Encapsulating Proton Inside C₆₀ Fullerene: A Density Functional Theory Study on the Electronic Properties of Cationic X⁺@C₆₀ (X⁺ = H⁺, H₃O⁺ and NH₄⁺)

Abstract

Confining protons into an enclosed carbon cage is expected to give rise to unique electronic properties for both the inner proton and the outer cage. In this work, we systematically investigated the geometric and electronic structures of cationic X⁺@C₆₀ (X⁺ = H⁺, H₃O⁺, and NH₄⁺), and their corresponding neutral species (X = H₂O, NH₃), by quantum chemical density functional theory calculations. We show that C₆₀ can trap H₂O, NH₃, H₃O⁺ and NH₄⁺ at the cage center and only slightly influence their geometries. The single proton clings to the inner wall of C₆₀, forming a C-H chemical bond. The encapsulated neutral species almost do not change the electronic structure of the C₆₀, while the internal cations have obvious effects. The charge transfer effect from the inner species to the C₆₀ cage was found for all X@C₆₀ (X = H₂O, NH₃) (about 0.0 e), X⁺@C₆₀ (X⁺ = H₃O⁺, NH₄⁺) (about 0.5 e) and H⁺@C₆₀ (about 1.0 e) systems. Encapsulating different forms of protons also regulates the fundamental physico-chemical properties of the hollow C₆₀, such as the HOMO-LUMO gaps, infrared spectra, and electrostatic potential, etc., which are discussed in detail. These findings provide a theoretical insight into protons’ applications, especially in energy.

1. Introduction

Protons in aqueous systems play a crucial role in various physical, chemical and biological processes [1,2]. For instance, they are involved in fuel cell membranes [3], ATP synthesis [4], enzymatic reactions in proteins [5], and more. When protons are in confined systems, they exhibit unique electronic, magnetic and optical properties [6,7]. Fullerenes, with hollow inner spaces, can encapsulate a wide variety of species, including atoms, molecules or ions, forming endohedral fullerenes [8,9,10]. They offer a potential platform for studying the behavior of protons in a confined setting. The unique structure of fullerenes not only provides a confined space but also may interact with the protons in ways that could further enhance our understanding of protons’ behavior and their associated properties [11,12,13,14,15]. The inner space of C₆₀, with a diameter of 3.53 Å, is suitable for entrapping a guest species [16,17]. It provides a remarkably simple model system through which to study the properties of species in confinement. As of now, a large number of experimental and theoretical methods have been used to research molecule endohedral fullerenes, such as H₂O@C₆₀ [17,18,19,20,21,22,23,24,25,26,27,28,29,30], HF@C₆₀ [26,31,32], H₂@C₆₀ [33,34,35,36], etc. These endohedral fullerenes have been synthesized by means of the arc discharge method [37] and molecular surgical method [38,39]. Some theoretical research has been carried out on H⁺ and NH₃ embedded into C₆₀ [40,41,42]. The studies focused on the geometry parameter, interaction energy, charge transfer, and spectra.

The proton, as an elementary particle, differs from all other ions that are stable in aqueous solutions. When introduced into water, a proton does not exist independently but rapidly combines with neighboring water molecules to form a hydronium cation (H₃O⁺) [43]. Protons show the same behavior in ammonia, forming ammonium ion (NH₄⁺) [44]. Moreover, the hydration of H₃O⁺ and NH₄⁺ plays an important role in the physical and natural sciences [45,46]. This is due to hydrogen bonding network formed in aqueous acid–base chemistry. Meanwhile, H₃O⁺ batteries are considered one of the most promising energy technologies as a next-generation power source, thanks to their cost-effectiveness and sustainability [47]. NH₄⁺ and other species react to form the ammonium salt complex species in the natural environment [48]. However, little is known about encapsulation of H₃O⁺ and NH₄⁺ inside C₆₀. Trapping H₃O⁺ and NH₄⁺ in a confined environment provides a unique opportunity to understand their novel properties. Hence, an in-depth study of the geometric and electronic structures of the cationic X⁺@C₆₀ (X⁺ = H⁺, H₃O⁺, and NH₄⁺), as well as their corresponding neutral species (X = H₂O, NH₃), would certainly be a worthwhile exercise.

