Synthesis, Mass Spectroscopy Detection, and Density Functional Theory Investigations of the Gd Endohedral Complexes of C 82 Fullerenols

: Gd endohedral complexes of C 82 fullerenols were synthesized and mass spectrometry analysis of their composition was carried out. It was established that the synthesis yields a series of fullerenols Gd@C 82 O x (OH) y ( x = 0, 3; y = 8, 16, 24, 36, 44). The atomic and electronic structure and properties of the synthesized fullerenols were investigated using the density functional theory calculations. It was shown that the presence of endohedral gadolinium increases the reactivity of fullerenols. It is proposed that the high-spin endohedral fullerenols are promising candidates for


Introduction
Studies of the properties of fullerenes and fullerene derivatives made it possible to determine the areas of their applications [1][2][3][4][5][6][7][8][9][10][11][12][13][14], including biomedical ones. The main biomedical feature of fullerenes and most of their derivatives is the low toxicity and the ability to be removed from the body [4]. In particular, pristine fullerenes [15] demonstrated low toxicity without substantial health risks for prolonged exposure under good hygiene conditions. It was shown that C 60 fullerenols demonstrate some toxicity due to the generation of reactive oxygen species caused by photoexcitation [16]. In particular, it was found that endohedral Gd@C 82 (OH) 22 species exhibited very low toxicity in tumor-bearing mice [17]. It was shown that most of the pristine and functionalized fullerenes are not overtly toxic, unless photoexcited or used at very high concentrations that are unlikely to be encountered environmentally or during therapy. The geometry and electronic structure of fullerenes allow them to form compounds containing various pharmacophore groups, which can easily pass to the excited state under the action of different physical and chemical factors and enclose metal atoms into their carbon cage with the formation of so-called endohedral metallofullerenes. The endohedral metal complexes are characterized by chemical stability, paramagnetism, and large specific surface, which can be easily functionalized [18].
Various functional groups can be attached to a fullerene cage, which makes it possible to obtain water-soluble fullerene derivatives. Fullerenols, due to their hydrophilic properties and ability to bind free radicals, can be used in chemotherapy, treatment of neurodegenerative diseases, and radiology [4,8,9,18]. Theoretical Molecular Dynamics (MD) simulations [19] of [C 60 (OH) n , where n = 2 -30] in aqueous solutions and survey of experimental data [20] demonstrate highly negative solvation free energies which directly indicate the thermodynamic feasibility of fullerenoles in water solutions.
In particular, hydroxylated fullerenes (fullerenols) exhibit pronounced antioxidant activity [3]. Fullerenols can react with most of the physiologically significant reactive oxygen species (ROS), including the OH • , O 2 • − , and H • radicals. Fullerenols can simultaneously contain the functional groups that can form radicals in aqueous solutions and anionic groups [4]. The calculation showed that the antioxidant activity with OH • depends on the distribution of hydroxyls over the C 60 fullerene cage. The fullerenols, in which the hydroxyl distribution lowers the redox potential ε, have the high trapping activity.
The Gd@C 82 endohedral fullerene complex and its derivatives are widely used in biomedicine [1][2][3][4][5][6][7][8][9]. The water-soluble gadolinium-containing metallofullerene derivatives can be excellent candidates to be used as novel magnetic resonance imaging (MRI) contrast agents, since they are characterized by the high relaxing ability and encapsulation of lanthanide ions (Gd 3+ ), which prevents their release into the bioenvironment [5]. The most widely used gadolinium-containing compounds are gadodiamide, gadopentetate dimeglumine, gadoterate meglumine, etc. [26,27]; however, there are fears that these substances may be toxic [27]. The metallofullerene derivatives trap toxic Gd 3+ ions into an inert yet strong carbon cage preventing their release and exhibit the 10 to 40 times higher proton relaxation ability as compared with that of conventional contrast agents and, in some cases, the much longer retention of the glioma brain tumor in mouse models [28].
