Electron-Transfer-Enhanced Cation–Cation Interactions in Homo- and

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Electron-Transfer-Enhanced Cation−Cation Interactions in Homoand Heterobimetallic Actinide Complexes: A Relativistic Density Functional Theory Study Ming Zheng, Fang-Yuan Chen, Jia-Nan Tian, and Qing-Jiang Pan* Key Laboratory of Functional Inorganic Material Chemistry of Education Ministry, School of Chemistry and Materials Science, Heilongjiang University, Harbin 150080, China S Supporting Information *

ABSTRACT: To provide deep insight into cation−cation interactions (CCIs) involving hexavalent actinyl species that are major components in spent nuclear fuel and pose important implications for the effective removal of radiotoxic pollutants in the environment, a series of homo- and heterobimetallic actinide complexes supported by cyclopentadienyl (Cp) and polypyrrolic macrocycle (H4L) ligands were systematically investigated using relativistic density functional theory. The metal sort in both parts of (THF)(H2L)(OAnVIO) and (An′)IIICp3 from U to Np to Pu, as well as the substituent bonding to Cp from electron-donating Me to H to electron-withdrawing Cl, SiH3, and SiMe3, was changed. Over 0.70 electrons are unraveled to transfer from the electron-rich UIII to the electron-deficient AnVI of the actinyl moiety, leading to a more stable AnV−UIV isomer; in contrast, uranylneptunium and uranylplutonium complexes behave as electron-resonance structures between VI−III and V−IV. These were further corroborated by geometrical and electronic structures. The energies of CCIs (i.e., Oexo−An′ bonds) were calculated to be −19.6 to −41.2 kcal/mol, affording those of OUO−Np (−23.9 kcal/mol) and OUO−Pu (−19.6 kcal/mol) with less electron transfer (ET) right at the low limit. Topological analyses of the electron density at the Oexo−An′ bond critical points demonstrate that the CCIs are ET or dative bonds in nature. A positive correlation has been built between the CCIs’ strength and corresponding ET amount. It is concluded that the CCIs of Oexo−An′ are driven by the electrostatic attraction between the actinyl oxo atom (negative) and the actinide ion (positive) and enhanced by their ET. Finally, experimental syntheses of (THF)(H2L)(OUVIO)(An′)IIICp3 (An′ = U and Np) were well reproduced by thermodynamic calculations that yielded negative free energies in a tetrahydrofuran solution but a positive one for their uranylplutonium analogue, which was synthetically inaccessible. So, our thermodynamics would provide implications for the synthetic possibility of other theoretically designed bimetallic actinide complexes.

1. INTRODUCTION Cation−cation interaction (CCI) was first recognized between UO22+ and NpO2+ in aqueous perchloric acid media,1 where the stronger Lewis basic oxo atom of neptunyl coordinates to the uranyl metal center. The concept is further extended to the interaction of one actinyl with cationic ions of s-, d-, and f-block metals.2−14 In solid-state chemistry, for instance, CCIs have been found to be capable of fabricating diverse structures of actinyl complexes such as dimers, oligomers, and one- to threedimensional networks.2−14 Apart from the fundamental interest, the understanding of CCIs is of great importance in the development of spent nuclear fuel processing technologies, the manipulation of nuclear waste, and the removal of radionuclides from the environment.15−19 Pentavalent actinyl ions (AnO2+, where An = U, Np, and Pu) dominate in cation−cation complexes because of the high Lewis basicity of -yl oxygen atoms.1−13 Comparatively, hexavalent uranyl-based complexes without the assistance of bridging ligands remain extremely scarce.14,20 As one of the © XXXX American Chemical Society

most stable and most prevalent in the formation of uranium(VI), the approximately linear UO22+ species has important environmental implications.15−18 It is highly soluble, and thus mobile, and biologically available, which makes it a key player in the long-term environmental risks involved in the disposal of radiotoxic waste. Relative to its pentavalent analogue, the very weak uranyl(VI) oxo basicity makes its CCI and/or functionalization greatly unfavorable. In this respect, a seminal uranyl complex, (THF)(UVIO2)(H2L) (labeled as UVIL; THF = tetrahydrofuran),21 with a “Pacman”-like structure was synthesized by Arnold, Love, and co-workers using a versatile Schiff-base polypyrrolic macrocycle (H4L);22,23 the uranyl was equatorially accommodated by one N4-donor compartment of the ligand and one additional THF solvent, and the other N4-donor compartment was left empty; the hydrogen bonds between the uranyl endo-oxo atom and the Received: January 6, 2018

