Introducing the ELF Topological Analysis in the Field of Quasirelativistic Quantum Calculations

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.

From the gas phase to the solid state: The chemical bonding in the superheavy element flerovium

As early as 1975, Pitzer suggested that copernicium, flerovium and oganesson are volatile substances behaving noble-gas like because of their closed-shell configurations and accompanying relativistic effects. It is, however, precarious to predict the chemical bonding and physical behavior of a solid by knowledge of the atomic or molecular properties only. Copernicium and oganesson have been analyzed very recently by our group. Both are predicted to be semi-conductors and volatile substances with rather low melting and boiling points, which may justify a comparison with the noble gas elements. Here we study closed-shell flerovium in detail to predict solid-state properties including the melting point from a decomposition of the total energy into many-body forces derived from relativistic coupled-cluster and from density functional theory. The convergence of such a decomposition for flerovium is critically analyzed, and the problem of using density functional theory is highlighted. We predict that flerovium is in many ways not behaving like a typical noble gas element despite its closed-shell 7$p_{1/2}^2$ configuration and resulting weak interactions. Unlike for the noble gases, the many-body expansion in terms of the interaction energy is not converging smoothly. This makes the accurate prediction of phase transitions very difficult. Nevertheless, a first prediction by Monte-Carlo simulation estimates the melting point at $284\pm 50$ K. Furthermore, calculations for the electronic band gap suggests that flerovium is a semi-conductor similar to copernicium

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.

The Topological Analysis of the ELFx Localization Function: Quantitative Prediction of Hydrogen Bonds in the Guanine-Cytosine Pair

In this contribution, we recall and test a new methodology designed to identify the favorable reaction pathway between two reactants. Applied to the formation of the DNA guanine (G) –cytosine (C) pair, we successfully predict the best orientation between the base pairs held together by hydrogen bonds and leading to the formation of the typical Watson Crick structure of the GC pair. Beyond the global minimum, some local stationary points of the targeted pair are also clearly identified.

Bond Dissociation Energies in Heavy Element Chalcogen and Halogen Small Molecules

Thermodynamic properties including bond dissociation energies (BDEs), heats of formation, and gas-phase acidities for the hydrides and dimers of chalcogens and halogens, H₂Y, HX, Y₂, and X₂ for Y = Se, Te, and At and X = Br, I, and At, have been predicted using the Feller-Peterson-Dixon composite-correlated molecular orbital theory approach. A full four-component CCSD(T) approach was used to calculate the spin-orbit effects on thermodynamic properties, except for Se₂, where the AoC-DHF value was used due to strong multireference effects in Se₂ for the SO calculations. The calculated results show that the At₂ BDE is quite small, 19.5 kcal/mol, with much of the low bond energy due to spin-orbit effects. H₂Po is not predicted to be stable to dehydrogenation to Po + H₂ in terms of the free energy at 298 K. In the gas phase, HAt is predicted to be a stronger acid than H₂SO₄. The current results provide insights into potential difficulties in the actual experimental observation of such species for heavy elements.

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⁺.

Astatine partitioning between nitric acid and conventional solvents: indication of covalency in ketone complexation of AtO. Chem Commun (Camb) 2020;56:9004-9007. [PMID: 32638758 DOI: 10.1039/d0cc03804k]

Astatine-211 has been produced at Texas A&M University on the K150 cyclotron, with a yield of 890 ± 80 MBq through the ²⁰⁹Bi(α,2n)²¹¹At reaction via an 8 h bombardment with a beam current of 4-8 μA and an α-particle beam energy of 28.8 MeV. The target was then dissolved in HNO₃ and the extraction of ²¹¹At was investigated into a variety of organic solvents in 1-3 M HNO₃. Extraction of ²¹¹At with distribution ratios as high as 11.3 ± 0.6, 12.3 ± 0.8, 42.2 ± 2.2, 69 ± 4, and 95 ± 6 were observed for diisopropyl ether, 1-decanol, 1-octanol, 3-octanone, and methyl isobutyl ketone, respectively, while the distribution ratios for ²⁰⁷Bi were ≤0.05 in all cases. The extraction of ²¹¹At into both methyl isobutyl ketone and 3-octanone showed a strong, linear dependence on the HNO₃ initial aqueous concentration and better extraction than other solvents. DFT calculations show stronger binding between the carbonyl oxygen of the ketone and the At metal center.

