The redox mechanism of Np^VI with hydrazine: a DFT study

Abstract

Valence state control and adjustment of neptunium in spent fuel reprocessing is very important for improving the separation efficiency of U/Np and Np/Pu. Hydrazine and its derivatives have been experimentally demonstrated to be effective in the reduction of Np^VI to Np^V. In this work, hydrazine was used as a representative reductant and the reduction mechanisms of Np^VI induced by hydrazine were investigated using density functional theory (DFT) calculations. Three reaction pathways were taken into account and characterized by gradually transferring a hydrogen atom from N₂H₄ to the “yl”-oxygen of [Np^VIO₂(H₂O)₅]²⁺ followed by the valence state adjustment from Np^VI to Np^V. The calculated results of the potential energy profiles (PEPs) revealed that Pathway I should be the most likely to occur as the process of forming ˙N₂H₃ is considered to be the rate-determining step with the highest energy barrier of 32.02 kcal mol⁻¹, which is in favor of the experimental results. Pathway II hardly occurs and Pathway III probably occurs. The bonding evolution, along with the reaction pathways, was explored through natural bond orbitals (NBOs), quantum theory of atoms-in-molecules (QTAIM) and electron localization function (ELF) analyses. This work can shed light on the understanding of redox mechanisms of Np^VI with N₂H₄ and its derivatives and help further attempts to design more efficient reductants for the separation of U/Np and Np/Pu in spent nuclear fuel reprocessing in the near future.

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Introduction

The treatment of neptunium in the nuclear fuel cycle is of significant concern since ²³⁷Np is present in non-negligible quantities in spent nuclear fuels and can migrate into the environment under specific conditions due to the stability of the pentavalent neptunyl ion (NpO₂⁺).¹ Recovery and recycling of Np, either to diminish the long term radiotoxicity or to reduce the heat burden on the geological repository, is therefore under investigation in most nuclear power countries.² It is known that in the so-called Plutonium URanium Extraction (PUREX) process,³ which is used for the commercial scale reprocessing of spent nuclear fuels, it is probable to recover and recycle Np through the valence state control of Np, as Np can be routed with Pu or U streams in the partition contactor, and disparate oxidation states of Np such as Np^IV, Np^V and Np^VI can emerge in this process. It is also well known that the extraction behaviors of neptunium towards TBP in nitric acid medium vary in different oxidation states;⁴ Np^VI was readily extractable, Np^IV was relatively poor extractable, and Np^V was barely extractable. However, the three oxidation states of Np can interconvert easily by various redox reactions under the conditions of solvent extraction-based spent nuclear fuel reprocessing.

So far, two approaches have been used to control and adjust the oxidation states of Np.^5,6 One was through in situ redox reaction based on photochemical induction^7–9 or electrochemistry.^10–12 For instance, Wada and his co-workers adjusted the oxidation states of Np to Np^V in nitric acid medium by a photochemical method.⁸ Kim et al. studied the electrochemical behavior of NpO₂²⁺ cation on platinum and glassy carbon electrodes,¹² where the NpO₂²⁺ cation was reduced to Np^V quasi-reversibly. The other was via ex situ redox reaction based on a specific redox reagent. For example, Bibler et al. employed ferrous sulfamate as a reductant for reducing Np^VI/V to Np^IV in the PUREX process.¹³ However, these redox reagents can introduce extra large amounts of salts to the process and will increase the amount of wastes. To avoid these defects, some new salt-free reductants, such as aldehydes,^14,15 hydroxylamine derivatives^16–18 and hydrazine derivatives^19–27 were developed and confirmed to be effective reductants. For instance, Koltunov and his co-workers investigated the reduction kinetics of Np^VI with hydrazine derivatives.²⁵ It was found that the reaction rate constants of Np^VI varied with respect to different substituent of the hydrazine derivatives. Recently, Ban et al. investigated the reduction kinetic of Np^VI with N,N-dimethylhydrazine in spent fuel reprocessing,¹⁹ in which Np^VI was quickly reduced to Np^V. Nevertheless, previous works about Np^VI reduction only focused on experimental researches. Reduction mechanisms were still unclear. In addition, to the best of our knowledge, theoretical investigations have been rarely addressed on this issue. Therefore, it was extremely necessary and meaningful to investigate the reduction mechanism of Np^VI by theoretical calculations, which can give reasonable description about geometries and properties of the actinide complexes.^28–31