Gadolinium endohedral complex Gd@C 82 increases the magnetic relaxivity of the contrast agent, which is a prerequisite for improved image contrast at lower gadolinium concentrations [29]. It was shown that Gd metallofullerenol in combination with chemotherapy improves the effectiveness of cancer therapy [30]. Gadolinium ions can inhibit calcium channels and exhibit neurological and cardiovascular toxicity [31]. To be used in clinical settings, the gadolinium ion must be placed in a chelating medium, which tightly binds the metal, but allows water to interact with unpaired gadolinium spins. The conventional approach implies the use of polyfunctional ligands, which strongly coordinate the Gd 3+ ion, but allow at least one water molecule to directly bind to Gd 3+ [5]. Due to the complexity of the synthesis of fullerenols with the gadolinium guest atom inside a carbon cage, the use of these compounds is still limited. Nevertheless, the Gd@C 82 O x (OH) y fullerenol is a good candidate for biomedical applications, since it has good solubility in water. Gadolinium enclosed in a carbon cage becomes nontoxic due to the easy removal of fullerenols from the body. In addition, a fullerenol can act as a substance for struggling against the ROSs.
In this work, the density functional theory (DFT) calculations were used to study the equilibrium atomic geometry and electronic structure of Gd endohedral complexes of C 82 fullerenols with different numbers of O and OH functional groups, which were synthesized in a high-temperature experiment and characterized by mass spectrometry. The reactivity of Gd@C 82 O x (OH) y endohedral complexes was estimated using the calculations of chemical electrophilicity (ω) and absolute electronegativity (χ) indices. It was found that the gadolinium guest atom increases the reactivity of fullerenol endohedral complexes with different ROSs. The endohedral complexes are proposed to be used for various MRI biomedical applications.

Experimental Procedures
A mixture of the Gd 2 O 3 powder and graphite in a weight ratio of 1:1 was processed in high-frequency arc plasma discharge by sputtering of graphite electrodes with 3-mm axial holes [32] with very low chemical yield. Fullerene mixture was extracted from carbon condensate by carbon disulfide in a Soxhlet apparatus. Using the technique described by Akiyama et al., a mixture of Gd@C 82 and higher fullerenes was isolated from the resulting solution. The sample was dried and redissolved in toluene. The Gd@C 82 fullerene was isolated from the solution by high-efficiency liquid chromatography on Agilent Technologies 1200 Series chromatograph with the only one Gd@C 82 endohedral complex detected in the mass spectrum, which signal clearly stands out against broadband background noise ( Figure S1).
According to the method proposed by Chiang and co-workers [12], the -O and -OH groups were attached to the isolated endohedral metallofullerene. Taking into account that the number of OH groups attached to the fullerene must be even [13,14], the composition of this product can be assumed as Gd@C 82 O x (OH) y (x = 10-12, y = 30-32, x + y = 40-42) [27].

Computational Details
The atomic and electronic structures of C 82 fullerene, Gd@C 82 endohedral complex, and Gd@C 82 O x (OH) y fullerenols and energy of solvation ( Figure 1) were calculated using DFT meta-hybrid exchange correlation MN15 functional [33] and def(2)-SVP basis set [34] for carbon (C), oxygen (O), and hydrogen (H) atoms and def(2)-SVP_ECP basis set for the gadolinium atom [35] using Gaussian 09 code [36]. The MN15 functional has a broader accuracy than any DFT potentials to reproduce bond energies, atomization energies, ionization potentials, electron affinities, proton affinities, reaction barrier heights, non-covalent interactions, hydrocarbon thermochemistry, isomerization energies, electronic excitation energies, absolute atomic energies, and molecular structures. In particular, it provides very accurate results for multi-, single-configurational, and non-covalent systems with mean unsigned error (MUE) 4.75, 1.85, and 0.25 kcal/mol, respectively, which is several times smaller than MUEs of conventional DFT potentials. The def(2)-SVP basis set is a balanced basis set to provide split valence, triple zeta valence, and quadruple zeta valence quality for H to Rn, which allows one to properly describe atomization energies, dipole moments, and structure parameters using density functional theory. The electronic structure calculations were performed within the restricted open-shell and unrestricted electronic structure calculations taking into account solvation effects using Universal solvation model based on density (SMD) [37]. Some details of taking into account solvation effects are presented in the SI Section. The Gd@C82 optimization was performed with spin S = 7/2, which corresponds to 4f 7 configuration of Gd +3 ion [38] (Figure 1a,b). The symmetrically distributed OH groups over the Gd@C82 were employed to develop the atomistic models of different fullerenols and to calculate their atomic and electronic structures ( Figure 1c). The fullerenols with three epoxy groups Gd@C82O3(OH)y (y = 8, 16, 24, 36, 44 (Figure 1d)) were developed by the uniform arrangement of hydroxyl and epoxy groups over fullerene carbon cage to reduce the number of possible intramolecular interactions and the atomic and electronic structures were studied as well. Some details of the development of structural models of Gd endohedral complexes of fullerenoles are presented in the SI Section.
