QTAIM Analysis in the Context of Quasirelativistic Quantum Calculations

The halogen(I) complex of astatine: a theoretical perspective on structural and bonding properties

Halonium ions (X+) can interact with two Lewis bases to form linear 3c4e halogen-bonded halogen(I) complexes ([D⋯X⋯D]+), which have been found to be useful in organic synthesis and supramolecular chemistry. However, current research is limited to lighter halogens (F, Cl, Br, and I) and does not include the At element owing to the lack of stable isotopes for experimental studies. Herein, we explore the structural and bonding properties of an At-mediated 3c4e halogen(I) complex ([D⋯At⋯D]+) and the effects of various Lewis bases, substituents, and halogens using relativistic density functional theory (DFT) and the coupled-cluster approach with single, double and perturbative triple excitation (CCSD(T)) calculations. Theoretical calculation results show that At, similar to other halogens, can form a linear [D⋯At⋯D]+ structure with equal bond lengths from the halonium ion to two donor atoms. The physical nature of the interaction and electronic structure of the At-mediated 3c4e halogen(I) complex are the same as those of the halogen(I) complexes of light halogens. Interestingly, the positive correlation between the polarizability of the halogen and the interaction between D and [D⋯X]+ fragments (X = F to At) observed at the scalar relativistic level does not hold when considering spin-orbit coupling effects on the At atom. This work deepens the understanding of the halogen bonds of At, and the stable [D⋯At⋯D]+ structure offers new insights into At coordination chemistry and the relevant experimental study of radiolabeling of At.

Comparative study of the therapeutic potential of C24, C32, B12N12, and B16N16 nanocages as drug delivery carriers for delivering an erlotinib derivative: DFT and QTAIM investigations

The use of nanostructures as drug delivery vehicles for a wide range of anticancer medications to lessen their severe side effects by delivering them to the targeted tumor cell location is presently a broadly studied innovative biomedical application of different nanostructures. To investigate the capability of C24 and C32, B12N12, and B16N16 nanocages as nanocarriers for delivering the methyl erlotinib molecule, we conducted density functional theory (DFT) computations using the M06-2X/6-311G(d,p) and M06-2X/6-31G(d) levels of theory. The calculation of the adsorption energy of methyl erlotinib on the nanocages was performed in aqueous and gaseous phases. The adsorption energy values associated with the interaction between the nanocages and methyl erlotinib were negative, indicating that this interaction was exothermic in nature. The adsorption energy values in the aqueous state were higher than those in the gaseous state, suggesting a stronger interaction in the aqueous state, with the exception of the C32 nanocage. Analyses of the density of states (DOS) and projected density of states (PDOS) were performed in order to examine the effect of methyl erlotinib adsorption on the electronic characteristics of selected nanocages. The findings indicated that the B12N12 nanocage following methyl erlotinib molecule adsorption came nearer to the Fermi level than the other nanocages examined. Calculations based on the Quantum Theory of Atoms in Molecules (QTAIM) indicated that methyl erlotinib had a weak interaction with all selected nanocages. According to the values of the adsorption energy derived from both methodologies, the interaction between methyl erlotinib and the B12N12 nanocage was determined to be more robust than the interaction between methyl erlotinib and the C24 nanocage, while the interaction between methyl erlotinib and the B16N16 nanocage was also stronger than that with the C32 nanocage. Notable variations in the ΔEg values were detected for methyl erlotinib@B12N12 and methyl erlotinib@B16N16 across all methods, suggesting that the conductivity of these two nanostructures improved more significantly following the adsorption of methyl erlotinib than that of other nanostructures. Consequently, the B12N12 and B16N16 nanocages can function as nanosensors for methyl erlotinib.

Probing the Redox Reactivity of Alkyl Bound Astatine: A Study on the Formation and Cleavage of a Stable At-C Bond

The formation of a stable alkyl At-C bond occurs during the shipment of 211At on a 3-octanone-impregnated column and the reactivity of 211At stripped from columns has been studied. The 211At could not be recovered from the 3-octanone organic phase using nitric acid or sodium hydroxide, even up to 10 and 15.7 M, respectively. Several reducing and oxidizing agents, including hydrazine, hydroxylamine, ascorbic acid, ceric ammonium nitrate, potassium permanganate, sodium hypochlorite, and calcium hypochlorite were used to promote the recovery of 211At. The most effective reducing agent was hydroxylamine, where ∼70% of the 211At was recovered, while among oxidizing agents ceric ammonium nitrate, potassium permanganate, and sodium hypochlorite all showed near quantitative recovery of 211At. These results indicate an At-C bond is being formed during the shipment of the column and a redox reaction is required for bond cleavage to occur. DFT calculations have been used to propose several products of an AtO+-3-octanone reaction, with 4-astato-5-hydroxy-octa-3-one being the most probable.

