Introduction

The nature of the multiple bonding between actinide (An) and main-group ligands (L) is of considerable research importance, due to interest in the behavior of 5f electrons [1–16]. A thorough understanding of An-L molecular structures could be helpful to ameliorating nuclear waste clean-up or devising new nuclear waste repositories. In addition to the well-known U≡O triple bonds in the uranyl ion, the U=O and U=NR multiple bonds in oxide and imido complexes are well established and understood classes of An-L multiple bonds [17].

It is found that the lone pair electrons of N atom in NH3 plays a vital role in the bonding of actinide imine molecules. Recently, laser-ablated Th or U atoms reacted with NH3 in the gas phase to form thorimine (HN=ThH2) or uranimine (HN=UH2) were detected and characterized by infrared spectroscopic identification in Andrews’ laboratories [18, 19]. On the theoretical side, Andrews et al. provided insights into the density functional theory study of thorimine (HN=ThH2) and uranimine (HN=UH2) molecule. Their calcuations showed that the HN=ThH2 and HN=UH2 have the analogous structure, and appreciable N≡Th and N≡U partial triple-bond character which has an important contribution from the f orbitals [18]. In our recent work, the reaction mechanism of U + NH3 in gas phase has been investigated in detail at different levels of theory [20]. Given the greater number of 5f orbitals available on Np and Pu atom, is the nature of the N-Np or N-Pu bonding in the actinide imine molecules as similar as in HN=ThH2 and HN=UH2?

The main objective of this work is to report the first detailed theoretical evidence of the neptunimine (HN=NpH2) and plutonimine (HN=PuH2) molecules. The bonding characters were investigated in terms of diverse analyses including electron localization function (ELF), atoms in molecules (AIM), and natural bond orbital (NBO). The roles of 5f orbitals were diagrams analyzed by total density of state (TDOS) and partial density of state (PDOS) together with overlap population density of state (OPDOS).

Computational details

Geometry optimization and frequency calculations of the minima structures were performed at the B3LYP [21, 22], PW91PW91 [23], B3PW91 [24], and PBE0 [25] methods, along with Stuttgart/Bonn relativistic effective core potential (RECP) [26] for Np and Pu atom, the 6-311++G(d,p) basis set for N and H atoms. This small-core RECP, is named SDD, replaces 60 electrons in inner shells, leaving the n ≥ 5 shell as the valence electrons. These calculations were carried out using the Gaussian 03 programs [27]. All of the structures were identified to be local minima without any imaginary frequencies. The present computational method has been successfully carried out in previous actinide systems calculations [28–32], and specifically, B3LYP/SDD and PW91/SDD methods were shown to have good performance in the structure and frequencies investigation for HN=ThH2 and HN=UH2 compounds [18, 19].

A topological description of all species with the aim of deeply understanding the nature of the bonding was performed. The wavefunction files (.wfn) which obtained by using the Gaussian 03 programs were used as input files of the Multiwfn [33] package to perform the ELF [34, 35] and AIM [36] analysis. It is worth mentioning that ELF and AIM are useful means of analyzing molecular interactions and have been successfully applied in many investigations. In order to gathering insights about the participation of 5f orbitals in the chemical bonds of complexes, TDOS, PDOS, and OPDOS were also calculated [37, 38]. In addition, CDA (charge decomposition analysis) were performed to obtain a deep insight into the nature of the charge transformation [39].

Results and discussion

Geometric structures

Many possible structures of HN=NpH2 and HN=PuH2 were constructed. Different possible spin states were considered. After optimization, the stable conformation in the gas phase was located. The optimized geometries of the HN=NpH2 and HN=PuH2 are shown in Fig. 1, and the optimized geometries show little dependence on the level of theory. The electronic state (ES) and relative energies of the stable structures are listed in Table 1.

Fig. 1
figure 1

Structures and geometric parameters of HN=NpH2 and HN=PuH2 molecules optimized at the B3LYP/SDD, B3PW91/SDD, PBE0/SDD, and PW91/SDD levels of theory (from top to bottom rows, respectively). Bond distances are in Å, and angles are in degrees

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Table 1 The electronic state and relative energies (in kcal mol−1) for the stable structures HNNpH2 and HNPuH2 molecules
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Our results indicate that the HN=NpH2 and HN=PuH2 molecules should be nonplanar and have a similar structure as HN=ThH2 and HN=UH2 [18, 19]. The HN=NpH2 molecule forms a stable nonplanar equilibrium structure with Np–N bond distances of 1.880Å, as can be seen from Fig. 1. The ground electronic state of HN=NpH2 molecule is identified as the quartet \( {\tilde{\mathrm{X}}}^4\mathrm{A} \). On the other hand, the calculation on HN=PuH2 predicted that the molecules have a quintet \( {\tilde{\mathrm{X}}}^5\mathrm{A} \) ground state. The N-Pu bond lengths were calculated as 1.887 Å. The N-An bonds are slightly shorter than the ones in HN=ThH2 and HN=UH2 (1.951 and 1.903Å at B3LYP/SDD level of theory, respectively).

