Extraction of actinyls: Systematic computational investigation on the complexation between actinyls and 2,2’- (Trifluoroazanediyl) bis (N,N’-dimethylacetamide)

2.1. Computational methods

Unrestricted DFT geometry optimizations and vibration frequency calculation were performed with the B3LYP [21,22] and PBE0 [23] method using Gaussian 16 [24] and ORCA 6.0 [25,26] package, respectively. In the calculations with the Gaussian 16, and the Stuttgart-Dresden-Bonn (SDD) [27] relativistic effective core potential for actinide atom, the Dunning’s correlation consistent basis sets, AUG-cc-pVTZ [28,29] for C, N, O, and F atoms. Nuclear magnetic resonance (NMR) shielding tensors were computed within the B972 [30] hybrid functionals together with SDD for actinide atom and Def2TZVP [31] for others, based on the stable structure obtained from the previous geometric optimization. The D3 version of Grimme’s dispersion with Becke-Johnson damping [32] was adopted to consider the dispersion correction.

In these calculations with ORCA 6.0, Zero-order regular approximation (ZORA) [33] was employed to account for the relativistic effects of the actinide atom. This method reliably captures the key relativistic phenomena, the effects on the valence 5f and 6d orbitals, that govern the ground-state geometry and bonding in uranyl complexes. For the basis set, segmented all-electron relativistically contracted (SARC) [34,35], def2-TZVPP were applied for the actinides and boron, respectively. D3 stood for the Grimme’s atom pairwise dispersion correction, and BJ for Becke–Johnson damping [36]. The influence of solvent effect was considered using the conductor-like polarizable continuum model (C-PCM) [37]. Ab initio molecular dynamics (AIMD) [38] simulations were performed for more than 2 ps with a time step of 1.0 fs at 300 K under the PBE0 functional to explore the thermal stability, and the initial configurations are the stable structure obtained by geometry optimization.

Interaction Region indicator (IRI) [39] analysis was used to visualize interactions within the complexes and was plotted. Furthermore, the atom-in-molecule (AIM) [40] theory was employed to investigate the topological attributes of bond critical points (BCPs) within the electron density gradient field. The molecular surface electrostatic potential (ESP) [41] is used to demonstrate the electrostatic interaction between complexes. The Multiwfn 3.8 (dev) [42,43] programs were employed for IRI, AIM, and ESP analysis.

3.1. Geometry structure and stability of the (AnO₂^{2 +}) CF₃ABDMA complexes

The calculated geometric structure of the (AnO₂²⁺)CF₃ABDMA in the ratio of 1:1 and 1:2 have been shown in Figure 2. The detailed geometric parameters of the ground state at PBE0/SARC/ZORA-def2-TZVPP/D3BJ have been presented in Table 1, and the detailed Cartesian coordinates are listed in Table S1.

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Figure 2.

Computed geometric structure of the (AnO₂²⁺)CF₃ABDMA in the ratio of 1:1 and 1:2 at PBE0/SARC/ZORA-def2-TZVPP/D3BJ levels of theory.

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It was found that the shorter An−O_C and longer An-O_A in the 1:2 complexes, except for the An-O_C of (UO₂²⁺)L and An−O_A of (NpO₂²⁺)L. The An−N bond is more elongated in the 1:2 complexes with respect to the 1:1 complex. The computed Np−N bond length in the 1:2 complex (in Vacuum) is longer (one at ∼2.9 Å and the other two at ∼2.8 Å) than that calculated at the same level of theory for the other 1:2 complex. The An−Oc bond shows minimal variation (average change of approximately 0.01 Å) from 1:1 to 1:2 species in U−O_C and Pu−O_C, while a more pronounced change is observed for Np−O_C (average change of approximately 0.2 Å). Furthermore, computational results suggest that these complexes could exist in solution, as geometric optimization in water does not significantly alter their structures.

Investigating the thermal stability of (AnO₂²⁺)CF₃ABDMA is crucial for analyzing the complex’s structure-property correlation. As shown in Figure 3, AIMD simulations were conducted at 300 K for 2 ps to examine the structural and energetic alterations of the complexes. It can be seen that (AnO₂²⁺)CF₃ABDMA remains stable throughout the simulation period, implying the favorable stability of these complexes under typical operational conditions. Taking (PuO₂²⁺)CF₃ABDMA as an example (Figure 3b), upon reaching approximately 200 femtoseconds of simulation, the system attains a temperature of 300 K, with energy stabilizing at –33337.11 Hartree. The energy exhibits minimal fluctuation, below 0.01 Hartree, while the key length fluctuates by less than 0.5 Å.