A

DOI: 10.1021/acs.inorgchem.8b00051 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry remaining hydrogen atoms of the pyrrolides of the empty pocket were found to be very important for promoting reduction of the uranium(VI) center and activating the opposite exo-oxo atom.24−30 Building on this molecular scaffold, significant contribution has been made by the same group to develop abundant cation−cation complexes. A variety of cations like lanthanide,31,32 transition metal,26,33 and maingroup metal27−30 were involved in the CCI with the uranyl(VI) unit; on the other hand, the CCI can be created in different positions of the UVIL complex, including uranyl endo-oxo or exo-oxo atoms and even both. In spite of considerable effort, however, encapsulating either the actinide ion or actinyl into the empty N4-donor compartment of UVIL, i.e., fabricating the interaction with uranyl endo oxgyen, was unsuccessful.21,26,33 Corresponding computational studies realized very high thermodynamic energies for their formation reactions.34 Excitingly, two impressive complexes, (THF)(H2L)(OUVIO)(An′)IIICp3 (An′ = U and Np), were achieved in 2016, which feature the intriguing uranyl exo-oxo and actinide interaction.20 Large electron transfer (ET) was revealed from UIIICp3 to the uranyl(VI) part, leading to the formation of UV−UIV in reality. Differently, modest ET was assigned to the neptuniumcontaining complex. Notably, these experimental complexes offer us an opportunity to investigate CCIs and unravel their nature at a molecular level, although posing theoretical challenges because of their large molecular systems, complicated electronic structures, and strong relativistic effects. In the work, a series of homo- and heterobimetallic actinide complexes were comprehensively examined using a relativistic density functional theory (DFT). We varied the metal sort both in the actinyl unit and in the (An′)IIICp3 part from U to Np to Pu in silo, which avoids experimental difficulties such as handling of the highly radiotoxic transuranics, scarcity of materials, rigid synthetic conditions, and extreme instability of complexes. Various substituted cyclopentadienyl ligands were considered for the actinide ion, while the actinyl unit was completed by the polypyrrolic macrocycle and one THF solvent. Structural, ET, and energetic properties were discussed in detail. The mechanism to form and stabilize cation−cation complexes was proposed. The nature of the CCIs was addressed according to topological analysis of the electron density.

Figure 1. Structures of (THF)(H 2 L)(OAn VI O)(An′) III (CpX) 3 (labeled as AnVI−(An′)IIIX; An and An′ = U, Np, and Pu; X = H, Me, Cl, SiH3, and SiMe3). Note that AnVI−(An′)III was used for clarity and X = H, and the complex with CpSiMe3 was not shown because of its long Oexo···U separation (4.547 Å).

Table 1. Formulas and Abbreviations of Investigated Complexes in This Work complex

abbreviation VI

(THF)(H2L)(OU O) (An′)IIICp3 (THF)(H2L)(OAnVIO) UIIICp3 (THF)(H2L)(OUVIO) UIII(CpX)3 [(THF)(AnmO2)(H2L)]z [(An′)nCp3]z UIII(CpX)3

U −(An′) VI

An −U VI

III

III

(An′ = U, Np, and Pu)

(An = Np and Pu)

UVI−UIIIX (X = Cl, Me, SiH3, and SiMe3) AnmL (An = U, Np, and Pu; m = VI and V; z = 0 and 1−) (An′)nCp (An = U, Np, and Pu; n = III and IV; z = 0 and 1+) UIIIX (X = Cl, Me, SiH3, and SiMe3)

out and neglected from the full Dirac equation.49 Default convergence criteria for gradients in the geometry optimization (10−5 au) and selfconsistent field (SCF; 10−6 au) were employed. The generalizedgradient-approximation Perdew−Burke−Ernzerhof (GGA-PBE) functional50, as well as the AE correlation-consistent double-ζ-polarized quality basis sets (marked as B-I), was used.47 In these calculations, UVI−UIII and UVI−UIIISiMe3 contain the smallest and largest numbers of atoms/electrons, corresponding to 127/791 and 163/935, respectively. The basis sets were taken as U/Np/Pu (34s33p24d18f6g)/(10s9p7d4f1g), Si/Cl (15s11p3d)/(4s3p1d), C/ N/O (10s7p3d)/(3s2p1d), and H (6s2p)/(2s1p). Thus, 1755 orbital basis functions with 4934 auxiliary basis functions were used for UVI− UIIISiMe3, for example. Analytical frequency calculations show no imaginary frequencies, which confirms the minimum nature of the optimized structure. Also, zero-point vibrational energies, entropies, and free energies at 298.15 K were obtained. With the ADF2014 program,51−53 the electronic properties and solvation energies were calculated at PRIRODA-optimized geometries. Previous studies have shown that this approximation is reliable because reoptimizations have only a very slight effect on the structural parameters and molecular properties.40,54−60 An integration parameter of 6.0, together with the default convergence criterion of 10−6 au, was applied. The conductor-like screening model (COSMO)61,62 was used to simulate solvent media around the complex, applying an Esurf type of cavity and a dielectric constant of 7.58 for THF. Klamt radii were used for the main-group atoms (H = 1.30 Å, C = 2.00 Å, N = 1.83 Å, O = 1.72 Å, Si = 2.40 Å, and Cl = 2.05 Å) and for the actinide atoms (U, Np, and Pu = 1.70 Å).63,64 We used the level of theory including

2. COMPUTATIONAL DETAILS Cation−cation complexes (THF)(H2L)(OAnVIO)(An′)III(CpX)3 (labeled as AnVI−(An′)IIIX; An and An′ = U, Np, and Pu; X = Me, H, Cl, SiH3, and SiMe3) were computationally explored in this work. Their structures are illustrated in Figure 1, where the uranyluranium and uranylneptunium ones have been experimentally synthesized and characterized recently.20 For comparison, precursors including [(THF)(AnmO2)(H2L)]z (AnmL; An = U, Np, and Pu; m = VI and V; z = 0 and 1−), [(An′)nCp3]z ((An′)nCp; An′ = U, Np, and Pu; n = III and IV; z = 0 and 1+), and UIII(CpX)3 (UIIIX; X = Cl, Me, SiH3, and SiMe3) were calculated. See their formulas and abbreviations in Table 1. Regarding open-shell systems, unrestricted calculations have been carried out in their highest electron-spin state, because reliable results were achieved in this work (Table S1) and previous studies.35−44 Moreover, spin contamination in the unrestricted Kohn−Sham wave function was calculated to be less than 0.14 for all of these complexes. Structural optimizations of the aforementioned complexes were accomplished by the PRIRODA code without any symmetry constraints.45−48 Unless otherwise noted, these structures will be used in the following work. A scalar relativistic all-electron (AE) Hamiltonian was applied, where the spin−orbit effect was projected B