For the system which does not have the experimental values about the structure parameters, we should routinely do our calculations with different functional and see if they give consistent results [40]. Our calculations contain pure GGA functional and hybrid density functional with small core relativistic effective potentials (RECP) and should give reliable results on geometries and energies of the HN=NpH2 and HN=PuH2 molecules. As shown by the relative energies of the stable structures listed in Table 1, the relative energies are consistent at various levels of theory. The only incongruity is that B3LYP/SDD underestimated the relative energies of HN=NpH2.

The ab initio MD simulations at 300 and 500 K, respectively, are performed at B3PW91 level of theory to further confirm the stability of the HN=NpH2 and HN=PuH2 structure. Both simulations are carried out for 5 ps using a BOMD [41] implemented in the Gaussian 03 program. The root mean square displacement (RMSD) of MD trajectory at different temperatures is depicted in Fig. 2. Within the time frame of our simulations, RMSD results indicate that HN=NpH2 icosahedral structure keeps its identity at both room temperature (300 K) and high temperature (500 K). However, one can see that the thermal distortions of HN=PuH2 have large fluctuations than that of HN=NpH2, which reveals that the HN=NpH2 is more stable than HN=PuH2.

Fig. 2
figure 2

The RMSD through time at different temperatures for the HN=NpH2 and HN=PuH2 molecules

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IR and Raman spectroscopy

The harmonic vibrational frequencies of the ground state HN=NpH2 and HN=PuH2 structure were calculated at the B3PW91 and PBE0 levels of theory as the geometry optimization. The results are collected in Table 2. Predicted IR spectra in the gas phase are depicted in Fig. 3. The strongest IR absorption for the HN=NpH2 molecule corresponds to the two Np-H stretching modes calculated at 1540.1 and 1493.8 (B3PW91) or 1544.5 and 1496.1 cm−1 (PBE0). Similarly to HN=NpH2, the strongest IR absorption for the HN=PuH2 molecule is the two Pu-H stretching modes. The frequencies 3554.7 cm−1 in the HN=NpH2 and 3521.1 cm−1 in HN=PuH2 are caused by N-H stretching vibrations. The Np=N stretching frequency calculated at 845.4 (B3PW91) or 860.3 cm−1 (PBE0), is higher than the Pu=N stretching frequency calculated at 781.3 (B3PW91) or 800.7 cm−1 (PBE0).

Table 2 Comparison of calculated harmonic frequencies for the HNNpH2 and HNPuH2
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Fig. 3
figure 3

Simulated IR spectra of HN=NpH2 and HN=PuH2 molecules

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Comparison between the vibrational frequencies of HN=NpH2, HN=PuH2, HN=ThH2, and HN=UH2 shows that vibrational modes are similar. This is because they have a similar structure. Taking the strongest IR absorption and N-H stretching as an example, the strongest IR absorption in all these cases are the two An-H stretching modes, and the frequency of N-H stretching vibrations are consistent. Predicted Raman spectra in the gas phase are depicted in Fig. 4. The result shows weak peaks in low frequencies and strong peaks in high frequencies.

Fig. 4
figure 4

Simulated Raman spectra of HN=NpH2 and HN=PuH2 molecules

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Bonding characteristics and orbital interactions

Bonding characteristics

The bonding properties of all of the species involved in this study have been investigated using two different topological methodologies (AIM, ELF) as well as using the natural bond orbital analysis.

The atoms in molecules (AIM) analysis is a powerful tool for the characterization of chemical bonds, and has been successfully utilized to explore the natures of chemical bonding in actinium-complexes [42, 43]. The AIM analyses were performed with wave functions obtained at the B3PW91/SDD level of theory. The topological properties of the (3,-1) bond critical points (bcp) were obtained in terms of the electron density ρ(r) and its Laplacian ∇2 ρ(r) at the critical bond, the total electron energy density H(r), the potential energy density V(r), and the kinetic electron energy density G(r). Higher V(r) value indicates the electrons are more localized in this regions, whereas large G(r) values correspond to regions where the electrons move faster [44]. The relationships between these parameters are shown in the following equations:

$$ {\nabla}^2\rho \left(\mathrm{r}\right)=2\mathrm{G}\left(\mathrm{r}\right)+\mathrm{V}\left(\mathrm{r}\right) $$
(1)
$$ \mathrm{H}\left(\mathrm{r}\right)=\mathrm{G}\left(\mathrm{r}\right)+\mathrm{V}\left(\mathrm{r}\right) $$
(2)

As the traditional topological criterion, a negative ∇2 ρ(r) corresponds to the covalent bonds. However, this criterion has been proved to be not sufficiently appropriate to describe the bond natures of heavy atoms [45, 46]. Cremer and Kraka [47] proposed that using H(r) as a criterion: for covalent interactions, |V(r)| > G(r), H(r) is negative; whereas closed-shell interactions, |V(r)| < G(r), H(r) is positive. H(r) was proved to be very adequate to characterize the nature of a bond for a heavy atom system [48, 49].

