Precursors to C60 fullerene formation

12-Membered Ring Carbides with Stabilization of Actinide Atoms

Actinide (Th and U) carbides as the potential nuclear fuels in nuclear reactors require basic research in order to understand the thermodynamic stability and performance of these substances. Here we report the structural characterization and bonding analyses of [C₁₂], ThC₁₂, and UC₁₂ clusters via a global-minimum search combined with relativistic quantum chemistry calculations to elucidate the stability and bonding nature of An-C bonds. We predict that these [C₁₂], ThC₁₂, and UC₁₂ compounds have a planar structure with C_6h, D_12h, and D_12h symmetry, respectively. [C₁₂] has a hyperconjugation structure containing alternating single and double bonds. The significant stabilization when forming AnC₁₂ predominantly comes from the electrostatic interaction between An⁴⁺ and [C₁₂]^4- and also from a certain degree of orbital interaction between the An 5f6d7s valence shell and [C₁₂] π orbitals. The covalent character of the An-C bonds exhibits a direct in-plane σ-type overlap of the C 2p-derived MOs of [C₁₂] and the An 5f_ϕ AO, thus leading to an unprecedented electronic configuration of d¹f¹ for U in UC₁₂. Our results present an example of the novel properties that can be expected for actinide compounds and would provide the knowledge required to obtain novel structures of AnC₁₂ in future experiments.

Potential molecular semiconductor devices: cyclo-Cn (n = 10 and 14) with higher stabilities and aromaticities than acknowledged cyclo-C18

Theoretical calculations reveal that the zero-dimensional allotropes of carbon atoms, cyclo-C_n (n = 10 and 14), have higher thermodynamic, kinetic, optical, and dynamic stabilities and aromaticity than the acknowledged cyclo-C₁₈.

Adsorption of Monocyclic Carbon Rings on Graphene: Energetics Revealed via Continuum Modeling

Gas-phase spectroscopic detection of tiny carbon clusters is a recent success story in the area of carbon cluster research. However, experimental production and isolation of these clusters are extremely difficult because of their high reactivity. One possibility to isolate the generated clusters would be to deposit them on graphene and to desorb them for subsequent use. One of the pertinent questions toward realizing this would be the energetics of the adsorption process. Therefore, in this work, the energetics for the adsorption of the monocyclic carbon rings (C _n with n = 10, 12, 14, 16, 18, 20, and 22) on a graphene sheet are investigated using the analytical approaches, developed earlier by Hill and co-workers. The adsorption process here is driven by the noncovalent interactions between the carbon rings and the graphene sheet. The analyses of the interaction energies as a function of both the vertical distance Z and the rotational angle ϕ are performed in order to determine the preferred orientations, equilibrium positions, and binding energies for the adsorption of various carbon rings on graphene. We find that the preferred orientation of the rings with respect to the graphene sheet is the parallel orientation. The results from continuum, discrete-continuum, and discrete models are in good agreement. Further, computations using density functional theory and quantum mechanics/molecular mechanics approaches are performed, and comparisons of the computed energetics with the data from the models are reported. Finally, we highlight the scope and the limitations of the analytical models.

MC19 (M = B, Si, Al and Ga) fullerenes: Adsorption mechanisms of 1,4-diformylpiperazine

Fullerenes and piperazines have been investigated, particularly, in the field of nanoscience and medicinal chemistry. In the present research, besides discussing structural and electronic properties, the most probable interaction mechanisms between C20, B-, Si-, Al-, Ga-doped C20 and 1,4-diformylpiperazine (1,4-dfp) were studied by employing density functional theory (DFT) in both the gas phase and water as the solvent. Stabilities of the investigated complexes were discussed based on the binding energy and electronic properties such as band gap energy, chemical hardness and electrophilicity index. It is found that doped complexes are more stabilized in water compared to the gas phase. However, the interaction between C20 and 1,4-dfp weakens upon the introduction of water as the solvent.