In this work, the three reduction mechanisms of Np^VI with N₂H₄ were carried out based on the results of DFT (density functional theory) calculations. And we investigated systematically the geometries and stabilities of stationary points of potential energy profiles (PEPs). The solvent effect had been taken into account. The optimal reaction pathway of Np^VI with N₂H₄ was obtained by comparing the energy barriers. This work can provide theoretical insights for having a command of the reduction mechanisms of Np^VI with N₂H₄ and its derivatives, and it is expected that more suitable reagents can be found to improve the separation efficiency of U/Np and Np/Pu in spent nuclear fuel reprocessing in the future.

Computational details

All quantum chemical calculations were performed using the hybrid B3LYP functional^32–37 within the Gaussian 09 program package.³⁸ For geometry optimizations, the quasi-relativistic small-core pseudopotential ECP60MWB coupled with ECP60MWB-SEG valence basis sets were employed for neptunium,^39–41 while the 6-31g* basis set was used for the other light atoms H, N, O. The quasi-relativistic small-core pseudopotential substituted 60 core electrons for neptunium, whereas the remaining 33 electrons were represented by the associated valence basis set. A small-core ECP was prevalently considered to obtain more accurate results compared to a large ECP.^42–44 Geometry optimizations of all the species were performed without symmetry restrictions in the aqueous phase at the B3LYP/ECP60MWB/6-31g* level of theory by using COSMO (conductor-like screening model).^45,46 Computations of open-shell systems were performed with spin-unrestricted methods. The minimal (without imaginary frequency) and transition states (with one imaginary frequency) of complexes in the three pathways were confirmed with harmonic frequency calculations and vibrational mode analyses which were performed by the GaussView program.⁴⁷ The intrinsic reaction coordinate (IRC)^48,49 calculations were carried out to confirm that the transition states connected reactants and products. The PEPs of three reaction pathways of [Np^VIO₂(H₂O)₅]²⁺ with N₂H₄ were obtained by calculating the relative bond energies of each species with respect to the ground-state reactant.

Recently, there are significant developments in understanding the accuracy and applicability of the DFT methods, especially for the chemistry of actinide complexes. Therefore, to achieve the accurate description of neptunium complexes, the influence of different functionals (B3LYP, PBE, BP86 and M06) and basis sets (6-31g*, 6-311+g* and 6-311++g**) on the geometries of [Np^VIO₂(H₂O)₅]²⁺ and [Np^VO₂(H₂O)₅]²⁺ have been investigated in this work. The more complete report of computational results is provided in ESI.† It is shown from Table S1† that the B3LYP functional and 6-31g* basis set for this work are reasonable and acceptable according to the comparison between the predicted bond lengths and available experimental data. In addition, for the neptunium atom with f-electron, effects of spin–orbital (SO) coupling are expected to be huge.⁵⁰ It has also been shown that SO coupling can affect reaction barrier dramatically.⁵¹ Therefore, further computations were undertaken for sake of evaluating the effects of spin–orbital coupling on the PEPs. In particular, the single-point computations were carried out on the B3LYP-optimized structures using the zero-order regular approximation (ZORA) associated with the spin–orbital correction (SO-ZORA). The SO-ZORA approximations were employed together with the BP86 functional and triple-ζ basis sets (TZP) without frozen core in the implementation of Amsterdam density functional (ADF 2013.01) package.^52,53 PEPs of the three pathways are obtained at the BP86-SO-ZORA/TZP level of theory.

The bonding properties of all the minima and transition states involved in the reaction pathways were explored with the electron localization function (ELF)^54–56 analysis and the quantum theory of atoms-in-molecules (QTAIM) method^57–59 by using Multiwfn program.⁵⁷ In particular, we explored the properties of the (3, −1) bond critical points (BCPs) in the gradient field of the electron density. Lastly, the Wiberg bond index (WBI)⁶⁰ and Mayer bond order⁶¹ of the related bonds were obtained by NBO (natural bonding orbital) analysis.

The abbreviations used in this work are as follows: (i) all species are denoted as icN^M, tsN^M and intN^M (ic = initial complex, ts = transition state, int = intermediate, M = I, II, III and N = 1 to 4); (iii) four hydrogen and two nitrogen atoms of N₂H₄ are labeled as H1, H2, H3, H4, N1 and N2 respectively.