To estimate the chemical reactivity of fullerenol gadolinium endohedral complexes, the absolute electronegativity index χ = (I−A)/2 (eV) [39], where I is the energy of the highest occupied molecular orbital (HOMO) and A is the energy of the lowest unoccupied molecular orbital (LUMO), and electrophilicity indexes ω = χ 2 /2η (η = -(I−A)/2 (in electron Volts, eV), which characterize the tendency of a molecule to attack the nucleophile, were calculated using the results of electronic structure calculations. The antioxidant properties of the fullerenols were estimated by calculating the electronic characteristics of oxygen molecules with different multiplicities (m) and charges (z), namely for O2 − m = 2 and z = −1; for O2 0 m = 1 and z = 0; for O2 0 m = 3 and z = 0; for hydrogen peroxide molecules H2O2 m = 1 and z = 0; and for HOO • m = 2 and z = 0. The density of states for fullerene and its derivatives were calculated with a peak smearing of 0.3 eV. The Gd@C 82 optimization was performed with spin S = 7/2, which corresponds to 4f 7 configuration of Gd +3 ion [38] (Figure 1a,b). The symmetrically distributed OH groups over the Gd@C 82 were employed to develop the atomistic models of different fullerenols and to calculate their atomic and electronic structures (Figure 1c). The fullerenols with three epoxy groups Gd@C 82 O 3 (OH) y (y = 8, 16, 24, 36, 44 (Figure 1d)) were developed by the uniform arrangement of hydroxyl and epoxy groups over fullerene carbon cage to reduce the number of possible intramolecular interactions and the atomic and electronic structures were studied as well. Some details of the development of structural models of Gd endohedral complexes of fullerenoles are presented in the SI Section.
To estimate the chemical reactivity of fullerenol gadolinium endohedral complexes, the absolute electronegativity index χ = (I−A)/2 (eV) [39], where I is the energy of the highest occupied molecular orbital (HOMO) and A is the energy of the lowest unoccupied molecular orbital (LUMO), and electrophilicity indexes ω = χ 2 /2η (η = −(I−A)/2 (in electron Volts, eV), which characterize the tendency of a molecule to attack the nucleophile, were calculated using the results of electronic structure calculations. The Gd guest atom in the Gd@C 82 endohedral complex is coordinated to the center of the hexagon on the C 2v axis of the C 82 cage [38]. An isolated Gd atom has the electron configuration 4f 7 5d 1 6s 2 and Gd 3+ ion has a 4f 7 configuration, which points out that Gd 5d-and Gd 6s-electrons are transferred to the carbon sphere, forming ionic bonds between Gd ion and C 82 cage. The Gd 4f 7 configuration is consistent with the Gd 3+ @C 82 3− ion model [40]. The Gd@C 82 ground spin state results from the intramolecular antiferromagnetic exchange between gadolinium ion with spin S Gd = 7/2 and S C82 = 1/2 [38] with the total spin S Gd@C82 = 6/2 of the complex.
