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The bond distance is the simplest and most obvious indicator of the nature of a given chemical bond. However, for rare chemistry, it may happen that it is not yet firmly established. In this communication, we will show that the formally-triple protactinium(V) mono-oxo bond is predicted longer than what was previously reported in the solid state and in solution, based on robust quantum mechanical calculations, supported by an extensive methodological study. Furthermore, additional calculations are used to demonstrate that the Pa-Ooxo bond of interest is more sensitive to complexation than the supposedly analogous U-Oyl ones, not only in terms of bond distance but also of finer bond descriptors associated with the effective bond multiplicity.

Quantum-chemical subsystem and embedding methods require complex workflows that may involve multiple quantum-chemical program packages. Moreover, such workflows require the exchange of voluminous data that goes beyond simple quantities such as molecular structures and energies. Here, we describe our approach for addressing this interoperability challenge by exchanging electron densities and embedding potentials as grid-based data. We describe the approach that we have implemented to this end in a dedicated code, PyEmbed, currently part of a Python scripting framework. We discuss how it has facilitated the development of quantum-chemical subsystem and embedding methods, and highlight several applications that have been enabled by PyEmbed, including WFT-in-DFT embedding schemes mixing non-relativistic and relativistic electronic structure methods, real-time time-dependent DFT-in-DFT approaches, the density-based many-body expansion, and workflows including real-space data analysis and visualization. Our approach demonstrates in particular the merits of exchanging (complex) grid-based data, and in general the potential of modular software development in quantum chemistry, which hinges upon libraries that facilitate interoperability.

In this work we introduce a novel subsystem-based electronic structure embedding method that combines the projection-based block-orthogonalized Manby-Miller embedding (BOMME) with the density-based Frozen Density Embedding (FDE) methods. Our approach is effective for systems in which the building blocks interact at varying strengths while still maintaining a lower computational cost compared to a quantum simulation of the entire system. To evaluate the performance of our method, we assess its ability to reproduce the X-ray absorption spectra (XAS) of chloride and fluoride anions in aqueous solutions (based on a 50-water droplet model) via real-time time-dependent density functional theory (rt-TDDFT) calculations. We employ an ensemble approach to compute XAS for the K- and L-edges, utilizing multiple snapshots of configuration space obtained from classical molecular dynamics simulations with a polarizable force field. Configurational averaging influences both the broadening of spectral features and their intensities, with contributions to the final intensities originating from different geometry configurations. We found that embedding models that are too approximate for halide-water specific interactions, as in the case of FDE, fail to reproduce the experimental spectrum for chloride. Meanwhile, BOMME tends to overestimate intensities, particularly for higher energy features because of finite-size effects. Combining FDE for the second solvation shell and retaining BOMME for the first solvation shell mitigates this effect, resulting in an overall improved agreement within the energy range of the experimental spectrum. Additionally, we compute the transition densities of the relevant transitions, confirming that these transitions occur within the halide systems. Thus, our real-time QM/QM/QM embedding method proves to be a promising approach for modeling XAS of solvated systems.

Polonium (Po, Z = 84) is a main-block element with poorly known physico-chemical properties. Not much information has been firmly acquired since its discovery by Marie and Pierre Curie in 1898, especially regarding its speciation in aqueous solution and spectroscopy. In this work, we revisit the absorption properties of two complexes, [PoCl5]^- and [PoCl6]^{2-}, using quantum mechanical calculations. These complexes have the potential to exhibit a maximum absorption at 418 nm in HCl medium (for 0.5 mol/L concentrations and above). Initially, we examine the electronic spectra of the Po^{4+} free ion and of its isoelectronic analogue, Bi^{3+}. In the spin-orbit configuration interaction (SOCI) framework. Our findings demonstrate that the SOCI matrix should be dressed with correlated electronic energies and that the quality of the spectra is largely improved by decontracting the reference states at the complete active space plus singles (CAS+S) level. Subsequently, we investigate the absorption properties of the [PoCl5]^- and [PoCl6]^{2-} complexes in two stages. Firstly, we perform methodological tests at the MP2/def2-TZVP gas phase geometries, indicating that the decontraction of the reference states can there be skipped without compromising the accuracy significantly. Secondly, we study the solution absorption properties by means of single-point calculations performed at the solvated geometries, obtained by an implicit solvation treatment or a combination of implicit and explicit solvation. Our results highlight the importance of saturating the first coordination sphere of the Po^{IV} ion to obtain a qualitatively correct picture. Finally, we conclude that the known-for-decades 418 nm peak could be attributed to a mixture of both the [PoCl5(H2O)]^- and [PoCl6]^{2-} complexes. This finding not only aligns with the behaviour of the analogous Bi^{III} ion under similar conditions but...