In this work, we present the results of first-principles computations to investigate the geometric and electronic structures of cationic X⁺@C₆₀ (X⁺ = H⁺, H₃O⁺, NH₄⁺), as well as their corresponding neutral species (X = H₂O, NH₃). This paper is organized as follows. First, the computational methodology is described. Then, we present results for the systems, including optimized geometry parameters, interaction energy, charge populations, electron density difference, HOMO-LUMO gaps, infrared spectra, electrostatic potentials, and hydration free energies. Finally, important results are summarized in the conclusions section, which may be useful for furthering sustainable and efficient energy sources.

2. Results

Figure 1 presents the optimized geometries of C₆₀, X⁺@C₆₀ (X⁺ = H⁺, H₃O⁺, NH₄⁺), and X@C₆₀ (X = H₂O, NH₃) at B3LYP-D3(BJ)/6-31G(d, p) at the theoretical level (for coordinates for optimized molecular structure, see Supplementary Materials). The optimized geometry parameters of isolated and confined species are compared to investigate the interaction between the C₆₀ cage and the confined species. The optimized geometry parameters are shown in

Table 1. Parameters optimized at the B3LYP-D3(BJ)/6-31G(d, p) level of theory (unit is Å).

Bond Length	H2O	H2O@C60
r(O-H)	0.965	0.964
r(O-H)	0.965	0.964
	NH3	NH3@C60
r(N-H)	1.018	1.014
r(N-H)	1.018	1.014
r(N-H)	1.018	1.014
		H+@C60
r(C-H)		1.130
	H3O+	H3O+@C60
r(O-H)	0.982	0.994
r(O-H)	0.982	0.994
r(O-H)	0.982	0.994
	NH4+	NH4+@C60
r(N-H)	1.027	1.027
r(N-H)	1.027	1.027
r(N-H)	1.027	1.027
r(N-H)	1.027	1.027

. For the neutral species X encapsulated inside C₆₀, species X is located at the center of the cage. The O-H and N-H bond lengths decrease by 0.001 Å and 0.004 Å, respectively, compared to the free molecule. Similar negligible changes have been reported in the literature [7,41,49], indicating that the computational level used in this work is reliable. Additionally, our calculations also show that the interaction between X and C₆₀ is minimal, with almost no perturbation of the C₆₀ geometry. It should be noted that in H⁺@C₆₀, the H⁺ is attached to C atom, indicating that the H⁺ directly interacts with the C atom of C₆₀. The C-H bond length in H⁺@C₆₀ is 1.130 Å, which is 3.5% longer than that (1.092) of free CH₄ due to C-H bond weakening. The H₃O⁺ encapsulated inside fullerene cage shows a slight deviation from the center. The comparison of the H₃O⁺ encapsulated inside C₆₀ and free H₃O⁺ in the gas phase reveals that the H₃O⁺ encapsulated inside C₆₀ has a particular conformation with a longer O-H (0.994 Å) than that of a free H₃O⁺ (0.982 Å), being about 1.2% larger than the O-H bond length, which is consistent with the results of reference [22,40]. The small increase in bond length shows that the attraction of H toward the cage causes the slight stretch. However, for NH₄⁺ encapsulated inside the fullerene cage, NH₄⁺ is located at the center of the cage. The computed N-H bond length of 1.027 Å for the NH₄⁺@C₆₀ is consistent with that of the free NH₄⁺ molecule. This result indicates that the interaction between H₃O⁺ and C₆₀ is stronger than that between NH₄⁺ and C₆₀.

3. Discussion

To generate the stable structure of H⁺ adsorbs, we previously considered proposed adsorption sites, atoms, bridges, and hollow sites. The optimization procedure of the C₆₀ geometrical structure yielded the 5-6 bonds at the junctions between a five- and a six-membered ring and the 6-6 bonds at the junctions between a six- and a six-membered ring. The lowest-energy adsorption site is the atom site, where a C-H bond is formed. Figure 2 displays the calculated energy profile along pathway from the atom site to the bridge site. In the transition state, the H⁺ is located on the 5-6 bond and 6-6 bond. We carried out intrinsic reaction coordinate (IRC) calculations in two parts. The corresponding energy barriers are 5.82 kcal/mol and 1.93 kcal/mol, respectively. Our results show that the transition from the atom to the 6-6 bond is much easier than that to the 5-6 bond due to the low energy barrier, suggesting that the pathway proposed here is reasonable.