The C 82 fullerene of C 2v symmetry consists of 12 pentagons and 32 hexagons (Figure 1a, Table 1). The formation of Gd@C 82 leads to the elongation of some carbon-carbon bonds from 1.42-1.43 to 1.44-1.45 Å (∆l = 0.02 Å) ( Table 1). In fullerenols, the C-C bond lengths are almost independent upon the number and positioning of the hydroxyl groups (8, 16, and 24) on the fullerene cage (l = 1.38-1.42 Å), as compared with pristine fullerene (Figure 2a, Table 1). However, an increase in the number of hydroxyl groups to 36 and 44 significantly changes the bond length, thus the global C 82 π system is almost annihilated with conversion of aromatic C-C bonds to separate single and double bonds with increases of the length of the single bond from 1.41-1.42 to 1.51-1.53 Å (∆l = 0.10-0.12 Å), while the length of the double bond decreases from 1.38-1.41 to 1.33-1.35 Å (∆l = 0.06-0.08 Å). In addition to the bond length, the angles between the carbon atoms of the carbon hexagon to which the gadolinium ion is coordinated also change, decreasing by 1-3 degrees in comparison with C 82 O x (OH) y . Gd@C 82 (OH) 8 Gd@C 82 (OH) 16 Gd@C 82 (OH) 24 Gd@C 82 (OH) 36 Gd@C 82 (OH) 44   The presence of gadolinium ion combined with epoxy and hydroxyl groups (8, 16 and 24) in the C82 fullerene slightly changes the bond angles between carbon atoms ( Figure  2a, Table 1). A greater number of hydroxyl groups increases the angle ∠С1-2-3 by 2-4°, from 120° to 124°, ∠С1-2-4 increases by 3-4°, from 109° to 112-113°, and ∠С3-2-4 decreases by 3-4°, for x = 36 hydroxyl groups from 122-125° to 118-119°. For x = 44 hydroxyl groups, the angles increase by 3-4°, as compared with the fullerenols with 36 hydroxyl groups from 118-119° to 121-122°.
It can be seen (Figures 1 and 2, Table 1) that C82Ox(OH)y and Gd@C82Ox(OH)y (x = 0, 3; y = 8, 16, 24, 36, 44) complexes can be assigned to two different groups, namely: (1) x = 0, 3 and y = 8, 16, 24 and (2) x = 0, 3; y = 36, 44. In the first group, the π-system is maintained even in the presence of gadolinium ion in the carbon cage, which can be seen for the fullerenols from the change in the angle of the hexagon with the gadolinium ion coordinated to the center (a change by 0-2 degrees relative to that in C82 and Gd@C82 Figure 2a, Table  1). However, as the number of hydroxyl groups increases, global C82 π-system is annihilated and uniform aromatic C-C bonds are replaced by the single and double bonds, which leads to a change in the geometry of the carbon cage (Figure 2b, Table 1).
The presence of 8, 16, and 24 hydroxyl groups on C82 carbon cage does not imply their significant mutual interaction (Figure 2a). When the number of hydroxyl groups increases to 36 and 44, they become close enough to each other and start interacting, forming a sys- The presence of gadolinium ion combined with epoxy and hydroxyl groups (8, 16 and 24) in the C 82 fullerene slightly changes the bond angles between carbon atoms (Figure 2a, Table 1 It can be seen (Figures 1 and 2, Table 1) that C 82 O x (OH) y and Gd@C 82 O x (OH) y (x = 0, 3; y = 8, 16,24,36,44) complexes can be assigned to two different groups, namely: (1) x = 0, 3 and y = 8, 16, 24 and (2) x = 0, 3; y = 36, 44. In the first group, the π-system is maintained even in the presence of gadolinium ion in the carbon cage, which can be seen for the fullerenols from the change in the angle of the hexagon with the gadolinium ion coordinated to the center (a change by 0-2 degrees relative to that in C 82 and Gd@C 82 Figure 2a, Table 1). However, as the number of hydroxyl groups increases, global C 82 π-system is annihilated and uniform aromatic C-C bonds are replaced by the single and double bonds, which leads to a change in the geometry of the carbon cage (Figure 2b, Table 1).
