid identification of CBZ degradation products. The structural elucidation of CBZ oxidation products was based on retention time, accurate mass, isotopic distribution and fragmentation pattern by using LC-HRMS an LC-HRMS2. The most important chemical reactions found to occur in the transformation of CBZ were hydrolysis and hydroxylation. EC-LC-MS and EC-MS analysis has made it possible to highlight the identification of degradation products of CBZ. In addition to previously known transformation products common to those observed during environmental degradation (monocarbomethoxyguanidine, benzimidazole-isocyanate, 2-aminobenzimidazole, hydroxy-2-aminobenzimidazole, hydroxycarbendazim, CBZ-CBZ dimer), two new degradation products were identified in this work: a quinone imine and a nitrenium ion. Electrochemistry mass spectrometry hyphenated techniques represent an accessible, rapid and reliable tool to elucidate the oxidative degradation of CBZ, including reactive degradation products and conjugates.

Questioning the Affinity of Electrophilic Astatine for Sulfur-containing Compounds: Unexpected Bindings Revealed.

The affinity of AtO+ for around 20 model ligands (L), carrying functionalized oxygen, sulfur, and nitrogen atoms, has been assessed through a combined experimental and theoretical methodology. Significant equilibrium constants (KL ∼ 104) have been measured for sulfur-containing compounds, in agreement with the previously highlighted, relatively stable radiolabeling of SH-containing proteins with 211At. Conversely, no interaction occurs in the aqueous phase for their oxygenated counterparts, but higher affinities (KL > 106) have been determined for nitrogen-based ligands, including aromatic nitrogen heterocycles. The quantum mechanical calculations definitively ruled out any rationale based on either the metallic character of astatine or its guessed softness; the favored interactions all involve specifically the oxygen atom of AtO+, leading to the formation of covalent O-S or O-C single bonds.

The electron affinity of astatine.

One of the most important properties influencing the chemical behavior of an element is the electron affinity (EA). Among the remaining elements with unknown EA is astatine, where one of its isotopes, 211At, is remarkably well suited for targeted radionuclide therapy of cancer. With the At- anion being involved in many aspects of current astatine labeling protocols, the knowledge of the electron affinity of this element is of prime importance. Here we report the measured value of the EA of astatine to be 2.41578(7) eV. This result is compared to state-of-the-art relativistic quantum mechanical calculations that incorporate both the Breit and the quantum electrodynamics (QED) corrections and the electron-electron correlation effects on the highest level that can be currently achieved for many-electron systems. The developed technique of laser-photodetachment spectroscopy of radioisotopes opens the path for future EA measurements of other radioelements such as polonium, and eventually super-heavy elements.

Quantum chemical topology at the spin-orbit configuration interaction level: Application to astatine compounds.

We report a methodology that allows the investigation of the consequences of the spin-orbit coupling by means of the QTAIM and ELF topological analyses performed on top of relativistic and multiconfigurational wave functions. In practice, it relies on the "state-specific" natural orbitals (NOs; expressed in a Cartesian Gaussian-type orbital basis) and their occupation numbers (ONs) for the quantum state of interest, arising from a spin-orbit configuration interaction calculation. The ground states of astatine diatomic molecules (AtX with X = AtF) and trihalide anions (IAtI- , BrAtBr- , and IAtBr- ) are studied, at exact two-component relativistic coupled cluster geometries, revealing unusual topological properties as well as a significant role of the spin-orbit coupling on these. In essence, the presented methodology can also be applied to the ground and/or excited states of any compound, with controlled validity up to including elements with active 5d, 6p, and/or 5f shells, and potential limitations starting with active 6d, 7p, and/or 6f shells bearing strong spin-orbit couplings.

Crystallographic structure and crystal field parameters in the [AnIV(DPA)3]2- series, An = Th, U, Np, Pu.

The [AnIV(DPA)3]2- series with An = Th, U, Np, Pu has been synthesized and characterized using SC-XRD and vibrational spectroscopy. First principles calculations were performed, the total electron density is analyzed using the Quantum Theory of Atoms in Molecules. Crystal field parameters and strength parameters are deduced following a previous work on the LnIII analog series e.g. [J. Jung et al., Chem. - Eur. J., 2019, 25, 15112]. The trends in the parameters along the series are compared to the LnIII complexes. They evidence larger covalent interactions and larger J mixing.

Towards a Stronger Halogen Bond Involving Astatine: Unexpected Adduct with Bu3 PO Stabilized by Hydrogen Bonding.

The halogen bond is a powerful tool for the molecular design and pushing the limits of its strength is of major interest. Bearing the most potent halogen-bond donor atom, astatine monoiodide (AtI) was recently successfully probed [Nat. Chem. 2018, 10, 428-434]. In this work, we continue the exploration of adducts between AtI and Lewis bases with the tributylphosphine oxide (Bu3 PO) ligand, revealing the unexpected experimental occurrence of two distinct chemical species with 1:1 and 2:1 stoichiometries. The 1:1 Bu3 PO⋅⋅⋅AtI complex is found to exhibit the strongest astatine-mediated halogen bond so far (with a formation constant of 10(4.24±0.35) ). Quantum chemical calculations unveil the intriguing nature of the 2:1 2Bu3 PO⋅⋅⋅AtI adduct, involving a halogen bond between AtI and one Bu3 PO molecular unit plus CH⋅⋅⋅O hydrogen bonds chelating the second Bu3 PO unit.

