Activation of CO2 on the Surfaces of Bare, Ti-Adsorbed and Ti-Doped C60

There is a growing interest in finding a suitable catalyst for the adsorption and activation of CO2 molecules to minimize the effect of global warming. In this study, density functional theorybased simulations are employed to examine the adsorption and activation of a CO2 molecule on the pure, Ti-supported and Ti-doped surfaces of C60. The adsorption on the pure surface is very week. Adsorption becomes significant on the Ti-supported C60 surface together with significant activation. Such strong adsorption is evidenced by the significant charge transfer between Ti and C60. The Ti-doped C60 surface adsorbs weakly, but the activation is not significant.

Buckminsterfullerene (C 60 ) has gathered a lot of interest due to its wide range of properties such as high thermal, chemical and mechanical stability [19]. Both inner and outer surfaces of C 60 have been thoroughly studied for encapsulation and adsorption of a variety of atoms and molecules respectively [20][21][22][23][24][25]. Alkali or transition metal adsorbed or doped C 60 surfaces have been considered for the adsorption and the activation of small molecules such H 2 , N 2 and CO 2 [20,22,23,25]. Transition metal-doped C 60 structures have some special features over alkali atoms-doped C 60 . They are size mismatch between highly charged metal ions and C 60 and small lattice energies of hypothetical M n+ −C 60 n− complexes. Titanium doped C 60 has been studied experimentally and theoretically as a candidate catalyst to adsorb H 2 and activate N 2 molecules [22,23]. It is anticipated that Ti atom supported on a C 60 molecule can introduce a charge transfer (Ti to C 60 ) due to the larger electronegativity of C 60 . The positively charged Ti is expected to enhance the adsorption of CO 2 molecule via strong Ti−O bond formation.
Here, computational modelling based on the density functional theory (DFT) is used to examine the adsorption efficacy of a CO 2 molecule on the surfaces of pure, Ti-adsorbed and Ti-doped C 60. The current methodology enabled us to determine the relaxed configurations together with electronic structures and charges on the adsorbed or doped Ti or CO 2 molecule.

Computational Methods
A DFT simulation code VASP (Vienna ab initio simulation program) [26] was used to perform all calculations. Projected augmented wave (PAW) potentials [27] and plane wave basis sets (cut-off of 500 eV) were used. The exchange correlation term was modelled using the generalized gradient approximation (GGA) as parameterized by Perdew, Burke, and Ernzerhof (PBE) [28]. All structures were optimized using the conjugate gradient algorithm [29]. The forces on the atoms were less than 0.001 eV/Å. A supercell with a Fuels 2022, 3 dimension of 25 × 25 Å × 25 Å was used to ensure that the adjacent molecules do not interact with each other in all directions. A single Ti atom was considered at different positions on the surface of C 60 for adsorption. The most favorable relaxed structure was allowed to interact a CO 2 molecule. Doping of Ti was carried out by replacing a C atom on the C 60 molecule with Ti atom. A 2 × 2 × 2 Monk-horst k-point mesh [30] was used to relax all structures. Semi-empirical dispersive interactions were included as described by Grimme et al. [31] The charges on the atoms were calculated using the Bader charge analysis [32]. Adsorption energy was calculated for a CO 2 molecule interacting the C 60 surface using the following equation. E ads = E CO 2 : C 60 -E C 60 -E CO 2 (1) where E CO 2 : C 60 is the total energy of a CO 2 molecule interacting the surface of C 60 , E C 60 is the total energy of a C 60 molecule and E CO 2 is the total energy of a CO 2 molecule.

