C20: fullerene, bowl or ring? New results from coupled-cluster calculations

Growth Patterns of Carbon Clusters Cn (n = 2-60) Identified via ABCluster Searching and DFT Benchmarking

Recently, novel algorithms and enhanced computational capabilities have created unprecedented opportunities to precisely determine the geometric structures of clusters through theoretical calculations. In this study, we extensively investigated and characterized the geometric arrangements of the carbon clusters Cn (n = 2-60), employing the efficient ABCluster algorithm in conjunction with the gradient-corrected PBE and higher-accuracy B3LYP hybrid functional in density functional theory (DFT). New structures and a discernible structural growth pattern have been discovered. We observed a distinct preference in carbon clusters that transform from the linear chains (n = 2-9) to closed single-ring and planar structures (n = 10-27) and finally evolve to carbon cages (n = 28-60). A shortcut to construct the cage clusters was unveiled by inserting or rotating specific atoms within a distinct structural unit. The research results obtained from combining ABCluster with DFT calculations offer valuable new insights into the growth mechanisms and evolutionary trajectories of carbon clusters, providing a crucial theoretical framework for the development of innovative carbon-based materials and their potential applications.

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.

In silico environmental chemical science: properties and processes from statistical and computational modelling

Quantitative structure-activity relationships (QSARs) have long been used in the environmental sciences. More recently, molecular modeling and chemoinformatic methods have become widespread. These methods have the potential to expand and accelerate advances in environmental chemistry because they complement observational and experimental data with "in silico" results and analysis. The opportunities and challenges that arise at the intersection between statistical and theoretical in silico methods are most apparent in the context of properties that determine the environmental fate and effects of chemical contaminants (degradation rate constants, partition coefficients, toxicities, etc.). The main example of this is the calibration of QSARs using descriptor variable data calculated from molecular modeling, which can make QSARs more useful for predicting property data that are unavailable, but also can make them more powerful tools for diagnosis of fate determining pathways and mechanisms. Emerging opportunities for "in silico environmental chemical science" are to move beyond the calculation of specific chemical properties using statistical models and toward more fully in silico models, prediction of transformation pathways and products, incorporation of environmental factors into model predictions, integration of databases and predictive models into more comprehensive and efficient tools for exposure assessment, and extending the applicability of all the above from chemicals to biologicals and materials.

Evolution of the interaction between C20cage and Cr(CO)5: A solvent effect, QTAIM and EDA investigation

This study used mpw1pw91 quantum chemical calculations in gas and solution phases to clarify the interaction between C20and Cr(CO)5fragment. It also sought to clarify the effects of solvent polarity on dipole moment, structural parameters, and frontier orbital energies of the complex. Energy decomposition analysis (EDA) was applied to analyze the bonding interaction between the C20and Cr(CO)5fragment. Percentage composition in terms of the defined groups of frontier orbitals for the complex was evaluated to characterize the metal–ligand bonds. The Cr–C bonds within the complex were examined using quantum theory of atoms in molecules (QTAIM) analysis. In order to determine the back-bonding effects in these bonds, QTAIM analysis was applied to calculate of the quadrupole polarization of the carbon atom.

Exploring the chemical bonding, infrared and UV-vis absorption spectra of OH radicals adsorption on the smallest fullerene

In the present work, the density-functional theory calculations were performed on C20 hydroxylated fullerene. B3LYP functionals with 6-31G(d,p) basis set were utilized to gain insight into the bonding characters and intramolecular interactions of hydroxyl groups adsorbed on the cage. Interestingly, we observed that the C20 cage has the bonding patterns with spherical orbitals configuration [1S(2)1P(6)1D(10)1F(2)], and the adsorbed hydroxyl groups significantly affect the chemical bonding of the cage surface. Analysis of vertical electron affinities and vertical ionization potentials indicates that the polyhydroxylated derivative with eight hydroxyl groups is more stable than others. The intramolecular interaction of these derivatives considered here reveals that the more the hydroxyl groups in derivatives, the stronger the interaction in stabilizing structures. On the basis of theoretical studies, the hydroxyl groups largely enhance the infrared intensities, especially for the polyhydroxylated derivatives.

A density functional approach toward structural features and properties of C20…N2X2 (X = H, F, Cl, Br, Me) molecules

In this work, the interaction of C 20 with N 2 X 2 ( X = H , F , Cl , Br , Me ) molecules has been explored using the B3LYP, M062x methods and 6-311G(d,p) and 6-311+G(d,p) basis sets. The interaction energies (IEs) obtained with standard method were corrected by basis set superposition error (BSSE) during the geometry optimization for all molecules at the same levels of theory. It was found C 20… N 2 H 2 interaction is stronger than the interaction of other N 2 X 2 ( X = F , Cl , Br , Me ) with C 20. Highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO, respectively) levels are illustrated by density of states spectra (DOS). The nucleus-independent chemical shifts (NICSs) confirm that C 20… N 2 X 2 molecules exhibit aromatic characteristics. Geometries obtained from DFT calculations were used to perform NBO analysis. Also, 14 N NQR parameters of the C 20… N 2 X 2 molecules are predicted.