Gas-phase ion chromatography: transition metal state selection and carbon cluster formation

Gas-phase ion chromatography can separate ions that have the same mass but differ in isomeric structure or electronic configuration. The main features of this technique are briefly outlined, and applications to a series of problems in transition metal chemistry and carbon cluster chemistry are described. Examples in transition metal chemistry include state-selective reactivity, excited state deactivation, and state-selective ligand binding energies. For clusters, ion chromatography was used to determine the structure of pure carbon cluster ions as a function of size from C(4) to C(84). The results indicate that carbon grows first in linear chains, transforms to monocyclic planar rings at about C(10), and forms new families of planar bi-, tri-, and tetracyclic rings at C(20), C(30), and C(40), respectively. Fullerenes, which mysteriously appear at C(30) and dominate by C(50), are generated by heating the planar ring systems above an isomerization barrier rather than by growth of graphite precursors.

Search for lowest-energy nonclassical fullerenes III: C22

Density functional and second-order Møller-Plesset perturbation (MP2) methods were employed in the investigation of low-lying C22 isomers. All cage structures with four-, five-, six-, and seven-membered rings were examined with the monocyclic ring, bowl, and other noncage structures. Cage isomers were first identified via graph theoretical methods, and noncages were identified by basin-hopping methods. Initial isomer screenings were carried out at the PBE/DND level of theory. Low-lying isomers, within 0.6 eV of the predicted lowest-energy isomer, were further evaluated at the PBE1PBE/cc-pVTZ and MP2/cc-pVTZ levels. Our results confirm that the cage structures are more stable than the ring structure and the bowl structure. The lowest-energy structure for C22 is predicted to be the C22-1 cage containing one four-membered ring. Anion photoelectron and optical spectra of the six lowest-lying isomers are also computed.

Isomers of C36 and free energy criteria for cluster growth

A molecular dynamics procedure is developed to search for cluster isomers and is used to study the isomer spectrum of C36 with the Brenner potential. Beginning with isolated carbon atom, the procedure quickly arrives at the D6h cage with the lowest potential and produces other 410 isomers. Among these isomers, we selected ones of typical cage, bowl, and sheet structures to calculate their free energies at 2300 K and performed molecular dynamics simulations starting either from 36 free carbon atoms diluted in He buffer gas kept at 2300 K or from the D6h cage under the same conditions, which show that the microsystem reaches a kinetic equilibrium within about 100 ns and that the isomer of the lowest free energy rather than the D6h cage of the lowest potential energy dominates in the resultant cluster.

Ab initio calculation of bowl, cage, and ring isomers of C20 and C20-

High-level ab initio calculations have been carried out to reexamine relative stability of bowl, cage, and ring isomers of C(20) and C(20)(-). The total electronic energies of the three isomers show different energy orderings, strongly depending on the hybrid functionals selected. It is found that among three popular hybrid density-functional (DF) methods B3LYP, B3PW91, PBE1PBE, and a new hybrid-meta-DF method TPSSKCIS, only the PBE1PBE method (with cc-pVTZ basis set) gives qualitatively correct energy ordering as that predicted from ab initio CCSD(T)/cc-pVDZ [CCSD(T)-coupled-cluster method including singles, doubles, and noniterative perturbative triples; cc-pVDZ-correlation consistent polarized valence double zeta] as well as from MP4(SDQ)/cc-pVTZ [MP4-fourth-order Moller-Plesset; cc-pVTZ-correlation consistent polarized valence triple zeta] calculations. Both CCSD(T) and MP4 calculations indicate that the bowl is most likely the global minimum of neutral C(20) isomers, followed by the fullerene cage and ring. For the anionic counterparts, the PBE1PBE calculation also agrees with MP4/cc-pVTZ calculation, both predicting that the bowl is still the lowest-energy structure of C(20)(-) at T=0 K, followed by the ring and the cage. In contrast, both B3LYP/cc-pVTZ and B3PW91/cc-pVTZ calculations predict that the ring is the lowest-energy structure of C(20)(-). Apparently, this good reliability in predicting the energy ordering renders the hybrid PBE method a leading choice for predicting relative stability among large-sized carbon clusters and other carbon nanostructures (e.g., finite-size carbon nanotubes, nano-onions, or nanohorns). The relative stabilities derived from total energy with Gibbs free-energy corrections demonstrate a changing ordering in which ring becomes more favorable for both C(20) and C(20)(-) at high temperatures. Finally, photoelectron spectra (PES) for the anionic C(20)(-) isomers have been computed. With binding energies up to 7 eV, the simulated PES show ample spectral features to distinguish the three competitive C(20)(-) isomers.