The presence of 8, 16, and 24 hydroxyl groups on C 82 carbon cage does not imply their significant mutual interaction (Figure 2a). When the number of hydroxyl groups increases to 36 and 44, they become close enough to each other and start interacting, forming a system of hydrogen bonds (Figure 2b). In particular, the distances between oxygen atoms of one hydroxyl group and hydrogen atoms of the other hydroxyl group ranges from 1.89 to 1.97 Å (Figure 2b).
The electronic structure calculations show that in C 82 O x (OH) y complexes with 8, 16, and 24 OH groups, the energy of interaction with solvent increases from 213 to 402 kJ/mol (Table S1), whereas Gd@C 82 O x (OH) y complex solvation is energetically favorable for 16 hydroxyl groups (793 kJ/mol, Table S1). An increase of the number of substituent hydroxyl groups in C 82 O x (OH) y and Gd@C 82 O x (OH) y (x = 0, 3; y = 36, 44) complexes leads to the formation of hydrogen bonds between oxygen and hydrogen atoms of the adjacent hydroxyl groups (the distance between hydroxyl groups decreased to 1.89-1.97 Å; Figure 2b). The energy of solvation was calculated for the complexes with larger numbers of C 82 O 8 (OH) y (y = 8, 16, 24, 36, 44) epoxy groups (Table S1). For the complexes with 8, 16, and 24 OH groups, the energy of interaction with the solvent increases from 165 to 298 kJ/mol (Table S1); for the complexes with 36 hydroxyl groups, it decreases to 258 kJ/mol; and for the complex with 44 hydroxyl groups, it increases to 288 kJ/mol (Table S1). The presence of gadolinium ion further increases the energy of solvation to 712-793 kJ/mol. All fullerenoles have good solubility in water whether or not they have endohedral guest atom inside the C 82 carbon cage. Consequently, for the complexes with a large number of hydroxyl groups, the interaction with the solvent is weaker (Table S1). The carbon cage is strongly distorted in the case of 36 and 44 hydroxyl groups, which leads to the breakdown of the π-system for the entire molecule and decreasing the electron affinity for the fullerenol, which is, according to the Koopmans theorem, the negative of LUMO energy, (Table 1, Figure 2b).

The C 82 O x (OH) y and Gd@C 82 O x (OH) y Electronic Structures
In Figure 3, the HOMO and LUMO diagrams are presented for free-standing Gd atom, C 82 fullerene (C 2v symmetry) in gas phase, and Gd@C 82 , and Gd@C 82 O 3 (OH) 24 (Figures S2 and S3) slightly affects both HOMO and LUMO energies. In particular, the ∆E (HOMO-LUMO) value for C 82 O 3 (OH) 24 is increased by 0.032 eV relative to that of C 82 (OH) 24 (Figures S2 and S3), keeping spatial localization of the HOMO and LUMO orbitals almost intact. The 4f Gd electrons lie below HOMO by 1.88 eV in the energy region from −6.24 to −6.69 eV. The HOMO states are localized mainly on carbon atoms of the fullerenol (Figure 3b-d), and, so the total high spin moment of the complex is maintained. The HOMO and LUMO of the C 82 fullerene are located at the top of the carbon cage (Figure 3b). In the Gd endohedral complex, the localization of α and β HOMOs is determined by endohedral gadolinium ion mostly at the top of the molecule in the vicinity of the carbon hexagon which coordinates Gd +3 (Figure 3c,d).
In this case, the spin-up and spin-down LUMOs are mostly localized at the carbon cage (Figure 3c). The hydroxy-and epoxy groups drive the localization of HOMOs and LUMOs states, i.e., the HOMO electron density is concentrated on carbon atoms near gadolinium and, vice versa, the LUMO electron density is localized at the opposite pole of the cage (Figure 3d). erenol, which is, according to the Koopmans theorem, the negative of LUMO energy, (Table 1, Figure 2b).