DOI: 10.1021/acs.inorgchem.8b00051 Inorg. Chem. XXXX, XXX, XXX−XXX

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Table 2. Electron-Spin Densities of Atoms, Groups, and Fragments in (THF)(H2L)(OAnVIO)(An′)III(CpX)3 [AnVI−(An′)IIIX; An and An′ = U, Np, and Pu; X = Me, H, Cl, SiH3, and SiMe3] Calculated at the PRIRODA: PBE/B-I/AE/Gas Level complex

An

Oexo

Oendo

H2L

THF

An′

3CpX

Frag.1a

Frag.2a

assignment

U −U UVI−NpIII UVI−PuIII NpVI−UIII PuVI−UIII UVI−UIIIMe UVI−UIIICl UVI−UIIISiH3 UVI−UIIISiMe3

1.014 0.800 0.687 2.260 3.570 1.089 0.973 0.932 0.389

−0.054 −0.051 −0.052 −0.097 −0.152 −0.058 −0.054 −0.050 −0.018

−0.048 −0.037 −0.031 −0.121 −0.223 −0.051 −0.047 −0.044 −0.016

−0.030 −0.027 −0.026 −0.046 −0.076 −0.030 −0.030 −0.028 −0.013

−0.004 −0.004 −0.003 −0.006 −0.012 −0.004 −0.004 −0.004 −0.001

2.266 3.590 4.874 2.166 2.044 2.183 2.297 2.302 2.734

−0.144 −0.272 −0.448 −0.157 −0.151 −0.130 −0.134 −0.107 −0.075

0.878 0.681 0.575 1.990 3.107 0.946 0.838 0.806 0.341

2.122 3.318 4.426 2.009 1.893 2.053 2.163 2.195 2.659

V−IV V−IV ↔ VI−III VI−III ↔ V−IV V−IV V−IV V−IV V−IV V−IV b

VI

III

a Frag.1 and Frag.2 denote (THF)(AnO2)(H2L) and (An′)(CpX)3, respectively. bThe state of UVI−UIIISiMe3 is not assigned because of the separate Frag.1 and Frag.2 (4.55 Å).

reports.36,37,74−76 Herein, we calculated the electron-spin density (S) of atoms and fragments in AnVI−(An′)IIIX (An and An′ = U, Np, and Pu; X = Me, H, Cl, SiH3, and SiMe3) and list them in Table 2. Let us first pay attention to the fragments (THF)(H2L)(OAnVIO) (marked as Frag.1) and (An′)III(CpX)3 (Frag.2). For the isolated Frag.1, hexavalent uranyl, neptunyl, and plutonyl ones are supposed to have formal values of 0, 1, and 2, respectively. Once cation−cation complexes formed, SFrag.1 was calculated to increase by 0.34− 1.11 relative to their corresponding formal values, and SFrag.2 reduced by exactly the same multitude. This confirms the occurrence of ET in cation−cation complexes with respect to their isolated precursors. Second, let us focus on the actinide centers. Regarding the uranyluranium series of complexes (UVI−UIIIX), almost one electron (0.93−1.09) was found to be localized on the uranium atom of the uranyl fragment, with the exception of UVI−UIIISiMe3, which shows nearly separate structures of Frag.1 and Frag.2 (4.55 Å Oexo−USiMe3 distance); accordingly, SU of the cyclopentadienyl part was calculated in the range from 2.18 to 2.31, indicating that this uranium center loses about 0.70−0.82 electrons relative to the formal value (3 is supposed for the trivalent uranium). Therefore, UVI−UIIIX (X = H, Me, Cl, and SiH3) is a V−IV state in reality, which agrees with the experimental characterizations of UVI−UIII.20 The same manners were found for AnVI−UIII (An = Np and Pu), which both have V−IV nature. Diagrams of the electronspin density are also intuitively shown in Figure S1. In addition, UVI−UIIISiMe3 was optimized to show a long separation between Frag.1 and Frag.2. This may be caused by the large steric effects of the SiMe3 substituent, for this is not so for UVI− UIIISiH3 with less steric effects. In the work, we will not discuss the former complex too much. We previously designed and investigated cation−cation complexes [(X)(OUVIO)(UIIIXn)](L) (n = 1 and 2; X is a donor atom/group), where the low-valence uranium atom was encapsulated in the empty N4-donor pocket of the precursor U VI L and formed the uranyl endo-oxo and uranium interaction.42 Although four coordination environments around the uranium centers were attempted, accompanied by changing X (11 complexes in total), the V−IV state was always found to be favored over VI−III. This is consistent with the results of the current work.42 Regarding all of these systems mentioned above, the AnVI ion (An = U, Np, and Pu) is formed by losing six valence electrons, being in an electron-deficient state. Also, the UIII ion keeps its three 5f single electrons and is electronrich. So, UIII → AnVI ET is most likely to occur, particularly given that there is an oxo ligand to bridge them.