Molecular engineering of BODIPY-bridged fluorescent probes for lysosome imaging - a computational study

Lysosome imaging plays an important role in diagnosing many diseases and understanding various intracellular processes. Recently, B0 was reported as a fluorescent probe capable of detecting lysosomal viscosity changes. BODIPY is fused into the molecule as a bridge between the acceptor and donor components of B0, yielding nine new B molecules. Computational design and analysis of their optoelectronic properties were conducted to evaluate their effectiveness as fluorescent probes for lysosome imaging, with a specific target of HSA inside lysosomes. Optimized geometries reveal excellent π electron delocalization, resulting in nearly planar molecular structures. Frontier molecular orbital analysis suggests intramolecular charge transfer, along with π-π* transitions, from donor to bridge. TD-DFT calculations were performed to study absorption properties in the solvent phase, with B3PW91 showing good agreement with experiments. Molecular docking studies indicate that B derivatives can bind with HSA, and molecular dynamics simulations confirm their HSA targeting ability. This investigation highlights the introduction of BODIPY as a bridge for developing new probes capable of producing NIR fluorescence for bio-imaging, aiding in disease diagnosis.

Comprehensive Computational Investigation of the Porphyrin-Based COF as a Nanocarrier for Delivering Anti-Cancer Drugs: A Combined MD Simulation and DFT Calculation

As nanomaterials have gained prominence in drug delivery technology, exploring their feasibility through computational methods is beneficial before practical tests. In this study, we aim to evaluate the capability of the porphyrin-based covalent organic framework COF-366 as a nanocarrier for two anticancer drugs, irinotecan (IRI) and doxorubicin (DOX). The optimal binding conformation of the drug molecules on the COF surface was predicted by using molecular docking. Subsequently, molecular dynamic simulation (MD) was performed to assess the adsorption mechanism of drug molecules on the COF in the aqueous environment. The free energy of adsorption for DOX and IRI was estimated to be -20.07 and -23.89 kcal/mol, respectively. The adsorption of both drugs on the COF surface is mainly influenced by the π-π interaction. Furthermore, density functional theory (DFT) calculation, natural bond orbital (NBO), and quantum theory of atoms in molecules (QTAIM) analyses were employed to investigate the structural stability of Drug@COF complexes and gain a detailed understanding of the interaction between them at the molecular level. Based on DFT results, it was found that in addition to π-π interaction, the bis-piperidine-phenylene interaction affects the adsorption of IRI on the COF surface. Moreover, the diffusion behavior of the drug molecule inside the COF pore was simulated using a ten-layer COF. Based on the mean square displacement analysis, the diffusion coefficients of DOX and IRI within the COF pore were calculated to be 108 and 97 um2/s, respectively. This computational study sheds light on how different types of interactions between the drug molecule and COF affect the adsorption and diffusion process. Our findings validated that the porphyrin-based COF-366 can serve as a nanobased platform for delivering DOX and IRI.

Preparation of Neptunyl and Plutonyl Acetates To Access Nonaqueous Transuranium Coordination Chemistry

Uranyl diacetate dihydrate is a useful reagent for the preparation of uranyl (UO22+) coordination complexes, as it is a well-defined stoichiometric compound featuring moderately basic acetates that can facilitate protonolysis reactivity, unlike other anions commonly used in synthetic actinide chemistry such as halides or nitrate. Despite these attractive features, analogous neptunium (Np) and plutonium (Pu) compounds are unknown to date. Here, a modular synthetic route is reported for accessing stoichiometric neptunyl(VI) and plutonyl(VI) diacetate compounds that can serve as starting materials for transuranic coordination chemistry. The new NpO22+ and PuO22+ complexes, as well as a corresponding molecular UO22+ complex, are isomorphous in the solid state, and in solution show similar solubility properties that facilitate their use in synthesis. In both solid and solution state, the +VI oxidation state (O.S.) is maintained, as demonstrated by vibrational and optical spectroscopy, confirming that acetate anions stabilize the oxidizing, high-valent +VI states of Np and Pu as they do for the more stable U(VI). All three acetate salts readily react with a model diprotic ligand, affording incorporation of U(VI), Np(VI), and Pu(VI) cores into molecular coordination compounds that occurs concomitantly with elimination of acetic acid; the new complexes are high-valent, yet overall charge neutral, facilitating entry into nonaqueous chemistry by rational synthesis. Computational studies reveal that the dianionic ligand framework assists in stabilizing the +VI O.S. via donation to the 5f shells of the actinides, highlighting the potential usefulness of protonolysis reactivity toward preparation of stabilized high-valent transuranic species.

