Adsorption of 5f-electron atoms (ThCm) on graphene surface: An all-electron ZORA-DFT study

Accepted Manuscript Adsorption of 5f-electron atoms (Th-Cm) on graphene surface: an all-electron ZORA-DFT study Jiguang Du, Gang Jiang PII: DOI: Reference:

S0021-9797(17)30921-9 http://dx.doi.org/10.1016/j.jcis.2017.08.015 YJCIS 22662

To appear in:

Journal of Colloid and Interface Science

Received Date: Revised Date: Accepted Date:

24 June 2017 22 July 2017 5 August 2017

Please cite this article as: J. Du, G. Jiang, Adsorption of 5f-electron atoms (Th-Cm) on graphene surface: an allelectron ZORA-DFT study, Journal of Colloid and Interface Science (2017), doi: http://dx.doi.org/10.1016/j.jcis. 2017.08.015

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Adsorption of 5f-electron atoms (Th-Cm) on graphene surface: an all-electron ZORA-DFT study ﹡ Jiguang Du1 , Gang Jiang2 1 College of Physical Science and Technology, Sichuan University, Chengdu 610064, China 2 Insitute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China Abstract All-electron calculations were performed to investigate the adsorption of 5f-electron atoms (An=Th-Cm) on graphene surface. The hollow site is energetically preferred for the An-graphene complexes studied. The interaction strengths between An and C decrease in the order of Th> Pa> U> Np> Pu> Cm>Am. The An-C interactions show predominately closed-shell characteristics, meanwhile Th-C chemical bond formed through orbital overlaps of Th (6d) and C (2p) possesses partial covalent nature. The participation of 6d(5f)-electron into bonding orbitals are gradually weakened (enhanced) from Th to Pu because the 5f electrons are more and more diffuse. The physisorption nature of Am on graphene was observed by the weak orbital overlaps between Am (6d) and C(2p) and the half-fill 5f occupancy. The magnetic moments of An-graphene species are mainly derived from the 5f-electron due to its high delocalization. The molecular orbital (MO) and charge decomposition analysis (CDA) indicate that the 6d orbitals of An atoms play a more important role in participation of bonds relative to the 5f orbital, as well as the strong linear correlation between 6d occupancy numbers and adsorption energy highlights the significant role of 6d-electron of An in the interaction.

Keyword: graphene surface; actinide atoms, bonding nature

1. Introduction Actinides were extensively used to advance nuclear energy and fuel efforts due to their active chemical properties and distinctive electronic structures [1, 2]. Meanwhile, ﹡

Corresponding author. E-mail: [email protected] (Jiguang Du) -1-

the nuclear wastes have significantly contributed to a global legacy of radioactive waste contamination in the environment [3-5]. In the last decades, the sorption of the radionuclides on minerals [6], oxides and nanomaterials were extensively studied to evaluate the possible application of these materials in nuclear waste management [7–10]. Recent advances in nanoscience and nanotechnology related to carbon-based nanomaterials [11,12] have led to the promising applications of carbon nanotubes (CNTs) and graphene for waste treatment and extraction of actinide materials [13-17]. In recent years, the removal of radionuclides from radioactive solutions with carbon materials such as carbon nanotubes [18-20], activated carbon [21], and graphene oxide [22-24] was investigated in experiments. Moreover, graphite materials [25] were popularly used as neutron moderators or reflectors in various nuclear reactors due to their superior properties such as high moderation ratio, low coefficient thermal expansion, and satisfactory radiation stability. In theory, the adsorptions of uranium dicarbide on primitive and defective graphene nanosheet were recently investigated by density functional theory (DFT) calculations in Wang’s group [26, 27]. The interaction between actinides ion complexes and the functioned graphene was studied [28] due to the vast application potential of graphene oxide (GO)-based materials in nuclear waste processing. The DFT calculations of U and Pu complexes with graphene and graphene oxide were also performed to examine the applicability of a graphene-based fissile sensor [29]. Although several works have paid attention to the adsorption of actinide complexes on pristine or functionalized graphene in theory as mentioned above, the fundamental understanding of interaction feature between actinide atoms and graphene surface is lacking, especially the periodic trend. Although the absorptions of 3d-, 4d- and 5d-electron atoms on graphene surface were recently investigated [30], the studies for the adsorption of 5f-electron atoms on graphene were missing. While the interaction between 5f-electron actinides and graphene is very important for the understandings of 5f-electron characteristics [31] and even the separation of nuclear elements [32]. In the present work, all-electron zero-order regular approximation (ZORA) DFT -2-