the scalar relativistic zeroth-order regular approximation (ZORA) Hamiltonian,65−68 PBE functional, and ZORA-TZP basis sets (denoted as B-II). Regarding the small-core ZORA basis sets, the core orbitals 1s−4f for U/Np/Pu, 1s for C, N, and O, and 1s−2p for Si and Cl were frozen. Computationally demanding spin−orbit coupling (SOC) energies were calculated for (THF)(H2L)(OUVIO)UIIICp3 (UVI−UIII) and its reactant precursors. Unfortunately, SCF calculation failed for UVI−UIII. Then we calculated several analogues [I(OUVIO)AnIVI](L) (An = Th, Pa, U, Np, and Pu), where the low-valence actinide atom was encapsulated into the empty N4-donor pocket of the precursor UVIL and formed the uranyl endo-oxo and actinide interaction. The U−Pa complex was chosen for the SOC calculations because it is the only one that possesses a pronounced ET (0.91 e) from low-valent AnIV to the hexavalent uranyl moiety. The contribution of SOC effects to its formation reaction was calculated to be only −2.4 kcal/mol, far smaller than its solvation effects (−18.4 kcal/mol). So, we did not consider SOC in this work. To explore the bonding properties in actinide complexes and particularly clarify the nature of the CCIs (i.e., Oexo−An′ bonds), we performed quantum-theory-of-atoms-in-molecule (QTAIM) calculations.69,70 This electron-density-based approach has been found to be sufficiently reliable and accurate for the rationalization of actinide− ligand bonds.35−37,71−76 First, single-point calculations were carried out using the Gaussian09 program.77 Stuttgart relativistic large-core effective core potentials (ECPs) and their corresponding basis sets were applied for actinides78−80 and 6-31G** for other atoms. These mixed basis sets were marked as B-III. The GGA-PBE functional was used. Then, the electron density ρ(r), Laplacian electron density ∇2ρ(r), and energy density H(r) at the Oexo−An′ bond critical point (BCP) were computed with the Multiwfn 3.3.3 package,81 together with the ellipticity (ε) and delocalization index δ(An′,Oexo), which is considered to be a measure of the bond order. In addition, the QTAIM properties at BCPs of AnOexo, AnOendo, and Oendo−H were also taken into account.

3. RESULTS AND DISCUSSION 3.1. Electron-Spin Density. In these homo- and heterobimetallic actinide complexes, the actinyl exo-oxo atom bridges two metal centers and constructs the CCI. From the structural point of view, the presence of the exo-oxo bridge facilitates ET between two actinides and plays an active role in stabilizing the formed cation−cation complexes. However, this ET, indeed, complicates assignment of the oxidation state of actinides because they may not retain the same valence as that in precursors. Therefore, it is of crucial importance to choose a good indicator to identify the actinide oxidation state. Our previous study of homo- and heterovalent diuranium complexes42 demonstrated that the electron-spin density around the actinide metal center (SAn) is capable of describing the uranium oxidation state well. The same was found in other C

DOI: 10.1021/acs.inorgchem.8b00051 Inorg. Chem. XXXX, XXX, XXX−XXX

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Table 3. Optimized Geometry Parameters and Bond Orders (in Parentheses) of Homo- and Heterobimetallic Actinide Complexes complex U −U VI

III

UVI−NpIII UVI−PuIII NpVI−UIII PuVI−UIII UVI−UIIIMe UVI−UIIICl UVI−UIIISiH3 UVI−UIIISiMe3

appr.a calcd expt calcd expt calcd calcd calcd calcd calcd calcd calcd

AnOexo 2.014 1.986 1.952 1.975 1.927 2.017 2.023 2.022 2.013 1.990 1.819

(1.48) (1.71) (1.81) (1.42) (1.36) (1.47) (1.49) (1.58) (2.36)

AnOendo 1.855 1.844 1.847 1.826 1.844 1.845 1.840 1.858 1.851 1.849 1.850

Oendo−H

(2.25)

2.379 (0.05)

(2.26)

2.427

(2.26) (2.25) (2.23) (2.24) (2.26) (2.27) (2.17)

2.450 2.374 2.356 2.378 (0.06) 2.379 2.406 3.531 (0.06)

An′−Oexo 2.253 2.245 2.355 2.249 2.403 2.227 2.192 2.244 2.257 2.309 4.547

An′−Cpcentb

α (deg)c

β (deg)c

2.496 2.456 2.474 2.413 2.474 2.494 2.481 2.493 2.500 2.492 2.470

178.9 176.9 178.6 176.9 177.2 179.6 179.5 179.5 179.2 179.9 175.7

170.0 171.2 168.8 170.5 167.4 170.4 170.5 170.8 170.4 172.2 146.4

(0.85) (0.63) (0.54) (0.91) (0.97) (0.88) (0.85) (0.76)

a

The theoretical approach corresponds to PRIRODA: PBE/B-I/AE/gas, and the experimental values come from ref 20. bAn′−Cpcent is the average distance of An′ and centroids of three Cp rings. cα and β denote the angles of OexoAnOendo and An′−Oexo−An, respectively.

Figure 2. DOS of α-spin orbitals of UVI−UIII, together with the diagrams of some orbitals on the right side.

