Structure, stability, MEP, NICS, reactivity, and NBO of Si–Ge nanocages evolved from C20 fullerene at DFT

Investigation of the substituted-titanium nanocages using computational chemistry

We are investigated substitution effects of titanium heteroatoms on band gap, charge and local reactivity of C_20-nTi_n heterofullerenes (n = 1-5), at different levels and basis sets. The C₁₈Ti_2-2 nanocage is considered as the most kinetically stable species with the widest band gap of 2.86 eV, in which two carbon atoms are substituted by two Ti atoms in equatorial position, individually. The charges on carbon atoms of C₂₀ are roughly zero, while high positive charge (1.256) on the surface of C₁₉Ti₁ prompts this heteofullerene for hydrogen storage. The positive atomic charge on Ti atoms and negative atomic charge on their adjacent C atoms implies that these sites can be influenced more readily by nucleophilic and electrophilic regents, respectively. We examined the usefulness of local reactivity descriptors to predict the reactivity of Ti-C atomic sites on the external surface of the heterofullerenes. The properties determined include Fukui function (F.F.); f (k) and local softness s (k) on the surfaces of the investigated hollow cages. Geometry optimization results reveal that titanium atoms can be comfortably incorporated into the CC network of fullerene. It is most likely associated with the triple-coordination characteristic of titanium atoms, which can well match with the sp²-hybridized carbon bonding structure. According to the values of f (k) and s (k) for the C₁₅Ti₅ heterofullerene; the carbon atoms in the cap regions exhibit a different reactivity pattern than those in the equatorial portion of the heterofullerene. The titanium impurity can significantly improve the fullerene's surface reactivity and it allows controlling their surface properties. The band gap of C_20-nTi_n …..(H₂)_n structures is decreased with increasing n. Hence, C₁₅Ti₅ is found as the best hydrogen adsorbent.

Density functional theory studies on C20 with substitutional TinNn impurities

In this paper, we have performed systematic theoretical surveys of C₂₀ and its C_20-2nTi_nN_n nanocages with n = 1-8 at DFT. Full optimization indicates none of the structures collapse to open deformed as segregated heterofullerene. Also, in order to avoid the resulted strain of fused five-pentagon configuration, some of them deform their cage at the Ti-N bonds and appear cubic-like. Binding energy (E_b) increases, and the absolute heat of atomization │ΔH_at│ of the designed C_20-2nTi_nN_n structures decreases, respectively, as the number of substituting Ti-N units increases. The calculated E_b of 57.05 eV/atom and │ΔH_at│ of 2437.40 kcal/mol display C₄Ti₈N₈ as the most thermodynamic stable heterofullerene where including eight separated Ti-N units through two double C═C bonds. In contrast, the calculated band gap of 2.06 eV shows C₁₈Ti₁N₁ as the best-insulated heterofullerene. Here isolable or extractable open-shell C₁₈Ti₁N₁ heterofullerene must be kinetic stable species, and closed-shell C₄Ti₈N₈ should be thermodynamic stable species. Compared to the suggested Ti-decorated B₃₈ fullerene as a high capacity hydrogen storage material with large E_b (5.67 eV/atom), our studied C_20-2nTi_nN_n heterofullerenes show the higher E_b with a range of 13.78 to 57.05 eV/atom, the higher stability, and the higher capacity hydrogen storage. Each Ti-N unit can bind up to two hydrogen molecules with an average adsorption energy of 0.073 eV/H₂. While the C₄Ti₈N₈ fullerene substituted with 8 Ti-N units can store 16 H₂ molecules, the hydrogen gravimetric density (the hydrogen storage capacity) reaches up to 5.61 wt% with an average adsorption energy of 0.587 eV/H₂. Based on these results, we infer that C₄Ti₈N₈ fullerene is a potential material for hydrogen storage with high capacity and might motivate active experimental efforts in designing hydrogen storage media.