calculations were performed to understand the adsorption characteristics of 5f-electron atoms, An=Thorium (Th), Protactinium (Pa), Uranium (U), Neptunium (Np), Plutonium (Pu), Americium (Am) and Curium (Cm) on graphene surface. We obtained the adsorption structures, magnetic properties and adsorption energy. The interaction nature between An atom and graphene was revealed with topological analysis of the electron density, molecular orbital (MO) and charge transfer analysis (CDA).

2. Computational methods The all-electron DFT calculations were carried out with ORCA-3.0.3 package [33]. The meta-generalized gradient approximation (meta-GGA) functional proposed by Tao-Perdew-Staroverov-Scuseria (TPSS) [34] was utilized to describe the electron correlation. The GGA functional BP86 [35] was also employed for the sake of comparison. The scalar relativistic effect was incorporated by the zero-order regular approximation (ZORA) [36]. Segmented all-electron relativistically contracted (SARC) [37] Gaussian-type basis set was employed to describe the actinide (An) atoms, and split valence basis set in relativistically recontracted version (SV-ZORA) [38] for the light C, H atoms. The natures of bonding in the titled species were observed by quantum theory of atoms in molecules (QTAIM) [39]. The all-electron wave functions obtained at the TPSS/SARC-ZORA level of theory were used in the QTAIM calculations with MULTIWFN program [40]. The orbital interactions in the molecular models (An-C6H6) were investigated based on charge transfer analysis (CDA) [41-42]. The deep understanding of charge transfer mechanism can be obtained with the molecule model description. The calculations for An-C6H6 molecular systems were carried out with Gaussian 09 package [43]. The small-core scalar-relativistic effective core potential (ECP60MWB) was adopted in combination with ECP60MWB_SEG basis set [44-46] to describe the An atoms, and cc-pVTZ basis set for the C, H atoms. The model cluster with a molecular formula of C54H18 was constructed to represent the graphene surface. Three different sites of the actinides atom with respect -3-

to the graphene surface, namely, top, hollow, and bridge (see Fig. 1), were relaxed as initial configurations. In the geometry optimization, all atoms in the systems were fully relaxed, followed by verifications using vibration frequency analysis at the same level of theory to ensure that the structures we obtained are at the real local minima on the potential energy surface. The high integration grid8 was chosen in the numerical integration to describe the actinide atoms in geometry optimization and frequency calculations. The electronic states with different spin multiplicities were calculated for each system to determine the ground electronic state. The adsorption energy of An atom on the graphene was calculated using the following equation Eads=EAn+Egraphene-EAn-graphene

(1)

where EAn, Egraphene and E An-graphene are the total energies of actinide atoms, C54H18 graphene cluster and An-graphene, respectively. 3. Results and discussions

3.1 Geometrical structures The structures of An-graphene (An=Th-Cm) were fully relaxed with TPSS, BP86, respectively. Three different adsorption sites represented in Fig. 1 were considered, and we found that the sites of top and bridge either have convergence problem or finally was relaxed to hollow site. Our results indicate that the hollow site was energetically preferred for all An-graphene species studied. Therefore, we will make detailed discussions for the hollow structures in the following. The ground electronic states were obtained by performing spin polarization calculations to understand the magnetic properties. The relative energies for different spin states of An-graphene (An=Th-Cm) are collected in Table S1 (TPSS) and Table S2 (BP86) of the electronic supporting information (ESI). The TPSS and BP86 functionals give the same ground electronic state for studied species except for Cm-graphene system, which was predicted the nonet state as ground state by TPSS, and septet state by BP86. The spin multiplicity increases from Th to Am gradually. The Cartesian coordinates of the lowest-energy structure obtained at the TPSS level of theory were given in the -4-