Results and discussion

According to the experimental results of Koltunov and his co-workers,²⁵ the total reaction equation of [Np^VIO₂(H₂O)₅]²⁺ with N₂H₄ in the aqueous phase can be depicted as follows:

4[Np^VIO₂(H₂O)₅]²⁺ + N₂H₄ → 4[Np^VO₂(H₂O)₅]⁺ + N₂ + 4H⁺ (1)

It has been known to be a consecutive reaction, hence, three probable pathways were designed to understand their reduction mechanisms. Because each stage of the same pathway is similar, here, we took the first stage of three pathways as an example, as shown in Scheme 1. It can be observed from Scheme 1 that the formation of int1 is the same process for the three pathways.

Scheme 1 The redox of [Np^VIO₂(H₂O)₅]²⁺ with N₂H₄ in the first stage of Pathways I, II and III.

(1) Pathway I via a free radical mechanism: from Scheme 1, it can be clearly seen that the H1 of ic1 is transferred to the “yl”-oxygen (O_yl) of [Np^VIO₂(H₂O)₅]²⁺ through N–H1 bond dissociation, forming the int1. After int1 direct dissociation, the products such as [Np^VO₂(H₂O)₅]⁺ and ˙N₂H₃ are obtained. The remaining hydrogen atoms are gradually transferred to the O_yl atom of [Np^VIO₂(H₂O)₅]²⁺ in the same way. Each stage of Pathway I can be expressed as following:

[Np^VIO₂(H₂O)₅]²⁺ + N₂H_x → [Np^VO₂(H₂O)₅]⁺ + N₂H_x−1 + 4H⁺ (2)

where x = 4–1.

(2) Pathway II via a free radical and ion mechanism: after forming int1, H atom of equatorial water molecule of int1 is close to N1 atom of int1 to form int1^II accompanying with the O_eq.–H_eq. bond dissociation. After that, H1 atom of int1^II is transferred to the hydroxyl of equatorial plane of int1^II to obtain [Np^VO₂(H₂O)₅]⁺ and ˙N₂H₄⁺. The other stages of Pathway II are similar to the first stage of Pathway I. Each stage of Pathway II can be expressed as following:

[Np^VIO₂(H₂O)₅]²⁺ + N₂H₄ → [Np^VO₂(H₂O)₅]⁺ + N₂H₄⁺ (3)

[Np^VIO₂(H₂O)₅]²⁺ + N₂H_x⁺ → [Np^VO₂(H₂O)₅]⁺ + N₂H_y⁺ + (x − y)H⁺ (4)

where y = x − 1, x = 4, 3; x = 2, y = 0.

(3) Pathway III via a free radical and disproportionation mechanism: in the first stage, both H1 and H2 are gradually transferred to O_yl atom and the products such as [Np^IVO₂H₂(H₂O)₅]²⁺ and N₂H₂ are obtained. Similarly, H3 and H4 are subsequently transferred to get [Np^IVO₂H₂(H₂O)₅]²⁺ and N₂. Eventually, [Np^IVO₂H₂(H₂O)₅]²⁺ reacts with [Np^VIO₂(H₂O)₅]²⁺ to obtain [Np^VO₂(H₂O)₅]⁺ by a disproportionation mechanism. Each stage of Pathway III can be expressed as following:

[Np^VIO₂(H₂O)₅]²⁺ + N₂H_x → [Np^IVO₂H₂(H₂O)₅]²⁺ + N₂H_x−2 (5)

[Np^VIO₂(H₂O)₅]²⁺ + [Np^IVO₂H₂(H₂O)₅]²⁺ → 2[Np^VO₂(H₂O)₅]⁺ + 2H⁺ (6)

where x = 4 and 2.

Pathway I via a free radical mechanism

Structures and energetics. PEPs of Pathway I obtained at the BP86-SO-ZORA/TZP level of theory are shown in Fig. 1. It can be seen from Fig. 1 that in the first and second stage, the formations of ic1 and ic2^I are exothermic process with values of −36.84 and −46.35 kcal mol⁻¹, respectively. Then ic1 and ic2^I are transformed into int1 and int2^I which need overcome 32.02 and 6.17 kcal mol⁻¹ energy barrier, respectively. Both of them are endothermic process with values of 17.67 and 1.14 kcal mol⁻¹, respectively. Similarly with the second state, the ic3^I and ic4^I converts into int3^I and int4^I with an energy barrier of 10.28 and 3.07 kcal mol⁻¹, and an exothermicity of −3.64 and −58.91 kcal mol⁻¹ respectively. Upon the comparison of energy barrier in the first stage to the fourth stage, it can be known that the energy barrier of the first stage is the highest among of the four stages for the Pathway I, suggesting that the first stage is the rate-determining step, which is in accord with the experimental result.²⁵ In addition, for each stage, intermediate can spontaneously decompose to the product of [Np^VO₂(H₂O)₅]⁺.