Energy decomposition analysis is a powerful method of assessing qualitative and quantitative interaction.

Table 2. Energy decomposition analysis of X@C₆₀ (X = H₂O, NH₃) and X⁺@C₆₀ (X⁺ = H⁺, H₃O⁺, NH₄⁺) at B3LYP-D3BJ/TZP in kcal/mol.

	∆Eint	∆Eelstat	∆EPauli	∆Eorb	∆Edisp
H2O@C60	−13.22	−6.02	13.60	−4.71	−16.09
NH3@C60	−14.18	−10.60	24.64	−5.95	−22.27
H+@C60	−174.08	82.43	0.00	−253.88	−2.63
H3O+@C60	−26.50	32.43	19.52	−58.23	−20.22
NH4+@C60	−22.97	33.45	17.07	−47.03	−26.46

presents the contributions of electrostatic (∆E_elstat), Pauli (∆E_Pauli), orbital (∆E_orb), and dispersion (∆E_dis) interaction to the total interaction energy (∆E_int). Clearly, for X@C₆₀ (X = H₂O, NH₃), the terms ∆E_elstat, ∆E_orb and ∆E_disp act as the stabilizing components, while the ∆E_Pauli term constitutes the destabilization factor for X@C₆₀. Decomposition of this term indicates that the total attractive interaction between the X and C₆₀ is dominated by the ∆E_elstat and ∆E_disp, the covalent term introduced by ∆E_orb. However, for cationic X⁺@C₆₀ (X⁺ = H⁺, H₃O⁺, NH₄⁺), the terms ∆E_orb and ∆E_disp act as the stabilizing components, while the ∆E_Pauli and ∆E_elstat terms constitute the destabilization factor. In general, the ∆E_elstat term is an attractive interaction. The results in Table 2 reinforce the observation that ∆E_elstat plays the most significant role in connection with the unfavorable nature of X⁺@C₆₀, as the ∆E_Pauli is of comparable magnitude to ∆E_disp, but the electrostatic term has a much more destabilizing effect. The ∆E_int results suggest that the interaction between X⁺ and C₆₀ is strong but significantly weaker in X@C₆₀. The ∆E_orb component of ∆E_int is rather stronger in X⁺@C₆₀ than in X@C₆₀, and its magnitude is sufficient to compensate for the destabilizing influence of ∆E_elstat and ∆E_Pauli, which is ultimately responsible for the stability of X⁺@C₆₀.

The electron density difference was calculated to explain the orbital interactions between X⁺ and C₆₀. Figure 3 displays the electron density difference, with green and blue parts corresponding to regions where the electron density is increased and decreased, respectively. Generally, significant electron polarization between the host and guest leads to a stronger electrostatic interaction. As shown in Figure 3, in X@C₆₀, the C₆₀ cage has almost no polarization of electron density. This result indicates that the interaction between the carbon cage and X is weak. In the X⁺@C₆₀ system, except for H⁺, there is electron accumulation localized in the C₆₀ cage, while there is electron depletion on X⁺. This corresponds to the electron transfer resulting from the interaction between X⁺ and C₆₀. For the H⁺@C₆₀ system, it is noteworthy that the H⁺ shows a very high density of polarized electrons, which verifies the strong binding fore of the C-H bond. Meanwhile, it can be found that there is obvious electron density electron polarization in the H atom of H₃O⁺@C₆₀. The relatively strong electron polarization between the H₃O⁺ and C₆₀ cage suggests the stronger electrostatic interaction between them. However, although the NH₄⁺ is confined in the C₆₀ cage, the cage shows only slight polarization. Our calculation result also indicates that the interaction between NH₄⁺ and C60 molecules is weak. These findings are thoroughly in accordance with previous studies based on energy decomposition analysis.

In order to quantitatively estimate the interaction between X/X⁺ and C₆₀, we performed atomic dipole moment corrected Hirshfeld charge fitting (ADCH), as shown in

Table 3. The ADCH charge populations of the neutral species X = H₂O ad NH₃ and the cationic species X⁺ = H⁺, H₃O⁺, NH₄⁺, and X/X⁺@C₆₀ (unit is e).