supporting information (see Table S3). No imaginary frequency (see Table 1) exists in all An-graphene species with hollow mode, confirming their thermal stability. The key structural parameters of the most stable structures obtained with TPSS are collected in Table 1. The An-C bonds are in the range of 2.56-2.87Å (dAn-C), and increase from Th to Am across An period. The An-C bond lengths are significantly larger than the sum of the covalent radii (shown in Table 1), and the largest difference for Am is as high as 20%. This implies that covalent interaction is not predominant for An-C bonds, which can also be confirmed by the Mayer bond order (MBO). Among all species studied, the Th-C (Am-C) interaction is strongest (weakest), as revealed by the MBO values. As shown in Table S4, the calculated parameters from BP86 are in excellent agreement with the results of TPSS.

Table 1. Distances between An and neighboring C atoms (dAn-C), Mayer bond order (MBO) for An-C bondings, the range of vibrational frequency (ωe), the Hirshfeld and the VDD (in parentheses) charges of the An atoms and dipole moments (μ) of An-graphene. max MBOAn Species rc+rAn (Å) MBO ωe/cm-1 Q(An) C max min /Å /Å d d An An  C C min An C

Th-graphene Pa-graphene U-graphene Np-graphene Pu-graphene Am-graphene Cm-graphene

2.546 2.713 2.693 2.712 2.745 2.851 2.705

2.639 2.720 2.703 2.714 2.791 2.866 2.711

2.48 2.42 2.43 2.44 2.45 2.39 2.39

0.31 0.25 0.25 0.23 0.18 0.11 0.20

0.51 0.26 0.25 0.23 0.19 0.13 0.22

34-3158 45-3159 53-3159 31-3159 37-3159 43-3159 44-3159

0.44 (0.35) 0.34 (0.25) 0.32 (0.20) 0.31 (0.19) 0.32 (0.22) 0.35 (0.24) 0.35 (0.24)

3. 2 Adsorption energies The adsorption energies of An-graphene species evaluated with equation (1) were obtained with BP86 and TPSS functionals for the sake of comparison, and the calculated values (in eV) are listed in Table 2. The adsorption energies obtained with TPSS functional are in the range of 0.35-1.84eV, and are slightly larger than those of BP86 by about 0.2eV. Both functionals predict the adsorption energy to decrease in the order of Th >Pa >U >Np >Pu >Cm >Am. The high adsorption energy of -5-

μ(D) 5.36 3.68 3.71 3.31 2.47 3.01 3.32

Th-graphene species implies the strong Th-C interaction, which is in line with its high Th-C MBO value of 0.51, as shown in Table 1. For Th, Pa, U, and Np adsorbed species, the adsorption energy is larger than 1eV, which suggests the existence of An-C chemical bonds. The U atom on graphene is less stable than that on carbon nanotube (CNT) [47]. The Pu and transplutonium (Am, Cm) atoms are weakly bound to the graphene surface, especially for Am, which corresponds to the adsorption energy of 0.35eV (TPSS) and 0.12eV (BP86), respectively, and is typically physisorbed state. On the whole, the adsorption energies of 5f-electron atoms on graphene are comparable with those of 3d transitional metals on graphene and CNT [48]. Table 2. The adsorption energies (Eads) in eV of An-graphene calculated with different functionals. Th Pa U Np Pu Am Cm TPSS 1.84 1.62 1.50 1.16 0.78 0.35 0.66 BP86 1.67 1.43 1.16 0.88 0.55 0.12 0.39