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Figure 3.

Time evolution of the system energy (black), the distance between An and N atoms (red), and the distance between An and O atoms (blue). (a) (AnO₂²⁺)CF₃ABDMA; (b) (PuO₂²⁺)CF₃ABDMA. The AIMD simulation of (NpO₂²⁺)CF₃ABDMA at PBE0/SARC/ZORA-def2-TZVPP/D3BJ level is included in Figure S1. The AIMD simulation of (NpO₂²⁺)CF₃ABDMA at PBE0/SARC/ZORA-def2-TZVPP/D3BJ level is included in the Supporting Information.

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3.2. Nuclear magnetic resonance (NMR)

In NMR spectroscopy, chemical shift serves as a crucial parameter indicating the local chemical milieu surrounding a specific nucleus. Variations in chemical environments lead to nuanced magnetic field interactions experienced by the nucleus, resulting in distinct resonance frequencies. The splitting between nuclear spin energy levels is given by the following (Eq. 1).

where σ is the shielding constant, γ is the spin-to-magnetic ratio of the nucleus, and ΔI_z is the change in spin quantum number [44]. The physical origin of this difference is due to the shielding effect of the electrons from the external magnetic field, which manifests itself in NMR spectra as chemical shifts (typically reported in ppm) in the NMR spectrum.

In this study, all presented ¹⁹F-NMR data are the results of theoretical simulations. The magnetic shielding value (σ) of the fluorine (F) atom in CFCl₃ is obtained by subtracting the σ of the F atom in the reference (AnO₂²⁺)CF₃ABDMA complexes. This calculation yields the chemical shift commonly used in NMR spectroscopy. Subsequently, the theoretical ¹⁹F-NMR spectrum was generated by applying a Lorentzian broadening function to the calculated chemical shifts.

The simulated 400 MHz ¹⁹F-NMR spectrum of the 1:2 complex (AnO₂²⁺)CF₃ABDMA has been shown in Figure 4. The peaks in the chemical shift diagram represent the resonance signals of the ¹⁹F nucleus in a particular chemical environment. Our simulations indicate that the NpO₂²⁺(L)₂ complex exhibits the most significant chemical shift in comparison to the unbound CF₃ABDMA. Additionally, the chemical shift of NpO₂²⁺(L)₂ closely approximates that of PuO₂²⁺(L)₂, with a difference of less than 0.5 ppm.

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Figure 4.

The 400 MHz ¹⁹F-NMR spectra of complexes AnO₂²⁺(L)₂.

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What needs to be clarified is that these results are purely predictive. The purpose is to provide a theoretical insight into the NMR characteristics of these actinyl complexes. We acknowledge that the absolute values of the chemical shifts are method-dependent and may exhibit systematic deviations from potential future experimental measurements. However, the computational protocol is well-established for reliably predicting relative trends, which is the primary focus of our discussion here.

3.3. Quantum theory of atoms in molecules (QTAIM) analysis

We conducted electron density topology analysis employing the QTAIM method to assess the characteristics and stability of the (AnO₂²⁺)CF₃ABDMA complexes, including their interaction modes and bonding patterns. The topology parameter for (AnO₂²⁺)CF₃ABDMA complexes in the ratio of 1:2. The topological parameters of the (AnO₂²⁺)CF₃ABDMA complex have been listed in Table 2, and the corresponding bond path between An-N and An-O_C is plotted together with other properties in Figure 5. The topology parameter for (AnO₂²⁺)CF₃ABDMA complexes in the ratio of 1:1 have been listed in Table S2.

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Figure 5.

The 3D isosurfaces and IRI scatter plots of the (AnO₂²⁺)CF₃ABDMA complexes in the ratio of 1:2. The green and blue isosurfaces correspond to their respective spikes in the scatter plot, while the red isosurfaces represent regions of intermolecular steric repulsion. The pure blue isosurface signifies a bonding interaction surpassing weak interactions. (Surface value is 0.05a.u.)

