Unanticipated favoured adsorption affinity of Th(IV) ions towards bidentate carboxylate functionalized carbon nanotubes (CNT–COOH) over tridentate diglycolamic acid functionalized CNT: density functional theoretical investigation

Abstract

The hybrid B3LYP density functional and TZVP basis set in conjunction with COSMO solvation approach have been used successfully to predict the free energy of adsorption for Th⁴⁺ ions with pristine CNTs, oxidized CNTs (CNT–COOH) and diglycolamic acid functionalized CNTs (CNT–DGA). Experimentally reported values of adsorption capacities of Th⁴⁺ by the above three types of CNT indicate that CNT–COOH has the strongest binding with Th⁴⁺, whereas p-CNT has the lowest; CNT–DGA shows less adsorption than CNT–COOH, although the former has tridentate ligands on CNTs' surfaces. This experimental observation has been demonstrated by DFT theoretical studies: gas phase calculation does not match with the above experimental fact, whereas, solvent phase calculation in the presence of nitrate ions, a more realistic approach, is able to explain. Free energy of complexation between Th⁴⁺ and CNT–COOH is higher than that of CNT–DGA in all available models of complexation reaction viz. bare Th⁴⁺ in aqueous nitrate medium, octahydrated Th⁴⁺ in nitrate and thorium nitrate ion pair in aqueous solution. The experimental fact that the presence of oxidized fullerene C₆₀ enhances the Th⁴⁺ adsorption by oxidized CNT has also been theoretically corroborated as oxidized C₆₀ has a quite high binding energy for Th⁴⁺. Present computational calculation in the search for the best nano carbon based Th⁴⁺ adsorbent parallel with experimental verification might be helpful for the design of effective nanomaterials to be used in the treatment of radioactive liquid waste.

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Introduction

Thorium is a long-lived naturally occurring radionuclide widely distributed over the earth's crust. The use of thorium as a source of fissile material for the manufacture of nuclear fuel as well as the reprocessing of nuclear fuel can also concentrate this element.¹ The presence of thorium metal ions in the environment is of important concern due to its toxicity and health effects on human. Although direct toxicity of thorium is low due to its stability at ambient temperature, when nitrate enters living organisms, it is mainly localized in the liver, spleen and marrow and precipitates in hydroxide form.² Efficient removal of thorium from waste streams before discharge to the environment is, hence, an essential field to explore. One indirect importance of thorium separation studies is that, it has only +IV stable oxidation state in solution and hence, has been selected as a chemical analogue for other tetravalent actinides.³

In recent years, attention has been paid to the use of nano-structured materials, especially carbon nanotubes (CNTs), as a high capacity adsorbent material.⁴ Due to their large specific surface area, hollow and porous structures along with high mechanical, chemical and thermal stability, CNTs are widely being used as a promising adsorbent for metal ions and organic pollutants.^5–9 The adsorption capacities of these hydrophobic materials have been enhanced by introducing hydrophilic sites on its surfaces by chemical oxidation process which results in the introduction of the oxygen-containing electro-donating functional groups such as COOH, OH or C=O. The improved adsorption by oxidized CNTs compared to its pristine form has been reported by several studies.^10–17 Oxidation thus by incorporating of carboxylic or phenolic hydroxyl group on the surface of CNTs provides active sites for further chemical modifications. Desired functionalities, e.g., amine,¹⁸ thiol,¹⁹ histidine,²⁰ tannic acid,²¹ hydroquinone,²² EDTA,²³ phosphinic acid,²⁴ starch,²⁵ polyacrylamide²⁶ etc., have been covalently introduced on to the surface of CNTs for selective and more sensitive separation of metal ions and organics.

Separation of tetravalent thorium, Th(IV), from aqueous solution by pristine multi-walled carbon nanotues (MWCNTs) and oxidized MWCNTs have been reported.^27–30 Diglycolamic acid (DGA), a tridentate and CHON based ligand, -functionalized CNTs³¹ were used for separation of Th(IV) from aqueous solution in our previous paper. From these studies it has been seen that oxidized CNTs have better adsorption performances than that of pristine and DGA functionalized CNTs. The presence of bi-dentate carboxylic acid ligands on the surface of the CNT enhances the Th(IV) binding up to adsorption capacity of 132 mg g⁻¹.³⁰ Whereas tridentate DGA ligand on CNT have shown nearly ten time lower adsorption.³¹ These interesting observations may be understood by considering the molecular approach of complexation of Th(IV) metal ion with pristine, oxidized and DGA-functionalized CNTs. Recent research has revealed that the presence of oxidized (carboxylated) fullerene enhances the Th(IV) adsorption efficiency of oxidized CNTs.³⁰ This interesting observations can also be theoretically examined parallel with above calculations to understand the nature of binding of Th(IV) with different kinds of carbon nanomaterials.

In this paper, quantum chemical calculations for the interaction of Th(IV) ion with pristine (p-CNT), oxidized or carboxylic acid (COOH) functionalized (CNT–COOH) and DGA functionalized CNTs (CNT–DGA) have been extensively studied by density functional theory (DFT). Electronic structures, energetics and thermodynamics of the interaction of Th(IV) ions with pristine CNT, CNT–COOH and CNT–DGA were described to look insight the complexation and hence, adsorption efficiencies of these carbon nano-structures towards Th(IV). The trend of variation of adsorption capacities of two types of CNTs is successfully correlated with theoretically calculated structural and thermodynamic parameters. The interactions of Th(IV) with oxidized fullerene was compared with the oxidized CNT.