3.3 Electronic structure The charge transfer between the graphene surfaces and the actinide atoms were calculated based on the Hirshfeld [49] and the Voronoi deformation density (VDD) [50] populations. Although the charges of An atoms in An-graphene calculated by these two populations are slightly different, the trends are very similar, as shown in Table 1. Both charge populations analyses suggest the positive charges on the An atoms. The charge transfers from the adatoms to the graphene implies electrostatic interactions between An atoms and graphene. Moreover, the calculated dipole moments μ of the An-graphene species (Table 1) suggest a degree of ionic character for the An-C bonds. The character of the An-C bonds is detailed addressed later by the electron density analysis. The magnitude of charge transfer from Th to the carbon surfaces was largest among all species studied, indicating the strong interaction between Th and C atoms, which is also revealed by the larger dipole moment of Th-graphene species. As shown in Table 3, the total magnetic moments of An-graphene species increase -6-

continuously and monotonically from Pa to Am with an increment of 1.0μ B. The moments of adsorbed An atoms except for Th and Cm are larger than those of isolated atoms. The contribution percentages from the actinide atom for total magnetic moment are in the range of 74.2%-95.6%, showing predominant contribution. As shown in Table 3, the unpaired electrons mainly come from 5f shell of An atoms with a little contribution from 7s and 6d shells due to the high delocalization of 5f-electron. It is also important to note that the contribution of magnetic moments from 5f-electron is gradually increased from left to right across An periodic series, along with the decrease of 6d-electron contribution. This because the 5f-electron is more and more diffuse across the An periodic table. Table 3. Magnetic moments of An-graphene (μT), adsorbed An atoms (μAn) and isolated An atoms (μI), and spin populations in valence shells of An atoms and the contribution percentages from different shells for total moments. Th Pa U Np Pu Am Cm μT (μb) 2 5 6 7 8 9 8 μAn (μb) 1.59 3.71 4.69 5.78 7.00 8.03 7.65 μI (μb) 2 3 4 5 6 7 8 7s 0.57 0.72 0.75 0.80 0.88 0.91 0.85 6d 1.07 1.07 0.86 0.62 0.32 0.23 0.40 5f -0.05 1.92 3.08 4.36 5.80 6.89 6.40 An% 79.5 74.2 78.2 82.6 87.5 89.2 95.6 An(7s)% 35.8 19.4 16.0 13.9 12.6 11.3 11.1 An(6d)% 67.3 28.8 18.3 10.7 4.6 2.9 5.2 An(5f)% -3.1 51.8 56.7 75.4 82.8 85.9 83.7

Table 4 shows the electron configurations (EC) of isolated and adsorbed actinides atoms. Compared to isolated atoms, the 7s electrons are promoted to 6d/5f orbitals in the adsorbed An atoms, resulting in single-electron occupancy (7s1) in 7s shell. This indicates that the s-d or s-f hybridization occurs in An atoms when involved in chemical bonds. In addition, the decrease of 6d electron populations accompany with increase of 5f electrons can be found from Th to Pu (Am/Cm). As shown in Fig. 2, it is very important to note that there exists strong linear correlation between 6d occupancy numbers and adsorption energy. This suggests that the 6d-electron of -7-

actinides play an important role in participation of chemical bonds. For example, the Th atom in Th-graphene which possesses 6d2 configurations has more electrons to participate into chemical bonds relative to other An atoms (as shown in Table 4), resulting into strong adsorption energy, on the other hand, the orbital overlap between Am and graphene is significantly weak due to low occupancy numbers of 6d electron (0.41) and half-fill 5f occupancy. Table 4. Electron configurations of isolated and adsorbed An in An-graphene. Systems isolated An An in An-graphene 0 2 2 Th 5f 6d 7s 5f0.436d1.897s0.78 Pa 5f26d17s2 5f2.006d1.427s0.86 U 5f36d17s2 5f3.166d1.197s0.90 Np 5f46d17s2 5f4.436d0.917s0.94 Pu 5f66d07s2 5f5.846d0.537s0.98 Am 5f76d07s2 5f6.926d0.417s1.00 Cm 5f76d17s2 5f7.536d0.727s1.00