Strucure of C 60
C 60 molecule is spherical and is formed by 12 pentagonal and 20 hexagonal molecules (see Figure 1a). It consists of two different carbon-carbon bonds (C-C and C=C) and their experimental values are reported to be 1.43 Å and 1.39 Å respectively [33]. First we optimized the C 60 molecule to determine the equilibrium bond lengths to validate the pseudo potentials and basis sets used for C, Ti and O in this study. In the relaxed structure, the C-C and C=C bond distances were calculated to be 1.44 Å and 1.40 Å respectively, agreeing well with the corresponding experimental values. The calculated density of the states plot is shown in Figure 1b. The calculated gap between the highest occupied level and the lowest unoccupied level is 1.30 eV in a reasonable agreement with the values (1.55 eV and 1.63 eV) calculated in previous DFT simulations [34,35]. The underestimation of the band gap (E gap ) can be attributed to the failure of GGA functionals describing the exchange-correlation effect. and Ernzerhof (PBE) [28]. All structures were optimized using the conjugate gradient algorithm [29]. The forces on the atoms were less than 0.001 eV/Å. A supercell with a dimension of 25 × 25 Å × 25 Å was used to ensure that the adjacent molecules do not interact with each other in all directions. A single Ti atom was considered at different positions on the surface of C60 for adsorption. The most favorable relaxed structure was allowed to interact a CO2 molecule. Doping of Ti was carried out by replacing a C atom on the C60 molecule with Ti atom. A 2 × 2 × 2 Monk-horst k-point mesh [30] was used to relax all structures. Semi-empirical dispersive interactions were included as described by Grimme et al. [31] The charges on the atoms were calculated using the Bader charge analysis [32]. Adsorption energy was calculated for a CO2 molecule interacting the C60 surface using the following equation.
where E : C is the total energy of a CO2 molecule interacting the surface of C60, E is the total energy of a C60 molecule and E is the total energy of a CO2 molecule.

Strucure of C60
C60 molecule is spherical and is formed by 12 pentagonal and 20 hexagonal molecules (see Figure 1a). It consists of two different carbon-carbon bonds (C-C and C=C) and their experimental values are reported to be 1.43 Å and 1.39 Å respectively [33]. First we optimized the C60 molecule to determine the equilibrium bond lengths to validate the pseudo potentials and basis sets used for C, Ti and O in this study. In the relaxed structure, the C-C and C=C bond distances were calculated to be 1.44 Å and 1.40 Å respectively, agreeing well with the corresponding experimental values. The calculated density of the states plot is shown in Figure 1b. The calculated gap between the highest occupied level and the lowest unoccupied level is 1.30 eV in a reasonable agreement with the values (1.55 eV and 1.63 eV) calculated in previous DFT simulations [34,35]. The underestimation of the band gap (Egap) can be attributed to the failure of GGA functionals describing the exchangecorrelation effect.

Encapsulation of CO2 Inside the Pure C60
A single CO2 molecule was encapsulated and its encapsulation energy was calculated. Encapsulation is endoergic with and without dispersion (see Table 1). Dispersion improved the encapsulation by ~0.70 eV. A very small amount of charge is transferred between the CO2 molecule and the C60 showing non-covalent interaction. The total DOS plot shows that the Fermi energy level and the value of the gap are almost unaffected (see Figure 2b). The charge density plot shows that there is no overlap between the CO2 molecule and the inner wall of C60 (see Figure 2c).

Encapsulation of CO 2 Inside the Pure C 60
A single CO 2 molecule was encapsulated and its encapsulation energy was calculated. Encapsulation is endoergic with and without dispersion (see Table 1). Dispersion improved the encapsulation by~0.70 eV. A very small amount of charge is transferred between the CO 2 molecule and the C 60 showing non-covalent interaction. The total DOS plot shows that the Fermi energy level and the value of the gap are almost unaffected (see Figure 2b). The charge density plot shows that there is no overlap between the CO 2 molecule and the inner wall of C 60 (see Figure 2c).

Adsorption of CO2 on the Surface of Pure C60
The adsorption of CO2 molecule was next considered. The relaxed structure is shown in Figure 2d. The adsorption is exoergic with dispersion and endoergic without dispersion, indicating the importance of dispersion (see Table 1). Charge transfer is negligible. The electronic structure is almost unaffected by the adsorption (see Figure 2e) as evidenced by the charge density plot in which there is no interaction of charge density (see Figure 2f).