Computational methodology

The optimized geometry, total energy and vibrational IR frequency of tetravalent thorium ion complexes with different type of CNTs were computed by generalized gradient approximation (GGA) using BP86 density functional employing SVP basis set³² as implemented in Turbomole suite of program^33,34 i.e. O(7s4p1d)/[3s2p1d], N(7s4p1d)/[3s2p1d], C(7s4p1d)/[3s2p1d], H(4s1p)/[2s1p], Th(14s13p10d8f1g)/[10s9p5d4f1g]. Small-core pseudopotentials with 60 electrons as the core for Th has been included in the basis set using relativistic effective core potential (ECP)³⁵ approach, while for light atoms C, H, O, and N the polarized all-electron basis set was considered. The zero point energy and thermodynamic correction to the total energy were made to compute the free energy at T = 298.15 K. Further, single point energy calculation was performed on all the optimized complexes using hybrid B3LYP functional³⁶ and TZVP basis set³³ i.e. O(11s6p2d1f)/[5s3p2d1f], N(11s6p1d)/[5s3p1d], C(11s6p2d1f)/[5s3p2d1f], H(5s2p1d)/[3s2p1d]. BP86 functional consists of Becke B88 exchange functional³⁷ and Perdew P86 correlation functional³⁸ and was found to be successful in predicting molecular geometries of lanthanides and actinides complexes.³⁹ The solvent effect in the energetic was incorporated employing conductor like screening model (COSMO).⁴⁰

The complexation ability of CNTs (p-CNT or o-CNT or f-CNT) with metal ions can be evaluated from the gas phase binding energy (ΔE). The ΔE of the metal ion (M⁴⁺) and CNTs (L) complexation reaction,

M⁴⁺ + L = M⁴⁺L (1)

is defined by the following general relation,

ΔE = E_{M⁴⁺–CNT} − (E_M⁴⁺ + E_CNT) (2)

where, E_{M⁴⁺–CNT}, E_M⁴⁺ and E_CNT refer to the energy of M⁴⁺–CNT complex, M⁴⁺ ion and the free CNT system, respectively.

The thermal correction to the electronic energy (E_el), enthalpy (H) and free energy (G) of the optimized structures has been performed to predict the thermodynamic parameters.⁴¹ The thermal and zero point energy corrected binding energy is

ΔU = U_{M⁴⁺–CNT} − (U_M⁴⁺ + U_CNT) (3)

where U_{M⁴⁺–CNT}, U_M⁴⁺, and U_CNT represent the internal energy of the M⁴⁺–CNT complex, M⁴⁺ ion and the free CNT system, respectively.

The binding enthalpy (ΔH) and binding free energy (ΔG) for the metal ion–CNT complexation reaction in eqn (1) are calculated using the following standard thermodynamic relations.

ΔH = ΔU + ΔnRT (4)

ΔG = ΔH − TΔS (5)

One of the key properties to be calculated in the metal ion–ligand complexation is the free energy of extraction (ΔG_ext). The metal ion–ligand complexation reaction is modelled using three schemes. In the Scheme–1, the metal ion and the nitrate ion is considered to be separately hydrated species as follows:

In Scheme–2, the complexation environment is similar as in Scheme–1, barring the Th⁴⁺ which is considered to be explicitly octa hydrated.

In Scheme–3, the thorium metal cation and nitrate anion is considered to be in the ion pair forms as frequently used by Wang et al.⁴² by citing the presence of high HNO₃ concentration.

We have performed single point energy calculation using optimized structures obtained from the BP86 functional with hybrid B3LYP functional as it includes the non-local HF contribution. Hybrid DFT was found to be superior to GGA functional for thermochemistry of actinides as reported earlier.⁴³ Relativistic effects, which are mandatory to include for heavy elements such as lanthanides and actinides, were accounted for by relativistic pseudopotentials, similar to previous studies.^42,43

Most of the metal ion extraction takes place from the aqueous solution phase aided by ligand. Hence, the consideration of solvent effect on the complexation of the ligand moiety with metal ion in the QM calculation is thus indispensable. COSMO is an improved solvation model, where the polarization charges of the solute is calculated in a continuum solvent using scaled conducting boundary condition and has been used successfully for the free energy calculation in solution containing the first solvation shell.⁴⁴ Further, there is very little effect on the solvation energy using the optimized geometry at the solvent phase.⁴⁵ Hence, the aqueous solvent effect was inducted by performing single point energy calculation using the optimized geometry obtained from BP86 level of theory employing COSMO solvation model as implemented in Turbomole quantum chemistry package.

The MOLDEN graphical program⁴⁶ was used for the visualization of various molecular geometry and structural parameters. Orbital population analysis was performed using natural population analysis (NPA)⁴⁷ which exhibits improved numerical stability and describes better the electron distribution in compound containing metal ions. Population analysis has also been performed by the natural bond orbital method⁴⁸ at B3LYP/TZ2P level of theory using natural bond orbital (NBO) program⁴⁹ under ADF program package.⁵⁰ NBO analysis focuses on the intermolecular orbital interaction between the filled donor and empty acceptor NBOs of M–L complexes by estimating their energy by second-order perturbation theory. For each donor NBO (i) and acceptor NBO (j), the stabilization energy E⁽²⁾ associated with electron delocalization between donor and acceptor is estimated as,

where q_i is the orbital occupancy, ε_i, ε_j are the diagonal elements and F_i,j is the off diagonal NBO Fock matrix element.

Strength of M–L interaction can also be evaluated by the amount of change transfer (ΔN)⁵¹ which can be calculated by equation eqn (9) as,

The χ and η, represent absolute electronegativity and absolute hardness of M or L, respectively, estimated as.