Protactinium ($Z$ = 91) is a very rare actinide with peculiar physico-chemical properties. Indeed, although one may naively think that it behaves similarly to either thorium or uranium by its position in the periodic table, it may in fact follow its own rules. Because of the quite small energy gap between its valence shells (in particular the 5$f$ and 6$d$ ones) and also the strong influence of relativistic effects on its properties, it is actually a challenging element for theoretical chemists. In this article, we combine experimental information, chemical arguments and standard first-principle calculations, complemented by implicit and explicit solvation, to revisit the stepwise complexation of aqueous protactinium(V) with sulfate and oxalate dianionic ligands (SO$_4$$^{2-}$ and C$_2$O$_4$$^{2-}$, respectively). From a methodological viewpoint, we notably conclude that it is necessary to at least saturate the coordination sphere of protactinium(V) to reach converged equilibrium constant values. Furthermore, in the case of single complexations (i.e. with one sulfate or oxalate ligand bound in the bidentate fashion), we show that it is necessary to maintain the coordination of one hydroxyl group, present in the supposed [PaO(OH)]$^{2+}$ precursor, to obtain coherent complexation constants. Therefore, we predict that this hydroxyl group is maintained in the formation of 1:1 complexes while we confirm that it is withdrawn when coordinating three sulfate or oxalate ligands. Finally, we stress that this work is a first step toward the future use of theoretical predictions to elucidate the enigmatic chemistry of protactinium in solution.

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 are not yet 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(H$_2$O)$_n$]$^{4+}$ 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 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 by 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.

The Frozen Density Embedding scheme represents an embedding method in which environmental effects onto a given subsystem are included by representing the other subsystems making up the surroundings quantum mechanically, by means of their electron densities. In the present paper, we extend the full 4-component relativistic Dirac-Kohn-Sham method, as implemented in the BERTHA code, to include environmental and confinement effects with the FDE scheme. This implementation has been enormously facilitated by BERTHA's python API (PyBERTHA), which provides a flexible framework of development by using all Python advantages in terms of code re-usability, portability while facilitating the interoperability with other FDE implementations available through the PyADF framework. The computational performance has been evaluated on a series of gold clusters (Au$_n$, with n=2,4,8) embedded into an increasing number of water molecules (5, 10, 20, 40 and 80 water molecules). We found that the procedure scales approximately linearly both with the size of the frozen surrounding environment (in line with the underpinnings of the FDE approach) and with the size of the active system (in line with the use of density fitting). Finally, we applied the code to a series of Heavy (Rn) and Super-Heavy elements (Cn, Fl, Og) embedded in a C_60 cage to explore the confinement effect induced by C_60 on their electronic structure. We compare the results from our simulations with more approximate models employed in the atomic physics literature, in which confinement is represented by a radial potential slightly affected by the nature of the central atom. Our results indicate that the specific interactions described by FDE are able to improve upon the cruder approximations currently employed, and thus provide a basis from which to generate more realistic radial potentials for confined atoms., Comment: 53 pages, 7 Figures

