Introduction

Fullerenes are a significant group of molecules in which large numbers of carbon atoms are locked together in an almost spherical shape. They have a graphite-like structure, but instead of all hexagonal sections, they also contain pentagons of carbon atoms that form a sheet in the shape of a sphere, oval, or cylinder. Putting these pentagons and hexagons together is essential for forming a spherical structure. A fullerene must have exactly 12 five-sided faces to close it in a spherical shape, but the number of hexagonal faces can be very different. It is an interesting molecule due to its symmetrical structure and reactivity to a variety of reagents.

Buckminsterfullerene [1] is one type of fullerene. Its molecules are spherical and contain 60 carbon atoms (12 pentagons and 20 hexagons). The most stable and abundant fullerenes are C60 and C70. Therefore, most of the properties mentioned in the case of fullerenes are focused on these two types. In the C60 structure, the carbon atoms of wall have a hybridization between the π and σ orbitals. This is due to its spherical structure, which limits the conjugate π bonding among the carbon atoms. Hence, this phenomenon leads to high reactivity of C60 [2].

Among the various nanostructures, fullerenes have received a great deal of attention due to their unique properties, which has made them attractive in a wide range of purposes. Known biomedical applications for fullerenes include the design of high-performance MRI contrast agents, X-ray imaging contrast agents, and photodynamic therapy [3,4,5,6,7,8,9]. They may also be used for drug and gene delivery systems in the body, in lubricants, and as catalysts. Other applications of fullerenes are mainly in the electronics, nanotechnology, materials science, and solar cells [10,11,12]. The doping fullerene has also attracted a lot of interest for its exploration due to its exclusive assets. For example, the K and Rb doping with C60 (KxC60 and RbxC60) causes these compounds to become superconductors [13,14,15,16,17,18]. In addition, the antibacterial activity [19], HIV-P inhibition [20], and photo cytotoxicity [21] are some of the potential applications of the C60 derivatives.

Fullerenes are known as zero-dimensional closed-cage nanomaterials. Hence, the spherical shape of fullerene nanomaterials gives this nanomaterial a large surface area [22,23,24,25]. This feature is important for biosensors and sensor systems. Although fullerenes can be dissolved in a variety of solvents, surface modification is an effective way to use them for biosensor and sensor technology. The most useful characteristic of the double bonds formed by the carbon structure in fullerenes is that they can be modified because they are able to easily respond to chemical reactions. Due to its spherical structure and 30 double bonds, it has the capacity to form 30 bonds that need to be modified with various chemical agents [26].

The choice of C60 in this study is due to the fact that it is one of the most plentiful fullerenes which is owing to minimize the strain of related instability by reducing the π overlap at adjacent pentagons sites [27]. C60 is an effective acceptor component with high electron affinity for charge transfer. The significant influences of chemical adsorption of the cations on the electrical sensitivity of pristine C60 and SiC59 nanocages could be the basis of new generation of electronic sensor design. It is well known that the heteroatom substitution of foreign atoms can modify and enhance the selectivity and sensitivity of C60s due to the different interactions of dopant and adsorbed factors [28]. The doping of C60 with the Si atom could modify the electronic properties due to inducted distortions in the neighboring positions. It can also alter the charge transfer and modifies the mechanic, chemical, and optic properties of C60.

The adsorption of metal ions on nanostructure surfaces has been observed in several theoretical and experimental studies [29,30,31,32,33,34,35,36,37,38,39,40,41]. The purpose of this work is to evaluate the adsorption of the alkali and alkaline–earth metal cations (M = Li+, Na+, K+, Be2+, Mg2+, Ca2+) on the pristine C60 and SiC59 nanocages. The titled interactions are theoretically investigated in terms of geometry, energies, and electronic structures using density functional theory (DFT). The topological parameters and charge transfer interactions are evaluated by AIM and NBO analyses, respectively. The effect of adsorbed cations on the electronic properties of pristine C60 and SiC59 nanocages is evaluated by frontier molecular orbital, energy gap, and chemical hardness and softness. These results may be useful for further studies on functionalization of the pristine and modified C60 nanocage as a sensor for the new compounds or drugs.