Fig. 1 Potential energy profile (ΔE, kcal mol⁻¹) of Pathways I computed at the BP86-SO-ZORA/TZP level of theory. The [Np^VIO₂(H₂O)₅]²⁺ and [Np^VO₂(H₂O)₅]⁺ were denoted as *1 and *2 respectively.

The optimized geometries and related bond lengths of all species in the Pathway I are presented in the ESI, Fig. S1.† As shown in Fig. S1(a), ESI† from ic1 to ts1 and int1, the N–H1/Np–O_yl bond length increases from 1.031/1.825 Å to 1.432/1.956 Å and 2.041/1.985 Å, respectively, while O_yl–H1 bond length decreases from 1.853 Å to 1.429 Å and 0.997 Å, indicating N–H1 bond dissociation and O_yl–H1 bond formation. Like the first stage, the trends of related N–H, Np–O_yl and O_yl–H bond lengths from ic to ts and int for the other stages of Pathway I as presented in Fig. S1(b)–(d), ESI† are similar.

Bonding evolution analyses. In order to gain a more in-depth understanding of redox mechanisms, the bonding evolution of all species in the Pathway I was explored by the bond order, QTAIM and ELF analyses.

It can be known that the Wiberg bond index between atom A and B is defined as

And Mayer bond order between atom A and B is defined as

where P and S are denoted as the density matrix and atomic orbital overlap matrix, respectively.^60,62 In general, the bond order index B_AB may more or less deviate from the integer values as well as exhibit some basis set dependences. It is expected, however, that the comparison of the values obtained by employing the same basis set for similar bonds in a series of related molecules may be instructive and provides some insights into the details of the bonding situation in the systems studied. The WBIs and Mayer bond orders of O_yl–H, N–H and Np–O_yl bond for all species in the Pathway I are shown in Table 1. The trends of Mayer bond orders are in accordance with those of corresponding WBIs. It can be clearly seen that with the reaction proceeding from initial complex to intermediate for each stage, the WBI of O_yl–H gradually increases, while that of N–H/Np–O_yl gradually decreases. Taking stage 2 (from ic2^I to int2^I) as an example, the WBI of O_yl–H2 increases from 0.091 to 0.509, whereas the WBI of N–H2/Np–O_yl decreases from 0.664/1.868 to 0.188/1.371. These results illustrate the dissociation of N–H bonds and formation of O_yl–H bonds.

Table 1 Calculated O_yl–H, Np–O_yl and N–H WBIs and Mayer bond orders of all species in the Pathway I at the B3LYP/ECP60MWB/6-31g* level of theory

	WBI			Mayer bond order
	Oyl–H^a	Np–Oyl	N–H^a	Oyl–H^a	Np–Oyl	N–H^a
a H represents H1–H4 in N2H4 corresponding to four stages of Pathway I.
ic1	—	1.924	0.729	—	1.940	0.641
ts1	0.298	1.584	0.409	0.338	1.557	0.385
int1	0.620	1.281	—	0.623	1.253	—
ic2^I	0.091	1.868	0.664	0.169	1.844	0.553
ts2^I	0.217	1.736	0.508	0.249	1.694	0.446
int2^I	0.509	1.371	0.188	0.491	1.360	0.196
ic3^I	—	2.233	0.801	—	2.168	0.791
ts3^I	0.186	1.678	0.545	0.278	1.630	0.407
int3^I	0.587	1.314	—	0.566	1.304	—
ic4^I	—	2.210	0.726	—	2.116	0.675
ts4^I	0.093	2.080	0.607	0.121	1.954	0.548
int4^I	0.638	1.277	—	0.609	1.262	—