A polarizable force-field (FF) model for short- and long-alkane chains and amide derivatives was constructed based solely on accurate quantum chemical (QC) calculations. First, the FF model accuracy was accessed by performing molecular dynamics (MD) simulations to calculate liquid-phase thermodynamic and structural properties for alkanes, for which experimental data are available. Second, The FF was then used to perform molecular dynamics simulations to calculate thermodynamic, structural and excess properties of monoamide/dodecane mixtures, namely DEHiBA/dodecane and DEHBA/dodecane. Aggregation phenomena appear for both types of mixtures and monoamide pure phases. A detailed structural analysis revealed, at small monoamide mole fraction the formation of dimers, while trimerization at larger monoamide concentrations and in their pure phases. Analysis of the relative orientation of the dimers have also been performed and showed a small difference for both phases., Comment: 15 pages, 11 figures

In this work we implement the real-time time-dependent block-orthogonalized Manby-Miller embedding (rt-BOMME) approach alongside our previously developed real-time frozen density embedding time-dependent density functional theory (rt-TDDFT-in-DFT FDE) code, and investigate these methods' performance in reproducing X-ray absorption spectra (XAS) obtained with standard rt-TDDFT simulations, for model systems comprised of solvated fluoride and chloride ions ([X@(H$_2$O)$_8$]$^-$, X = F, Cl). We observe that, for ground-state quantities such as core orbital energies, the BOMME approach shows significantly better agreement with supermolecular results than FDE for the strongly interacting fluoride system, while for chloride the two embedding approaches show more similar results. For the excited states, we see that while FDE (constrained not to have the environment densities relaxed in the ground state) is in good agreement with the reference calculations for the region around the K and L$_1$ edge, and is capable of reproducing the splitting of the $\mathrm{1s^{1} (n+1)p^1}$ final states ($n+1$ being the lowest virtual p orbital of the halides), it by and large fails to properly reproduce the $\mathrm{1s^{1} (n+2)p{^1}}$ states and misses the electronic states arising from excitation to orbitals with important contributions from the solvent. The BOMME results, on the other hand, provide a faithful qualitative representation of the spectra in all energy regions considered, though its intrinsic approximation of employing a lower-accuracy exchange-correlation functional for the environment induces non-negligible shifts in peak positions for the excitations from the halide to the environment. Our results thus confirm that QM/QM embedding approaches are viable alternatives to standard real-time simulations of X-ray absorption spectra of species in complex or confined environments., Comment: 15 pages, 5 figures

We investigated isolated sodium/chloride aqueous droplets at the microscopic level, which comprise from about 5k to 1M water molecules and whose salt concentrations are 0.2$m$ (brackish water) and 0.6$m$ (sea water), by means of molecular dynamics simulations based on an \emph{ab initio}-based polarizable force field. The size of our largest droplets is at the submicron particle marine aerosol scale. From our simulations, we investigated ion spatial distributions, ion aggregates (size, composition, lifetime and distribution), droplet surface potentials and the densities of the water vapor surrounding the droplets. Regarding ions, they form a weak electrostatic double layer extending from the droplet boundary to 2~nm within the droplet interior. Free $\mathrm{Na^+}$ and ion aggregates are more repelled from the boundary than free $\mathrm{Cl^-}$. Most of the droplet properties depend on the droplet radius $R$ according to the standard formula $A=A_\infty(1 - 2 \delta/R) $, where $A_\infty$ is the bulk magnitude of the quantity $A$ and $\delta$ is a length at most at the~nm scale. Regarding the water vapor densities they obey a Kelvin relation corresponding to a surface tension whose Tolman length is negative and at the 1~nm scale. That length is about one order of magnitude larger than for pure water droplets, however it is weak enough to support the reliability of a standard Kelvin term (based on planar interface surface tensions and water densities) and of the related K{\"o}lher equation to model sub-micron salty aerosols., Comment: 54 pages, 10 figures, 3 tables