		ADCH			ADCH
H2O	O	−0.714	H2O@C60	O	−0.538
	H	0.357		H	0.266
	H	0.357		H	0.266
NH3	N	−0.968	NH3@C60	N	−0.680
	H	0.323		H	0.223
	H	0.323		H	0.223
	H	0.323		H	0.222
H+	H	1	H+@C60	H	0.053
H3O+	O	−0.480	H3O+@C60	O	−0.165
	H	0.493		H	0.268
	H	0.493		H	0.266
	H	0.493		H	0.265
NH4+	N	−0.249	NH4+@C60	N	−0.134
	H	0.312		H	0.203
	H	0.312		H	0.204
	H	0.312		H	0.206
	H	0.312		H	0.206

. Generally, the ADCH charge is a good charge population analysis method for confined systems [14]. The ADCH charge on X/X⁺@C₆₀ is higher than that on free X/X⁺ because the electronegativity of C is greater than that of X/X⁺. Here, it can be seen that the H₂O (O: −0.714 e) and NH₃ (N: −0.968 e) possess larger negative charges than H₂O@C₆₀ (O: −0.538 e) and NH₃@C₆₀ (N: −0.538 e), and H₂O (H: 0.357 e) and NH₃ (H: 0.323 e) possess larger positive charges than H₂O@C₆₀ (H: 0.266 e) and NH₃@C₆₀ (H: 0.233 e), indicating the interaction between H₂O, NH₃ and C₆₀. However, the ADCH charges of H⁺@C₆₀ (H: 0.053 e) are noticeably smaller than that of free H⁺(H: 1 e), indicating stronger interaction between H⁺ and C₆₀. The H₃O⁺ (O: −0.480 e) has a relatively larger negative charge than H₃O⁺@C₆₀ (O: −0.165 e). The charges are less accumulated in the H₃O⁺@ C₆₀, which implies a charge transfer effect from H₃O⁺ to the C₆₀ cage. In addition, the ADCH charges of H (0.493 e) are the same in the H₃O⁺, while the ADCH charges of H are not equal in H₃O⁺@C₆₀. This may be because the H₃O⁺ encapsulated inside the fullerene cage shows a slight deviation from the center. The ADCH charges of NH₄⁺ (N: −0.249 e) possess a larger negative charge than NH₄⁺@C₆₀ (N: −0.134 e). However, The ADCH charges of NH₄⁺ (H: 0.312 e) are the same, and the charges of H are also not equal in NH₄⁺@C₆₀.

To gain a deeper insight into the effect of confined species X/X⁺ on the electronic structure of C₆₀ cage, the density of states (DOS) of C₆₀ and X/X⁺@C₆₀ are calculated (as shown in Figure 4). In Figure 4, the red and blue lines represent the contributions of two fragments of C₆₀ cage and X/X⁺ to the DOS. H and L represent the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (HOMO), respectively. The HOMO-LUMO gaps (i.e., the energy difference between HOMO and LUMO levels) of C₆₀ and X/X⁺@C₆₀ are marked in Figure 4. Compared with the total density of state (TDOS) distributions of C₆₀, the TDOS distributions of X@C₆₀ are basically unchanged. This implies that there is only a slight interaction between X and C₆₀. Moreover, the TDOS is mostly attributed to the contribution from C₆₀, indicating that there are few electrons occupied by embedded species in the molecular orbital. The energy gaps of C₆₀, H₂O@C₆₀ and NH₃@C₆₀ are 2.77 kcal/mol, 2.75 kcal/mol and 2.74 kcal/mol, respectively. The results reveal that the energy gap of X@C₆₀ is slightly smaller than that of the C₆₀ cage. Therefore, this indicates a weak interaction between X and the C₆₀ cage. This is consistent with the results of previous encapsulated species studies [27,50,51,52]. However, the DOS curves of X⁺@C₆₀ change significantly, especially for H⁺@C₆₀ and H₃O⁺@C₆₀ in the TDOS curves. This is attributed to the H atom adsorbed on the C₆₀ cage in H₃O⁺@C₆₀, which is different from other systems. For the H₃O⁺@C₆₀ system, it indicates a strong interaction between the H₃O⁺ and C₆₀. In contrast, the DOS curves of NH₄⁺@C₆₀ show only slight variations, indicating the weak interaction between NH₄⁺ and C₆₀. Meanwhile, the calculated energy gap of H⁺@C₆₀ is 2.24 kcal/mol, which is the lowest energy gap of H⁺@C₆₀ among all the systems. This is because H⁺ is attached to the C atom. In the H⁺@C₆₀ system, the LUMO orbitals split into two small peaks. This state is a hybrid of C-2p and H-1s orbitals, causing novel peaks in DOS. The energy gaps of H₃O⁺@C₆₀ and NH₄⁺@C₆₀ are 2.75 kcal/mol and 2.79 kcal/mol, respectively. The H₃O⁺@C₆₀ and H₂O@C₆₀ have the same energy gap. In contrast, the energy gap of H₃O⁺@C₆₀ is reduced by 0.02 kcal/mol compared to that of NH₄⁺@C₆₀.