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Certainly, the process of the bonding evolution is also supported by the QTAIM analysis. It is well worth mentioning that QTAIM is a ubiquitous approach for studying the properties and evolution of chemical bonds.^63–65 In principle, at BCP the electron density ρ(r) > 0.20 au and Laplacian ∇²ρ(r) < 0 present a covalent bond (shared shell interaction), while ρ(r) < 0.10 au and Laplacian ∇²ρ(r) > 0 indicate an ionic bond (closed shell interaction). The total energy density H(r) at the BCP is negative for interactions with significant sharing of electrons, which magnitude can reflect the “covalence” of the interaction.⁶⁶ However, it is unanticipated that the above criteria of QTAIM analysis are not available for strong polar covalent bond. Therefore, the other criteria that ρ(r) > 0.20 au and H(r) < 0 present a covalent bond (shared shell interaction), while ρ(r) < 0.10 au and H(r) > 0 indicate an ionic bond (closed shell interaction) are employed.^66,67 The ρ(r), ∇²ρ(r) and H(r) at the BCPs are listed in Table 2. It is shown that the ρ(r) at O_yl–H BCP for each intermediate are over 0.2 au with negative ∇²ρ(r). Moreover, with reaction proceeding from initial complex to intermediate for each stage, the ρ(r) at N–H BCP gradually decreases. From these results, we conclude that N–H bond is dissociated and O_yl–H bond is formed in every stage of Pathway I. In addition, Np–O_yl bond is a strong polar covalent bond with the value of larger ρ(r) and negative H(r) for each stationary point. And the strength of Np–O_yl gradually weakens with ρ(r) decreasing from initial complex to intermediate for each stage, which indirectly reflects the formation of O_yl–H bond. Besides, we also perform the ELF analysis to further confirm the characteristic of bonding interaction. It has been discovered that the ELF analysis can afford effective information on chemical bonds.^68–70 In generally, ELF falls within the scope of 0 and 1, ELF = 1 suggests the faultless electron localization, whereas ELF = 0 reveals the perfect electron delocalization.^54,55 The ELF value is closer to 1 suggesting stronger covalence of a chemical bond. Fig. 2 presents two-dimensional colored ELF pictures of all species on Np–O_yl–N plane. It is obviously known that from initial complex to intermediate for each stage, the ELF value of N–H bond gradually decreases, and that of O_yl–H bond increases, suggesting the dissociation of N–H bonds and formation of O_yl–H bonds.

Table 2 Electron density [ρ(r), au], its Laplacian [∇²ρ(r), au], and the total energy density [H(r), au] at the O_yl–H, N–H and Np–O_yl BCPs of all species in the Pathway I

	Oyl–H^a			N–H^a			Np–Oyl
	ρ(r)	∇^2ρ(r)	H(r)	ρ(r)	∇^2ρ(r)	H(r)	ρ(r)	∇^2ρ(r)	H(r)
a H represents H1–H4 in N2H4 corresponding to four stages of Pathway I.
ic1	0.030	0.104	0.001	0.320	−1.782	−0.486	0.261	0.263	−0.206
ts1	0.094	0.073	−0.028	0.108	−0.056	−0.048	0.191	0.335	−0.102
int1	0.301	−1.520	−0.434	—	—	—	0.171	0.367	−0.008
ic2^I	0.047	0.149	−0.001	0.287	−1.416	−0.389	0.256	0.291	−0.200
ts2^I	0.082	0.141	−0.018	0.154	−0.364	−0.125	0.256	0.323	−0.199
int2^I	0.252	−1.044	−0.326	0.067	0.136	−0.010	0.186	0.379	−0.095
ic3^I	—	—	—	0.328	−1.673	−0.457	0.326	0.216	−0.323
ts3^I	0.057	0.114	−0.005	0.188	−0.700	−0.210	0.188	0.350	−0.098
int3^I	0.294	−1.450	−0.420	0.038	0.109	−0.001	0.178	0.367	−0.087
ic4^I	0.014	0.046	0.001	0.294	−1.430	−0.397	0.325	0.200	−0.324
ts4^I	0.048	0.136	−0.002	0.186	−0.544	−0.171	0.321	0.224	−0.317
int4^I	0.314	−1.660	−0.467	0.019	0.067	0.002	0.170	0.378	−0.077

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Fig. 2 Two dimensioned ELF contours of all species on the Np–O_yl–N plane for four stages of Pathway I.