The values of SU and SAn′ calculated for UVI−(An′)III (An′ = Np and Pu) are somewhat different (Table 2). Relative to their formal values, SU of UVI−NpIII increases by 0.80 and SNp reduces by 0.41. We related the complex to an electronresonance structure between V−IV and VI−III. It is a little more difficult to assign the oxidation state for UVI−PuIII in that SU has an increase of 0.69e, but SPu only loses 0.13e. Careful inspection finds that the three Cp ligands bonding to the plutonium center have nonnegligible 0.45e loss. Considering large interference of the ancillary ligands, we attribute UVI− PuIII to an electron-resonance state, similar to that of UVI− NpIII. The subtle difference is that UVI−NpIII contains the major V−IV state, while UVI-PuIII involves more VI−III. These results will be further evidenced by analyses of the electronic structures. Notably, for convenient discussion, we still use the original abbreviations of AnVI−(An′)IIIX, as shown in Table 1, throughout this work, although real metal oxidation states were assigned differently for some of them. 3.2. Structural Properties. Selected geometry parameters of the complexes are presented in Table 3. Representative structures are illustrated in Figure 1. One can observe that the OexoAnOendo (α) and An′−Oexo−An (β) angles are approximately linear, which would facilitate electron communication around the whole An′OexoAnOendo unit. Interestingly, the An′−Oexo−U angles of UVI−(An′)III (An′ = Np and Pu) were calculated as 169° and 167°, respectively, showing the largest deviation from linearity (180°). This

coincides with a small amount of ET in them, as indicated above; on the other hand, the resulting Oexo−An′ bonds (CCIs) in the two complexes are conjectured to be relatively weak in strength, which will be proven by the QTAIM data below. Easy ET is also reflected by large elongation of the AnOexo bond lengths in AnVI−(An′)IIIX with respect to their actinyl precursors AnmL (An = U, Np, and Pu; m = VI and V). A comparison finds that the AnOexo distances in AnVI− (An′)IIIX lengthen by about 0.19/0.16 Å (An = U; An′ = U, Np, and Pu; mean value), 0.23/0.20 Å (An = Np; An′ = U), and 0.24/0.22 Å (An = Pu; An′ = U) relative to AnVIL/AnVIL (Tables 3 and S2). Obviously, these large changes are caused by the presence of Oexo−An′ bonding interactions, which are “socalled” CCIs. The Oexo−An′ distances were calculated between 2.19 and 2.31 Å, and the corresponding bond orders (Meyer) of 0.54−0.97 indicate their strength being close to a single bond in some cases. Comparatively, the calculated AnOendo distances show a slight change when AnVI−(An′)IIIX is compared with AnmL. With respect to UVI−UIII, the bond lengths of Oexo−U, U− Cpcent, UOexo, and UOendo were calculated as 2.25, 2.50, 2.01, and 1.86 Å, respectively, which are close to the experimental values of 2.25, 2.46, 1.99, and 1.84 Å.20 Comparable U−Oexo−U and OexoUOendo angles were afforded, with less than 2° difference. Similarly, the experimental values of UVI−NpIII were well reproduced by our calculation, as seen in Table 3.20 D

DOI: 10.1021/acs.inorgchem.8b00051 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Table 4. QTAIM Dataa (au) at the An′−Oexo BCP in Homo- and Heterobimetallic Actinide Complexes, Together with the Ellipticity ε, Delocalization Index δ(An′,Oexo), and Interaction Energy Eint (kcal/mol) complex

ρ(r)

∇2ρ(r)

V(r)b

G(r)b

H(r)b

δ(An′,Oexo)

ε

Eintc

U −U UVI−NpIII UVI−PuIII NpVI−UIII PuVI−UIII UVI−UIIIMe UVI−UIIICl UVI−UIIISiH3

0.0865 0.0680 0.0578 0.0913 0.0993 0.0884 0.0864 0.0792

0.3046 0.2639 0.2437 0.3257 0.3511 0.3124 0.3028 0.2873

−0.1049 −0.0763 −0.0625 −0.1154 −0.1314 −0.1088 −0.1044 −0.0923

0.0906 0.0712 0.0617 0.0984 0.1096 0.0934 0.0901 0.0821

−0.0144 −0.0052 −0.0008 −0.0170 −0.0218 −0.0153 −0.0144 −0.0103

0.6357 0.4978 0.4103 0.6538 0.7152 0.6346 0.6405 0.5807

0.0307 0.0375 0.0518 0.0368 0.0528 0.0254 0.0415 0.0524

−32.91 −23.94 −19.61 −36.21 −41.23 −34.14 −32.76 −28.96

VI

III

QTAIM data include the electron density ρ(r), Laplacian ∇2ρ(r), and energy density H(r). bH(r) is the sum of the potential V(r) and kinetic G(r) energy densities. cEint of the An′−Oexo bond is estimated by 0.5V(r) according to refs 82−84.