Most stable structure of fullerene[20] and its novel activity toward addition of alkene: A theoretical study

Structures and stabilities of fullerene C20 and C20- have been investigated by the density functional theory and CCSD(T) calculations. In consideration of the Jahn-Teller distortion of Ih-symmetric C20, possible subgroup symmetries have been used in the full geometry optimization. On the basis of relative energetics, vibrational analyses, and electron affinities, fullerenes C20 and C20- have most stable D2h and Ci structures, respectively. The controversy on the relative stability of fullerene[20] arises from the use of different subgroups in calculation and the basis set dependence in vibrational analysis. Predicted nucleus-independent chemical shift values show that the most stable fullerene C20 and its derivatives C20(C2H2)n and C20(C2H4)n (n=1-3) exhibit remarkable aromaticity, while C20(C2H2)4 and C20(C2H4)4 have no spherical aromaticity. The C20 (D2h) cage has remarkable activity toward the addition of olefin, and such feasibility of the addition reaction is ascribed to strong bonding interactions among frontier molecular orbitals from C20 and olefin. Calculations indicate that both C20(C2H2)n and C20(C2H4)n have similar features in electronic spectra.

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.

A Family of Stable Silica Fullerenes with Fully Coordinated Structures

Theoretical electronic structure techniques have become an indispensable and powerful tool for predicting molecular properties and designing new materials. The discovery of C(60) opened a challenging field in nanoscale materials science, and since then people have been looking for its inorganic analogues. On the basis of the B3LYP/6-31G(d) calculations, here we provide theoretical evidence for a family of stable silica fullerenes with fully coordinated structures, which exhibit highly structural and energetic stabilities, very large energy gaps, and extremely good resistibilities to breakdown of the insulating capability in an applied electric field. Our calculations indicate that the discrete silica fullerenes are a possible polymorph of silica and can be synthesized under some conditions. They are expected to find novel applications in silica-based molecular devices. The present results may provide an aid in the experimental design for controllably producing desired silica clusters.

Toward a Reversible Isolation of a C20 Fullerene Inside a Tetraureacalix[4]arene Dimer. A Theoretical Study

The potential stabilization of normally unstable C20, the smallest fullerene, via its encapsulation inside a tetraureacalix[4]arene dimer has been analyzed using molecular mechanics calculations with different force fields, the self-consistent-charge density-functional tight-binding with dispersion correction (SCC-DFTB-D) model, and standard density-functional-theory (DFT) calculations. The interaction energies obtained for the C20 complex have been compared with analogous values calculated for numerous complexes of the tetraureacalix[4]arene dimer with other guests. Results of the calculations with all force fields and SCC-DFTB-D predict that the binding of C20 occurs with the highest selectivity. On the other hand, standard DFT calculations fail to correctly describe the stabilization of the complexes under study as standard DFT generally does not treat dispersion interactions properly. Predicted relative stabilities of the complexes are discussed in conjunction with available experimental data. Molecular dynamics simulations reveal the instability of the guest-free capsular dimer, which decomposes on a 1-ns time scale, while dimeric complexes with guests remained intact during the 5-ns simulation time, indicating the guest-driven formation of the molecular capsule.

A path from Ih to C1 symmetry for C20 cage molecule

The symmetry of the C20 cage is studied based on the intrinsical relationship among point groups (Bradley, C. J.; Cracknell, A. P. The Mathematical Theory of Symmetry in Solids; Claredon Press: Oxford, 1972). The structure of the C20 cage with I(h) symmetry is constructed, as are eight other structures with subgroup symmetry. A path from I(h) symmetry to C1 symmetry is obtained for the closed-shell electronic state, and the structure with D2h symmetry is the most stable on this path. Using the D2h structure the correlation energy correction is studied on the condition of restricted excitation space at the CCSD(T) level. We obtain curves on the relation between the orbital numbers and the total energy at the CCSD(T), CCSD, and MP2 level, respectively. The results of these curves obtained from MP2 and CCSD(T) methods have the same tendency, while the results of CCSD gradually diverge with an increase in orbital numbers. When the orbitals used in the calculation reach 460, the total energy is -759.644 hartree at MP2 level and is -759.721 hartree by the CCSD(T) method. From the calculation results, we find that a large basis set can improve the reliability of the MP2 method, and to restrict excitation space is necessary when using the CCSD(T) method.

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

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.

Monte Carlo methods in electronic structures for large systems

Quantum Monte Carlo methods have recently made it possible to calculate the electronic structure of relatively large molecular systems with very high accuracy. These large systems range from positron complexes [NH(2),Ps] with approximately 10 electrons to C(20) isomers with 120 electrons, to silicon crystal structures of 250 atoms and 1000 valence electrons. The techniques for such calculations and a sampling of applications are reviewed.