The Chemical Bond at the Bottom of the Periodic Table: The Case of the Heavy Astatine and the Super-Heavy Tennessine

In this work, we study the chemical bond in molecules containing heavy and super-heavy elements according to the current state-of-the-art bonding models. An Energy Decomposition Analysis in combination with Natural Orbital for Chemical Valence (EDA-NOCV) within the relativistic four-component Dirac-Kohn-Sham (DKS) framework is employed, which allows to successfully include the spin-orbit coupling (SOC) effects on the chemical bond description. Simple halogen-bonded adducts ClX⋯L (X=At, Ts; L=NH3, Br-, H2O, CO) of astatine and tennessine have been selected to assess a trend on descending along a group, while modulating the ClX⋯L bond features through the different electronic nature of the ligand L. Interesting effects caused by SOC have been revealed: i) a huge increase of the ClTs dipole moment (which is almost twice as that of ClAt), ii) a lowering of the ClX⋯L bonding energy arising from different contributions to the ClX…L interaction energy strongly depending on the nature of L, iii) a quenching of one of the π back-donation components to the bond. In the ClTs(CO) adduct, the back-donation from ClTs to CO becomes the most important component. The analysis of the electronic structure of the ClX dimers allows for a clear interpretation of the SOC effects in these systems.

Estimation of thermodynamic and physicochemical properties of the alkali astatides: On the bond strength of molecular astatine (At2 ) and the hydration enthalpy of astatide (At- )

The recent accurate and precise determination of the electron affinity (EA) of the astatine atom At0 warrants a re-investigation of the estimated thermodynamic properties of At0 and astatine containing molecules as this EA was found to be much lower (by 0.4 eV) than previous estimated values. In this contribution we estimate, from available data sources, the following thermodynamic and physicochemical properties of the alkali astatides (MAt, M = Li, Na, K, Rb, Cs): their solid and gaseous heats of formation, lattice and gas-phase binding enthalpies, sublimation energies and melting temperatures. Gas-phase charge-transfer dissociation energies for the alkali astatides (the energy requirement for M+ At- ➔ M0  + At0 ) have been obtained and are compared with those for the other alkali halides. Use of Born-Haber cycles together with the new AE (At0 ) value allows the re-evaluation of ΔHf (At0 )g (=56 ± 5 kJ/mol); it is concluded that (At2 )g is a weakly bonded species (bond strength <50 kJ/mol), significantly weaker bonded than previously estimated (116 kJ/mol) and much weaker bonded than I2 (148 kJ/mol), but in agreement with the finding from theory that spin-orbit coupling considerably reduces the bond strength in At2 . The hydration enthalpy (ΔHaq ) of At- is estimated to be -230 ± 2 kJ/mol (using ΔHaq [H+ ] = -1150.1 kJ/mol), in good agreement with molecular dynamics calculations. Arguments are presented that the largest alkali halide, CsAt, like the smallest, LiF, will be only sparingly soluble in water, following the generalization from hard/soft acid/base principles that "small likes small" and "large likes large."

Stability of the protactinium(V) mono-oxo cation probed by first-principle calculations

This study explores the distinctive behavior of protactinium (Z=91) within the actinide series. In contrast to neighboring elements like uranium or plutonium, protactinium in the pentavalent state diverges by not forming the typical dioxo protactinyl moiety PaO2 + in aqueous phase. Instead, it manifests as a monooxo PaO3+ cation or a Pa5+ . Employing first-principle calculations with implicit and explicit solvation, we investigate two stoichiometrically equivalent neutral complexes: PaO(OH)2 (X)(H2 O) and Pa(OH)4 (X), where X represents various monodentate and bidentate ligands. Calculating the Gibbs free energy for the reaction PaO(OH)2 (X)(H2 O)→Pa(OH)4 (X), we find that the PaO(OH)2 (X)(H2 O) complex is stabilized with Cl- , Br- , I- , NCS- , NO3 - , and SO4 2- ligands, while it is not favored with OH- , F- , and C2 O4 2- ligands. Quantum Theory of Atoms in Molecules (QTAIM) and Natural Bond Orbital (NBO) methods reveal the Pa mono-oxo bond as a triple bond, with significant contributions from the 5f and 6d shells. Covalency of the Pa mono-oxo bond increases with certain ligands, such as Cl- , Br- , I- , NCS- , and NO3 - . These findings elucidate protactinium's unique chemical attributes and provide insights into the conditions supporting the stability of relevant complexes.