3.4 Topological analyses of electron density To understand the interaction characteristics between actinide atom and the coordinating carbon atoms of graphene surface, the topological parameters at (3,-1) bond critical points (BCPs) were calculated based on the wavefunction obtained at TPSS/SARC-ZORA level of theory. The bond paths and located ciritical points (CP) are depicted in Fig. 3. According to QTAIM criteria, the covalent interaction corresponds to a negative ▽2ρ at the critical point (CP). However, previous works indicated that this criterion is not sufficient to describe the bond natures of heavy atoms. Another property, the total energy density (defined as the sum of local kinetic energy density G(r) and the local potential energy density V(r)) proposed by Cremer and Kraka [51] was very appropriate to characterize the degree of covalency of a bond, the more negative the H(r) value, the more stabilizing the interaction. One can also employ the -V(r)/G(r) ratio as another useful description, the -V(r)/G(r)<1 is characteristic of a typical ionic bond; and -V(r)/G(r)>2 is diagnostic of a classical covalent interaction. As shown in Table 5, the ▽2ρ values are positive for all An-C bonds studied, which indicates the predominant closed-shell An-C interaction. -8-

Meanwhile, from negative H(r) values and low -V(r)/G(r) ratio (slightly larger than 1), it can be concluded that the An-C bonds have extremely weak covalent nature. The Th-C bond has higher covalency than the rest An-C bonds, as revealed by its larger ρBCP(r) values, -V(r)/G(r) ratio and more negative H(r) values, this result is consistent with the shorter Th-C bonds and higher adsorption energy mentioned above. On the other hand, the interaction of Am with graphene surface is typically physisorption nature as evidenced by its topological parameters shown in Table 5. On the whole, all topological parameters indicate that the An-C bonds in studied An-graphene are predominantly ionic, which is also supported by the results of electron localization function (ELF) [52-54] and localized orbital locator (LOL) [55], as shown in Table 5. Table 5. Topological parameters for An-C bond critical points (BCP) in studied species Species

ρ(r)

▽2ρ

H(r)

G(r)

V(r)

-V(r)/G(r)

G(r)/ρ(r)

ELF

LOL

Th-graphene Pa-graphene U-graphene Np-graphene Pu-graphene Am-graphene Cm-graphene

0.066 0.041 0.042 0.040 0.038 0.028 0.038

0.097 0.117 0.120 0.117 0.115 0.088 0.113

-0.017 -0.004 -0.004 -0.003 -0.002 -0.001 -0.003

0.041 0.033 0.034 0.033 0.031 0.023 0.031

-0.058 -0.037 -0.038 -0.036 -0.034 -0.023 -0.034

1.415 1.121 1.118 1.091 1.097 1.000 1.097

0.621 0.805 0.810 0.825 0.816 0.821 0.816

0.36 0.16 0.16 0.15 0.13 0.11 0.14

0.43 0.30 0.30 0.29 0.28 0.26 0.29

3.5 Molecular orbital analyses To deeply understand the interactions between actinide atoms and the graphene surface, the molecular orbitals (MOs) relevant to the An-C bonds were displayed in Fig. 4, and the orbital compositions are collected in Table 6. The energy levels of the bonding MOs for studied complexes gradually ascend from Th to Am, and then decrease to Cm, suggesting the affinities between the actinides and graphene surface decrease in the order of Th>Pa>U>Np>Pu>Cm>Am, showing the similar trends to the adsorption energy. The energy levels of Am-graphene and Cm-graphene complexes are much higher than those of other studied complexes (Fig. 4), which indicate the weaker affinities between Am/Cm and graphene surface. As Fig. 4 shows, one bonding orbital (HOMO) and one antibonding orbital (LUMO) relevant to An-C -9-