The AIM parameters calculated at the (3,-1) bcp for HN=NpH2 and HN=PuH2 molecules are listed in Table 3. At all BCPs in the HN=NpH2 and HN=PuH2 molecules, the H(r) values are negative, the |V(r)|/G(r) ratio exceeds 1.0. All of these quantities mean that the An–H and An–N bonds have covalent character. In order to facilitate comparison of data, we also listed the AIM parameters of HN=ThH2 and HN=UH2 at B3PW91/SDD method using the geometric result of the Andrews’ study [18, 19]. The results included in Table 3 suggest that the Th–N and U-N bonds also have a covalent character. A lower H(r) value (−0.1551 au) is observed in the Np-N, as compared to H(r) in the Th-N (−0.1212 au), U-N (−0.1443 au), and Pu-N (−0.1483 au) bonds. The ∇2 ρ(r) values of the An-N bonds rise steadily with increasing atomic number (from Th to Pu).

Table 3 Topological properties of the charge density calculated at the (3,-1) bond critical points for HNNpH2 and HNPuH2 molecules at B3PW91/SDD level of theory
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ELF is another useful tool for identifying the bonding characteristics in molecules. It is worth mentioning that the effective core potential (ECP) seems make the ELF calculation fail to provide a clear core-valence separation on the Np and Pu center. However, studies have shown that the deeper actinium core has little impact on the topological properties of valence [29]. The electron density obtained from a small-core ECP calculation is good enough to reproduce not only the correct topology of the actinium-ligand bonds but the values of the local properties as well [43, 49]. Therefore, the small-core RECP we used in this work is probably responsible for these analysis. Figure 5 shows the behavior of two-dimensional (2D) filled-color diagrams of ELF (η = 0.70). One can see that there is a disynaptic valence basin between Np and the N atom, which indicates that there is a covalent bond formation between Np and N in complex HN=NpH2. This conclusion is supported by the AIM analysis, our result shows that there is a (3,-1) BCP between Np and N atom with a relatively low charge density, ρ(r) 0.2227 au, while negative H(r) value (−0.1551) indicates that Np–N bond has a covalent character. This characteristic is also found in the HN=PuH2. Despite the qualitative similarity there are differences in the Np-H and Pu-H bond. The ELF diagram shows that the combination of Np-H in HN=NpH2 are more tightened than Pu-H bonds in HN=PuH2 molecule, this may due to the large atomic covalent radius of Pu (note that 7s orbital is much more diffuse than 5f).

Fig. 5
figure 5

Two-dimensional (2D) filled-color diagrams of ELF (η = 0.70) at the B3PW91/SDD level of theory

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Bond dissociation energies (BDE) are a measure of the bond strength in a chemical bond. Firstly, BDE of HN=NpH2 and HN=PuH2, calculated by different methods as well as the results for HN=ThH2 and HN=UH2 [19], are collected in Table 4. It can clearly be seen that, as the atomic number increases (from Th to Pu case), the BDE of An-N bond in these complexes decrease. This fact may be due to the delocalization effect of 5f electrons has steadily diminished from Th to Pu atom. Mayer bond order analysis indicated that An-N bond order are decreased from Th to Pu, the results are reported in Table 5. In these studies, the 6-311++G(d,p) were replaced with 6-311G(d,p) to generate wavefunctions, because the Mayer bond order was not sufficiently appropriate if diffusion functions were used.

Table 4 Bond dissociation energies (BDE in kcal mol−1) and An-N bond lengths (r(An-N) in Å) obtained with four different theoretical methods
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Table 5 Mayer bond order of An-N bond obtained with four different theoretical methods
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With the aim of investigating the nature of An=N bonds, we performed NBO analysis. The results are compared in Table 6. The ionic character (i AB) is also listed in Table 6. The ionic character (i AB) is a good indicator of the chemical bond, indicating the ionicity of the A-B bond, as determined from NBO polarization coefficients cA, cB. The i AB is formulated by the following equation [50]:

Table 6 Natural bond orbital analysis for HN=AnH2 (An=Th, U, Np, and Pu) molecules at B3PW91 level of theory
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$$ {i}_{\mathrm{A}\mathrm{B}}=\left|\left({{\mathrm{c}}_{\mathrm{A}}}^2-{{\mathrm{c}}_{\mathrm{B}}}^2\right)/\left({{\mathrm{c}}_{\mathrm{A}}}^2+{{\mathrm{c}}_{\mathrm{B}}}^2\right)\right| $$

Where cA and cB are the coefficients of natural hybrid orbital.