Topology of electrostatic potential and electron density reveals a covalent to non-covalent carbon-carbon bond continuum

The covalent and non-covalent nature of carbon-carbon (CC) interactions in a wide range of molecular systems can be characterized using various methods, including the analysis of molecular electrostatic potential (MESP), represented as V(r), and the molecular electron density (MED), represented as ρ(r). These techniques provide valuable insights into the bonding between carbon atoms in different molecular environments. By uncovering a fundamental exponential relationship between the distance of the CC bond and the highest eigenvalue (λv1) of V(r) at the bond critical point (BCP), this study establishes the continuum model for all types of CC interactions, including transition states. The continuum model is further delineated into three distinct regions, namely covalent, borderline cases, and non-covalent, based on the gradient, , with the bond distance of the CC interaction. For covalent interactions, this parameter exhibits a more negative value than -5.0 a.u. Å-1, while for non-covalent interactions, it is less negative than -1.0 a.u. Å-1. Borderline cases, which encompass transition state structures, fall within the range of -1.0 to -5.0 a.u. Å-1. Furthermore, this study expands upon Popelier's analysis of the Laplacian of the MED, denoted as ∇2ρ, to encompass the entire spectrum of covalent, non-covalent, and borderline cases of CC interactions. Therefore, the present study presents compelling evidence supporting the concept of a continuum model for CC bonds in chemistry. Additionally, this continuum model is further explored within the context of C-N, C-O, C-S, N-N, O-O, and S-S interactions, albeit with a limited dataset.

The LRESC-Loc Model to Analyze Magnetic Shieldings with Localized Molecular Orbitals

The leading electronic mechanisms of relativistic effects in the NMR magnetic shieldings of heavy-atom (HA) containing molecules are well described by the linear response with elimination of small components model (LRESC). We show here first results from a new version of the LRESC model written in terms of localized molecular orbitals (LMOs) which is coined as LRESC-Loc. Those LMOs resemble "chemist's orbitals", representing lone-pairs, atomic cores, and bonds. The whole set of relativistic effects are expressed in terms of non-ligand-dependent and ligand-dependent contributions. We show the electronic origin of trends and behavior of different mechanisms in molecular systems which contain heavy elements that belong to any of the IB to VIIA groups of the periodic table. The SO mechanism has a well-defined dependence with the LPs (LPσ and LPπ) when the HAs have them, but the non-SO mechanisms mostly depend on other LMOs. In addition we propose here that the SO mechanism can be used to characterize interactions involving LPs and the non-SO mechanisms to characterize covalent and close-shell interactions. All our main results are in accord with previous findings, though we are now able to analyze them in a different manner.

Geometries, interaction energies and bonding in [Po(H2O)n]4+ and [PoCln]4-n complexes

Polonium (Z = 84) is one of the rarest elements on Earth. More than a century after its discovery, its chemistry remains poorly known and even basic questions have not yet been satisfactorily addressed. In this work, we perform a systematic study of the geometries, interactions energies and bonding in basic polonium(IV) species, namely the hydrated [Po(H₂O)_n]⁴⁺ and chlorinated [PoCl_n]^4-n complexes by means of gas-phase electronic structure calculations. We show that while up to nine water molecules can fit in the first coordination sphere of the polonium(IV) ion, its coordination sphere can already be filled with eight chloride ligands. Capitalising on previous theoretical studies, a focused methodological study based on interaction energies and bond distances allows us to validate the MP2/def2-TZVP level of theory for future ground-state studies. After discussing the similarities and differences between complexes with the same number of ligands, we perform topological analyses of the MP2 electron densities in the quantum theory of atoms in molecules (QTAIM) fashion. While the water complexes display typical signatures of closed-shell interactions, we reveal large Po-Cl delocalisation indices, especially in the hypothetical [PoCl]³⁺ complex. This "enhanced" covalency opens the way for a significant spin-orbit coupling (SOC) effect on the corresponding bond distance, which has been studied using two independent approaches (i.e. one a priori and one a posteriori). We finally conclude by stressing that while the SOC may not affect much the geometries of high-coordinated polonium(IV) complexes, it should definitely not be neglected in the case of low-coordinated ones.