chemical bonds exist in Am/Cm-graphene complexes, on the other hand, there are two bonding orbitals relevant to An-C interaction in other studied complexes. The orbital overlaps between actinides and graphene surface in Am-graphene and Cm-graphene are weaker than other studied complexes, as revealed by orbital compositions. The contribution from Am/Cm atom (6d) to bonding orbital is only 9%/18%, and is significantly less than other counterparts, as shown in Table 6. In Th-graphene species, the bonding orbitals show π characteristics derived from orbital overlaps of 6d (Th) and 2p (C) electrons. Th-graphene species has the lowest energy levels of bonding orbitals, and is consistent with its high stability. In Pa-graphene, U-graphene and Np-graphene species, both 6d and 5f electrons of actinides participate in the chemical bondings. The orbital overlaps between Pu-5f and C-2p result into σ characteristics of Pu-C bonds (Fig. 4). It is interesting that the 6d-electron contributions to bonding orbitals are gradually decreased from Th to Pu, in consistent with the change trends of adsorption energy and MO energy level. It is meanwhile to note that the 5f-electron contribution to bonding orbitals increase because that the 5f electrons are more and more diffuse from Th to Pu. On the other hand, the 5f electrons were not involved in chemical bonds in Am/Cm-graphene systems due to half-fill 5f occupancy as shown in Table 4. The orbital overlaps in Cm-graphene species are more significantly than that in Am-graphene species, which is inconsistent with the higher stability of Cm-graphene species. We also analyzed the overlap population density-of-states (OPDOS) between An atoms and the neighboring carbon atoms in graphene to understand the interaction between An atoms and graphene. As Fig. 5 shows, one distinct peak is found below -3eV, which can be ascribed to the direct orbital overlaps between An atoms and graphene, this is in line with molecular orbital analyses aforementioned. The predominant electrostatic interaction between Pu/Am/Cm and graphene is clearly revealed by their weak OPDOS peaks. Moreover, the intensity of OPDOS is gradually decreased from left to right across actinide series, suggesting the decreasing interaction between An atoms and graphene.

- 10 -

Table 6. Bonding orbitals composition for the studied An-graphene. Species

Orbitals

Th-graphene

HOMO

Th (5f)

-

Th (6d)

48%

C (2p)

42%

HOMO-1 HOMO-2 HOMO-3 HOMO HOMO-1 HOMO HOMO-1 HOMO-1 HOMO-2 LUMO HOMO LUMO HOMO

Th (5f) Pa (5f) Pa (5f) U (5f) U (5f) Np (5f) Np (5f) Pu (5f) Pu (5f) Am (5f) Am (5f) Cm (5f) Cm (5f)

9% 20% 9% 14% 25% 25% 50% 50% -

Th (6d) Pa (6d) Pa (6d) U (6d) U (6d) Np (6d) Np (6d) Pu (6d) Pu (6d) Am (6d) Am (6d) Cm (6d) Cm (6d)

34% 21% 16% 31% 29% 18% 18% 9% 9% 24% 18%

C (2p) C (2p) C (2p) C (2p) C (2p) C (2p) C (2p) C (2p) C (2p) C (2p) C (2p) C (2p) C (2p)

52% 59% 49% 45% 50% 45% 43% 28% 21% 78% 84% 62% 71%

Pa-graphene U-graphene Np-graphene Pu-graphene Am-graphene Cm-graphene

Orbital composition

3.6 Charge Decomposition Analysis (CDA) We reviewed the interaction of orbitals in the molecular models (An-C6H6) to provide useful description of orbital interaction nature by analyzing charge transfer between An and C6H6 fragments. The CDA [41] and ECDA [42] methods were used to probe how charges are transferred between different fragments in targeted complexes. The idea of CDA is to quantify the charge donation and back-donation between the metal fragment and ligands in the complexes based on fragment orbitals. The most remarkable feature of CDA is that electron transfer can be decomposed to the contribution of complex orbitals. ECDA takes into account the electron polarization effect (PL) in addition to the charge-transfer effect (CT). These two methods were extensively used to understand the charge transfer mechanism of actinyl complexes [56-57]. Table S5 in the ESI collects the amount of the net charge transfer from the An atoms to benzene fragment in AnC6H6 molecules calculated with ECDA method. The net charge transfer from the An atoms to benzene fragment in the analogous molecules decreases in the order of Th> Pa> U> Np> Pu> Cm> Am, and shows an excellent consistency with the results of stability. This trend is also evidenced by the - 11 -