From the NBO analysis we can conclude that the multiple bonding in HN=AnH2 is similar: (1) there are three BD type in N-An; (2) these N-An bond are very polarized, indeed, the An contributions make up only 17.01–21.1 %. Despite these qualitative similarities, there are significant differences. First of all, the N-Th bond in HN=ThH2 is a triple bond, and each BD has two electrons. However, in U, Np, and Pu cases, each BD has almost one electron. Secondly, ionic character (i AB) of N-An bond is gradually decreasing from Th, to Np, but have a maximum value in the Pu case. Finally, from Th to Pu, the 5f orbitals play a more and more important role in An-N bonding.

Orbital interactions

The TDOS, PDOS, and OPDOS were created by convoluting the molecular orbital information with Gaussian curves of unit height and full width at half maximum (FWHM) of 0.05 a.u using Multiwfn. The TDOS, PDOS, and OPDOS curves of HN=NpH2 and HN=PuH2 at the B3PW91/SDD levels of theory are plotted in Fig. 6. Fragment 1 is defined as Np or Pu atom, fragment 2 is defined as N atom. The vertical dashed line indicates the position of HOMO and LUMO level.

Fig. 6
figure 6

The TDOS, PDOS, and OPDOS curves of HN=NpH2 and HN=PuH2 at the B3PW91/SDD levels of theory

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As seen in Fig. 6, the behavior of the DOSs are similar in both HN=NpH2 and HN=PuH2 cases. At the position of HOMO level, the orbitals of Np (Pu) atom nearly approaches the TDOS line, which means most of the contributions to HOMO came from the Np (Pu) atom orbitals. The PDOS and OPDOS diagrams also show that the Np (Pu) atom and N have bonding characters around −8.16 eV (below the HOMO), as evidenced by the positive OPDOS value. In the region of −21.77 to −9.0 eV, the OPDOS values are negative, indicating in this energy region Np (Pu) and N atom have anti-bonding characters.

In addition to the similarities, the differences are noteworthy. It is readily seen in Fig. 6, the energy gap between HOMO and LUMO of HN=NpH2 is larger than that of HN=PuH2, indicating the HN=NpH2 is more stable than HN=PuH2. This fact is also consistent with previous dynamics simulation results. The OPDOS values of HN=PuH2 are more negative than that of HN=NpH2 in the region of −21.77 to −9.0 eV, suggesting in this energy region the anti-bonding character of Pu=N bond is stronger.

The CDA analyses were performed to obtain a deep insight into the nature of the charge transformation. The results are displayed in Fig. 7, the occupied orbitals are represented by solid lines, and virtual orbitals are represented by dashed lines. The LUMO and HOMO∼HOMO-4 of HN=NpH2 and HN=PuH2 were primarily comprised of the corresponding orbitals of NpH2 and PuH2, respectively. Therefore, the above electron transitions happened inside NpH2 and PuH2. The HOMO and HOMO-1 molecular orbitals for HN=NpH2 and HN=PuH2 were also shown in Fig. 7. These two orbitals correspond most closely to two π bonds found by the NBO analyses.

Fig. 7
figure 7

Orbital-interaction diagram of HN=NpH2 and HN=PuH2

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Conclusions

The structures, stabilities, nature of bonding, and spectroscopic properties of HN=NpH2 and HN=PuH2 were studied using tools derived from the density functional theory. Ab initio MD calculations indicated that the HN=NpH2 is more stable than HN=PuH2. Our calculation indicated that both the HN=NpH2 and HN=PuH2 should be nonplanar, and have a quartet (\( {\tilde{\mathrm{X}}}^4\mathrm{A} \)) and quintet (\( {\tilde{\mathrm{X}}}^5\mathrm{A} \)) ground state, respectively. The nature of the chemical bonding in these molecules were investigated by employing topological methods including electron localization function (ELF), atoms in molecules (AIM) as well as natural bond orbital analysis (NBO). AIM analysis suggested that the Np=N and Pu=N bonds have a covalent character. NBO results showed that these actinide complexes possess relatively strong Np=N and Pu=N bonds between the Np (Pu) 6d-5f hybrid orbitals with N 2s-2p orbitals. The charge decomposition analysis (CDA) diagram demonstrated that the transition of electrons mainly happened inside the AnH2 of HN=AnH2. Total and partial density of state (TDOS and PDOS) and also overlap population density of state (OPDOS) diagrams analysis were implemented. The OPDOS diagrams showed interactions for Np (Pu) and N atom have bonding character near HOMO, but have anti-bonding character at the energy region which is much lower than the HOMO. We hope that the results of this study will help researchers toward synthesis of new actinide imine materials.