Covalency of Trivalent Actinide Ions with Different Donor Ligands: Do Density Functional and Multiconfigurational Wavefunction Calculations Corroborate the Observed "Breaks"?

A comprehensive ab initio study of periodic actinide-ligand bonding trends for trivalent actinides is performed. Relativistic density functional theory (DFT) and complete active-space (CAS) self-consistent field wavefunction calculations are used to dissect the chemical bonding in the [AnCl₆]^3-, [An(CN)₆]^3-, [An(NCS)₆]^3-, [An(S₂PMe₂)₃], [An(DPA)₃]^3-, and [An(HOPO)]^- series of actinide (An = U-Es) complexes. Except for some differences for the early actinide complexes with DPA, bond orders and excess 5f-shell populations from donation bonding show qualitatively similar trends in 5f ⁿ active-space CAS vs DFT calculations. The influence of spin-orbit coupling on donation bonding is small for the tested systems. Along the actinide series, chemically soft vs chemically harder ligands exhibit clear differences in bonding trends. There are pronounced changes in the 5f populations when moving from Pu to Am or Cm, which correlate with previously noted "breaks" in chemical trends. Bonding involving 5f becomes very weak beyond Cm/Bk. We propose that Cm(III) is a borderline case among the trivalent actinides that can be meaningfully considered to be involved in ground-state 5f covalent bonding.

A new iron-phosphate compound (Fe7P11O38) obtained by pyrophosphate stoichiometric glass devitrification

Iron phosphates are a wide group of compounds that possess versatile applications. Their properties are strongly dependent on the role and position of iron in their structure. Iron, because of its chemical character, is able to easily change its redox state and accommodate different chemical surroundings. Thus, iron-phosphate crystallography is relatively complex. In addition, the compounds possess intriguing magnetic and electric properties. In this paper, we present crystal structure properties of a newly developed iron-phosphate compound that was obtained by devitrification from iron-phosphate glass of pyrophosphate stoichiometry. Based on X-ray diffraction (XRD) studies, the new compound (Fe₇P₁₁O₃₈) was shown to adopt the hexagonal space group P6₃ (No. 173) in which iron is present as Fe³⁺ in two inequivalent octahedral and one tetrahedral positions. The results were confirmed by Raman and Mössbauer spectroscopies, and appropriate band positions, as well as hyperfine interaction parameters, are assigned and discussed. The magnetic and electric properties of the compound were predicted by ab initio simulations. It was observed that iron magnetic moments are coupled antiferromagnetically and that the total magnetic moment of the unit cell has an integer value of 2 µ_B. Electronic band structure calculations showed that the material has half-metallic properties.

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.

Capture of Fullerenes in Cages and Rings by Forming Metal-π Bond Arene Interactions

Nowadays, the task of the selectively capture of fullerene molecules from soot is the subject of several studies. The low solubility of fullerenes represents a drawback when the goal is to purify them and to carry out chemical procedures where they participate. There are different molecules that can act as a kind of cocoon, giving shelter to the fullerene cages in such a way that they can be included in a solution or can be extracted from a mix. In this work, a theoretical study of some known and new proposed organic molecules of this kind is presented. In all cases, the interaction occurs with the help of a metallic atom or ion which plays the role of a bridge, providing a place for a metallocene like interaction to occur. The thermodynamic arguments favoring the formation of this adduct species are addressed as well as the nature of the bond by means QTAIM parameters and frontier molecular orbitals analysis.

New insights in chemical reactivity from quantum chemical topology

Based on the quantum chemical topology of the modified electron localization function ELF_x , an efficient and robust mechanistic methodology designed to identify the favorable reaction pathway between two reactants is proposed. We first recall and reshape how the supermolecular interaction energy can be evaluated from only three distinct terms, namely the intermolecular coulomb energy, the intermolecular exchange-correlation energy and the intramolecular energies of reactants. Thereafter, we show that the reactivity between the reactants is driven by the first-order variation in the coulomb intermolecular energy defined in terms of the response to changes in the number of electrons. Illustrative examples with the formation of the dative bond B-N involved in the BH₃ NH₃ molecule and the typical formation of the hydrogen bond in the canonical water dimer are presented. For these selected systems, our approach unveils a noticeable mimicking of E_dual onto the DFT intermolecular interaction energy surface calculated between the both reactants. An automated reaction-path algorithm aimed to determine the most favorable relative orientations when the two molecules approach each other is also outlined.