The C82Ox(OH)y and Gd@C82Ox(OH)y Electronic Structures
In Figure 3, the HOMO and LUMO diagrams are presented for free-standing Gd atom, C82 fullerene (C2v symmetry) in gas phase, and Gd@C82, and Gd@C82O3(OH)24 complexes in solvent as well as O2 0 (m = 1, m= 3), O2 − (m = 2), and HOO • in the solvent.   16,24,36,44) fullerenols, the HOMO-LUMO energy gaps for O 2 species are much greater than the UV threshold (3.5 eV) and they are equal to 8.90 and 11.32 eV, respectively (Figure 3e). One can speculate that an electronic excitation that is less demanding in energy is an excitation from a reactive oxygen species to fullerenol LUMO states with alpha and beta energies equal to −1.54 and −2.56 eV, respectively. For a neutral singlet oxygen molecule, the HOMO-LUMO gap is 2.64 eV; therefore, the excited electrons may be transferred to the fullerenole's LUMO state (Figure 3e). The energies of HOMO and LUMO states of the hydroxyperoxide radical HOO • are −5.55 eV and 2.07 eV, respectively, with the HOMO-LUMO gap equal to 7.62 eV (Figure 3f), which is also greater than the UV energy threshold. The α-and β-LUMO energies of fullerenol Gd@C 82 O 3 (OH) 24 (−1.54 and −2.56 eV for α and β partners, Figure 3d) are also much lower than HOO • LUMO. The ROS molecules have large energy gaps and their unoccupied molecular orbitals are high in energy, which complicates the excitations of the electron from HOMOs to LUMOs. The boundary molecular orbitals of fullerenols are located between HOMOs and LUMOs of the ROSes; therefore, these molecules can easily interact with the chemical environment.
The C 82 O 3 (OH) 24 complex has an electrophilicity index of ω = 11.6 eV, which promotes chemical attacks of ROS nucleophiles. The guest gadolinium ion changes the ability to accept electrons in both α and β channels with ω = 5.76 eV for 16 hydroxyl groups and 3.1 and 5.86 eV for 24 hydroxyl groups for α and β electrons, respectively.

Conclusions
The C 82 O x (OH) y and Gd@C 82 O x (OH) y (x = 0, 3; y = 8, 16, 24, 36, 44) complexes perspective for biomedical applications were synthesized and characterized using massspectroscopy. Following mass-spectrometry experimental detection, a number of atomistic models of endohedral fullerenoles Gd@C 82 O x (OH) y (x = 0, 3; y = 8, 16, 24, 36, 44) were developed and studied using ab initio DFT calculations. It was shown that the guest Gd atom promotes the chemical reactivity and electrophilic properties of fullerenol cages. For a relatively small number of hydroxyl groups, the C 82 carbon cage of C 82 O x (OH) y and Gd@C 82 O x (OH) y (x = 0, 3; y = 24) complexes still maintain the π-electron system. The complexes display high electron affinity, which ensures advanced antioxidant properties. Increasing the number of hydroxyl groups (y > 24) in Gd@C 82 O x (OH) y complexes leads to the formation of intramolecular hydrogen bonds between the hydroxyl groups, which prevents chemical interactions with water solvent with decreasing of reactivity and solubility of the complexes with consequent degradation of antioxidant properties. Based on combined experimental and theoretical investigation, the endohedral Gd@C 82 O x (OH) y complexes with 24 hydroxyl groups are considered as the best candidate for biomedical applications.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/ 10.3390/computation9050058/s1, Figure S1: Mass spectrum of the chromatographic fraction with Gd@C82 (positive mode); Description of Solavatation models; Table S1: Energy of solvation of Gd@C 82 O 3 (OH) y , C 82 O 3 (OH) y and C 82 O 8 (OH) y ; Figure S2: Diagram of the boundary molecular orbitals of C 82 O x (OH) 24  Data Availability Statement: All supporting data can be found in SI section available online.