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.

Valence-Shell Electron-Pair Repulsion Theory Revisited: An Explanation for Core Polarization

Valence-shell electron-pair repulsion (VSEPR) theory constitutes one of the pillars of theoretical predictive chemistry. It was proposed even before the advent of the concept of "spin", and it is still a very useful tool in chemistry. In this article we propose an extension of VSEPR theory to understand the core structure and predict core polarization in the main-group elements. We show from first principles (Electron Localization Function analysis) how the inner- and outer-core shells are organized. In particular, electrons in these regions are structured following the shape of the dual polyhedron of the valence shell (3^rd period) or the equivalent polyhedron (4^th and 5^th periods). We interpret these results in terms of "hard" and "soft" core character. All the studied systems follow this trend, providing a framework for predicting electron distribution in the core. We also show that lone pairs behave as "standard ligands" in terms of core polarization. The predictive character of the model was tested by proposing the core polarization in different systems not included in the original set (such as XeF₄ and [Fe(CN)₆ ]^3- ) and checking the hypothesis by means of a posteriori calculations. From the experimental point of view, the extension of VSEPR to the core region has consequences for current crystallography research. In particular, it explains the core polarization revealed by high resolution X-ray experiments.

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.

Testing the tools for revealing and characterizing the iodine-iodine halogen bond in crystals

To understand what tools are really suitable to identify and classify the iodine-iodine non-covalent interactions in solid organic polyiodides, we have examined the anisotropy of the electron density within the iodine atomic basin along and across the iodine-iodine halogen bond using the Laplacian of electron density, one-electron potential and electron localization function produced by Kohn-Sham calculations with periodic boundary conditions. The Laplacian of electron density exhibits the smallest anisotropy and yields a vague picture of the outermost electronic shells. The one-electron potential does not show such a deficiency and reveals that the valence electron shell for the halogen-bond acceptor iodine is always wider than that for the halogen-bond donor iodine along its σ-hole direction. We have concluded that the one-electron potential is the most suitable for classification of the iodine-iodine bonds and interactions in complicated cases, while the electron localization function allows to distinguish the diiodine molecule bonded with the monoiodide anion from the typical triiodide anion.

Electron localization function from density components

This work addresses the decomposition of the Electron Localization Function (ELF) into partial density contributions using an appealing split of kinetic energy densities. Regarding the degree of the electron localization, the relationship between ELF and its usual spin-polarized formula is discussed. A new polarized ELF formula, built from any subsystems of the density, and a localization function, quantifying the measure of electron localization for only a subpart of the total system are introduced. The methodology appears tailored to describe the electron localization in bonding patterns of subsystems, such as the local nucleophilic character. Beyond these striking examples, this work opens up opportunities to describe any electronic properties that depend only on subparts of the density in atoms, molecules, or solids. © 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.

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

The hydration-induced ground-state change of AtO⁺ is confirmed by means of multiconfigurational wave-function-based calculations. The involved states are identified for the first time.

Plutonium and transplutonium element trioxides: molecular structures, chemical bonding, and isomers

The stability of the An·3O (An = Pu through Cf) lowest-energy isomers should decrease in the series Pu(vi)O₃ > Am(v)O₃ ≈ Bk(v)O₃ > Cm(iii)O(O₂) > Cf(iii)O(O₂).

QTAIM Analysis in the Context of Quasirelativistic Quantum Calculations

Computational chemistry currently lacks ad hoc tools for probing the nature of chemical bonds in heavy and superheavy-atom systems where the consideration of spin-orbit coupling (SOC) effects is mandatory. We report an implementation of the Quantum Theory of Atoms-In-Molecules in the framework of two-component relativistic calculations. Used in conjunction with the topological analysis of the Electron Localization Function, we show for astatine (At) species that SOC significantly lowers At electronegativity and boosts its propensity to make charge-shift bonds. Relativistic spin-dependent effects are furthermore able to change some bonds from mainly covalent to charge-shift type. The implication of the disclosed features regarding the rationalization of the labeling protocols used in nuclear medicine for (211)At radioisotope nicely illustrates the potential of the introduced methodology for investigating the chemistry of (super)heavy elements.