Relativistic four-component potential energy curves for the lowest 23 covalent states of molecular astatine (At2)

The potential energy curves (PECs) of all covalent states of Molecular Astatine (At₂) have been investigated in this work within a four-component relativistic framework using the MOLFDIR program package. The ground state was determined using multireference configuration interaction with all single and double excitations including Davidson size-extensivity correction (MRCISD+Q) whereas the 22 excited states were treated by complete open shell configuration interaction (COSCI). Spectroscopic constants (R_e,ω_e,ω_ex_e,ω_ey_e, D_e,B_e,α_e,β_e,T_e) are presented for all states as well as vertical excitations obtained at COSCI, MRCISD and MRCISD+Q levels. In addition, it is also presented accurate extended Rydberg analytical form for the ground state X: (1)0_g⁺.

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.

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.

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.

Molecular QTAIM Topology Is Sensitive to Relativistic Corrections

The topology of the molecular electron density of benzene dithiol gold cluster complex Au₄ -S-C₆ H₄ -S'-Au'₄ changed when relativistic corrections were made and the structure was close to a minimum of the Born-Oppenheimer energy surface. Specifically, new bond paths between hydrogen atoms on the benzene ring and gold atoms appeared, indicating that there is a favorable interaction between these atoms at the relativistic level. This is consistent with the observation that gold becomes a better electron acceptor when relativistic corrections are applied. In addition to relativistic effects, here, we establish the sensitivity of molecular topology to basis sets and convergence thresholds for geometry optimization.

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.

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.

Quantum calculations of At-mediated halogen bonds: on the influence of relativistic effects

If astatine is generally a stronger halogen-bond donor than iodine, an inversion is sometimes observed owing to the spin–orbit coupling.

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 C_2V equilibrium structures with the heavier of them, AtF₃ , also revealing an almost isoenergetic planar D_3h 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 D_3h 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 C_2v and the planar D_3h 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 D_3h structures than at the C_2v ones for X = Cl - I, but not with X = At. This comes with the increasing stabilization, along the XF₃ series, of the planar D_3h structure with respect to the global T-shaped C_2v 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 D_3h structures in AX₃ E₂ systems. © 2017 Wiley Periodicals, Inc.

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.

(211)At-labeled agents for alpha-immunotherapy: On the in vivo stability of astatine-agent bonds

The application of (211)At to targeted cancer therapy is currently hindered by the rapid deastatination that occurs in vivo. As the deastatination mechanism is unknown, we tackled this issue from the viewpoint of the intrinsic properties of At-involving chemical bonds. An apparent correlation has been evidenced between in vivo stability of (211)At-labeled compounds and the At-R (R = C, B) bond enthalpies obtained from relativistic quantum mechanical calculations. Furthermore, we highlight important differences in the nature of the At-C and At-B bonds of interest, e.g. the opposite signs of the effective astatine charges, which implies different stabilities with respect to the biological medium. Beyond their practical use for rationalizing the labeling protocols used for (211)At, the proposed computational approach can readily be used to investigate bioactive molecules labeled with other heavy radionuclides.

Investigation into the metallophilic interaction in coinage-metal halides: an ab initio study of CMX (CM = Cu and Ag, X = F - I)

Investigation of the metallophilic interactions of the title coinage-metal halide series, CMX (CM = Ag and Cu, X = F - I), and their cationic and anionic systems, were performed at CCSD(T) theoretical level with extended basis sets. Natural bond orbital analysis shows that the interactions come mainly from the overlap of the sp hybrid on the halogen and the spd hybrid on the coinage-metal atom. Electron density deformation analysis demonstrates a pronounced electron accumulation in the interaction region between the heavier X and the coinage-metal atoms, and suggests a covalent character of the interaction. Positive Laplacian values and negative total energy densities at bond critical points (BCPs) show the "intermediate" character of the interactions. Reduced density gradient analysis visualizes the interaction; a linear relationship between energy densities and eigenvalues can be found at BCPs.