To understand the electronic properties, we displayed the frontline molecular orbital diagrams of C₆₀ and X/X⁺@C₆₀. The HOMO and LUMO orbitals for C₆₀ and X/X⁺@C₆₀ are plotted in Figure 5. The molecular orbitals involved for the first time by confined species are also depicted in Figure 5. The corresponding frontier molecular orbitals are similar in all these cases. The HOMO iso-surface of C₆₀ is symmetrically distributed on its surface, formed by contribution of π-π bonds and some contribution of σ bonds located on C atoms. The LUMO iso-surface is located on C atoms due to contribution of s electrons, and some π-π bonds are displayed on the rest of its surface as well. For X/X⁺@C₆₀ systems, the HOMO orbitals are also mainly located on the C₆₀ cage, whereas the LUMO orbitals of X/X⁺@C₆₀ are located on both confined species and the C₆₀ cage, similar to those reported for other endohedral fullerenes [53,54]. For the H₂O@C₆₀ system, the HOMO electronic distributed is on the C₆₀ cage, and the π bonds remain in both parts; the LUMO iso-surface is uniformly distributed on the surface with π-π bonds. The HOMO-32 orbital is mainly constructed by the O-2p orbital, with a very small contribution from the C-2p orbital. For the HOMO frontier orbital associated with the NH₃@C₆₀ system, it is concentered on the C₆₀ cage displaying π-π bonds, whereas the LUMO electronic distribution is exhibited on C atoms that come from π-π bonds around the surface, alongside the contribution of p electrons. Whereas for the HOMO-12 orbital, the contribution comes from N-2p and C-2p orbitals in NH₃@C₆₀, for the H⁺@C₆₀ system, the HOMO iso-surface is concentrated on the C₆₀ cage displaying π-π bonds. The electronic distribution of LUMO is located on the C-H bond, whereas π-π bonds are displayed on the surface of the C₆₀ cage. It can be seen that the main contribution in HOMO-13 comes from H-1s and C-2p orbitals. For the H₃O⁺@C₆₀ system, the HOMO iso-surface is concentered on the C₆₀ cage displaying π-π bonds, the electronic distribution of LUMO is located on the bond of O-H and C₆₀ cage, and the HOMO-37 orbital involved in confined species is mainly constructed by the C-2p orbitals and a few H-s orbitals. For NH₄⁺@C₆₀ systems, similar features are shown on the HOMO iso-surface; the electronic distribution of LUMO is located on the C₆₀ cage. The HOMO-37 orbital is involved in confined species and is mainly constructed by the C-2p orbital displaying π-π bonds.

