Computational Design of New N-Heterocyclic Silyl Pincer Fullerenes

A density functional theory study was performed to design new N-heterocyclic silyl pincer fullerenes based on the reactions of diaminofullerene with chlorosilanes SiHRCl2. Reaction energies of the formation of pincer fullerene ligands increased through the substitution of flanking arms with CH3 and phenyl groups. However, substituting hydrogen of SiH2 with methyl slightly increased the corresponding reaction energies; replacing hydrogen with phenyl group decreased the reaction energies of the considered pincer fullerenes. While the calculated electrophilicity values of the pincer fullerenes are larger than the electrophilicity values obtained for the fullerene derivatives, the substitution of hydrogen atoms of central SiH2 and PH2 did not has a noticeable impact on the electrophilicity values of the pincer fullerenes. The only exception was SiHPh(NCH2PH2)2C60. Natural bonding orbital analysis showed that the delocalization of electrons from the lone pairs of phosphorous atoms to the n* orbital of transition metal atoms was a key factor for stabilizing the considered complexes. The strongest interaction was due to the delocalization of electrons from lone pairs of phosphorous atoms in the flanking arms to the LP* of transition metals, which was followed by the delocalization of electrons of the Si-H σ* orbitals to the LP* of transition metals.


Introduction
There has been extensive growth in the interest in the chemistry of complexes of transition metals of pincer ligands after Moulton and Shaw's outstanding report in 1976 about a wide range of pincer-ligated metal complexes [1]. Strong binding to the metal center is made by the tridentate coordination of pincer ligands and this outcomes in high stability of the pincer metal unit and decomposition on heating happens only at a temperature higher than 100°C [2]. The robustness of pincertype complexes together with hemilability of donor group positions are very significant for designing the catalysts that should be satisfactorily stable to resist the harsh reaction conditions [2][3][4][5][6][7]. On the other hand, the donor groups don't need to be strongly bonded to make sure that it might reversibly dissociate and form a coordination site needed for activating inert bonds. They can react with external ligands (e.g. isocyanides, H 2 , CO, CO 2 , dihalides, water, acids, oxidizing and reducing agents, or even Na metal) with the assistance of the thermal stability and tight binding of pincer complexes [8][9][10]. Simultaneously, they keep the pincer coordination of the ligand even at a raised temperature. This explains how several pincer-type complexes can be utilized as catalysts for extensively endothermic reactions like the dehydrogenation of organic substrates [7,8]. There has been a great deal of attention to this among researchers after the main report by Jensen et al. [11] of an example of iridium pincer complex for alkane dehydrogenation. Therefore, the reasonable design and synthesis of pincer-type ligands, of which stereoelectronic properties are controllable using practical modification, have been long an objective in inorganic and organometallic chemistry [12].
In the pincer ligands, a central moiety supplies two electrons from the donor atom (like phosphorus, nitrogen, oxygen, and carbon) to the transition metal. The two atoms are donated through a covalent bond that is also an "anchor." Two neutral pendant arms are on either side of the central donor atom, which provide a lone pair of electrons from heteroatoms (e.g. nitrogen, oxygen, sulfur, or phosphorus). These aspects play a critical role in stabilizing the metal center and characterizing the "active sector" in the coordination of the complex, see Fig. 1. As seen, there is a straight impact on the steric hindrance about the metal in bulky R groups that can add chirality in the complex through chiral LR n groups. However, the ring size relies upon the size of the linker arms (Y); consequently, it affects the reactivity of the complex and the bite angle. It is feasible to modulate the adjustments in the electronic properties of the pincer ligands utilizing the fine control given by the nature of the substituent on the central aromatic ring (Z). This minimally affects the steric of the ligand. The nature of the central donor atom (X, typically C, N, O, or P) may likewise have a significant electronic effect, particularly through the variety of the trans impact [11][12][13]. The probability of including other less conventional donor atoms as the equatorial donor is another field of study. Silicon, as a donor, has gotten a unique consideration as electropositive σ-silyl ligands