Computational details

In this paper, the structure of SiC59 is obtained by replacing the C atom at the head of a pentagon ring with the Si atom (Fig. 1). The complete optimization of geometry and the calculation of properties on the pristine C60 and SiC59 surfaces with and without the metal cations of Be2+, Mg2+, Ca2+, Li+, Na+, and K+ are done using the B3LYP function [42, 43] combined with the standard 6-31G(d) basis set. B3LYP has been revealed to be a reliable and commonly used functional for the study of different nanostructures [44,45,46,47,48,49,50,51,52,53]. The quantum chemistry package GAMESS [54] has been used to carry out all these calculations. The adsorption energies (Eads) of metal cations on the nanocages are determined by the following equations:

$${E}_{\mathrm{ads}}={E}_{(\mathrm{M}@\mathrm{C}60)}-{E}_{(\mathrm{M})} - {E}_{(\mathrm{C}60)}$$
(1)
$${E}_{\mathrm{ads}}={E}_{(\mathrm{M}@\mathrm{SiC}59)}-{E}_{(\mathrm{M})} - {E}_{(\mathrm{SiC}59)}$$
(2)

where E(M@C60) and E(M@SiC59) are the total energies of the metal cations adsorbed on the pristine C60 and SiC59 nanocages, and E(C60), E(SiC59), and E(M) are referred to the energies of an isolated pristine C60, SiC59, and the mentioned metal cations, respectively. The adsorption energies of complexes are corrected for basis set superposition error (BSSE) using the counterpoise correction scheme predetermined by Boys and Bernardi [55]. The atoms in molecules (AIM) theory of Bader [56] is applied to evaluate the nature of the intermolecular interactions by means of AIM 2000 software [57]. In this calculation, the B3LYP/6-31G(d) wave functions are used as input. The NBO analysis [58, 59] is also performed at the same level of theory in order to evaluate the natural electron configuration of adsorbing metal cations and the electron charge transfer between metal cations and nanocages. The GaussSum program [60] is applied to calculate the density of state (DOS) results and to get a more precise insight into the electronic properties of the analyzed structures. Finally, the quantum molecular descriptors of complexes such as softness (S), chemical hardness (η) [61], and electronegativity (χ) [62] are analyzed using the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energies.

Fig. 1
figure 1

The optimized structures and DOS plots of a fullerene C60 and b SiC59

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Results and discussion

Molecular geometry and interaction energy

The complete optimization of geometry in the pristine C60 and SiC59 structures as well as metal cations adsorbed on pristine C60 (M@C60) and SiC59 (M@SiC59) nanocages (M = Li+, Na+, K+, Be2+, Mg2+, and Ca2+) are performed using the DFT calculations at the B3LYP level of theory with the 6-31G(d) basis set. Figures 1, 2, and 3 show a number of the structures considered in this study. In the C60 nanocage, the two typical bond lengths C–C and C = C are about 1.453 Å and 1.395 Å, respectively. The single bond exists between the pentagonal and hexagonal rings, whereas the double bond is present in the hexagonal rings.

Fig. 2
figure 2

The optimized structures and DOS plots of fullerene C60 with divalent metal cations (M = Be2+, Mg2+, and Ca2+) adsorbed at the center of a pentagon ring

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Fig. 3
figure 3

The optimized structures and DOS plots of SiC59 with divalent metal cations (M = Be2+, Mg2+, and Ca2+) adsorbed at the center of a pentagon ring

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Our findings also show that in the SiC59 nanocage, the bond lengths of C–C and C = C connected to the Si atom are 1.456 Å and 1.397 Å, respectively. These results are close to the same bonds in pristine C60 and do not change significantly. On the other hand, the calculations indicate that the C–Si–C angle in the SiC59 nanocage is 90.7°, which is less than the C–C–C angle with sp3 hybridization (109.5°) in the C60 nanocage. When metal cations are adsorbed on the SiC59 nanocage, the C–Si–C angle for alkali and alkaline earth cations changes during the complexation. It can be expressed as Li+ (88.3°), Na+ (88.5°), K+ (89.0°), Be2+ (83.6°), Mg2+ (86.9°), and Ca2+ (87.7°).