I and A correspond to ionization potential and electron affinity respectively and can be obtained using Koopmans' theorem⁵² as,

I = −E_HOMO, A = −E_LUMO (11)

E_HOMO and E_LUMO are the energy of highest occupied and lowest unoccupied molecular orbital of the M or L respectively and can be determined from the DFT calculation. Point to be noted that the Koopmans' theorem does not include the orbital relaxation in the calculation of I and A, and is quite accurate only for restricted Hartree–Fock system.

Recent literature reports on DFT based theoretical studies of adsorption of gases^53–56 and drug molecules on CNTs⁵⁷ have revealed that dispersion-corrected-DFT should be used instead of DFT for studying the interactions between CNT surface and gases/drug molecules. Long-range electron correlation which is responsible for van der Waals (dispersive) forces is very important for the interaction of organic molecules on surfaces. As the dispersive interactions play a key role for determining the orientation of the organic molecules on the CNT surfaces, it is necessary to add the dispersion-corrected energy term with the standard DFT energy. Our study involves the adsorption of tetra positive charged thorium metal ion on CNTs. To study the effect of dispersion interaction, we have carried out dispersion-corrected DFT calculation of interaction of Th⁴⁺ ion with CNT-side surface, CNT-open end, CNT–COOH and CNT–DGA in absence of nitrate anions. Initially, all the structures were optimized at BP86/SVP level of theory with dispersion-corrected DFT of Grimme's D3 scheme as implemented in Turbomole suit of program. The single point energy was calculated at two level of theory – (i) B3LYP/TZVP, and (ii) Grimme's D3 scheme dispersion-corrected B3LYP/TZVP. Adsorption binding energies of Th⁴⁺ with all CNT structures were calculated and compared with the same calculated from DFT without dispersion-correction.

Results and discussion

Structural parameters

The chemical species of interest are hydrated thorium and hydrated thorium nitrate, and hence these species are optimized and the structures are presented in Fig. 1. In hydrated Th⁴⁺–(H₂O)₈, the central Th metal ion was coordinated to 8 water molecules in distorted octa coordinated fashion. The calculated Th–O (see Table 1) bond distance of 2.48 Å was found to be very close to the experimental results of 2.45 Å and hence confirm the reliability of the present method of calculation. The coordination of 8 water molecules was reported earlier using LUX experiment.⁵⁸ But, EXAFS studies reported a varied coordination number of Th⁴⁺ ion of 9–11 with a Th–O distance of about 2.45Å.^59–61 Hence, further, hydrated Th⁴⁺ with 9, 10 and 11 numbers of H₂O molecules were optimized and shown in Fig. 1. The calculated Th–O (see Table 1) bond distances of 2.52 Å (Th⁴⁺–(H₂O)₉) and 2.55 Å (Th⁴⁺–(H₂O)₁₀) were found to be higher compared to the experimental results. It can clearly be seen from the structure of Th⁴⁺–(H₂O)₁₁ that 11 water molecules cannot be accumulated in the first sphere of solvation shell; 9 water molecules reside in the first shell and rest 2 nest in the second solvation shell. The average Th–O bond distances of the H₂O's of first solvation shell are same (2.52 Å) as Th⁴⁺–(H₂O)₉ which is higher compared to the experimentally reported value. Owing to the impact of second water coordination sphere in the hydration of Th⁴⁺, a structure of 24H₂O hydrated Th⁴⁺ was optimized and it is seen that 8H₂O molecules occupy the first coordination sphere with 2.45 Å Th–O bond length which is exactly same with experimental results. In order to find out the most stable hydrated species, free energy of hydration was calculated after inclusion of standard state entropy correction.⁶² The calculated results are presented in Table 2. From the table it is seen that the free energy of hydration for Th⁴⁺–(H₂O)₈ ion is higher than that of Th⁴⁺–(H₂O)₉ (by −0.15 kcal mol⁻¹), Th⁴⁺–(H₂O)₁₀ (by −7.18 kcal mol⁻¹) and Th⁴⁺–(H₂O)₂₄ (by −19.90 kcal mol⁻¹) indicating its higher stability and hence higher chance of occurrence in the aqueous environment. Although the difference in Gibb's hydration energy between Th⁴⁺–(H₂O)₈ and Th⁴⁺–(H₂O)₉ or Th⁴⁺–(H₂O)₁₀ is small, Th–O bond length of latter does not tally with the experimental one whereas former shows very similar length. On the other hand, although the Th–O bond length is very good match with experimental one for Th⁴⁺–(H₂O)₂₄, the free energy of hydration is quite lower than that of Th⁴⁺–(H₂O)₈. Therefore, aqueous Th⁴⁺ ion is modelled using Th⁴⁺–(H₂O)₈ species. The coordination of 8 water molecules in the first solvation shell was further confirmed performing ab initio molecular dynamics simulation (AIMD) using VASP package (ESI, Fig. S7†). In presence of nitric acid, the nitrate ions displace the water molecules from the first shell of solvation leading to the formation of Th(NO₃)₄ which is confirmed from the free energy of reaction (Table 2). The optimized structure of Th(NO₃)₄ is presented in Fig. 1. All four nitrate ions are found to be coordinated in bidentate mode. It is interesting to check whether the Th(NO₃)₄ species remains as hydrated form in the aqueous environment. In view of this, di-hydrated structure of Th(NO₃)₄ is optimized and the structure is shown in Fig. 1. In Th(NO₃)₄(H₂O)₂, the central Th metal ion was coordinated to the 4 nitrate ion in bidentate mode and 2 water molecules leading to deca coordination. The formation of Th(NO₃)₄(H₂O)₂ was confirmed by the negative free energy of reaction (Table 2).