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According to QTAIM, the presence of a bond path and a bond critical point (BCP) indicates a bonded interaction. To rigorously classify the nature of these interactions, we adopted established criteria [40,45]. The key indicators are the electron density ρ(r), its Laplacian ∇²ρ(r), and the total energy density H(r). Crucially, for bonds involving heavy atoms (such as actinides), the sign of ∇²ρ(r) can be misleading, and H(r) is a more robust descriptor [46]. Typically: 1) Shared (Covalent) Character is signified by a negative H(r), indicating a dominance of potential energy density at the BCP. 2) Closed-Shell (Electrostatic) Character is indicated by a positive H(r). As shown in Table 2, the An-N BCPs exhibit positive ∇²ρ(r) but negative H(r) values. This profile is characteristic of interactions with significant partial covalent character. This is analogous to the bonding in the Co–Co bond of Co₂(CO)₆(AsPh₃)₂, which was experimentally shown to be covalent based on its negative H(r), despite a positive ∇²ρ(r) [46].

In contrast, the An-Oc BCPs show more negative H(r) values, indicating a stronger covalent contribution. The character of the An-Oc bond thus aligns more closely with a coordinate covalent bond. The comparative analysis confirms that the bonding strength follows the order An-Oc > An-N, consistent with the relative hardness of the oxygen donor atom.

3.4. Analysis of interaction types

To efficiently discern the region and type of interactions within the (AnO₂²⁺)CF₃ABDMA complex, we employ the interaction region IRI to visually represent the various interaction modes between the actinide atoms and CF₃ABDMA ligands. IRI is essentially the gradient norm of electron density weighted by scaled electron density, defined as follows (ie Eq 2) [39].

where a is an adjustable parameter, a = 1.1 is adopted for standard definition of IRI. The sign(λ₂)$\rho$ function is projected onto the IRI isosurfaces by different colours to distinguish the strength and character of the action in different regions. Here λ₂ represents the second largest eigenvalue of the electron density Hessian matrix.

Figure 5 displays the 3D isosurfaces and IRI scatter plots of (AnO₂²⁺)CF₃ABDMA complexes at a 1:2 scale, while the scatter plots of the 1:1 complex can be found in Figure S2 in the Supporting Information. The interactions’ type and extent are depicted through the color and shape of the isosurfaces. A surface value of 0.05a.u. was utilized for generating these 3D isosurfaces. In Figure 5, the blue-biased green isosurfaces between An-N correspond to similarly colored spikes in the scatterplot, indicating a weak interaction between An-N. The pure blue isosurface observed between An-O_C signifies a bonding interaction surpassing weak interactions. Intermolecular site resistance is illustrated by the red isosurfaces.

To gain further insight into the charge interactions and distribution dynamics during the complexation of AnO₂²⁺ with the CF₃ABDMA ligand, we analysed the electrostatic potential (ESP) and generated electron density difference maps. The ESP reveals the potential for electrostatic interactions between the species, while the electron density difference maps clarify the charge redistribution and transfer processes. Figure 6 presents detailed views of the complexes’ ESPs, complemented by overlayed surface ESP maps. These visualizations in Figure 6 illustrate that the interaction of the maximum point of AnO₂²⁺ with the minimum value point of CF₃ABDMA satisfies the characteristics of the electrostatic effect and contributes to the complex stability.

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Figure 6.

Surface ESP overlap diagram of (AnO₂²⁺)CF₃ABDMA in the ratio of 1:2 and electrostatic potential distribution of CF₃ABDMA and AnO₂²⁺. To highlight the variations in the ESP of different regions on the molecular surface, the darker the colour in the figure, the greater the ESP value, and the bluer the colour, the smaller the ESP value.

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Figure 7 depicts the electron density difference maps of the complexes, and there is a positive region between An-O_C, indicating that the formation of covalent bonds leads to an accumulation of electron densities between the bonded atoms. The density difference map for PuO₂²⁺(L)₂ differs from that of UO₂²⁺(L)₂ and NpO₂²⁺(L)₂ due to the higher number of 5f electrons in plutonium, enabling it to display increased reducibility and complex chemical behaviour during chemical reactions. Unlike uranium and neptunium, which each possess one electron in the 6d orbital, plutonium lacks an electron in the 6d orbital. This distinction implies that in uranium and neptunium, the 6d orbital begins to fill, whereas in plutonium, the filling of the 6d orbital is superseded by the filling of the 5f orbital.

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Figure 7.