The adsorption energies (Eads) of M@C60 and M@SiC59 are also computed to evaluate the stability of the considered complexes. The negative value of Eads indicates the exothermic character of the adsorption process. Therefore, the addition of M cations leads to the formation of stable configurations. The theoretical results display that the alkaline earth cations increase the stability of all complexes more than the alkali ones. As shown in Table 1, Eads is highly dependent on the nature of the different cations. For each ion group (alkali metal and alkaline earth), the calculations demonstrate that the Eads values for the M@C60 and M@SiC59 complexes are approximately close to each other (see Table 1). Since these complexes are largely electrostatic in nature, it is easy to see that cations with higher charge density interact more strongly with nanocages. The data also show that the adsorption of alkaline earth cations on the SiC59 nanocage is stronger than the C60 one. However, the large values of Eads denote that the adsorption process is chemisorption and the related nanocages are highly sensitive to divalent cations.

Table 1 Adsorption energies of alkali and alkaline earth cations on C60 and SiC59 nanocages (Eads, in eV), energies of HOMO and LUMO (in eV), gap energy (Eg, in eV), energy of Fermi level (EFL, in eV), change of Eg upon adsorption of cations (ΔE (%)), work function (ϕ, in eV), electronegativity (χ, in eV), hardness (η, in eV), softness (S, in eV−1), number of electrons transferred (ΔN), and dipole moment (μ, in debye)
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Electronic properties

Density of state (DOS) analysis is performed on the pristine C60 nanocage, SiC59, and the different M@C60 and M@SiC59 complexes to provide a comprehensive investigation of the effects of X-doping (X = Si) on the electronic structure and adsorption behavior of the metal cations on the C60 nanocages. As shown in Table 1, the energy gap value for the pristine C60 nanocage is equal to 2.76 eV, which means that it is a semiconductor material. The calculated DOS plots (Figs. 1, 2, and 3) exhibit that the electronic properties of the C60 and SiC59 nanocages significantly change with the addition of metal cations. According to the M@C60 and M@SiC59 DOS plots (Figs. 2 and 3), the Eg and Fermi level (EFL, middle of the Eg at 0 K) of the alkaline earth complexes considerably change and shift toward lower energies. On the other hand, the results show that in the alkali complexes, Eg changes slightly downwards, which is negligible; thus, the DOS plots of alkali-adsorbed nanocages (plots not shown) are approximately close to the C60 and SiC59 nanocages.

The work function (ϕ) of a semiconductor can be calculated as the difference between the Fermi level energies and the vacuum level, which is the minimum energy required to separate one electron from the Fermi level to the infinite distance from the surface. The following equation indicates the calculated work function as:

$$\phi ={E}_{\mathrm{inf}}-{E}_{\mathrm{FL}}$$
(3)

where Einf is the electrostatic potential at infinity (assumed to be zero) and EFL is the Fermi level energy. In accordance with this guess, ϕ is equivalent to the negative amount of the Fermi level energy. It is obvious from Table 1 that the reduction in Fermi level is accompanied with the increment in work function. There is also a relationship between the emitted electron current density in vacuum (J) with the work function in exponential form (Richardson-Dushman equation), as given below:

$$J=A{T}^{2}\mathrm{ exp }(-\phi /kT)$$
(4)

According to this formula, A is the Richardson constant, T is the temperature, ϕ is the work function, and k is the Boltzmann constant. As can be seen, with increasing ϕ, the field emission properties (J) decrease. Hence, the work function is a major factor in evaluating the field electron emission.