can stabilize higher oxidation states and gratitude to their solid trans impact they can labialize trans ligands, while both have likely uses in catalysis. Stobart et al. [14] were the first group to introduce the phosphine/silylbased pincer ligands with flexible alkyl backbones and then extended to the NSiN [15,16], PSiP [17,18], and SSiS [19] pincer frameworks. Dixon et al. [20] depicted silicon-based pincer ligands and enforced the meridional geometry by adding an appropriately stiff backbone. They announced the synthesis of the primary instances of N-heterocyclic σ-silyl pincer ligands that are highlighted with a PSiP-LXL donor triad with reactions of 1,2-C 6 H 4 (NHCH 2 PPh 2 ) 2 with c h l o r o s i l a n e s S i H R C l 2 ( R = P h , C l ) a l o n g w i t h trimethylamine, see Fig. 2. Regardless of the relevance between experimental and theoretical efforts about the pincerligated metal complexes, we tracked down no theoretical/ experimental work about pincer ligands on the fullerene surface. Thinking about a similar procedure, diamino fullerene C 60 (NH 2 ) 2 can be used as precursors and for designing of new pincer fullerene ligands [21][22][23]. The reactions of 1,2-C 6 H 4 (NHCH 2 PPh 2 ) 2 with chlorosilanes SiHRCl 2 (R = H, CH 3 , and Ph) were taken into account in the design of SiHR(NCH 2 PPL 2 ) 2 C 60 R and L = H, CH 3 and phenyl, see Fig. 2. Nine pincer fullerene ligands SiHR(NCH 2 PL 2 ) 2 C 60 , R and L = H, CH 3 and phenyl were taken into account, see Fig. 3. Then, the pincer-ligated metal complexes were developed by adding a transition metal (Fe, Co, Ni and Cu) to the pincer bites to examine their formation using their electronic properties and stability. Such systems are selected to address the structure, stability, electronic properties, steric hindrance, bite angle, and the reactivity of the considered N-Heterocyclic silyl pincer fullerenes by variety the nature, size, and reactivity of their flanking arms and central moieties. Our expectation here in this work is to respond to the following questions. Could fullerenes be utilized in designing pincer ligands? How does the fullerene moiety influence the electronic properties of the pincers? How does the change of bulky L groups of the flanking arms impact the electronic and steric properties of the pincer-ligated metal complexes? How does the modification of bulky R groups of the central moieties influence the electronic and steric properties of the pincer-ligated metal complexes? What is the nature of the transition metals on the electronic impact, especially through the variation of the transition metal?

Computational Aspects
Taking into account the immensity of investigated systems, the optimization method is qualified bit by bit. The geometries of the fullerene pincer ligands SiHR(NCH 2 PPL 2 ) 2 C 60 R and L = H, CH 3 and phenyl (1-9, Fig. 3) were optimized at the beginning at the M06-2X/3-21G level of theory. Thereafter, the optimal geometries of the structures determined in past stages were calculated based on standard 6-311G(d, p) and 6-311G+(d, p) basis set. Frequency calculations were performed for the whole systems at the same level of theory, and the actual frequencies were supported as all of them were structures with minimum energy. The geometries of these pincer fullerene ligands together with the significant geometrical parameters are illustrated by Fig. 3. The pincerligated metal complexes were determined by adding transition metals and then optimal geometries for all the structures were obtained at the same level of theory. The M06-2X functional is in a new generation of hybrid metageneralized gradient approximation exchange-correlation functionals consisting an accurate treatment of the dispersion energy. The M06-2X functional [24] and 6-311G+(d, p) basis sets were utilized for optimization of geometry and single-point energy calculations. The basis set superposition error (BSSE) effects on the energies are also considered via a counterpoise [25] method. All density functional theory (DFT) calculations are performed utilizing GAMESS suite of programs [26,27]. Wave functions determined at the M06-2X/6-311 + G(d, p) level of theory were analyzed by the natural bond orbital (NBO) method [28,29]. Twelve pentagons in six pyracylene units design C 60 fullerene cage with icosahedral (I h ) symmetry which lead to a single type of carbon atom and two types of C-C bonds including the [6] and [5,6] ring fusion sites. The length of the bond at [6] and [5,6] [30,31]. Each amination reaction added the elements NRR and H across a [6] π-bond on fullerene. Several regiochemistries are possible but experimental data recommend that aminations prefer either a 1,2-or a 1,4-addition.