Fig. 1 Optimized structures of hydrated Th⁴⁺ ions and Th(NO₃)₄ at BP/SVP level of theory.

Table 1 Structural parameters of hydrated species of Th⁴⁺ and Th(NO₃)₄

Chemical species	M–OH (Å)	M–ON (Å)
a Experimental values are given in parenthesis.
Th^4+(H2O)8	2.48
	(2.45)^a^,49
Th^4+(H2O)9	2.52
Th^4+(H2O)10	2.55
Th^4+(H2O)24	2.45, 4.54
	(1st shell, 2nd shell)
Th(NO3)4		2.44
Th(NO3)4(H2O)2	2.59	2.48
	(2.57)^48	(2.46)^48

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Table 2 Free energy of hydration (in kcal mol⁻¹) for hydrated species of Th⁴⁺ and Th(NO₃)₄ at B3LYP/TZVP level of theory

Chemical reaction	Gas phase	Aqueous phase
Th^4+ + 8H2O = Th^4+–(H2O)8	−693.92	−1325.39
Th^4+ + 9H2O = Th^4+–(H2O)9	−716.41	−1325.24
Th^4+ + 10H2O = Th^4+–(H2O)10	−725.12	−1318.21
Th^4+ + 24H2O = Th^4+–(H2O)24	−932.73	−1305.49
Th^4+–(H2O)8 + 4NO3 = Th(NO3)4 + 8H2O	−913.29	−60.23
Th(NO3)4 + 2H2O = Th(NO3)4–(H2O)2	−13.91	−13.23

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For our modelling studies, we have considered pristine CNT, COOH and DGA functionalized CNT. The CNT considered here is a (8, 0) zigzag single-walled CNT which consists of four unit cells with tubular length of 5.78 Å width of 6.40 Å. We have considered one COOH and DGA unit anchored on the open pore of the (8, 0) zig-zag CNT with 4 unit cells as earlier studied.⁶³ The optimized geometries of pristine and COOH and DGA functionalized CNT are displayed in Fig. 2. In the optimized structures, the C–C and C–H bond distance of CNT unit was found to be 1.44 Å and 1.10 Å. In CNT–COOH, the COOH group was found to be aligned along the axis of the CNT. It has been seen that the diglycolamic acid group was wrapping around the cylindrical backbone of nanotubes (Fig. 2). In the DGA unit, the carbonyl, C=O bond distance was found to be 1.22 Å and carboxylate C=O bond distance was found to be 1.31 Å. The ethereal C–O bond distance was found to be 1.39 Å. Three oxygen donor atoms are projecting in similar directions like in free diglycolamic acid. The bond length of two C=O groups of DGA unit was found to be 1.21 Å and 1.22 Å respectively.

Fig. 2 Optimized geometries of pristine and COOH and DGA functionalized CNT at BP/SVP level of theory.

The optimized structures of complexes of Th⁴⁺ with p-CNT with and without nitrate ions are presented in Fig. 3 and S1,† respectively. Although open edges are more reactive than the sidewall surface of p-CNT, we have considered the binding of thorium from both directions. The Th(NO₃)₄(H₂O)₂ species was found to be lying outside of the side surface and open end of the CNT. The calculated Th–O (O from NO₃ and H₂O) and Th–C are displayed in Table 3.

Fig. 3 Optimized structure of complexes of Th⁴⁺ with non-functionalized/pristine CNT along with nitrate ion: (a) interaction from sidewall of CNT (CNT_S) and (b) from open edges of CNT (CNT_O).

Table 3 Bond distances in Å from Th⁴⁺ metal centre for complexes/system under consideration

Bond	System of Th^4+ bonded with
	CNT-side surface (in presence of NO3 and H2O)	CNT-open end (in presence of NO3 and H2O)	CNT–COOH (in absence of NO3 & H2O)	CNT–DGA (in absence of NO3 & H2O)	CNT–COOH (in presence of NO3 & H2O)	CNT–DGA (in presence of NO3 & H2O)
a M–C: distances between metal and nearest six carbon atoms of a hexagon the CNT.b First one is the distance of M–O=C bond and second one is of M–O–C of –COOH group.c Average bond distance of two Th–Ocarbonyl of DGA unit of CNT–DGA.
Th–O(NO3)	2.49	2.49	—	—	2.52	2.47
Th–O(H2O)	2.56	2.58	—	—	2.63	2.45
Th–C^a(CNT)	5.451	—	—	—	—	—
Th–H(CNTedge)	—	4.703	—	—	—	—
Th–O^b(COOH)	—	—	2.11, 2.42	—	2.36, 3.82	—
Th–Ocarbonyl^c(DGA)	—	—	—	2.21	—	2.62
Th–Oether(DGA)	—	—	—	2.48	—	2.71

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The optimized structures of complex of Th⁴⁺ with functionalized CNT–COOH and CNT–DGA in absence of nitrate ion are presented in Fig. 4 and the characteristic bond distances are shown in the figure as well as given in Table 3. From the Fig. 4(a) it is seen that the COOH group is little tilted from the axis of the CNT after complexation with Th⁴⁺ ion. Th–O bond distance was found to be 2.11 Å and 2.42 Å. In Fig. 4(b), the Th⁴⁺ ion is found to be directly coordinated to the three donors O atoms of the DGA moiety. All three donor O atoms and the coordinated metal ion are lying in the same plane. It is interesting to mention that though the metal ions and three donor O atoms are lying in the same plane, the M–O bond length with three O atoms are not same in length. The M–O (O of C=O group) bond length were found to be 2.20 and 2.21 Å and one M–O (ethereal O) bond length was found to be 2.48 Å. The shorter M–O bond length for C=O group compared to M–O bond length of ethereal O suggest that former has stronger interaction ability than the later. In order to find out the effect of CNT on the interaction, we have performed the calculation by replacing CNT with H atom in the CNT–COOH and CNT–DGA motifs. The optimized structures are presented in Fig. S2† and characteristics bond distances are shown in Table S1.†

Fig. 4 Optimized structures of Th⁴⁺ complex with (a) COOH and (b) DGA functionalized CNT in absence of nitrate ions at BP/SVP level of theory.