The results of calculations also show that the adsorption of alkaline earth cations relative to the alkali ones in both the C60 and SiC59 nanocages leads to a significant increase in the work function and thus a noteworthy decrease in the emitted electron current density during the complexation. In fact, increasing the work function in these complexes can be attributed to the more charge transfer from the active sites of C60 and SiC59 nanocages to the alkaline earth cations compared to the alkali ones. Therefore, it can be concluded that adsorption of the alkaline earth cations may be more effective in evaluating the field emission properties of C60 and SiC59 nanocages.

In the DOS diagrams of the C60 and SiC59 nanocages containing alkaline earth cations compared to alkali cations, the valence level appreciably shifts to lower energies, which is in accordance with a significant reduction in their band gaps (see Figs. 2 and 3). This means that the selected nanocages are more sensitive to alkaline earth cations with respect to alkali ones; thus, the Fermi level for alkaline earth cations adsorbed on nanocages would diminish from − 4.60 and − 4.73 eV in C60 and SiC59 to − 11.16 and − 11.21 eV in Be2+, − 11.24 and − 11.03 eV in Mg2+, and − 10.51 and − 10.43 eV in Ca2+, respectively.

The energy gap (Eg) is a major factor in determining the electrical conductivity of the materials, and a classic relation between them is as follows [63]:

$$\sigma \alpha \mathrm{ exp }(-{E}_{g}/2kT)$$
(5)

where values of σ and k are the electric conductivity and the Boltzmann constant, respectively. It is clear that there is an inverse relationship between the energy gap values and their corresponding electrical conductivity. In other words, a decrease in Eg is associated with an increase in the electrical conductivity (σ) and vice versa. Table 1 presents the obtained values of Eg for the pristine C60 and SiC59 nanocages and their analogous complexes. By comparing the Eg values, it is found that after the adsorption of metal cations on the nanocages, the energy gaps in both systems change to some extent, so that these changes are more in the alkaline earth cations than in the alkali ones.

AIM analysis

The AIM theory allows one to study the concept of chemical bond and the bond strength in terms of the electron density distribution function [56, 64]. It exploits the topological features of electron density, ρ(r), and thereby the definition of chemical bonding through the bond path and the bond critical point (BCP). The Laplacian of the electron density, 2ρ(r), is also a measure of the local concentrations of electron density and may be positive or negative. The total energy density in a BCP, H(r), is another useful topological descriptor that provides supplementary information about the nature of the interactions.

A negative value of 2ρ(r) (i.e., covalent interactions) denotes the electron concentration at a particular point, while a positive value of 2ρ(r) (i.e., ionic interactions, van der Waals or hydrogen bonds) implies electron depletion [56]. The former interactions have a high value of the electron density in BCP of the order > 10−1 a.u., and for the latter cases, the value of ρ is quite small (~ 10−2 a.u. or less). It has also been reported that if 2ρ(r) > 0 and H(r) < 0, this interaction is at least partly covalent in nature [65,66,67,68]. Figure 4 shows the typical molecular graphs obtained from AIM analysis for the Be2+@C60 and Be2+@SiC59 complexes.

Fig. 4
figure 4

The molecular graphs of a Be2+@C60 and b Be2+@SiC59 complexes obtained from the DFT calculation

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The calculated topological parameters for the M@C60 and M@SiC59 complexes are shown in Table 2. As shown in this table, for all M@SiC59 complexes, the BCPs of interaction have low ρ, 2ρBCP > 0 and HBCP > 0. These values indicate that the cation–π interaction in the studied complexes may be classified as the van der Waals interactions. However, in the Be2+ complex, the corresponding HBCP value is negative, meaning that this interaction is at least partly covalent (see Table 2). It is also apparent from this table that the values of ρSi…M and 2ρSi…M for the divalent complexes are greater than the values of the monovalent. This denotes that the interaction between the divalent cations and SiC59 nanocage is stronger than the monovalent cations.