The addition reaction of C 60 with amines is a widely studied topic [21][22][23]. Moreover, 1,2-addition of amine to the [6, 6]bond of fullerene C 60 led to the formation of two newly C-N bonds with 1.469 Å at the M06-2X/6-311 + G(d, p) level of theory. The [6] C-C bond lengths of 1,2-diamino fullerene were equal to 1.628 Å, which are lengthier than normal C-C bond lengths in fullerene (1.401 Å) [30,31]. To design nine pincer fullerene ligands in this study, 1,2-diamino fullerene was utilized as precursors. The geometries of these pincer fullerene ligands together with the significant geometrical parameters are illustrated in Fig. 3.  [20]. As mentioned above, the IR vibrational frequencies were computed for the systems at the same level of theory. In addition, the actual frequencies showed that they were structures with minimized energy. The distinctive IR spectroscopic fingerprints yielded valuable insight into future experimental detections. However, it is notable that at the beginning, theoretical frequencies are overestimated universally in comparison with the results even in the case of more accurate methods. Therefore, the present study is not an attempt to predict the exact frequencies. This study is aimed at finding patterns in the data that can help us determining different forms of pincer fullerenes. Figure 4 shows the simulated IR vibrational spectra of the SiH 2 -(NCH 2 PH 2 ) 2 C 60 , and the prominent peaks are quite clear. Thus, it is better to discuss the spectra region by region. In the different vibrational frequencies theoretically found for SiH 2 (NCH 2 PH 2 ) 2 C 60 , two lowest-energy modes of 505.6 and 612.0 cm −1 correspond to out-of-plane bending of C-C bonds and breathing mode of fullerene cage. On the other hand, the following vibrations at 830.8 and 1011.6 cm −1 are due to the out-of-plane wagging and in-plane scissoring of HSiH angles, respectively. The vibrational frequency at 2285.2 cm −1 with the highest intensity is assigned to the symmetric stretching of the SiH bonds coupled with the symmetric stretching of the PiH bonds. The SiH 2 (NCH 2 PH 2 ) 2 C 60 exhibits symmetric and asymmetric stretching of CH bonds at 3034.7 and 3113.6 cm −1 respectively. Similar data were obtained for the pincer fullerene ligands, which are in agreement with those values obtained for N-Heterocyclic σ-siliyl pincer ligands. The IR spectrum simulated for the other pincer fullerene ligands along with their assignments can be found in the supplementary material.
To investigate the formation of the pincer fullerene ligands SiHR(NCH 2 PL 2 ) 2 C 60 , R and L = H, CH 3 and phenyl, the reactions of C 60 (NHCH 2 PPh 2 ) 2 with chlorosilanes SiHRCl 2 (R = H, CH 3 and phenyl) were taken into account (Fig. 2), and the reaction energies (E r ) were obtained in the standard way as follows: where E SiHR(NCH2PL2)2C60 and E [C60(NHCH2PPh2)2] are total energies of the pincer fullerenes and C 60 (NHCH 2 PPh 2 ) 2 and E [Cl2] and E [SiHRCl2] refer to energies of Cl 2 and chlorosilanes, respectively. As listed in Table 1, the calculated E r values of the formation of the considered pincer fullerenes are calculated to be 46.8-61.6 kcal/mol, which is lower than the E r values obtained for the SiHR(NCH 2 PPh 2 ) 2 C 6 H 4 at the same theory level. In comparison between the calculated reaction energies of pincer fullerenes, some important results were found. As noted, to analyze the influence of the nature of the flanking arms and central silicon atom on fullerene pincer ligands, the substitution of flanking arms and central silicon atom with CH 3 and phenyl groups was changed. Substituting flanking arms with CH 3 and phenyl groups increased the reaction energies of the pincer fullerene ligands formation. While substituting hydrogen of SiH 2 with methyl led to a slight increase of the reaction energies, replacing hydrogen with phenyl groups decreased the reaction energies of the considered pincer fullerenes.
To examine the electronic properties of the considered pincer ligands, electrophilicity was calculated, which can be used as a base to examine the electrophilic competency of the system under consideration through using the electronic chemical potential (μ) to the measure tendency of the system to obtain an extra electron from next electron-rich species. At the same time, it uses hardness (η) to describe the system resistance to electron exchange with the environment. Parr et al. defined a general index for the electrophilicity strength [32]. The definition is based on the quantitative chemical concepts in DFT such as the electronic chemical potential (μ) and hardness (η) [33,34]. Employing a quadratic and finite difference approximation, Parr et al. [32] interpreted that μ and η may be equal Finally, the electrophilicity index was defined as ω = μ 2 /2η [33]. Therefore, electrophilicity ω values were obtained for the pincer ligands based on the mentioned formula and listed in Table 1. As listed in Table 1, the obtained electrophilicity values of the pincer fullerenes are in 4.11-4.23 eV range, which are larger than the electrophilicity values obtained for the fullerene derivatives with heterocyclic ring systems. Notably, the substitution of hydrogen atoms of central SiH 2 and PH 2 does not have a noticeable impact on the electrophilicity values of the pincer fullerenes, except for SiHPh(NCH 2 PH 2 ) 2 C 60 in which substituting flanking arms with CH 3 and phenyl increases the electrophilicity of the considered pincer fullerenes.