The optimized structures of complex of Th⁴⁺ ion with functionalized CNT–COOH and CNT–DGA in presence of nitrate ion are presented in Fig. 5 and the characteristic bond distances are shown in the figure as well as given in Table 3. From the Fig. 5(a) it is seen that the only the carbonyl O of COOH group (unlike in case of Th⁴⁺ complex with CNT–COOH in absence of nitrate ions where both the O centres were bonded to metal ions) is coordinated to the Th⁴⁺ ion and it is lengthened to 2.36 Å in presence of nitrate ion from 2.11 Å in absence of nitrate ions. The presence of nitrate ions and water molecules made the carboxylic group to bind in monodentate mode with more electro-donating carbonyl O centre. Thorium ion coordinated to four nitrate ion in bidentate mode and one each with water and carbonyl O of COOH group. The Th–O (O of NO₃) bond distance was lengthened due to the strong coordination from the carbonyl O atom of CNT–COOH adsorbent. In CNT–DGA complex, Fig. 5(b), The Th⁴⁺ ion is found to be directly coordinated to the three donor O atoms of the DGA moiety, six donor atoms from four nitrate ions (two bidentate and two monodentate mode) and one from aqua leading to deca coordination. The Th–O (oxygen of NO₃) is found to be varied from 2.32 Å to 2.59 Å and the Th–O (carbonyl oxygen of DGA) is found to be varied from 2.53 to 2.72 Å indicating asymmetrical nature of bonding from the identical carbonyl bonding. The Th–O (etheric oxygen of DGA) is found to be 2.71 Å. Further, the M–O bond length in hydrated species was found to be larger than the M–O bond length of H₂O attached to the CNT–DGA–Th complex. The M–O bond distance of NO₃⁻ ion is found to be smaller than the M–O of H₂O indicating the stronger interaction of metal ions with NO₃⁻ ion group than H₂O. In the complex of Th⁴⁺ ion with CNT–DGA, the elongation of the of the two carbonyl C=O bonds (1.31, 1.30 Å) from free CNT–DGA (1.21, 1.22 Å) and ethereal C–O bonds (1.45 Å) from free CNT–DGA (1.39 Å) refers to its participation in the binding, whereas the same carboxylic C=O bond distance before (1.30 Å) and after (1.31 Å) binding refers its non-participation in the complexation. The shorter Th–O bond of the C=O (2.36 Å) of the CNT–COOH than that of C=O (2.62 Å) of CNT–DGA clearly aimed towards the greater affinity of CNT–COOH for Th⁴⁺ adsorption than CNT–DGA.

Fig. 5 Optimized structures of Th⁴⁺ complex with (a) CNT–COOH and (b) CNT–DGA in presence of nitrate ion at BP/SVP level of theory.

Binding energy/free energy of complexation in absence of nitrate ions

The gas phase binding energy, which plays an important role in the initial screening as well as predicting adsorption capacity of an adsorbent material towards metal ions, is calculated using different possible reaction routes. The calculated values of binding energy are presented in Table 4. The gas phase binding energy of p-CNT with bare metal ion was found to be quite high; the interaction of Th⁴⁺ from sidewall and open edge surface of p-CNT have nearly similar binding energy. The aqueous phase free energy of the binding is four times higher for sidewall interaction than that of open edges of p-CNT; may be the consequence of interaction of water molecules with the reactive dangling bonds at the open edges of CNT. It is seen that the binding energy of bare Th⁴⁺ ion with CNT–COOH and CNT–DGA in gas phase in absence of nitrate ion is very high. The CNT–DGA shows more electronic binding capacity than CNT–COOH. This might be due to the more number of donor atom (3 in CNT–DGA) than CNT–COOH (2 donor atoms). In order to have further insights, NPA (Table 5), HOMO–LUMO (Table S2†) and NBO (Table 6) analysis were performed. There is a considerable transfer of charge to the ligands as evident from the residual charge values in Table 5 on the metal centre leading to higher interaction energy. Increase of electronic population in the s, d and f orbitals of the metal ions after complexation signals to the strong covalent bonding between the metal and ligands. The absolute electronegativity and absolute hardness of CNT–COOH and CNT–DGA are almost close, the HOMO–LUMO gap of CNT–COOH and CNT–DGA is also identical (Table S2†). These has also been reflected in the identical values of ΔN which indicates that their interaction with Th⁴⁺ ion should be very close (Table S2†). But actually, the gas phase interaction energy of CNT–DGA is higher that of CNT–COOH and hence, ΔN unable to correlate the interaction energy values. Further it was seen that the higher interaction of CNT–DGA compared to CNT–COOH is reflected neither from the residual charge on the thorium metal ion which is found to be higher for the former than of latter (NPA analysis) nor from the stabilization energy by NBO analysis in Table 6. NBO analysis resulted higher stabilization energy for Th⁴⁺–CNT–COOH interaction than that of Th⁴⁺–CNT–DGA establishing higher binding energy for the former. In order to investigate the role of CNT in the functionalized CNT–COOH and CNT–DGA unit, the interaction energy of the metal ions was further evaluated by replacing the CNT unit with H atom in the CNT–COOH and CNT–DGA motif. The gas phase interaction energies were found to be reduced considerably in absence of CNT (see Table S3†). The selectivity trend remains the same.