a

withdrawing) are able to tune the electronic structures of UVI− UIIIX to some extent. Although changes of the substituents slightly affect the amount of ET between fragments of UVIL and UIII(CpX)3, both electron-spin densities around the uranium centers and metal-dominated orbitals yield the V−IV state for UVI−UIIIX. 3.3. Topology of the Electron Density. In this section, we will use the topology of the electron and energy densities to characterize the bonding properties of CCIs in AnVI−(An′)IIIX (An and An′ = U, Np, and Pu; X = H, Me, Cl, and SiH3) and quantify their strength to some degree. Focusing on the electron density, the QTAIM properties at BCPs afford a clear definition of a chemical bond.69,70 More importantly, they have been found to be reliable and accurate for analyses of actinide and ligand/actinide bonds in recent studies.35−37,71−76 Generally, the types of chemical bonds can be classified according to the QTAIM values (au) at the corresponding BCPs.73,81 Values of H(r) < 0, ρ(r) > 0.15, and ∇2ρ(r) < 0 indicate the typical covalent (shared-shell) bonds; in this case, strong polarity is involved in a covalent bond if ∇2ρ(r) > 0. By contrast, ionic (closed-shell) interactions have values of H(r) > 0, ρ(r) > 0, and ∇2ρ(r) > 0. With the condition of H(r) < 0, the values of 0 < ρ(r) < 0.1 and ∇2ρ(r) > 0 show ET or dative bonds; associated with the similar range of the H(r) and ρ(r) values but the unknown sign for ∇2ρ(r), a hydrogen bond is suggested. In Table 4, the calculated QTAIM parameters at the An′− Oexo BCP are listed, where the energy density H(r) is decomposed into kinetic G(r) and potential V(r) parts. The interaction energy (Eini) of An′−Oexo was computed by the 0.5V(r) used in previous reports.82−84 First, all computed H(r) values are negative, with ∇2ρ(r) > 0. The ρ(r) values are small, ranging from 0.058 to 0.099. According to the aforementioned criterion, an ET or dative bond is attributed to An′−Oexo interaction; i.e., CCI is the dative bond in nature. This agrees with the previous study of CCIs between NpVO2+ species.85 Eini of the CCI was calculated to be between −19.6 and −41.2 kcal/ mol, which are comparable to the previously calculated association energies of (ONpVO−ONpVO)2+ (−42.1 kcal/ mol) and (ONpVO → OUVIO)3+ (−29.2 kcal/mol).86 Second, the regular trend is found by analyzing the QTAIM data of these cation−cation complexes. In the series of UVI−(An′)III, ρ(r) decreases upon going from An′ = U to Np to Pu; the corresponding delocalization index δ(An′,Oexo), which is considered to be a measure of the bond order, as well as Eini, decreases. All of these indicate a decrease of the CCI strength. Absolute values of H(r), also decreasing along the series, suggest a reduction of the covalency in An′−Oexo. Differently,

Because of the mutual interaction in the approximately linear An′−OexoAnOendo domain, it is difficult to clearly distinguish the oxidation state of the actinide center only from those of the geometrical structures. Now, we will divert to their electronic structures and help to understand the electron arrangement around the actinide centers. Similarity is found by inspection of the frontier molecular orbitals of UVI−(An′)III (An′ = U, Np, and Pu). All of them possess actinide-character low-lying unoccupied orbitals and high-lying occupied ones; the polypyrrolic-ligand-based occupied orbitals are present in the further low-energy area. One can note that the number of high-lying occupied (α-spin) orbitals with the most actinide character is equal to the number of their supposed 5f single electrons. For example, UVI−UIII has three uranium-dominated α-spin orbitals [highest occupied molecular orbital (HOMO), H-1, and H-2] and also three 5f single electrons regardless of where they are localized. The diagrams of the orbitals in Figure 2 (right side) show that the electron in HOMO is localized on the uranyl uranium atom, with a slight distribution around the cyclopentadienyl uranium atom. In the H-1 and H-2 orbitals, an electron cloud almost resides in the cyclopentadienyl uranium center. The lowerenergy H-3 orbital is mainly contributed by the polypyrrolic ligand. π(U−Cp) bonding is found in H-7, contributed by the overlap of 22% U 5f and 52% Cp. In a much lower-energy area (−6.92 eV), σ(UO) character forms the H-24 orbital. Associated with the density of states (DOSs) in Figure 2 (left side) and orbital compositions in Table S3, a real UV−UIV complex is assigned, which agrees with the aforementioned electron-spin-density analyses. Electronic structures support the assignment that UVI−NpIII is a major V−IV state, mixed with VI−III. Table S4 quantitatively gives one uranium−neptunium mixed HOMO (63% U 5f and 26% Np 5f) and three pure neptunium orbitals (H-1−H-3, over 93% Np 5f character), which are qualitatively reflected by Figure S2. Similarly, an electron-resonance structure between VI−III and V−IV is attributed to the UVI−PuIII complex (Figure S3 and Table S5). Along the series of complexes AnVI−UIII, the actinyl unit is changed from U to Np to Pu. Transuranic complexes have the general character of frontier orbitals, quite similar to that of UVI−UIII. Electron distributions (Figures S4 and S5) and orbital contributions (Tables S6 and S7) assigned the V−IV state to AnVI−UIII (An = Np and Pu). This agrees with the above results of electron-spin-density analyses. When we vary the substituents (X = Me, H, Cl, and SiH3) bonding to cyclopentadienyl ligands in UVI−UIIIX, the energy levels of the frontier orbitals show an overall descending tendency. Obviously, the electronic effects of X (donating and E

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Figure 3. Plots of the QTAIM parameters (au) at the An′−Oexo BCP and δ(An′,Oexo) versus Eint (kcal/mol) for homo- and heterobimetallic actinide complexes.