On the Interplay between Charge-Shift Bonding and Halogen Bonding.

The nature of halogen-bond interactions has been analysed from the perspective of the astatine element, which is potentially the strongest halogen-bond donor. Relativistic quantum calculations on complexes formed between halide anions and a series of Y3 C-X (Y=F to X, X=I, At) halogen-bond donors disclosed unexpected trends, e. g., At3 C-At revealing a weaker donating ability than I3 C-I despite a stronger polarizability. All the observed peculiarities have their origin in a specific component of C-Y bonds: the charge-shift bonding. Descriptors of the Quantum Chemical Topology show that the halogen-bond strength can be quantitatively anticipated from the magnitude of charge-shift bonding operating in Y3 C-X. The charge-shift mechanism weakens the ability of the halogen atom X to engage in halogen bonds. This outcome provides rationales for outlier halogen-bond complexes, which are at variance with the consensus that the halogen-bond strength scales with the polarizability of the halogen atom.

Spin-orbit coupling as a probe to decipher halogen bonding.

The nature of halogen-bond interactions is scrutinized from the perspective of astatine, the heaviest halogen element. Potentially the strongest halogen-bond donor, its ability is shown to be deeply affected by relativistic effects and especially by the spin-orbit coupling. Complexes between a series of XY dihalogens (X, Y = At, I, Br, Cl and F) and ammonia are studied with two-component relativistic quantum calculations, revealing that the spin-orbit interaction leads to a weaker halogen-bond donating ability of the diastatine species with respect to diiodine. In addition, the donating ability of the lighter halogen elements, iodine and bromine, in the AtI and AtBr species is more decreased by the spin-orbit coupling than that of astatine. This can only be rationalized from the evolution of a charge-transfer descriptor, the local electrophilicity ω+S,max, determined for the pre-reactive XY species. Finally, the investigation of the spin-orbit coupling effects by means of quantum chemical topology methods allows us to unveil the connection between the astatine propensity to form charge-shift bonds and the astatine ability to engage in halogen bonds.

Theoretical 0-0 Energies with Chemical Accuracy.

Ab initio calculation of electronic excitation energies with chemical accuracy (ca. 1 kcal·mol-1 or 0.043 eV with respect to experiment) is a long-standing challenge in electronic structure theory. Indeed, the most advanced theories can, in practice, only be used to estimate vertical transition energies that cannot be measured experimentally, whereas the calculation of 0-0 energies requires excited-state structures and vibrations for both the ground and excited states, which drastically restrains the number of applicable methods. In this Letter, we present a composite computational protocol able to deliver chemically accurate theoretical 0-0 energies, with a mean absolute deviation of 0.018 eV for a set of 35 singlet valence states. Such accuracy, achievable for the valence states of small- and medium-sized molecules only, allows pinpointing questionable experimental assignments with very high confidence and constitutes a step toward quantitative prediction of excited-state properties.

Experimental and computational evidence of halogen bonds involving astatine.

The importance of halogen bonds-highly directional interactions between an electron-deficient σ-hole moiety in a halogenated compound and an acceptor such as a Lewis base-is being increasingly recognized in a wide variety of fields from biomedicinal chemistry to materials science. The heaviest halogens are known to form stronger halogen bonds, implying that if this trend continues down the periodic table, astatine should exhibit the highest halogen-bond donating ability. This may be mitigated, however, by the relativistic effects undergone by heavy elements, as illustrated by the metallic character of astatine. Here, the occurrence of halogen-bonding interactions involving astatine is experimentally evidenced. The complexation constants of astatine monoiodide with a series of organic ligands in cyclohexane solution were derived from distribution coefficient measurements and supported by relativistic quantum mechanical calculations. Taken together, the results show that astatine indeed behaves as a halogen-bond donor-a stronger one than iodine-owing to its much more electrophilic σ-hole.

The bonding picture in hypervalent XF3 (X = Cl, Br, I, At) fluorides revisited with quantum chemical topology.

Hypervalent XF3 (X = Cl, Br, I, At) fluorides exhibit T-shaped C2V equilibrium structures with the heavier of them, AtF3 , also revealing an almost isoenergetic planar D3h structure. Factors explaining this behavior based on simple "chemical intuition" are currently missing. In this work, we combine non-relativistic (ClF3 ), scalar-relativistic and two-component (X = Br - At) density functional theory calculations, and bonding analyses based on the electron localization function and the quantum theory of atoms in molecules. Typical signatures of charge-shift bonding have been identified at the bent T-shaped structures of ClF3 and BrF3 , while the bonds of the other structures exhibit a dominant ionic character. With the aim of explaining the D3h structure of AtF3 , we extend the multipole expansion analysis to the framework of two-component single-reference calculations. This methodological advance enables us to rationalize the relative stability of the T-shaped C2v and the planar D3h structures: the Coulomb repulsions between the two lone-pairs of the central atom and between each lone-pair and each fluorine ligand are found significantly larger at the D3h structures than at the C2v ones for X = Cl - I, but not with X = At. This comes with the increasing stabilization, along the XF3 series, of the planar D3h structure with respect to the global T-shaped C2v minima. Hence, we show that the careful use of principles that are at the heart of the valence shell electron pair repulsion model provides reasonable justifications for stable planar D3h structures in AX3 E2 systems. © 2017 Wiley Periodicals, Inc.