Quantitative predictions of the release of volatile radiocontaminants of ruthenium (Ru) in the environment from either nuclear power plants (NPP) or fuel recycling accidents present significant uncertainties while estimated by severe accidents nuclear analysis codes. Observations of Ru from either experimental or modeling works suggest that the main limitations relate to the poor evaluation of the kinetics of gaseous Ru in the form of RuO$_3$ and RuO$_4$. This work presents relativistic correlated quantum chemical calculations performed to determine the possible reactions pathways leading to the formation of gaseous Ru oxides under NPP severe accident conditions, as a result of reactions of RuO$_2$ gaseous with air radiolysis products, namely nitrous and nitrogen oxides. The geometries of the relevant species were optimized with the TPSSh-5%HF functional of the density, while the total electronic energies were computed at the CCSD(T) level with extrapolations to the complete basis set CBS limit. The reaction pathways were fully characterized by localizing the transition states and all intermediate structures using the internal coordinate reaction algorithm (IRC). The rate constants were determined over the temperature range 250-2500 K. It is revealed that the less kinetically limiting pathway to form Ru gaseous fraction is the oxidation of Ru by nitrogen oxide, corroborating experimental observations., Comment: 9 pages, 7 tables, 5 figures

Polycyclic aromatic compounds (PACs) constitute an important class of molecules found in various environments and are considered important pollutants of the Earth's atmosphere. In particular, functionalization of PACs modify the ring aromaticity, which greatly influences the chemical reactivity of these species. In this work we studied several oxygen-containing PACs, relevant to atmospheric chemistry. We investigated the conformational landscape of four naphthalene-derivative molecules -- namely ,1- and 2-hydroxynaphthalene and 1- and 2-naphthaldehyde -- by means of rotational and vibrational spectroscopy supported by quantum chemical calculations. For 1-hydroxynaphthalene and 1-naphthaldehyde, intramolecular hydrogen bonding and steric effects drive the conformational preferences while for 2-hydroxynaphthalene and 2-naphthaldehyde, the charge distributions allow us to understand the conformational landscape. This work not only demonstrates how the localization of the substitution group in the ring influences the conformational relative energies and but also constitutes a step toward a better understanding of the different chemical reactivity of such functionalized PACs.

We investigate the ability of mechanical and electronic density functional theory (DFT)-based embedding approaches to describe the solvent effects on nuclear magnetic resonance (NMR) shielding constants of the $^{95}$Mo nucleus in the molybdate ion in aqueous solution. From the description obtained from calculations with two- and four-component relativistic Hamiltonians, we find that for such systems spin-orbit coupling effects are clearly important for absolute shielding values, but for relative quantities a scalar relativistic treatment provides a sufficient estimation of the solvent effects. We find that the electronic contributions to the solvent effects are relatively modest yet decisive to provide a more accurate magnetic response of the system, when compared to reference supermolecular calculations. We analyze the errors in the embedding calculations by statistical methods as well as through a real-space representation of NMR shielding densities, which are shown to provide a clear picture of the physical processes at play., Comment: 14 pages, 6 figures

The luminescence properties of the $\mathrm{[UO_2Cl_4]^{2-}}$ complex in an organic phase, especially the influence of large organic counter cations, have been studied by time-resolved laser-induced fluorescence spectroscopy (TRLFS) and ab initio modeling. The experimental spectrum was assigned by vibronic Franck-Condon calculations on quantum chemical models based on relativistic density functional approaches. The shape of the luminescence spectrum of the uranyl tetrachloride complex is determined by symmetrical vibrations and geometrical change upon emission. The possible change of the luminescence properties depending on the first and second uranyl coordination sphere was predicted theoretically for $\mathrm{[UO_2Br_4]^{2-}}$ and $\mathrm{[R_4N]_2[UO_2Cl_4]}$ ($\mathrm{R_4N}$ = $\mathrm{[Bu_4N]}$, $\mathrm{[{A336}]}$) systems. The computations reveal that for U(VI), the second coordination sphere has little influence on the spectrum shape, making speciation of uranyl complexes with identical first coordination-sphere ligands tedious to discriminate. The computed structural changes agreed well with experimental trends; theoretical spectra and peaks attribution are in a good accordance with TRLFS and magnetic circular dichroism (MCD) data respectively.