Pathway II via a free radical and ion mechanism

Structures and energetics. PEPs of Pathway II obtained at the BP86-SO-ZORA/TZP level of theory are shown in Fig. 3. As stated in Scheme 1 and Fig. 3, the first stage of three pathways has the same reaction route before the int1 formation. Then int1 can be converted with distinct patterns. Following Pathway II, int1^II can be formed via H⁺ transferring from the equatorial water of int1 to ˙N₂H₃ fragment. This process need surmount an energy barrier of 0.83 kcal mol⁻¹ and is exothermic by −8.13 kcal mol⁻¹. In the second stage, ic2^II is converted into int2^II with an energy barrier of 44.90 kcal mol⁻¹. In the third and fourth stage, ic3^II and ic4^II are transformed into int3^II and int4^II with an energy barrier of 24.50 and 59.53 kcal mol⁻¹, respectively. The former process is endothermic by 5.40 kcal mol⁻¹. In the end of each stage, intermediate exothermically dissociated to get the product of [Np^VO₂(H₂O)₅]⁺. The energy barrier (59.53 kcal mol⁻¹) of the fourth stage in Pathway II is higher than that of the other stages of Pathway II (32.02, 44.90 and 24.50 kcal mol⁻¹, respectively), which suggests that the fourth stage of Pathway II is the rate-determining step. It is obvious that this result is not consistent with the experimental result.²⁵ Furthermore, in the latter three stages of Pathway II, the formation of initial complexes is extremely unfavorable thermodynamically. Hence, it can be inferred that the Pathway II is hardly occurred based on the kinetically and thermodynamically factors. Fig. S2, ESI† presents the structures and the related bond lengths of all species in the Pathway II. As shown in Fig. S2(a), ESI† it is obvious that the O_eq.–H_eq. bond length gradually increases from 1.030 Å to 1.653 Å and N–H_eq. bond length decreases from 1.636 Å to 1.054 Å, which indicates the H transfer of the first stage in the Pathway II. It should be pointed out for the Pathway II that the trends of related N–H, Np–O_yl and O_yl–H bond lengths from ic to ts to int of other stages are in consistent with the first stage, as presented in Fig. S2(b)–(d), ESI.†

Fig. 3 Potential energy profile (ΔE, kcal mol⁻¹) of Pathways II computed at the BP86-SO-ZORA/TZP level of theory. The [Np^VIO₂(H₂O)₅]²⁺ and [Np^VO₂(H₂O)₅]⁺ were denoted as *1 and *2 respectively.

Bonding evolution analyses. For all species in the Pathway II, the WBIs, Mayer bond orders and QTAIM parameters are tabulated in Tables 3 and S2, ESI.† From Table 3, the O_eq.–H WBI and Mayer bond order decrease from 0.536 and 0.526 to 0.104 and 0.198, while those of N1–H bond increase from 0.178 and 0.209 to 0.678 and 0.580 with the reaction proceeding from int1 to int1^II. It suggests the successful transfer of H in the first stage of Pathway II. In stages of 2, 3 and 4 of Pathway II, the trends of WBIs and Mayer bond orders of O_yl–H, N–H and Np–O_yl bonds are in accordance with that in Pathway I.

Table 3 Calculated O_yl–H, Np–O_yl and N–H WBIs and Mayer bond orders of all species in the Pathway II at the B3LYP/ECP60MWB/6-31g* level of theory

	WBI			Mayer bond order
	Oyl–H^a	Np–Oyl	N–H^a	Oyl–H^a	Np–Oyl	N–H^a
a H represents H2–H4 in N2H4 corresponding to stages 2, 3 and 4 of Pathway II.b H and O represent the Heq.–Oeq. of H2O in the equatorial plane corresponding to stage 1 of Pathway II.
int1	0.536^b	—	0.178^b	0.526^b	—	0.209^b
ts1^II	0.361^b	—	0.386^b	0.375^b	—	0.324^b
int1^II	0.104^b	—	0.678^b	0.198^b	—	0.580^b
ic2^II	—	2.201	0.761	—	2.096	0.699
ts2^II	0.138	2.058	0.591	0.143	1.925	0.600
int2^II	0.648	1.276	—	0.683	1.224	—
ic3^II	—	2.186	0.728	—	2.068	0.664
ts3^II	0.145	2.034	0.540	0.163	1.888	0.532
int3^II	0.650	1.262	—	0.685	1.208	—
ic4^II	—	2.237	0.709	—	2.177	0.677
ts4^II	0.148	2.010	0.471	0.195	1.856	0.415
int4^II	0.652	1.263	—	0.680	1.202	—

