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.

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.

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.

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-).

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.

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.

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.

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.

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.

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.

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.

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.

Influence of Alcohol ß-Fluorination on Hydrogen-Bond Acidity of Conformationally Flexible Substrates.

Rational modulations of molecular interactions are of significant importance in compound properties optimization. We have previously shown that fluorination of conformationally rigid cyclohexanols leads to attenuation of their hydrogen-bond (H-bond) donating capacity (designated by pKAHY ) when OH⋅⋅⋅F intramolecular hydrogen-bond (IMHB) interactions occur, as opposed to an increase in pKAHY due to the fluorine electronegativity. This work has now been extended to a wider range of aliphatic ß-fluorohydrins with increasing degrees of conformational flexibility. We show that the observed differences in pKAHY between closely related diastereomers can be fully rationalized by subtle variations in populations of conformers able to engage in OH⋅⋅⋅F IMHB, as well as by the strength of these IMHBs. We also show that the Kenny theoretical Vα (r) descriptor of H-bond acidity accurately reflects the observed variations and a calibration equation extended to fluorohydrins is proposed. This work clearly underlines the importance of the weak OH⋅⋅⋅F IMHB in the modulation of alcohol H-bond donating capacity.

Scrutinizing "Invisible" astatine: A challenge for modern density functionals.

The main-group 6p elements did not receive much attention in the development of recent density functionals. In many cases it is still difficult to choose among the modern ones a relevant functional for various applications. Here, we illustrate the case of astatine species (At, Z = 85) and we report the first, and quite complete, benchmark study on several properties concerning such species. Insights on geometries, transition energies and thermodynamic properties of a set of 19 astatine species, for which reference experimental or theoretical data has been reported, are obtained with relativistic (two-component) density functional theory calculations. An extensive set of widely used functionals is employed. The hybrid meta-generalized gradient approximation (meta-GGA) PW6B95 functional is overall the best choice. It is worth noting that the range-separated HSE06 functional as well as the old and very popular B3LYP and PBE0 hybrid-GGAs appear to perform quite well too. Moreover, we found that astatine chemistry in solution can accurately be predicted using implicit solvent models, provided that specific parameters are used to build At cavities. © 2016 Wiley Periodicals, Inc.

Advances on the Determination of the Astatine Pourbaix Diagram: Predomination of AtO(OH)2 (-) over At(-) in Basic Conditions.

It is generally assumed that astatide (At(-) ) is the predominant astatine species in basic aqueous media. This assumption is questioned in non-complexing and non-reductive aqueous solutions by means of high-pressure anion-exchange chromatography. Contrary to what is usually believed, astatide is found to be a minor species at pH=11. A different species, which also bears a single negative charge, becomes predominant when the pH is increased beyond 7. Using competition experiments, an equilibrium constant value of 10(-6.9) has been determined for the formation of this species from AtO(OH) with the exchange of one proton. The identification of this species, AtO(OH)2 (-) , is achieved through relativistic quantum mechanical calculations, which rule out the significant formation of the AtO2 (-) species, while leading to a hydrolysis constant of AtO(OH) in excellent agreement with experiment when the AtO(OH)2 (-) species is considered. Beyond the completion of the Pourbaix diagram of astatine, this new information is of interest for the development of (211) At radiolabeling protocols.

Unraveling the hydration-induced ground-state change of AtO+ by relativistic and multiconfigurational wave-function-based methods.

The AtO+ cation is one of the main chemical forms that appear in the astatine Pourbaix diagram. This form can react with closed-shell species in solution, while in the gas phase, it has a spin-triplet ground spin-orbit-free (SOF) state. Spin-orbit coupling (SOC) mixes its MS = 0 component with the 1Σ+ singlet-spin component, while keeping an essentially-spin-triplet SOC ground-state. Therefore, it was suggested that AtO+ undergoes a hydration-induced ground-state change to explain its reactivity in solution with closed-shell species [J. Phys. Chem. B, 2013, 117, 5206-5211]. In this work, we track the nature of the low-lying SOF and SOC states when the hydration sphere of AtO+ is stepwise increased, using relativistic and multiconfigurational wave-function-based methods. This work clarifies previous studies by (i) giving additional arguments justifying a solvation-induced ground-state change in this system and (ii) clearly identifying for the first time the nature of the involved SOF and SOC many-electron states. Indeed, we find at the SOF level that AtO+ undergoes a ground-state reversal between 3Σ- and the closed-shell component of 1Δ, which leads to an essentially-spin-singlet and closed-shell SOC ground-state. This explains the observed reactivity of AtO+ with closed-shell species in solution.