Substitution effects via aromaticity, polarizability, APT, AIM, IR analysis, and hydrogen adsorption in C20-nTin nanostructures: a DFT survey

In this paper, the substitution effects of titanium heteroatom(s) on aromaticity, the average isotropic polarizability (< α >), the atomic polar tensor (APT) charge, the electrostatic potential (ESP) map, and the atoms in molecule (AIM) analysis along with infrared (IR) spectroscopy of C₂₀ fullerene and its C_20-nTi_n derivatives (n = 1-5) are probed via density functional theory (DFT). The nucleus-independent chemical shifts (NICS) specify that substitution effect causes more aromaticity character of the optimized heterofullerenes than benzene molecule and higher APT charge distribution upon surfaces of them than pure cage. The highest negative and positive APT charge distribution on carbons of C₁₅Ti₅ and titanium substitutions of C₁₆Ti_4-2 implies that these sites can be attacked more readily by electrophilic and nucleophilic regents, respectively. We are very pleased to state that isolating the Ti-Ti single bonds by intermediacy of one or two C atoms is an applicable strategy for attaining the highest APT charge distribution on Ti atoms of C₁₆Ti_4-2 as suitable hydrogen storage. AIM analysis of the studied C_20-nAl_n derivatives signifies the highest electron density (ρ (r)) of 0.294 a.u. and the highest positive Laplacian of electron density (∇²ρ (r)) of 0.190 a.u., at bond critical points (BCPs) of C-Ti bond in the most stable C₁₉Ti₁ species. This heterofullerene shows the lowest < α > between the studied structures. IR spectroscopy shows that exclusive of C₁₆Ti_4-1 (as transition state), the other optimized hollow cages (as global minima) have no imaginary frequency.

Characterization of titanium influences on structure and thermodynamic stability of novel C20-nTin nanofullerenes (n=1-5): a density functional perspective

In this survey, effects of titanium heteroatom(s) on structural parameters and thermodynamic stability of C₂₀ fullerene and its C_20-nTi_n derivatives (n = 1-5) are compared and contrasted, at DFT levels of theory. The results show that in going from C₁₉Ti₁ to C₁₅Ti₅, binding energy increases while absolute value heat of atomization decreases. According to vibrational frequency analysis, excepting C₁₆Ti_4-1, the other optimized structures give no imaginary frequency as true minima. The calculated binding energy of 887.12 kcal mol^-1/atom displays C₁₅Ti₅ as the most thermodynamically stable heterofullerene. It has C_s symmetry and contains five titanium atoms alternatively in equatorial position. The substitutional doping of C₂₀ fullerene leads to high Mülliken charge distribution upon the surfaces of the resulted heterofullerenes especially C₁₉Ti₁ as suitable hydrogen storage. The contour plots indicate the most negative electrostatic potential by red color for C atoms, whereas the most positive electrostatic potential by yellow color for Ti heteroatoms. The contour plots and multiwfn analysis exhibit charge transfer from titanium heteroatoms to the neighboring carbon atoms. Furthermore, the resulted electron density maps from multiwfn qualitatively confirm the contour plot's findings. The hydrogen adsorption is an endothermic process for C₂₀ fullerene and exothermic process for C_20-nTi_n heterofullerenes. Major criteria examined for thermodynamic stability; from C₁₉Ti₁ to C₁₅Ti₅, binding energy and hydrogen adsorption increase while heat of atomization decreases.

Thermodynamic stability, structural and electronic properties for the C20-nAln heterofullerenes (n = 1-5): a DFT study

DFT calculations are utilized to compare and contrast the substituted aluminum-heterofullerenes, C_20-nAl_n (with n = 1-5) from thermodynamically view point, at density functional theory (DFT). Vibrational frequency analysis confirms that apart from C₁₅Al₅, all studied species are true minima. Considering the optimized geometries shows that all heterofullerenes are isolated-pentagon cage and none collapse to open deformed as segregated structure. The highest binding energy (5.56 eV/atom) and absolute heat of atomization (3323.68 kcal mol^-1) reveals open-shell C₁₉Al₁ as the most stable thermodynamic heterofullerene. The most NICS (0) (isotropic and anisotropic parameters, -49.58 and - 46.47 ppm, respectively) introduces closed-shell C₁₈Al_2-2 as the most aromatic structure. Also, closed-shell C₁₆Al_4-1 heterofullerene emerges with the most polarizability (307.71 a.u.) and hence activity to interact with the surrounding polar species. The lowest and the highest charge transfer on the surfaces of C₂₀ and C₁₆Al_4-2 without weak Al-Al bond, as the worst and the best candidate, respectively, provokes further investigation on impossible and possible application for hydrogen storage, respectively. We wish that the present survey will stimulate new experiments.