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As expected, these bonding interactions are also confirmed by QTAIM and ELF analyses. It can be known from Table S2, ESI† that ρ(r) at N–H_eq. BCP for int1^II is 0.288 au with negative ∇²ρ(r), revealing the H transfer from int1 to int1^II. In stages 2, 3 and 4, the trends of ρ(r) at N–H, Np–O_yl and O_yl–H BCPs for Pathway II are similar to that of Pathway I. In addition, the two-dimensional colored ELF pictures of all species on Np–O_eq.–N and Np–O_yl–N planes are provided in Fig. S3 ESI.† The ELF value of O_eq.–H_eq. decreases and that of N–H_eq. increases, revealing the transfer of H from int1 to int1^II. Moreover, in stages 2, 3 and 4, the ELF results of N–H and O_yl–H bonds for Pathway II are in analogy with those for Pathway I. These results suggest that the N–H bond is dissociated and O_yl–H bond is formed with the reaction proceeding from initial complex to intermediate for each stage of Pathway II.

Pathway III via a free radical and disproportionation mechanism

Structures and energetics. PEPs of the first and second stages of Pathway III obtained at the BP86-SO-ZORA/TZP level of theory are presented in Fig. 4. As can be seen from the first stage of Pathway III in Scheme 1 and Fig. 4, int1 can be transformed into int1^III by continuous transferring H2 to O_yl after H1 transferring. This process requires overcoming an energy barrier of 21.71 kcal mol⁻¹ and is endothermic by 15.85 kcal mol⁻¹. It should be noted that the second stage in Pathway III are the same with that in Pathway I. Nevertheless, it is unexpected that int2^III is formed rather than int3^I when H3 is transferring. The process from ic3^I to int2^III is necessary to surmount an energy barrier of 10.28 kcal mol⁻¹. After that, int2^III is converted into int3^III accompanying with H4 transferring. The energy barrier is 13.86 kcal mol⁻¹. In the third stage, [Np^IVO₂H₂(H₂O)₅]²⁺ reacts with [Np^VIO₂(H₂O)₅]²⁺ to get the product of [Np^VO₂(H₂O)₅]⁺ by a disproportionation mechanism along with the relative energy of −174.34 kcal mol⁻¹. It is found that the first stage of Pathway III is also the rate-determining step with the highest energy barrier. However, it can be clearly seen from Fig. 1 and 4 that Pathway I is also more kinetically and thermodynamically favorable than Pathway III due to the lower relative energy for initial complexes and intermediates and energy barrier in the Pathway I.

Fig. 4 PEP (ΔE, kcal mol⁻¹) of stages 1 and 2 of Pathway III computed at the BP86-SO-ZORA/TZP level of theory. The [Np^VIO₂(H₂O)₅]²⁺ and [Np^IVO₂H₂(H₂O)₅]²⁺ were denoted as *1 and *3 respectively.

Fig. S4, ESI† shows structures and related bond lengths of all species in the first and second stages of Pathway III. As seen from Fig. S4(a)† and 4, the O_yl–H2 bond length decreases from 1.466 Å (ts1^III) to 1.008 Å (int1^III), while the N–H2/Np–O_yl bond length increases from 1.019/1.985 Å of int1 to 1.763/2.461 Å of int1^III, which suggests H2 is successfully transferred to O_yl atom. The transfer of H4 to O_yl atom as shown in Fig. S4(b)† and 4 is similar to that of H2.

Bonding evolution analyses. The WBIs and Mayer bond orders as well as QTAIM parameters for all species in the stages 1 and 2 of Pathway III are listed in ESI, Tables S3 and S4† respectively. It is apparent that the O_yl–H WBI and Mayer bond order gradually increase, while N–H WBI and Mayer bond order gradually decrease with the reaction proceeding from initial complex to intermediate for each stage. It suggests the dissociation of N–H bonds and formation of O_yl–H bonds. Moreover, these bonding evolutions can be supported by the QTAIM and ELF analyses. It can be seen from ESI, Tables 2 and S4† that, the ρ(r) at O_yl–H BCP is over 0.2 au and ∇²ρ(r) is negative for intermediate. Besides, for each stages of Pathway III, the ρ(r) at N–H and Np–O_yl BCPs gradually decrease with reaction proceeding from initial complex to intermediate. Fig. S5, ESI† presents the two-dimensional colored ELF pictures of stationary points on the Np–O_yl–N plane for the transfer of H2 and H4. It can be distinctly seen that the ELF values of O_yl–H2 and O_yl–H4 bonds gradually increase, indicating the formation of O_yl–H2 and O_yl–H4 bonds.