Table 2 Topological parameters of the metal cations adsorbed on C60 and SiC59 nanocages (in a.u.)
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In the M@C60 complexes, the low ρC…M values and positive 2ρC…M also indicate a decrease in the electronic charge along the bond paths, which is specification of the van der Waals interactions (see Table 2). The interaction of the Be2+ complex is also the partially covalent in nature, due to the negative HBCP in this compound. It is also observed that for each ion group (alkali metal and alkaline earth), with an increase in the cation size from up to down, the values of ρBCP and 2ρBCP decrease as one goes from Be2+ (Li+) to Mg2+ (Na+) then to Ca2+ (K+) (Table 2). For the analyzed complexes, this trend corresponds to a decrease in the cation–π interactions strength in each group.

NBO analysis

The NBO analysis [58] is achieved to provide a complete investigation of the adsorption behavior of the metal cations on the C60 and SiC59 nanocages. It is originally developed as a way to quantify the contribution of the resonance structure to molecules [69,70,71,72,73,74,75,76,77]. Table 3 shows the results of the NBO analysis including the second order perturbation interaction energy, E(2), and the occupation numbers of the donor and acceptor orbitals at the B3LYP/6-31G(d) level of theory. As shown in this Table, the charge transfer takes place from C60 and SiC59 nanocages to the alkali and alkaline cations. In other words, the dominant interaction in the analyzed complexes is between the σ-electrons of the donor species and an antibonding lone pair of the metal cations (σ → LP*). The result of calculations demonstrates that σC–C of the C60 and σC–Si of the SiC59 nanocages participate as donors and LP*cation acts as acceptor.

Table 3 NBO analysis of M@C60 and M@SiC59 complexes, occupation numbers of donor (O.N.D) and acceptor (O.N.A) orbitals and their energies (in kcal/mol) of some important orbitals
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Based on the results of E(2) obtained from the NBO analysis, the interaction between cations with C60 and SiC59 nanocages decreases with an increase in the atomic number and the size of the metals cations from up to down (see Table 3). The order of E(2) in the M@SiC59 complexes is as Be2+  > Mg2+  > Ca2+ ≈ Li+  > Na+  > K+. Hence, the results confirm that the SiC59 surface has the stronger interaction with the alkaline earth cations with respect to the alkali ones; as a result, larger values of E(2) are associated with stronger donor–acceptor interactions and greater stability of the complexes [28].

Frontier molecular orbital analysis

Our final study in this paper is to evaluate the reactivity of C60s by analyzing their electronic structure. Figures 5 and 6 show the schematic diagrams of the HOMO and LUMO orbitals of the pristine C60, SiC59, and M@C60 and M@SiC59 complexes related to Be2+ as the most stable structure studied in this work. Table 1 shows variable information about quantum molecular descriptors such as softness (S), chemical hardness (η) [61], and electronegativity (χ) [62], which can be expressed as follows:

Fig. 5
figure 5

The calculated orbitals localized at a HOMO and LUMO of isolated C60 b HOMO and LUMO of isolated SiC59

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Fig. 6
figure 6

The calculated orbitals localized at a HOMO and LUMO of the Be2+@C60 complex and b HOMO and LUMO of the Be2+@SiC59 complex

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$$\eta = \frac{({E}_{\mathrm{LUMO}}- {E}_{\mathrm{HOMO}})}{2}$$
(6)
$$\chi = \frac{-({E}_{\mathrm{LUMO}}+ {E}_{\mathrm{HOMO}})}{2}$$
(7)
$$S= \frac{1}{2\eta }$$
(8)

As can be seen, these parameters are computed using HOMO and LUMO energies (EHOMO and ELUMO) according to Koopman’s theorem equations [78].