Figure 4. Plots of the QTAIM parameters (au) at the An′−Oexo BCP and δ(An′,Oexo) versus ΔSav (average value of ΔSAn and |ΔSAn′|) for homo- and heterobimetallic actinide complexes.

all QTAIM data are increasing for AnVI−UIII along An = U, Np, and Pu. Interestingly, the substituent on the cyclopentadienyl ligand is also able to tune the QTAIM data and CCI strength. With increasing electron-withdrawing ability of X (Me, H, Cl, and SiH3), the QTAIM values and CCI strength decrease

accordingly. This would provide an additional possibility to tune CCI in homo- and heterobimetallic actinide complexes and might be exploited to guide future experimental synthesis. In brief, a positive correlation is established between the QTAIM data and CCI strength. This is intuitively described by F

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Inorganic Chemistry

3.4. Reaction Energies. Recently, two cation−cation complexes UVI−(An′)III (An′ = U and Np) have been experimentally synthesized and characterized.20 According to the synthetic route, we designed and calculated the following formation reactions. From the thermodynamic point of view, these results would provide implications for the synthetic possibility of complexes.

the plots of QTAIM data versus Eini in Figure 3. Larger QTAIM data (absolute value) correspond to more negative Eini values, i.e., larger CCI strength. Moreover, the least-squares linear regression correlation coefficient R2 ranges from 0.962 to 0.998. Recently, Kaltsoyannis and Mountain found that the QTAIM metrics correlate well with the strength of heavy-element bonds.36,71 Our work provides more evidence to support this point. Now one may question whether the amount of ET in the formation of AnVI−(An′)IIIX is related to the QTAIM data. If so, one can further extend ET to correlate with the strength of the CCIs. To achieve this goal, the QTAIM data and δ(An′,Oexo) were plotted against the ET amount determined by ΔSAn, ΔSAn′, and their averaged value ΔSav. The first two spin values were obtained by subtracting the formal value from the calculated SAn. As seen in Figure 4, a good linear correlation was built for ΔSav, with the R2 values ranging from 0.910 to 0.985; the plots also show a positive correlation. Also, a linear correlation was found for ΔSAn and ΔSAn′ in Figures S6 and S7. Because the linear correlations of the QTAIM data are built against both the strength of the CCIs and the amount of ET, a positive correlation can be extrapolated to the latter two. Building on the analyses of the electron-spin density and geometrical/electronic structures as well as the positive correlation of CCIs’ strength and ET amount, it is concluded that the CCIs in AnVI−(An′)IIIX are driven by the electrostatic attraction between negative -yl exo-oxo and positive An′ atoms and enhanced by ET. Except for the Oexo−An′ bond (i.e., CCI), we also performed QTAIM analyses at other BCPs of AnOexo, AnOendo, and Oendo−H. On the one hand, these bonds most likely affect the CCI via direct and indirect electronic effects; on the other hand, all bonds together provide perfect models in a single complex to compare and understand chemical bonds with diverse types (covalent, dative, ionic, and hydrogen bonds) and to quantify the strengths and also further test the applicability of QTAIM in actinides, particular in heterobimetallic ones. Using the criterion of the QTAIM parameters indicated earlier, AnOexo and AnOendo were recognized for covalent bonds with strong polarity, showing large values of ρ(r) (>0.15), ∇2ρ(r), and absolute H(r) (Tables S8 and S9). The calculated δ(An,Oexo/Oendo) indicates that AnOexo and AnOendo lie between single and double bonds, which are obviously weaker than those in their precursors AnmL. As seen in Tables S10 and S11, Oendo−H is a hydrogen bond per se, having small values of QTAIM and δ(An,H). Its Eint value was calculated in the range from −3.2 to −4.0 kcal/mol, being lower than those of typical hydrogen bonds (>5.0 kcal/mol). This results from the fact that the most electrons of the endo-oxo atom are involved in the AnOendo bonding. Notably, the criterion of ρ(r) with 0.15 au used in the work is different from the previously suggested 0.20 au for a classified covalent bond.36,73 Regarding the QTAIM data for AnOexo bonds (Table S8), calculated ρ(r) values ranging from 0.15 to 0.20, δ(An,Oexo) lying between 1.13 and 1.43, and Eint falling within −70.3 and −101.4 kcal/mol would attribute AnOexo to be a covalent bond. Therefore, the criterion of ρ(r) is valid in the present study. In addition, QTAIM calculations were also performed on complex UVI−UIII with the AE scalar relativistic SARC-DKH and SARC-ZORA for uranium atoms.87 It is found that ECPs used in this work have a very slight effect on the QTAIM results (Table S12).

(THF)(UVIO2 )(H 2L) + (An′)III Cp3 = (THF)(H 2L) (OUVIO)(An′)III Cp3

(An′ = U, Np, and Pu)

(THF)(An VIO2 )(H 2L) + UIIICp3 = (THF)(H 2L) (OAn VIO)UIIICp3

(An = Np and Pu)

(THF)(UVIO2 )(H 2L) + UIII(CpX)3 = (THF)(H 2L) (OUVIO)UIII(CpX)3

(X = Cl, Me, SiH3, and SiMe3)

As seen in Table 5, all AnVI−(An′)IIIX have negative free energies ΔrG in the gas phase with the exception of UVI− Table 5. Calculated Energies (kcal/mol) of Homo- and Heterobimetallic Actinide Complexes complex

ΔrEa

ΔrE0a

ΔrGa

ΔrG(sol)b

U −U UVI−NpIII UVI−PuIII NpVI−UIII PuVI−UIII UVI−UIIIMe UVI−UIIICl UVI−UIIISiH3 UVI−UIIISiMe3 UVI−UIII c

−28.66 −23.03 −14.35 −40.33 −48.69 −30.69 −29.11 −23.66 −10.60 −114.09

−27.30 −21.58 −13.17 −38.70 −46.93 −29.19 −27.81 −22.29 −9.75 −112.27

−12.24 −8.09 −1.95 −23.68 −31.98 −15.09 −12.68 −7.67 1.62 −98.81

−5.24 −1.39 4.75 −17.01 −25.93 −9.12 −4.83 0.41 7.96 −25.74

VI

III

a ΔrE, ΔrE0, and ΔrG are the total energy, total energy including zeropoint vibrational energy, and free energy of formation reaction (see the text) in the gas phase, respectively. bΔrG(sol) stands for the reaction free energy in a THF solution and is the sum of ΔrG and ΔrGsol. ΔrGsol = ∑νBGsol(B), where Gsol(B) is the calculated solvation energy of each species (B) in the formation reaction. cFrom the reaction of [(THF)(UVO2)(H2L)]− + [UIVCp3]+ = (THF)(H2L)(OUVO)UIVCp3 (UV−UIV or UVI−UIII).