Table 4 Electronic and thermodynamic energies (in kcal mol⁻¹) of Th⁴⁺ ion with non-functionalized and functionalized CNT in absence of nitrate ion at B3LYP/TZVP level of theory^a

Complexation reaction	ΔE	ΔS	ΔH	ΔG	ΔGaq
a CNTS and CNTO refers to the surface side and open end of CNT; unit of ΔE, ΔH and ΔG = kcal mol^−1; ΔS = kcal mol^−1 K^−1.
Th^4+ + CNTS = CNTS–Th^4+	−759.60	−0.029	−759.23	−750.49	−86.82
Th^4+ + CNTO = CNTO–Th^4+	−754.57	−0.03	−754.19	−745.22	−22.31
CNT–COOH + Th^4+ = CNT–COOH–Th^4+	−792.84	−0.02	−792.00	−783.86	−105.64
CNT–DGA + Th^4+ = CNT–DGA–Th^4+	−875.61	−0.04	−874.29	−861.90	−114.57
Th^4+(H2O)8 + CNTS = CNTS–Th^4+ + 8H2O	24.94	0.238	14.63	−56.59	33.35
Th^4+(H2O)8 + CNTO = CNTO–Th^4+ + 8H2O	29.98	0.238	19.66	−51.32	97.86
CNT–COOH + Th^4+(H2O)8 = CNT–COOH–Th^4+ + 8H2O	−8.21	0.239	−18.53	−89.98	48.82
CNT–DGA + Th^4+(H2O)8 = CNT–DGA–Th^4+ + 8H2O	−90.98	0.225	−100.83	−168.02	39.89

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Table 5 Gas phase NPA for complexes/system under consideration

NPA parameters	System of Th^4+ bonded with
	CNT-side surface	CNT-open end	CNT–COOH	CNT–DGA
Charge on Th^4+ metal ion	1.902	1.892	1.719	1.768
Electron population on the orbital of s	4.201	4.20	5.312	5.179
Electron population on the orbital of p	11.998	11.998	11.973	11.962
Electron population on the orbital of d	11.056	11.059	10.643	10.788
Electron population on the orbital of f	0.835	0.844	0.349	0.299
Electron population on the orbital of g	0.004	0.004	0.002	0.002

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Table 6 Average second order stabilization energies E⁽²⁾_ij for the complexes of Th⁴⁺ with CNT–COOH and CNT–DGA using NBO analysis at B3LYP/TZ2P level of theory as implemented in ADF package^a

Complex	Donor nbo (i)	Acceptor nbo (j)	Avg. E^(2)ij kcal mol^−1
a LP = lone pair; LV = energy-sorted lone vacant orbitals.
CNT–COOH	LP-O	LV-Th	10.38
CNT–DGA	LP-O	LV-Th	7.43

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In aqueous phase, though the CNT–DGA shows higher free energy, the value has been reduced considerably due to the solvent dielectric screening on the interaction (Table 4). Since the metal ion mainly exist in hydrated form in the solution, the binding energy was evaluated using the stable hydrated Th⁴⁺–(H₂O)₈ ion species. The gas phase interaction as well as free energy was found to be reduced considerably. Even, the free energy of complexation has become positive indicating no adsorption of metal ion from the solution either by CNT–COOH or CNT–DGA if the modelling is carried out without nitrate ion in the complexation reaction. In addition, The HOMO–LUMO analysis in the aqueous phase is also not in accord with the calculated interaction energies values; the fraction of electron transfer should have been more for CNT–DGA than that of CNT–COOH (Table S2†).

One interesting observation can be seen from entropy change values of the eight reactions considered in Table 4. The first four reactions where Th⁴⁺ taken as a bare metal ions ΔS values are negative whereas in the next four reactions where Th⁴⁺ taken as octa-hydrated it is positive. The adsorption of Th⁴⁺ metal ions from aqueous to the surface of the CNTs involve two steps: (i) partial or complete dehydration of the hydrated Th⁴⁺ metal ions, and (ii) condensation of the dehydrated metal ion onto the surface of CNTs by chemical and/or physical adsorption process. The ΔS of the first step is positive as it releases the bonded water molecules from the hydrated cluster, whereas, ΔS of the second step is negative. The dehydration step is not required for the initial four reactions of Table 4 and hence owing to the condensation of random bare Th⁴⁺ ions onto the CNT surface the entropy change turn as negative. The negative free energy of these entropy disfavoured reactions has come from the high and negative enthalpy change values (Table 4). In the case of the reactions involving the octa-hydrated Th⁴⁺, although reactions are entropy favoured due to the positive or less negative values of electronic enthalpy change, the free energy change turned to be positive. Thus for the complexation reactions of hydrated Th⁴⁺ with CNTs the electronic effect dominate over the entropy effect in the calculation of Gibb's free energy.