Structural, dynamical, and transport properties of the hydrated halides: How do At(-) bulk properties compare with those of the other halides, from F(-) to I(-)?

The properties of halides from the lightest, fluoride (F(-)), to the heaviest, astatide (At(-)), have been studied in water using a polarizable force-field approach based on molecular dynamics (MD) simulations at the 10 ns scale. The selected force-field explicitly treats the cooperativity within the halide-water hydrogen bond networks. The force-field parameters have been adjusted to ab initio data on anion/water clusters computed at the relativistic Möller-Plesset second-order perturbation theory level of theory. The anion static polarizabilities of the two heaviest halides, I(-) and At(-), were computed in the gas phase using large and diffuse atomic basis sets, and taking into account both electron correlation and spin-orbit coupling within a four-component framework. Our MD simulation results show the solvation properties of I(-) and At(-) in aqueous phase to be very close. For instance, their first hydration shells are structured and encompass 9.2 and 9.1 water molecules at about 3.70 ± 0.05 Å, respectively. These values have to be compared to the F(-), Cl(-), and Br(-) ones, i.e., 6.3, 8.4, and 9.0 water molecules at 2.74, 3.38, and 3.55 Å, respectively. Moreover our computations predict the solvation free energy of At(-) in liquid water at ambient conditions to be 68 kcal mol(-1), a value also close the I(-) one, about 70 kcal mol(-1). In all, our simulation results for I(-) are in excellent agreement with the latest neutron- and X-ray diffraction studies. Those for the At(-) ion are predictive, as no theoretical or experimental data are available to date.

The Heaviest Possible Ternary Trihalogen Species, IAtBr- , Evidenced in Aqueous Solution: An Experimental Performance Driven by Computations.

Evidencing new chemical species in solution is particularly challenging when one works at ultra-trace concentrations, as is likely to happen with radioelements such as astatine (Z=85). Herein, quantum mechanical calculations were used to predict the narrow experimental domain in which it is possible to detect the presence of an exotic ternary trihalogen anion, IAtBr- , and thus to guide a series of experiments. By analyzing the outcomes of competition experiments, we show that IAtBr- exists and can even predominate in aqueous solution. The equilibrium constant associated with the reaction At+ +I- +Br- ⇌IAtBr- was determined to be 107.5±0.2 , which is in fair agreement with that predicted by density functional theory (106.9 ). This system not only constitutes the very first example of a ternary trihalogen species that involves the element astatine but is also the first trihalogen species reported to predominate in solution. Moreover, we show that the oxidation number of At is zero in this species, as in the other molecules and anions that At+ can form with Cl- , Br- , and I- ligands.

Influence of Fluorination on the Conformational Properties and Hydrogen-Bond Acidity of Benzyl Alcohol Derivatives.

The effect of fluorination on the conformational and hydrogen-bond (HB)-donating properties of a series of benzyl alcohols has been investigated experimentally by IR spectroscopy and theoretically with quantum chemical methods (ab initio (MP2) and DFT (MPWB1K)). It was found that o-fluorination generally resulted in an increase in the HB acidity of the hydroxyl group, whereas a decrease was observed upon o,o'-difluorination. Computational analysis showed that the conformational landscapes of the title compounds are strongly influenced by the presence of o-fluorine atoms. Intramolecular interaction descriptors based on AIM, NCI and NBO analyses reveal that, in addition to an intramolecular OH⋅⋅⋅F interaction, secondary CH⋅⋅⋅F and/or CH⋅⋅⋅O interactions also occur, contributing to the stabilisation of the various conformations, and influencing the overall HB properties of the alcohol group. The benzyl alcohol HB-donating capacity trends are properly described by an electrostatic potential based descriptor calculated at the MPWB1K/6-31+G(d,p) level of theory, provided solvation effects are taken into account for these flexible HB donors.