predictions of MO and OPDOS analyses mentioned above. We take ThC6H6 and AmC6H6 as an example to analyze the charge transformation between An and C6H6 fragments. As Fig. 6 (a) shows, there are obvious orbital interactions between the 6d (7s) orbitals of Th and the frontier orbitals of benzene in bonding orbitals of ThC6H6 molecule. On the other hand, none orbital interaction between Am and benzene can be found for AmC6H6 as shown in Fig. 6 (b), this can be used to explain the extremely weak affinity between Am and graphene surface. By reviewing the orbital-interaction diagrams of the analogous AnC6H6 molecules (Fig S1-Fig S5 in ESI), we can conclude that the 6d orbitals of An atoms participate in the bonding to a higher degree than the 5f orbital. Overall, the CDA method provides us a useful evaluation of the donor-acceptor interaction in actinide complexes.

4. Conclusion In summary, the structures and bonding nature of actinides (Th-Cm) adsorbed graphene were studied with all-electron ZORA-DFT methods. The actinide atoms are stably attached on the hollow site of graphene surface. Analyses on magnetic moments show that unpaired electrons mainly come from 5f shell with a little contribution from 7s and 6d shells due to the 5f-electron delocalization. The values of adsorption energies increase in the order of Th >Pa >U >Np >Pu > Cm >Am. Interestingly, the strong linear correlation between 6d occupancy numbers and adsorption energy was found, implying the importance of 6d-electron of actinides in participation of chemical bonds. QTAIM results indicate that An-C interactions show predominately closed-shell characteristics. Th-C chemical bonds is partial covalent, as observed by its topological parameters due to the formation of π-character bonds from the overlaps of 6d (Th) and 2p (C), however, Am-C bond is a type of electrostatic interaction. Molecular orbital analyses were also performed to understand the bonding interaction. The participation of 5f (6d)-electron (An) into bonding orbitals are gradually enhanced (weakened) from Th to Pu. The CDA analyses indicate that charge transfers from An to benzene decrease in the order of Th >Pa >U >Np >Pu > Cm >Am, showing the same trend to the stability. The CDA also suggests that the 6d - 12 -

orbitals of An atoms participate in the bonding to a higher degree than the 5f orbital. We hope that our work is useful for the understanding of interaction nature in An-graphene complexes.

Acknowledgments This work was supported by the National Natural Science Foundation of China (NO.11204193).

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Fig 1. Scheme representation of actinide atoms adsorbed on graphene (C 54H18) surface.

Fig 2. Linear correlation between 6d occupancy numbers and adsorption energy, a) at BP86 level of theory, b) at TPSS level of theory.

Fig 3. Molecular graphs of An-graphene with topview (a) and sideview (b). The colour scheme identifying critical points is as follows: cyan ball for attractors, blue ball for bond critical points (BCP), red ball for ring critical points (RCP), green ball for cage critical points (CCP). - 19 -

Fig 4. Isosurfaces and energy levels of α-spin molecular orbitals relevant to An-C bonds in titled An-graphene species

Fig 5. Overlap population density of states (OPDOS) for An-graphene systems studied.

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Fig 6. Partial CDA of Kohn–Sham orbital (α-spin) energy diagram of Th-C6H6 (a) and Am-C6H6 (b).

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All-electron ZORA-DFT calculations were performed to understand the adsorption of actinide atoms (An=Th-Cm) on graphene surface. The delocalization of 5f-electron result to high magnetic moments. An-C interactions are predominately closed-shell characteristics. The participation of 6d(5f)-electron into bonding orbitals are gradually weakened (enhanced) from Th to Pu suggesting the diffuse of 5f electrons. The 6d orbitals of An atoms participate in the bonding to a higher degree than the 5f orbital.

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