In the context of nuclear fuel recycling and environmental issues, the understanding of the properties of radio-elements with various approaches remains a challenge regarding their dangerousness. Moreover, experimentally, it is imperative to work at sufficiently high concentrations to reach the sensitivities of the analysis tools, which often leads to precipitation for some of them, and stabilizing of specific oxidation states of some actinides remains a challenge, thus making it difficult to extract general trends across the actinide series. Complementary to experiments, modelling can be used to unbiasedly probe the actinide's properties in aquatic environment and offers a predictive tool. We report the first molecular dynamics simulations based on homogeneously built force fields for the whole series of the tetravalent actinides in aqueous phase from $\mathrm{Th^{IV}}$ to $\mathrm{Bk^{IV}}$ and including $\mathrm{Pu^{IV}}$. The force fields used to model the interactions among the constituents include polarization and charge donation microscopic effects. They are built from an automated iterative \textit{ab initio} based engine, the core element of a future machine learning procedure devoted to generate accurate force fields. The comparison of our simulated hydrated actinide properties to available experimental data show the model robustness and the relevance of our parameter assignment engine. Moreover our simulated structural, dynamical and hydration free energy data show that, apart from $\mathrm{Am^{IV}}$ and $\mathrm{Cm^{IV}}$, the actinides properties change progressively along the series., Comment: 7 pages, 4 figures

The ability to predict the nature and amounts of plutonium emissions in industrial accidents, such as in solvent fires at PUREX nuclear reprocessing facilities, is a key concern of nuclear safety agencies. In accident conditions and in the presence of oxygen and water vapor, plutonium is expected to form the three major volatile species $\rm{PuO_2}$, $\rm{PuO_3}$, and $\rm{PuO_2(OH)_2}$, for which the thermodynamic data necessary for predictions (enthalpies of formation and heat capacities) presently show either large uncertainties or are lacking. In this work we aim to alleviate such shortcomings by obtaining the aforementioned data via relativistic correlated electronic structure calculations employing a two-step multi-reference approach (MS-CASPT2 with SO-RASSI), which is able to describe the multireference character of the ground-state wave functions of $\rm{PuO_3}$ and $\rm{PuO_2(OH)_2}$. We benchmark this approach by comparing it to relativistic coupled cluster calculations for the ground, ionized, and excited states of $\rm{PuO_2}$. Our results allow us to predict enthalpies of formation $\Delta_fH^\ominus(\rm{298.15~K})$ of $\rm{PuO_2}$, $\rm{PuO_3}$ and $\rm{PuO_2(OH)_2}$ to be $\rm{-449.5\pm8.8}$, $\rm{-553.2\pm27.5}$, and $\rm{-1012.6\pm38.1~kJ\;mol^{-1}}$, respectively, which confirm the predominance of plutonium dioxide, but also reveal the existence of plutonium trioxide in the gaseous phase under oxidative conditions, though the partial pressures of $\rm{PuO_3}$ and $\rm{PuO_2(OH)_2}$ are nonetheless always rather low under a wet atmosphere. Our calculations also permit us to reassess prior results for $\rm{PuO_2}$, establishing that the ground state of the $\rm{PuO_2}$ molecule is mainly of $\rm{^{5}\Sigma_{g}^+}$ character, as well as to confirm the experimental value for the adiabatic ionization energy of $\rm{PuO_2}$., Comment: 17 pages, 5 figures, 9 tables and supplementary information