The pincer-ligated metal complexes were prepared by adding a transition metal (Fe, Co, Ni, and Cu) to the pincer bites. Through this, their formation based on structure, electronic properties, stability was predicted. Two five-member metallocyclic rings were formed by the complexation of metal to three adjacent coplanar sites of pincer fullerene ligands. Figure 5 illustrates the geometries and the important geometrical parameters of these complexes. The criteria of stability of different pincer-ligated metal complexes namely the difference between the total energy of pincer-ligated metal complexes, the constituent, and individual transition metals, and pincer fullerene ligands were used to calculate binding energies (E b ). Using the counterpoise (CP) method [25], the binding energies were corrected for basis set superposition error (BSSE). Clearly, binding energies range from −84.24 to −88.59 eV. Notably, the metal-silicon bonds are shorter than expected for single covalent bonds. For example, Co-Si and Co-P bond lengths in Co-SiH(NCH 2 PH 2 ) 2 C 60 (2.271 and 2.201 Å) is smaller than the corresponding single Co-Si and Co-P bond lengths (2.43 and 2.19 Å). When the hybrid orbitals of the ligands and the hybrid orbitals of the metal atoms in the metal complexes are overlapped, the delocalization of electrons happens. Therefore, we perform NBO analysis to have a deeper insight into the nature of electronic conjugation among the bonds in the pincer-ligated metal complexes. The NBO analysis is a useful tool to determine these delocalizations of the electrons. The NBOs have a close relationship with the picture of localized bonds and lone pairs as basic units of molecular structure. It is possible to interpret ab initio wave-functions based on the classical Lewis structure concepts through transforming these functions to NBO form [28]. The present study is mostly about the results of second-order perturbation theory analysis of Fock matrix in NBO of the complexes. Concerning each donor NBO(i) and Fig. 4 Simulated IR spectra of SiH 2 -(NCH 2 PH 2 ) 2 C 60 together with the assignment of some important modes Table 1 The total energies (Et in hartree), reacton energies (Er in kcal/mol), electrophilicities (ω in eV) and natural charge Q/e (e = 1.6 × 10 −19 C), for for the N-Heterocyclic Silyl Pincer Fullerenes RSiH-(NCH 2 PL 2 ) 2 C 60 at the M06-2X/6-311 + G(d, p) level of theory acceptor NBO(j), the stabilization energy E (2) pertinent to delocalization is obtained as follows [28,29].
where q i represents the donor orbital occupancy, ϵ i and ϵ j represent the orbital energies, and ij b Fjj D E stands for the offdiagonal NBO Fock matrix element. With higher values of the E (2) , the interaction between the donors and acceptors is intensified [10]. The strongest interactions of n* orbitals of transition metal atoms with lone pairs of phosphorous atoms and the Si-H σ* orbitals of central silicon atoms are listed in Table 2. As seen, the strongest interaction of all happens because of the delocalization of electrons from lone pairs of phosphorous atoms (donor) in the flanking arms to the LP* of transition metals (acceptor) followed by the Si-H σ* orbitals of central silicon atoms (donor) to the LP* of transition metals (acceptor). For example the delocalization of electrons from the lone pairs of flanking arms phosphorous atoms to the n* orbitals of Fe atom resulted in the interaction of LP P with LP* Fe stabilizing the complex by about 48.41 kcal/mol. On the other hand, the delocalization of electrons from the Si-H σ* orbitals of central silicon atoms to the LP* orbitals of Fe atom stabilizes the complex by only 13.37 kcal/mol. Therefore, it seems that the delocalization of electrons from the lone pairs of flanking arms phosphorous atoms to the n* orbitals of Fe atoms is a more important factor for stabilizing the complexes in comparison to the orbitals of central silicon atoms.

Conclusion
A DFT study was carried out to design of new n-heterocyclic silyl pincer fullerenes. The reactions of C 60 (NH 2 ) 2 with chlorosilanes SiHRCl 2 (R = H, CH 3 , and Ph) were taken into account to design the nine pincer fullerene ligands SiHR(NCH 2 PL 2 ) 2 C 60 , R and L = H, CH 3 , and Ph and the pincer-ligated metal complexes achieved by adding a transition metal to the pincers. According to the findings, the following points are notable. Substituting flanking arms with CH 3 and phenyl groups increases the reaction energies of the formation of the pincer fullerene ligands. While substituting the hydrogen of SiH 2 with methyl leads to a slight increase of the reaction energies, replacing hydrogen with phenyl groups decreases the reaction energies of the considered pincer fullerenes. In addition, the calculated electrophilicity values of the pincer fullerenes range are larger than the electrophilicity values obtained for the fullerene derivatives. Therefore, the substitution of hydrogen atoms of central SiH 2 and PH 2 does not have an obvious impact on the electrophilicity values of the pincer fullerenes, except for SiHPh(NCH 2 PH 2 ) 2 C 60 . Natural bonding orbital analysis (NBO) showed that the interaction of the phosphorous lone pairs in the flanking arms with the n* orbitals of transition metal atoms was stronger than the interaction of Si-H σ* orbitals of central silicon atoms with the LP* of transition metals.

Supplementary Information
The online version contains supplementary material available at https://doi.org/10.1007/s12633-021-01168-3 Acknowledgements We gratefully acknowledge for the financial support from the Research Council of Alzahra University.
Code availability Not applicable.