The IR spectra of X = H₂O, NH₃, X⁺ = H⁺, H₃O⁺, NH₄⁺, and X/X⁺@C₆₀ are presented in Figure 6. The vibrational spectra of H₂O@C₆₀, H₃O⁺@C₆₀, and NH₄⁺@C₆₀ share many characteristics with spectrum of C₆₀. Figure 6 shows that the spectrum of H₂O@C₆₀ closely resembles the spectrum of the pristine C₆₀. In addition, the vibrational features of H₂O are very weak in the IR spectrum of H₂O@C₆₀, indicating the potential screening effect of the fullerene cage [17]. However, most of the bands in the spectrum of the NH₃@C₆₀ look quite similar to that of C₆₀, except for one weak peak observed (marked with a circle in Figure 6). This peak is mainly derived from the N-H wagging mode and is slightly blue-shifted compared to NH₃. The IR spectrum of H⁺@C₆₀ is much more complicated than that of the other embedded systems. This is mainly due to the formation of the C-H bond between the H and C₆₀ cage. The IR spectrum of the H₃O⁺@C₆₀ looks quite similar to that of C₆₀, except for two weak peaks and a strong peak (marked with a square in Figure 6). These peaks are mainly derived from the O-H stretching mode. For the H₃O⁺@C₆₀ system, except for the O-H free stretch mode, all the normal modes of confined H₃O⁺ are slightly red-shifted compared to free H₃O⁺. Interestingly, in the O-H stretching mode, a small peak is observed inside H₃O⁺ (marked with arrows in Figure 6). The peak change due to encapsulation can be attributed to the interaction effect between H₃O⁺ and the C₆₀ cage. Moreover, the NH₄⁺@C₆₀ and C₆₀ spectra show similarity in the whole spectral region, except for the N-H free stretch mode. This result indicates a weak interaction between NH₄⁺ and the C₆₀ cage.

Electrostatic potential has been widely used in the study of interactions and has become one of the most common means of analyzing the interaction between molecules. Moreover, the electrostatic potential explains the charge distribution on a molecule and indicates electrophilic positively charged or nucleophilic negatively charged properties. Therefore, we calculated the electrostatic potential of C₆₀ and X/X⁺@C₆₀. Blue and red colors represent negative potential and positive potential, respectively. As shown in Figure 7, for the electrostatic potential of the C₆₀ cage, the positive electrostatic potential region is mainly distributed in center of the cage, and the surface of the cage is close to neutral. For the electrostatic potential of X@C₆₀, there is no obvious change in the electrostatic potential due to encapsulation of neutral species inside the cage. Encapsulation of X⁺ induces positive electrostatic potential both inside and outside the C₆₀ cage; it can be seen from the figure that the electrostatic potential distribution of H⁺@C₆₀ in C₆₀ cage is different from that of H₃O⁺@C₆₀ and NH₄⁺@C₆₀. This is mainly due to the H⁺ adsorbing on the C atom. For H₃O⁺@C₆₀, the positive electrostatic potential is more distributed on the O atom. This result indicates that there is electron polarization between H₃O⁺ and C₆₀, which is consistent with our previous result. For NH₄⁺@C₆₀, NH₄⁺ is at the center of the cage, and there is a uniform distribution of the electrostatic potential. However, when the guest species is in an off-centered position, the electrostatic potential is more localized inside the cage. This shows the electron polarization of the X⁺ system compared to the X species located at the center of the cage.

To explore the effects of H₂O on the adsorption behavior, we calculated the structure of H₂O adsorbed on the surface of C₆₀, X⁺@C₆₀ (X⁺ = H⁺, H₃O⁺, NH₄⁺), and X@C₆₀ (X = H₂O, NH₃). The lowest-energy structures are shown in Figure 8 (for coordinates of the optimized molecular structure, see Supplementary Materials). For H₂O adsorption on neutral species X@C₆₀, the H atoms of H₂O point towards the C atoms of the C₆₀ cage. However, when H₂O adsorbs on ionic species X⁺@C₆₀, the O atom of H₂O is most likely to point towards the six-membered ring of the C₆₀ cage. This result indicates that O atoms prefer to be located in the region of positive electrostatic potential outside the C₆₀ cage. For H₂O adsorbed on H⁺@C₆₀, the O atom of H₂O is close to the C atoms of C₆₀. This is probably due to the H atom being absorbed on the C atom and having the lowest adsorption energy (−9.23 kcal/mol). Furthermore, from Figure 8, we can also learn that the interaction between H₂O and X⁺@C₆₀ is much stronger than that with X@C₆₀, indicating the presence of positive electrostatic potential.