Isomers of C20: an energy profile III

Semiempirical calculations, at the PM3 level provided within the Winmopac v2.0 software package, are used to geometrically optimize and determine the absolute energies (heats of formation) of a variety of C(20) isomers that are predicted to exist in and around the ring and cage isomers. Using the optimized Cartesian coordinates for the ring and the cage isomers, a saddle-point calculation was performed. The resulting energy profile, consisting of a series of peaks and valleys, is used as a starting point for the identification and location of fifteen additional isomers of C(20) that are predicted to be energetically stable, both via geometry optimizations and force constant analysis. These additional isomers were subsequently determined to lie adjacent to one another on the potential surface and establish a step-wise transformation between the ring and the cage. Transition-state optimization of the Cartesian coordinates at the saddle point between adjacent isomers was performed to quantify the energy of the transition state. The step-wise process from one isomer to another, which extends out over the three-dimensional surface, is predicted to require approximately 15% less energy than that of the direct, two-dimensional transformation predicted in the bowl-cage profile. However, the net atomic rearrangement for the step-wise process is about four times greater than that of the direct process. Although less in energy, the amount of atomic rearrangement in the step-wise process would make the occurrence of such a route prohibitive. Utilizing the direct distance separating the three primary isomers (ring, bowl, cage), the method of triangulation is performed to quantitatively position other C(20) structures on the potential surface, relative to the ring, bowl, and cage isomers.

Isomers of C(20): an energy profile II

Semi-empirical calculations, at the PM3 level provided within the Winmopac v2.0 software package, are used to geometrically optimize and determine the absolute energies (heats of formation) of a variety of C(20) isomers that are predicted to exist in and around the bowl and cage isomers. Using the optimized Cartesian coordinates for the bowl and the cage isomers, a saddle-point calculation was performed. The output file generated, containing energy, distance, and geometry information, is then organized into a graphical format. The resulting graph, which plots the energy of the 20-atom system as a function of the distance from the geometric midpoint, is a two-dimensional energy profile. This profile illustrates an estimation of the contours on the potential energy surface, showing energy minima and maxima that are encountered as the bowl evolves into the cage structure, or vice-versa. To expand the surface into three dimensions, geometry optimizations were performed on the sets of Cartesian coordinates that correspond to energy minima in the bowl-cage profile. Based on these optimizations, eight additional isomers of C(20) have been identified and are predicted to be energetically stable. These additional isomers were subsequently subjected to saddle-point calculations in order to identify those isomers that lie adjacent to one another on the three-dimensional surface. Two isomers that are adjacent to each other will exhibit an energy profile that progresses smoothly from the potential well of each isomer up to the saddle point separating them. Consequently, these adjacent pairs of isomers establish a step-wise transformation between the bowl and the cage. This process, which extends out over the three-dimensional surface, is predicted to require less energy than that of the direct, two-dimensional transformation predicted in the bowl-cage profile.

Isomers of C(20): an energy profile

Semiempirical calucaltions, at the PM 3 level, are used to geometrically optimize and determine the absolute energies (heats of formation) of a variety of C(20) isomers. Based on the geometrically optimized Cartesian coordinates of the ring and the bowl isomers, and the subsequent saddle-point calculation, a two-dimensional energy profile between these two isomers is generated. Performing geometry optimization on the Cartesian coordinates that correspond to energy minima within the ring-bowl profile, we have been able to identify several more isomers of C(20) that are predicted to be energitically stable. With these additional stable structures, we have identified pairs of isomers that lie adjacent to one another on the potential energy surface, as is evidenced by the form of their respective energy profiles. These adjacent pairs of isomers establish a step-wise transformation between the ring and the bowl. This process, which extends out over the three-dimensional surface, is predicted to require less energy than that of the direct, two-dimensional transformation predicted in the ring-bowl profile.