A subsystem approach for obtaining electron binding energies in the valence region and apply it to the case of halide ions (X$^-$, X = F-At) in water. This approach is based on electronic structure calculations combining the relativistic equation of motion coupled-cluster method for electron detachment (EOM-IP-CCSD) and density functional theory via the frozen density embedding (FDE) approach, using structures from classical molecular dynamics with polarizable force fields for discrete systems (in the present study, droplets containing the anion and 50 water molecules). Our results indicate one can accurately capture both the large solvent effect observed for the halides as well as the splitting of their ionization signals due to the increasingly large spin-orbit coupling of the p$_{3/2}$-p$_{1/2}$ manifold across the series, at an affordable computational cost. Furthermore, due to the quantum mechanical treatment of both solute and solvent, electron binding energies of semi-quantitative quality are also obtained also obtained for (bulk) water as by-products of the calculations for the halogens (in droplets).

Tributyl-phosphate (TBP), a ligand used in the PUREX liquid-liquid separation process of spent nuclear fuel, can form explosive mixture in contact with nitric acid, that might lead to violent explosive thermal runaway. In the context of safety of a nuclear reprocessing plant facility, it is crucial to predict the stability of TBP at elevated temperatures. So far, only the enthalpies of formation of TBP is available in the literature with a rather large uncertainties, while those of its degradation products, di-(HDBP) and mono-(H$_2$MBP}) are unknown. In this goal, we have used state-of-the art quantum chemical methods to compute the formation enthalpies and entropies of TBP and its degradation products di-(HDBP), mono-(H$_2$MBP) in gas and liquid phases. Comparisons of levels of quantum chemical theory revealed that there are significant effects of correlation on their electronic structures, pushing for the need of not only high level of electronic correlation treatment, namely local coupled cluster with single and double excitation operators and perturbative treatment of triple excitations [LCCSD(T)], but also extrapolations to the complete basis to produce reliable and accurate thermodynamics data. Solvation enthalpies were computed with the conductor like screening model for real solvents [COSMO-RS], for which we observe errors not exceeding 22 kJ mol$^{-1}$. We thus propose with final uncertainty of about 20 kJ mol$^{-1}$ standard enthalpies of formation of TBP, HDBP, and H$_2$MBP which amounts to -1281.7$\pm$24.4, -1229.4$\pm$19.6 and -1176.7$\pm$14.8 kJ mol$^{-1}$, respectively, in the gas phase. In the liquid phase, the predicted values are -1367.3$\pm$24.4, -1348.7$\pm$19.6 and -1323.8$\pm$14.8 kJ mol$^{-1}$, to which we may add about -22 kJ mol$^{-1}$ error from the COSMO-RS solvent model. From these data, we predict the complete hydrolysis of TBP to be nearly thermoneutral.

Actinide-containing complexes present formidable challenges for electronic structure methods due to the large number of degenerate or quasi-degenerate electronic states arising from partially occupied 5f and 6d shells. Conventional multi-reference methods can treat active spaces that are often at the upper limit of what is required for a proper treatment of species with complex electronic structures, leaving no room for verifying their suitability. In this work we address the issue of properly defining the active spaces in such calculations, and introduce a protocol to determine optimal active spaces based on the use of the Density Matrix Renormalization Group algorithm and concepts of quantum information theory. We apply the protocol to elucidate the electronic structure and bonding mechanism of volatile plutonium oxides (PuO$_3$ and PuO$_2$(OH)$_2$), species associated with nuclear safety issues for which little is known about the electronic structure and energetics. We show how, within a scalar relativistic framework, orbital-pair correlations can be used to guide the definition of optimal active spaces which provide an accurate description of static/non-dynamic electron correlation, as well as to analyse the chemical bonding beyond a simple orbital model. From this bonding analysis we are able to show that the addition of oxo- or hydroxo-groups to the plutonium dioxide species considerably changes the pi-bonding mechanism with respect to the bare triatomics, resulting in bent structures with considerable multi-reference character., Comment: 12 pages, 5 figures