To explicitly assess the effect of solvent on X/X⁺@C₆₀ interactions, the IEFPCM (integral equation formalism–PCM model) was calculated (see Figure 9). All the negative solvation energies indicate spontaneous solvation. It can be inferred from the above data that a smaller value of solvation energy leads to improved solubility of the complex in the aqueous phase. Solvation studies also reveal that the solvent medium, i.e., water, stabilizes the complex by decreasing its solvation energy. The solvation energies for C₆₀, H₂O@C₆₀ and NH₃@C₆₀ are −8.08 kcal/mol, −14.26 kcal/mol, and −8.51 kcal/mol, respectively. It is observed that the solvation energy of C₆₀ is slightly higher than the calculated solvation energy of NH₃@C₆₀. Among the neutral species, the solvation energy of H₂O@C₆₀ is the lowest, indicating that H₂O@C₆₀ is stable in the aqueous phase. However, the solvation energies for H⁺@C₆₀, H₃O⁺@C₆₀ and NH₄⁺@C₆₀ are −51.42 kcal/mol, −63.94 kcal/mol, and −58.02 kcal/mol, respectively. H₃O⁺@C₆₀ has the lowest solvation energy, followed by NH₄⁺@C₆₀. H⁺@C₆₀ has a relatively lower solvation energy, suggesting that H⁺@C₆₀ is stable in the aqueous phase. This is consistent with the results from the adsorption energy analysis.

4. Materials and Methods

In this work, the cationic X⁺@C₆₀ (X⁺ = H⁺, H₃O⁺, and NH₄⁺), as well as their corresponding neutral species (X = H₂O, NH₃), have been studied using the hybrid generalized gradient approximation (hybrid GGA) B3LYP [55,56] function. Grimme’s empirical dispersion correction with Beck-Johnson damping (D3BJ) was used to consider weak interactions. The 6-31G(d, p) was used to describe all the atoms. In this case, all atoms were allowed to relax. To ensure we obtained the minimum energy structures, vibrational frequency verifications were also performed at the same level of theory. All the structures were assessed with the Gaussian 09 package [57]. The energy decomposition analysis was performed using the B3LYP-D3BJ and TZP basis sets in ADF 2016 [58]. Multiwfn 3.8 [59] programs were used to obtain the electronic structure data.

The interaction energy $∆{\mathrm{E}}_{\mathrm{i}\mathrm{n}\mathrm{t}}$ can be decomposed into electroatatic interaction $∆{\mathrm{E}}_{\mathrm{e}\mathrm{l}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}$, repulsive exchange (Pauli) interaction $∆{\mathrm{E}}_{\mathrm{P}\mathrm{a}\mathrm{u}\mathrm{l}\mathrm{i}}$, orbital interaction $∆{\mathrm{E}}_{\mathrm{o}\mathrm{r}\mathrm{b}},$ and dispersion interaction $∆{\mathrm{E}}_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{p}}$.

$$∆{\mathrm{E}}_{\mathrm{i}\mathrm{n}\mathrm{t}}=∆{\mathrm{E}}_{\mathrm{e}\mathrm{l}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}+∆{\mathrm{E}}_{\mathrm{P}\mathrm{a}\mathrm{u}\mathrm{l}\mathrm{i}}+∆{\mathrm{E}}_{\mathrm{o}\mathrm{r}\mathrm{b}}+∆{\mathrm{E}}_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{p}}$$

(1)

where $∆{\mathrm{E}}_{\mathrm{e}\mathrm{l}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}$ is the conventional electrostatic interaction between two molecules. $∆{\mathrm{E}}_{\mathrm{P}\mathrm{a}\mathrm{u}\mathrm{l}\mathrm{i}}$ is the repulsive Pauli interaction between the occupied orbitals of two different molecules. $∆{\mathrm{E}}_{\mathrm{o}\mathrm{r}\mathrm{b}}$ stands for the stabilizing interactions between the occupied molecular orbitals in one molecule and the unoccupied molecular orbitals in the other molecule along with the interaction of occupied and virtual orbitals within the same molecule in the final geometry. $∆{\mathrm{E}}_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{p}}$ represents the dispersion forces.