Adsorption of CO2 on the Surface of C60 Supported with Ti
Next, I considered a CO2 molecule adsorbed on the Ti-supported C60 surface. Five different starting configurations were considered (see Figure 3) for the Ti interacting with C60. In the configurations H and P, the Ti atom is positioned on the hexagonal ring and the pentagonal ring respectively. The configurations 66 and 65 accommodate the Ti atom above the bonds bridging hexagonal-hexagonal and hexagonal-pentagonal rings respectively. In the initial structure C, Ti atom is located above the C atom on the C60 surface. All initial configurations were fully relaxed. Table 2 lists the relative energies of the final configurations. The most stable configuration is found to be the configuration H. The inclusion of dispersion does not affect the trend in the relative energies. Corresponding information (d-f) is also provided for a CO 2 molecule adsorbed on the surface of C 60 .

Adsorption of CO 2 on the Surface of Pure C 60
The adsorption of CO 2 molecule was next considered. The relaxed structure is shown in Figure 2d. The adsorption is exoergic with dispersion and endoergic without dispersion, indicating the importance of dispersion (see Table 1). Charge transfer is negligible. The electronic structure is almost unaffected by the adsorption (see Figure 2e) as evidenced by the charge density plot in which there is no interaction of charge density (see Figure 2f).

Adsorption of CO 2 on the Surface of C 60 Supported with Ti
Next, I considered a CO 2 molecule adsorbed on the Ti-supported C 60 surface. Five different starting configurations were considered (see Figure 3) for the Ti interacting with C 60 . In the configurations H and P, the Ti atom is positioned on the hexagonal ring and the pentagonal ring respectively. The configurations 66 and 65 accommodate the Ti atom above the bonds bridging hexagonal-hexagonal and hexagonal-pentagonal rings respectively. In the initial structure C, Ti atom is located above the C atom on the C 60 surface. All initial configurations were fully relaxed. Table 2 lists the relative energies of the final configurations. The most stable configuration is found to be the configuration H. The inclusion of dispersion does not affect the trend in the relative energies.  The relaxed structure of Ti adsobed on the hexagonal ring of C60 (H) is shown in Figure 4a. The adsorbed Ti forms strond bonds with C in the hexagonal ring are described by the shorter Ti-C bond lenghts (see Figure 4b). The Bader charge analysis shows that there is a significant charge transfer from Ti to the C in the hexagonal ring (see Figure 4b). This is further confirmed by the positive Bader charge on the Ti atom and the negative Bader charges on the C. The adsorption energy was calculated using a Ti atom as a reference state. Adsorption is negative and its value is −1.71 eV with dispersion. Exclusion of dispersion reduces the adsorption by 0.04 eV as expected. The total DOS plot exhibits that the Ti-supported C60 is metallic (see Figure 5a). This is due to strong perturbation of C60 with Ti. The atomic DOS plots shows that the Fermi energy level is mainly populated with d states of Ti (see Figure 5b).  The relaxed structure of Ti adsobed on the hexagonal ring of C 60 (H) is shown in Figure 4a. The adsorbed Ti forms strond bonds with C in the hexagonal ring are described by the shorter Ti-C bond lenghts (see Figure 4b). The Bader charge analysis shows that there is a significant charge transfer from Ti to the C in the hexagonal ring (see Figure 4b). This is further confirmed by the positive Bader charge on the Ti atom and the negative Bader charges on the C. The adsorption energy was calculated using a Ti atom as a reference state. Adsorption is negative and its value is −1.71 eV with dispersion. Exclusion of dispersion reduces the adsorption by 0.04 eV as expected.  