Contour plots of the electron density difference between AnO₂²⁺ and CF₃ABDMA fragments. Solid lines (red) represent regions where electron density increases, and the dotted lines (blue) represent regions where the electron density decreases. Relative to UO₂²⁺(L)₂ and NpO₂²⁺(L)₂, the PuO₂²⁺(L)₂ complex exhibits a distinct density difference map, attributed to the higher 5f electron count and lack of a 6d electron in Pu, leading to enhanced reducibility and complex behavior.

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3.5. Hirshfeld surface analysis

Hirshfeld analysis elucidates interactions between atoms in the central molecule and those in the surrounding molecule, while local contact analysis pinpoints the specific atoms from both molecules involved in the Hirshfeld analysis. The positioning of the scatter distribution on the fingerprint map enables the detailed examination of interaction characteristics between AnO₂²⁺ and its neighbouring ligands.

Using (UO₂²⁺)CF₃ABDMA as a case study, Figure 8 illustrates localized Hirshfeld surfaces and fingerprints. The Hirshfeld surface isosurfaces map highlights regions with higher electron density in red, indicating stronger interactions. Each point on the fingerprint map corresponds to a vertex on the Hirshfeld surface and is color-coded based on dot density, with yellow representing denser regions and purple indicating sparser areas. Notably, the U-N and O-N bonds exhibit relatively weaker interactions in (UO₂²⁺)CF₃ABDMA. The presence of a distinct spike in the fingerprint plot for U-O_C atoms suggests a more robust U-O_C interaction compared to the U-N bond. The relative positions of these spikes, with d_i > d_e, suggest that U acts as the acceptor and O_C as the donor in the bonding arrangement.

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Figure 8.

The localized Hirshfeld surface and molecular fingerprints of (UO₂²⁺)CF₃ABDMA at a 1:2 ratio are depicted. The horizontal coordinate d_i represents the shortest distance from an interior atom (from the central molecule) to the Hirshfeld surface at the given point. The vertical coordinate d_e signifies the nearest distance from exterior atoms to the surface.

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3.6. Energy decomposition analyses

The preceding discourse focused on electron density topological properties or orbital interactions; in this section, we shift the focus to characterizing interactions through an energy composition perspective. Energy decomposition analyses (EDA) enable the dissection of interaction energy into distinct physical components, facilitating an understanding of the pivotal factors influencing the interaction.

Here we have used the sobEDA [47,48] method based on the definition of DFT dispersion correction. The sobEDA decomposes the interaction energy ΔE_int into five different components, that is, Eq 3.

These symbols represent electrostatic ΔE_els, orbital ΔE_orb, and exchange-reciprocal interactions ΔE_xrep, as well as Coulomb correlation ΔE_DFTc and dispersion correction ΔE_dc, respectively. The exchange-repulsion term ΔE_xrep is defined as the sum of ΔE_x and ΔE_rep.

The specific values analysed for energy decomposition are listed in Table 3. The electrostatic interaction magnitudes suggest the following trend for the complexes: UO₂²⁺(L)₂ > NpO₂²⁺(L)₂ > PuO₂²⁺(L)₂. The total interaction energy of PuO₂²⁺(L)₂ is higher than that of NpO₂²⁺(L)₂ due to the combined effect of the weak orbital interaction in NpO₂²⁺(L)₂ and the small site-barrier interaction in PuO₂²⁺(L)₂, yet it remains lower than that of UO₂²⁺(L)₂.

This observed trend finds its origin in the evolving electronic structure across the actinide series. It is well-established that the 5f orbitals of the early actinides are more spatially extended and accessible for bonding compared to their lanthanide counterparts, allowing for a significant covalent contribution [49]. However, across the series from Uranium to Plutonium, these 5f orbitals undergo a pronounced contraction and energetic stabilization due to the increasing nuclear charge.

This contraction leads to a systematic shift in the bonding mechanism. In the UO₂²⁺ complex, the more expanded 5f orbitals (as well as the 6d orbitals) can effectively participate in covalent overlap with ligand orbitals. In contrast, for PuO₂²⁺, the contracted 5f orbitals participate less effectively, resulting in bonds that are predominantly electrostatic. The NpO₂²⁺ system represents an intermediate case. This mechanistic picture is fully consistent with our EDA, which shows a decreasing trend in the orbital interaction component from U to Pu (Table 3)

The analysis in Table 3 indicates that electrostatics and orbitals predominantly govern the (AnO₂²⁺)CF₃ABDMA interactions. This finding aligns with the results of the ESP and QTAIM analyses, where electrostatic interactions stabilize the complexes, and bond critical point analyses reveal the covalent interactions.