Binding energy/free energy of complexation in presence of nitrate ions

In view of the failure of the model without nitrate ion, next we have calculated the binding/free energy for the above complexation reaction in presence of nitrate ion and the calculated values are presented in Table 7. In case of p-CNT, for both the surface and open face of CNT, the interaction energy of thorium nitrate species in gas phase was found to be negative whereas the free energy was found to be positive. Further, the CNT surface have slightly higher electronic interaction energy compared to open face of the CNT. Furthermore, the free energy of adsorption for thorium nitrate with either type of pristine CNT shows positive value confirming its inability to adsorb in solution phase which is also observed from experiments.^27,28 The next question arises whether oxidised CNT can adsorb Th⁴⁺ metal ion from the solution or not. In view of that, the binding energy and free energy for bare Th⁴⁺ metal ion in presence of nitrate ion in gas phase is evaluated and the values are presented in Table 7. It is interesting to note that both the binding energy and free energy of complexation of Th⁴⁺ ion was found to be higher with CNT–COOH than that of CNT–DGA in presence of nitrate ion which was inverse in absence of nitrate ion (Scheme – 1). Although, the role of entropy is similar as observed in the absence of nitrate ion (see Table 4). Even in solution phase also, CNT–COOH shows higher adsorption capacity than CNT–DGA and matter of fact is that the experimental results also show the same trend of adsorption capacity by this two CNT-based sorbents.^27–31 As we know that the metal ion in solution phase remains as hydrated form and hence next calculation is performed using stable hydrated Th⁴⁺–(H₂O)₈ ion species. The binding and free energy both in gas and solution phase follows the same trend i.e. CNT–COOH shows higher binding capacity over CNT–DGA (Scheme – 2). Recently, there is a practice of considering hydrated ion pair of actinide nitrate instead of their isolated species in higher nitric acid concentration.⁴² In view of this, we have also calculated the binding and free energy of complexation using hydrated ion pair (Scheme – 3). The calculated results are presented in Table 7. The calculated binding and free energy values both in gas and solution phase for thorium nitrate with CNT–COOH is shown to be negative. For CNT–DGA, binding energy is negative but the free energy is positive either in gas and solution phase. This clearly indicates that the hydrated nitrate ion pair of Th⁴⁺ ion seems to be unsuitable for modeling the adsorption reaction of ions with functionalized CNT.

Table 7 Electronic and thermodynamic energies (in kcal mol⁻¹) of Th⁴⁺ ion with non-functionalized and functionalized CNT in presence of nitrate ion at B3LYP/TZVP level of theory^a

Complexation reaction	ΔE	ΔS	ΔH	ΔG	ΔGaq
a Unit of ΔE, ΔH and ΔG = kcal mol^−1; ΔS = kcal mol^−1 K^−1.
Th(NO3)4(H2O)2 + CNTS = CNT–Th(NO3)4(H2O)2	−8.21	−0.04	−8.40	4.02	11.12
Th(NO3)4(H2O)2 + CNTO = CNT–Th(NO3)4(H2O)2	−5.70	−0.03	−6.12	4.14	16.47
Scheme – 1
CNT–COOH + Th^4+ + 4NO3 + H2O = CNT–COOH–Th(NO3)4(H2O)	−1699.0	−0.22	−1695.24	−1629.35	−200.98
CNT–DGA + Th^4+ + 4NO3 + H2O = CNT–DGA–Th(NO3)4(H2O)	−1696.83	−0.23	−1691.37	−1620.54	−188.98
Scheme – 2
CNT–COOH + Th^4+(H2O)8 + 4NO3 = CNT–COOH–Th(NO3)4(H2O) + 7H2O	−914.46	0.047	−921.36	−935.45	−46.40
CNT–DGA + Th^4+(H2O)8 + 4NO3 = CNT–DGA–Th(NO3)4(H2O) + 7H2O	−912.27	0.03	−917.50	−926.64	−34.40
Scheme – 3
Th(NO3)4(H2O)2 + CNT–COOH = CNT–COOH–Th(NO3)4(H2O) + H2O	−9.28	−0.009	−10.94	−8.23	−7.23
Th(NO3)4(H2O)2 + CNT–DGA = CNT–DGA–Th(NO3)4(H2O) + H2O	−7.09	−0.02	−6.48	1.16	5.35

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Effect of presence of C₆₀–COOH

Oxidized/carboxylated form of fullerene has also been emerging as more efficient adsorbent in recent times. Presence of hydroxylated and carboxylated fullerene (C₆₀) enhances the adsorption capacity of oxidized CNT has been established by experimentation.³⁰ Calculations have been performed for the interactions of Th⁴⁺ with carboxylated C₆₀ fullerene (C₆₀–COOH), the optimized structure of the related complex has been shown in Fig. S3,† characteristic Th–O bond lengths are shown in Table S1,† and energetic results are displayed in Table S3.† It is evident from the binding energy values that C₆₀–COOH can enhance the adsorption while companying CNT; interaction energy (−697 kcal mol⁻¹) is more than twice as compared with formic acid, replacing C₆₀ with H in C₆₀–COOH, (−292 kcal mol⁻¹). The higher absolute electronegativity and HOMO–LUMO gap (see Table S2†) of C₆₀–COOH also indicate for the strong interaction with thorium ions. It can also be seen that for the complexation with Th⁴⁺ or hydrated Th⁴⁺ the C₆₀–COOH has lower ΔN values than that of CNT–COOH and CNT–DGA. This supports the fact that former have lower binding energy (−627.06 kcal mol⁻¹) than the later (−792.84 and −930.24 kcal mol⁻¹, respectively) (Table S3†) but the considerable binding energy of C₆₀–COOH is sufficient to increase the adsorption capacity of CNT–COOH (or CNT–DGA) for Th⁴⁺ adsorption when C₆₀–COOH would be added with the functionalized CNT.