To obtain a deep insight into the nature of the charge transformation, we calculated the electron density difference between X/X⁺ and the C₆₀ cage. This can be exactly calculated as

$$∆\mathsf{\rho }={\mathsf{\rho }}_{\mathrm{X}/{\mathrm{X}}^{+}@{\mathrm{C}}_{60}}-{\mathsf{\rho }}_{{\mathrm{C}}_{60}}-{\mathsf{\rho }}_{\mathrm{X}/{\mathrm{X}}^{+}}$$

(2)

where ${\mathsf{\rho }}_{\mathrm{X}/{\mathrm{X}}^{+}@{\mathrm{C}}_{60}}$, ${\mathsf{\rho }}_{{\mathrm{C}}_{60}}$, and ${\mathsf{\rho }}_{\mathrm{X}/{\mathrm{X}}^{+}}$ represent the electron density of X/X⁺@C₆₀, C₆₀, and X/X⁺, respectively.

The adsorption energy (${\mathrm{E}}_{\mathrm{a}\mathrm{d}\mathrm{s}}$) is an important factor in measuring the adsorption capacity of a structure. When molecule A is adsorbed on surface B, the calculation formula of adsorption energy is as follows:

$${\mathrm{E}}_{\mathrm{a}\mathrm{d}\mathrm{s}}={\mathrm{E}}_{{\mathrm{H}}_2\mathrm{O}-\mathrm{X}/{\mathrm{X}}^{+}@{\mathrm{C}}_{60}}-{\mathrm{E}}_{\mathrm{X}/{\mathrm{X}}^{+}@{\mathrm{C}}_{60}}-{\mathrm{E}}_{{\mathrm{H}}_2\mathrm{O}}$$

(3)

where ${\mathrm{E}}_{{\mathrm{H}}_2\mathrm{O}-\mathrm{X}/{\mathrm{X}}^{+}@{\mathrm{C}}_{60}}$ is the total energy after H₂O adsorption, and ${\mathrm{E}}_{\mathrm{X}/{\mathrm{X}}^{+}@{\mathrm{C}}_{60}}$ and ${\mathrm{E}}_{{\mathrm{H}}_2\mathrm{O}}$ are the total energy of adsorbate $\mathrm{X}/{\mathrm{X}}^{+}@{\mathrm{C}}_{60}$ and H₂O, respectively. A negative value indicates a favorable exothermic adsorption.

The integral equation formalism-PCM model (IEFPCM) was applied [60]. Being an essential part of the living system, water was chosen as a solvent with which to study the solubility and stability of the complex. The stability and solubility of X/X⁺@C₆₀ can be calculated using the following expression:

$${\mathrm{E}}_{\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{v}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}={\mathrm{E}}_{\mathrm{s}\mathrm{o}\mathrm{l}}-{\mathrm{E}}_{\mathrm{g}\mathrm{a}\mathrm{s}}$$

(4)

where ${\mathrm{E}}_{\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{v}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}$ represents system’s total solvation energy, while ${\mathrm{E}}_{\mathrm{s}\mathrm{o}\mathrm{l}}$ and ${\mathrm{E}}_{\mathrm{g}\mathrm{a}\mathrm{s}}$ stand for the energy in the solvent phase and gas phase, respectively. All the negative solvation energies indicate a spontaneous solvation.

5. Conclusions

In this study, we performed a systematic theoretical investigation on the geometric and electronic structures of cationic X⁺@C₆₀ (X⁺ = H⁺, H₃O⁺, and NH₄⁺) as well as their corresponding neutral species (X = H₂O, NH₃). A deeper understanding of cationic X⁺@C₆₀ was obtained. Our results revealed that the confined species almost did not change the geometric structure of the C₆₀ cage, except for H⁺. For the H⁺@C₆₀ system, the H⁺ was attached to C atom in H⁺@C₆₀, forming a C-H chemical bond. Meanwhile, we found that orbital interaction plays a significant role between the cationic X⁺ species and the C₆₀ cage. Electronic structure analysis showed that the electron polarization of X⁺@C₆₀ was stronger than that of X@C₆₀. This has important implications for energy applications. For instance, the unique electronic properties of these systems could potentially be harnessed in the development of advanced energy storage materials. The strong electron polarization in X+@C₆₀ could lead to more efficient charge transfer and storage capabilities. Additionally, understanding the interactions between protons and the C₆₀ cage could contribute to the design of novel fuel cells or batteries that utilize proton conduction. The encapsulated protons could offer a stable and controlled environment for energy conversion processes. We hope that this work will pave the way for further development of proton applications in the future, especially in the field of energy, where innovative solutions are desperately needed to meet the growing demand for sustainable and efficient energy sources.