The relaxed structure of Ti adsobed on the hexagonal ring of C60 (H) is shown in Figure 4a. The adsorbed Ti forms strond bonds with C in the hexagonal ring are described by the shorter Ti-C bond lenghts (see Figure 4b). The Bader charge analysis shows that there is a significant charge transfer from Ti to the C in the hexagonal ring (see Figure 4b). This is further confirmed by the positive Bader charge on the Ti atom and the negative Bader charges on the C. The adsorption energy was calculated using a Ti atom as a reference state. Adsorption is negative and its value is −1.71 eV with dispersion. Exclusion of dispersion reduces the adsorption by 0.04 eV as expected. The total DOS plot exhibits that the Ti-supported C60 is metallic (see Figure 5a). This is due to strong perturbation of C60 with Ti. The atomic DOS plots shows that the Fermi energy level is mainly populated with d states of Ti (see Figure 5b). The total DOS plot exhibits that the Ti-supported C 60 is metallic (see Figure 5a). This is due to strong perturbation of C 60 with Ti. The atomic DOS plots shows that the Fermi energy level is mainly populated with d states of Ti (see Figure 5b). A single CO2 molecule was allowed to adsorb on the surface of Ti-supported C60. The relaxed configuration is shown in Figure 6a. In this structure, the CO2 molecule exhibits a nonlinear structure. There is a significant elongation in the bond lengths of C-O in comparison with those found in molecular CO2 (1.18 Å) (see Figure 6b). This indicates that depletion of CO2 can be enhanced by the support of Ti on the surface of C60. The Bader charge analysis shows that the net charge on the CO2 molecule is −1.19. Adsorption energy of the CO2 molecule was calculated. Adsorption is exoergic with an adsorption energy of −1.57 eV. Adsorption becomes less negative (by 0.06 eV) without dispersion. Adsorption is exoergic as confirmed by the strong bonding between Ti and oxygen in the CO2 molecule. The resultant configuration exhibits a narrow-gap semiconductor (see Figure 6c). The states appearing around the Fermi level are contributed to by the d states of Ti (see Figure 6d). A single CO 2 molecule was allowed to adsorb on the surface of Ti-supported C 60 . The relaxed configuration is shown in Figure 6a. In this structure, the CO 2 molecule exhibits a nonlinear structure. There is a significant elongation in the bond lengths of C-O in comparison with those found in molecular CO 2 (1.18 Å) (see Figure 6b). This indicates that depletion of CO 2 can be enhanced by the support of Ti on the surface of C 60 . The Bader charge analysis shows that the net charge on the CO 2 molecule is −1.19. A single CO2 molecule was allowed to adsorb on the surface of Ti-supported C60. The relaxed configuration is shown in Figure 6a. In this structure, the CO2 molecule exhibits a nonlinear structure. There is a significant elongation in the bond lengths of C-O in comparison with those found in molecular CO2 (1.18 Å) (see Figure 6b). This indicates that depletion of CO2 can be enhanced by the support of Ti on the surface of C60. The Bader charge analysis shows that the net charge on the CO2 molecule is −1.19. Adsorption energy of the CO2 molecule was calculated. Adsorption is exoergic with an adsorption energy of −1.57 eV. Adsorption becomes less negative (by 0.06 eV) without dispersion. Adsorption is exoergic as confirmed by the strong bonding between Ti and oxygen in the CO2 molecule. The resultant configuration exhibits a narrow-gap semiconductor (see Figure 6c). The states appearing around the Fermi level are contributed to by the d states of Ti (see Figure 6d). Adsorption energy of the CO 2 molecule was calculated. Adsorption is exoergic with an adsorption energy of −1.57 eV. Adsorption becomes less negative (by 0.06 eV) without dispersion. Adsorption is exoergic as confirmed by the strong bonding between Ti and oxygen in the CO 2 molecule. The resultant configuration exhibits a narrow-gap semiconductor (see Figure 6c). The states appearing around the Fermi level are contributed to by the d states of Ti (see Figure 6d).

Adsorption of CO 2 on the Surface Ti-Doped C 60
The efficacy of Ti-doped surface for the adsorption of CO 2 was next considered. The relaxed structure of Ti-doped C 60 is shown in Figure 7a. In the relaxed structure, the Ti atom is displaced forming longer Ti−C bond lengths compared to C−C bond lengths (see Figure 7b). There is a significant distortion in the relaxed structure. The Bader charge analysis exhibits a significant charge transfer between Ti and three C atoms directly bonded to it. The Bader charge on the Ti is +2.21. The loss of 2.21 electrons is gained by three nearest neighbor C atoms. The total DOS plot exhibits that the resultant structure is a semi-conductor with a band gap of 0.6 eV. This value is lower than that found for the pure C 60 . The atomic DOS plots shows that states near the Fermi level are mainly associated with the d sates of Ti.