According to the principle of electronegativity equalization, formulated primarily by Sanderson [79,80,81,82], “when two or more atoms initially different in electronegativity are combined chemically, their electronegativities become equal in the molecule.” In the studied complexes, due to different electronegativity and chemical hardness, the electron density flux is from that of with less χ to that with more χ. In other words, the electron is transferred to the lower electronic chemical potential, until the electronic chemical potentials become equal. Because, the electronegativity of Mulliken is characterized by the negative of electronic chemical potential (χ =  − µ); thus, it must be constant everywhere. Hence, the values of χ and η obtained for calculating the number of electrons transferred (ΔN) from one system (nanocages) to another system (cations) [83] are applied as follows:

$$\Delta N= \frac{1}{2} \frac{({\chi }_{SiC59 \mathrm{or} C60} - {\upchi }_{M})}{({\eta }_{SiC59 \mathrm{or} C60} + {\eta }_{M})}$$
(9)

In this equation, χSiC59 or C60, χM and ηSiC59 or C60, ηM are the electronegativity and chemical hardness of the SiC59 or pristine C60 nanocages and the M cations, respectively. A positive value of ΔN shows that charge flows from the cations to the nanocages and the nanocages act as electron acceptors, while a negative value of ΔN displays that charge flows from the nanocages to the cations and the nanocages act as electron donors. Table 1 shows the number of electrons transferred (ΔN) in the studied systems. As shown in table, the absolute values of ΔN in the divalent complexes are more than the monovalent ones. Hence, the electron-donating ability in the former cases is greater than the latter.

Another major electronic property that affects the selected complexes is the dipole moment (μ). Table 1 shows the dipole moment of the pristine C60 and SiC59 nanocages and their complexes computed by the DFT method. It is well known that the large dipole moments exhibit the high reactivity of molecules [84, 85]. In other words, the more adsorption between adsorbent and adsorbate can be attributed to the high dipole moment in the compounds [86]. It can be noted that during the adsorption process of metal cations on the nanocage surface, depending on the adsorption configurations, the size and direction of the electric dipole moment vector change. The results shown in Table 1 display that in most cases, the highest dipole moments belong to divalent complexes and the lowest of those correspond to monovalent ones.

Conclusion

In the present study, the adsorption of alkali (Li+, Na+, K+) and alkaline earth (Be2+, Mg2+, Ca2+) cations on the pristine C60 and SiC59 nanocages as sensors with high electron donor is investigated, and their results are compared with together. The detection of these cations by the mentioned nanocages is considered by means of DFT calculations. From the obtained results, it can be understood that cations with a larger charge density interact more strongly with nanocages. The data show that the adsorption of alkaline earth cations on the SiC59 nanocage is stronger than the C60 one. The large values of Eads denote that the adsorption process is chemisorption and the related nanocages are highly sensitive to divalent cations. The results of AIM analysis show that the investigated interactions in complexes are from type of the van der Waals. It is apparent that the values of ρ and 2ρ for the divalent complexes are higher than those of the monovalent ones. This denotes that the interaction between the divalent cations and nanocages is stronger than the monovalent cations. The NBO analysis also shows that the SiC59 surface has the stronger interaction with the alkaline earth cations with respect to the alkali ones; hence, larger values of E(2) are associated with stronger donor–acceptor interactions and greater stability of the complexes. The calculated DOS plots show that the Eg and Fermi levels of the alkaline earth complexes considerably change and shift toward lower energies, while in the alkali complexes, Eg changes slightly downwards, which is negligible and approximately close to the selected nanocages. The results of calculations also show that the adsorption of alkaline earth cations relative to the alkali ones in both the C60 and SiC59 nanocages leads to a significant increase in the work function and thus a noteworthy decrease in the emitted electron current density during the complexation. By comparing the Eg values, it is found that after the adsorption of metal cations on the nanocages, the energy gaps in both systems change to some extent, so that these changes are more in the alkaline earth cations than in the alkali ones. Thus, the nanocages used in this study could be interest sensors for the detection of the alkaline earth cations.