The three pathways with different mechanisms for reduction of Np^VI with hydrazine molecule are proposed, and the feasibilities of three pathways are testified by DFT computation. According to the calculated PEPs, it can be inferred that the Pathway I is the most likely to occur, the Pathway II is hardly realized and Pathway III is probably taken place through comparing the energy barriers and the stability of species. The reason of high energy barrier in the Pathway II is likely to be that the nitrogen atom electron density of ˙N₂H₄⁺ is smaller together with the smaller electronegative of nitrogen atom compared to those of ˙N₂H₃, resulting in the weaker polarization of N–H bond that makes the dissociation of N–H bond become more difficult. In the Pathway III, the energy barriers of the second and fourth stages are relative higher than those of Pathway I. It is probably that the activity of neptunyl ion is so small that the first H atom transfer is relative easy, but successive transferring the second H atom becomes difficult. In addition, the nature of Np^VI reduction is gradually transferring hydrogen atom from N₂H₄ to “yl”-oxygen of [Np^VIO₂(H₂O)₅]²⁺, which is embodied by the analyses of bond length, bond order, QTAIM and ELF. All the calculated results suggest that the N–H bond gradually dissociated and O_yl–H bond gradually formed with the reaction proceeding from initial complex to intermediate for each stage.

Conclusions

In this work, the redox mechanisms of Np^VI with N₂H₄ in aqueous solution were investigated based on the difficult control and adjustment of neptunium valence state in spent fuel reprocessing. The three reaction pathways with free radical, free radical and ion, as well as free radical and disproportionation mechanism were proposed. And it is supposed that the redox nature of [Np^VIO₂(H₂O)₅]²⁺ with N₂H₄ was the gradual transfer of hydrogen atoms along with the dissociation of N–H bonds and formation of O_yl–H bonds. To verify the pathway reasonability, we have performed a series of theoretical calculations. All the structures of species of the three pathways are optimized at the B3LYP/ECP60MWB/6-31g* level of theory. Consideration the importance of spin–orbital coupling of neptunium atom, we performed the single-point computation based on the B3LYP-optimized structures at the BP86-SO-ZORA/TZP level of theory. The PEPs of three pathways were depicted based on the relative bond energies of each species with respect to the ground-state reactant. The results show that the Pathway I is the most reasonable among the three ones. Moreover, the stage of forming ˙N₂H₃ of Pathway I has the highest energy barrier of 32.02 kcal mol⁻¹ and is the rate-determining step, which is in accordance with the experimental observation.²⁵ In addition, in order to prove the redox nature, the analyses of bond length, the WBIs and Mayer bond orders, QTAIM and ELF were provided for whole reaction process. The calculated results explicitly explained the redox nature with the transferring H atoms step by step. In summary, this work has been provided the understanding of reduction mechanisms of Np^VI with N₂H₄ and its derivatives. It is expected this work can provide theoretical basis on designing more efficient reductants for the separation of U/Np and Np/Pu in spent nuclear fuel reprocessing.

Acknowledgements

This work was supported by the Natural Science Foundation of China (Grant No. 21477130, 91426302, 91326202) and the “Strategic Priority Research Program” of the Chinese Academy of Sciences (Grant No. XDA030104). The results describle in this work were obtained on the ScGrid of Supercomputing Center, Computer Network Information Center of Chinese Academy of Sciences.

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Footnotes

† Electronic supplementary information (ESI) available: The structures and related bond length of all species in the Pathways I, II and III (Fig. S1, S2 and S4 respectively), Np–O bond length of [Np^VIO₂(H₂O)₅]²⁺ and [Np^VO₂(H₂O)₅]²⁺ (Table S1), the QTAIM parameters and ELF pictures of Pathways II and III (Tables S2 and S4, Fig. S3 and S5) as well as the WBIs and Mayer bond orders (Table S3) are provided. See DOI: 10.1039/c6ra13339h

‡ The first two authors contributed equally to this work.

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