UIIISiMe3. Considering the influence of solvent media, ΔrG(sol) values in THF solutions of UVI−PuIII and UVI− UIIISiH3 become positive, being 4.8 and 0.4 kcal/mol. UVI−UIII and UVI−NpIII were calculated to show ΔrG(sol) values of −5.2 and −1.4 kcal/mol. These reveal that uranyluranium/ neptunium complexes are synthetically accessible and the uranylplutonium one is not favored thermodynamically, which agrees with experimental results.20 When we change the actinyl part with respect to UVI−UIII, the resulting NpVI−UIII and PuVI−UIII possess ΔrG(sol) values of −17.0 and −25.9 kcal/ mol, respectively. The much lower reaction energies are interpreted by the increased -yl oxo basicity of NpO22+ and PuO22+ relative to UO22+. Featuring a relatively strong electrondonating methyl group, UVI−UIIIMe (−9.1 kcal/mol) is found to have a more negative ΔrG(sol) value than UVI−UIII (−5.2 kcal/mol). Comparatively, a little more positive ΔrG(sol) value (−4.8 kcal/mol) was calculated for UVI−UIIICl, which has the electron-withdrawing chloro group. The substituents bonding G

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Inorganic Chemistry to cyclopentadienyls show some influence on the reaction energies of the complexes. Because UVI−UIII turned out to be UV−UIV, we designed a reaction according to the reactants of [(THF)(UVO2)(H2L)]− and [UIVCp3]+. A much more negative ΔrG(sol) value (−25.74 kcal/mol) was calculated. It can be envisaged that complex UVI−UIII (to be precise, it is the notation UV−UIV) would be more easily synthetically accessible if one started from sources of uranyl(V) and organouranium(IV). Interestingly, a linear correlation has been found between the calculated reaction energies and the average amount of An′ → An ET (ΔSav). The R2 values fall between 0.863 and 0.934, as seen in Figure S8. A larger ET amount corresponds to a lower reaction energy, which results in more stable cation−cation complexes.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (Q.-J.P.). ORCID

Qing-Jiang Pan: 0000-0003-2763-6976 Notes

4. CONCLUSIONS In the work, a series of actinylactinide CCI complexes were systematically calculated at the relativistic DFT level. Exploration of the structures, electron-spin densities, QTAIM properties, and reaction energies, particularly centering on the CCI, has come to the following points. Analyses of the electron-spin densities of formed cation− cation complexes demonstrate that AnVI−UIII (An = U, Np, and Pu) and UVI−UIIIX (X = Me, Cl, and SiH3) have the real V−IV state because of their considerable amount of ET. In contrast, electron-resonance structures of V−IV and VI−III are assigned to UVI−(An′)III (An = Np and Pu); the subtle difference is that the former complex has a major V−IV state and the latter possesses more VI−III character. The assignment is also corroborated by the results of geometrical and electronic structures. Associated with the electron-spin density, structural parameters, and orbital structures, the QTAIM properties attributed CCIs (i.e., Oexo−An′) of these complexes to ET or dative bonds in nature. Their energies (Eini) were calculated to be −19.6 to −41.2 kcal/mol. A positive linear correlation has been established between the ET amount and CCIs’s strength (also reaction energy). Thus, it is concluded that the CCI is driven by the electrostatic attraction between a negatively charged actinyl oxo atom and a positively charged actinide ion and strengthened by their ET. The reaction free energies in a THF solution to form experimentally synthesized complexes UVI−(An′)III (An′ = U and Np) were calculated to be negative, but a positive one for UVI−PuIII was synthetically inaccessible. Changing the actinyl sorts and substituents of the cyclopentadienyl ligands allows one to tune the free energies of formed complexes, which would provide implications for possible syntheses of some designed bimetallic actinide complexes. In summary, the present investigation of the CCIs between actinyl and actinide is anticipated to help separate hexavalent actinyl species in spent nuclear fuel, as well as eliminate these highly soluble/mobile and biologically available species as much as possible from the environment. A study of the kinetic process of the formation of bimetallic actinide complexes is in progress.

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Diagrams of the electron-spin density and α-spin orbitals of several CCI complexes, plots of the QTAIM data and reaction energies versus ET amount, tables of the electron-spin density calculated at different levels of theory, the optimized geometry parameters of polypyrrolic precursors, QTAIM data at BCPs, and orbital compositions (%) of six cation−cation complexes, and the full references of the ADF and Gaussian codes (PDF)

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported by the National Natural Science Foundation of China (Grants 21671060 and 21273063) and the Scientific Foundation of Heilongjiang Province for the Returned Overseas Chinese Scholars. The authors are grateful to Dr. Dimitri Laikov for providing us with the PRIRODA code.

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