Comparison with dispersion-corrected DFT (DFT-D)

The DFT-D optimized geometric structures of pristine-CNT, CNT–COOH and CNT–DGA are shown in Fig. S4† and their complexes with Th⁴⁺ ion are shown in Fig. S5 and S6.† It is seen that all structures are similar with the DFT optimization, except the orientation of the DGA unit on CNTs is different in free CNT–DGA structure; although the Th⁴⁺ complexes of CNT–DGA structures are similar for both the cases (see Fig. 4(b) and S6(b)†). Due to the dispersive interaction the DGA molecule has taken a different orientation from the DFT optimized structure. Other conformations of the CNT–DGA may also possible owing to the flexible nature of the DGA unit attached with the CNT. But once Th⁴⁺ ion bonded with the DGA unit through tridentate chelation, the flexibility of the unit would be nearly diminished and that is why geometrical structures of Th⁴⁺ complex of CNT–DGA are similar at DFT and DFT-D level of optimization. Table S4† compares the characteristic bond distances of Th⁴⁺ complexes with CNTs, CNT–COOH and CNT–DGA without and without optimization at DFT and DFT-D. It is found that all the bond lengths are almost same and refers to identical binding environment around the metal ion.

Adsorption binding energies of CNTs, CNT–COOH and CNT–DGA with Th⁴⁺ were calculated by considering bare and hydrated metal ions. The results are depicted in Table 8. It is clearly found that the binding energy values are very close to the DFT based calculations. Difference in the energy values between DFT and DFT-D calculation is more when hydrated metal ions are considered for the complexation. This is evident as, in case of hydrated model, the presence of water molecules near the CNT surface create more dispersion interaction compared to bare Th⁴⁺ ions. Binding energy of the interactions were also compared between the energy calculations at DFT level after structural optimization at DFT-D level and the energy calculations at DFT-D level after structural optimization at DFT-D of theory (Table S5†) and it is seen that the difference in the adsorption binding energy values are not significant. Although the adsorption binding energy values are not same, but the trend of binding energy of adsorption of Th⁴⁺ by CNT-open edge, CNT-side surface, CNT–COOH and CNT–DGA are identical with the DFT calculation. Hence, there would not be any difference in the adsorption preferences of Th⁴⁺ towards above four types of CNTs considered between computational calculations done at DFT and DFT-D.

Table 8 Electronic and thermodynamic energies (in kcal mol⁻¹) of Th⁴⁺ ion with non-functionalized and functionalized CNT in absence of nitrate ion at B3LYP/TZVP level of theory with dispersion-corrected DFT of Grimme's D3 scheme

Complexation reaction	ΔE
Th^4+ + CNTS = CNTS–Th^4+	−764.28
Th^4+ + CNTO = CNTO–Th^4+	−765.84
CNT–COOH + Th^4+ = CNT–COOH–Th^4+	−793.96
CNT–DGA + Th^4+ = CNT–DGA–Th^4+	−884.54
Th^4+(H2O)8 + CNTS = CNTS–Th^4+ + 8H2O	35.14
Th^4+(H2O)8 + CNTO = CNTO–Th^4+ + 8H2O	33.58
CNT–COOH + Th^4+(H2O)8 = CNT–COOH–Th^4+ + 8H2O	5.46
CNT–DGA + Th^4+(H2O)8 = CNT–DGA–Th^4+ + 8H2O	−85.11

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Conclusion

The structures, interaction, bonding and thermodynamic parameters for the complexation of Th⁴⁺ ion with pristine CNT, oxidized CNT or CNT–COOH and CNT–DGA using DFT levels of theory are reported here. The free energy of adsorption for Th⁴⁺ ion by the three CNT based ligands was computed using the hybrid B3LYP density functional and TZVP basis set in conjunction with COSMO solvation approach. The coordination number of hydrated Th⁴⁺ ion in gas phase was determined to be 8 and was further corroborated by performing AIMD simulation using PW91 density functional. Gas phase results though provide qualitative idea about the complexation reaction it is not realistic as it does not represent the real system which takes place in solution phase. Results of aqueous phase calculation are comparable with the experimentally obtained trend of adsorption capacity of Th⁴⁺ with p-CNT, CNT–COOH and CNT–DGA. The p-CNT has positive free energy of adsorption implying zero interaction with Th⁴⁺ in aqueous phase. DGA being tridentate ligand compared to bidentate COOH, CNT–DGA was expected to be shown higher interaction/complexation with Th⁴⁺ metal ion. But, CNT–COOH has higher free energy of adsorption than that of CNT–DGA; same is reflected from their experimental Th⁴⁺ adsorption capacity values. Carboxylated C₆₀ fullerene has quite high value of binding energy with Th⁴⁺ indicating enhancement of adsorption by CNT–COOH in presence of C₆₀–COOH. Inclusion of the Grimme's dispersion correction in the calculation does not alter the preferences of adsorption of Th⁴⁺ towards all three types of CNTs studied. The present study was a modest attempt to model the complex chemical problem like the complexation reaction of Th⁴⁺ ion pristine as well as COOH and DGA functionalized CNT and can be used further for future design of functionalized CNT for the removal of Th⁴⁺ and other radionuclides from nuclear waste.

Acknowledgements

Computer Division BARC is acknowledged for providing ANUPAM Supercomputing facility.

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Footnote

† Electronic supplementary information (ESI) available: Tables S1–S5 and Fig. S1–S5. See DOI: 10.1039/c5ra16651a

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