Adsorption of CO2 on the Surface Ti-Doped C60
The efficacy of Ti-doped surface for the adsorption of CO2 was next considered. The relaxed structure of Ti-doped C60 is shown in Figure 7a. In the relaxed structure, the Ti atom is displaced forming longer Ti−C bond lengths compared to C−C bond lengths (see Figure 7b). There is a significant distortion in the relaxed structure. The Bader charge analysis exhibits a significant charge transfer between Ti and three C atoms directly bonded to it. The Bader charge on the Ti is +2.21. The loss of 2.21 electrons is gained by three nearest neighbor C atoms. The total DOS plot exhibits that the resultant structure is a semiconductor with a band gap of 0.6 eV. This value is lower than that found for the pure C60. The atomic DOS plots shows that states near the Fermi level are mainly associated with the d sates of Ti. Adsorption of CO2 was next considered on the surface of Ti-doped C60. The relaxed structure is shown in Figure 8a. In the relaxed structure, one of the oxygen atoms in the CO2 molecule forms a strong bond with Ti (see Figure 8b). In the relaxed structure, the CO2 molecule is slightly bent. The net charge on the CO2 molecule is −0.23 according to the Bader charge analysis. The activation of the C-O bond is not significant as its bond lengths are not significantly elongated with respect to its isolated molecule. The energy required to adsorb a CO2 molecule is −0.41 eV with dispersion, indicating that Ti-doped C60 can accommodate a CO2 molecule. Adsorption is endothermic without dispersion and its adsorption energy is +1.71 eV, again indicating the importance of dispersion. There is a small band gap of 0.50 eV observed in the total DOS plot. The states associated with the d orbitals of Ti are mainly localized near the Fermi energy level. Adsorption of CO 2 was next considered on the surface of Ti-doped C 60 . The relaxed structure is shown in Figure 8a. In the relaxed structure, one of the oxygen atoms in the CO 2 molecule forms a strong bond with Ti (see Figure 8b). In the relaxed structure, the CO 2 molecule is slightly bent. The net charge on the CO 2 molecule is −0.23 according to the Bader charge analysis. The activation of the C-O bond is not significant as its bond lengths are not significantly elongated with respect to its isolated molecule. The energy required to adsorb a CO 2 molecule is −0.41 eV with dispersion, indicating that Ti-doped C 60 can accommodate a CO 2 molecule. Adsorption is endothermic without dispersion and its adsorption energy is +1.71 eV, again indicating the importance of dispersion. There is a small band gap of 0.50 eV observed in the total DOS plot. The states associated with the d orbitals of Ti are mainly localized near the Fermi energy level.

Conclusions
Computer simulations based on the DFT together with dispersion were applied to examine the efficacy of the pure, Ti-supported and Ti-doped C60 surface for the adsorption of a CO2 molecule. The results show that there is no significant adsorption on the surface of pure C60. Adsorption becomes significantly stronger once the Ti is supported on the surface of C60. Such adsorption distorts and activates the CO2 molecule significantly. The enhancement of adsorption is confirmed by the significant charge transfer between the Ti and the C60 molecule. Thus, the Ti-supported C60 molecule is the most efficient for CO2 adsorption. The Ti-doped C60 surface has the ability to adsorb the CO2 molecule. However, the activation is not significant.
Funding: This research received no external funding.

Data Availability Statement:
The data presented in this study are available upon reasonable request from the author.

Conclusions
Computer simulations based on the DFT together with dispersion were applied to examine the efficacy of the pure, Ti-supported and Ti-doped C 60 surface for the adsorption of a CO 2 molecule. The results show that there is no significant adsorption on the surface of pure C 60 . Adsorption becomes significantly stronger once the Ti is supported on the surface of C 60 . Such adsorption distorts and activates the CO 2 molecule significantly. The enhancement of adsorption is confirmed by the significant charge transfer between the Ti and the C 60 molecule. Thus, the Ti-supported C 60 molecule is the most efficient for CO 2 adsorption. The Ti-doped C 60 surface has the ability to adsorb the CO 2 molecule. However, the activation is not significant.
Funding: This research received no external funding.

Data Availability Statement:
The data presented in this study are available upon reasonable request from the author.