On the structure and vibrational frequencies of C20

Bound states and symmetry breaking of the ring C20 - anion

Determining the geometry of carbon rings is an ongoing challenge. Based on our calculations at a state-of-the-art level, we found that the C₂₀ ^- ring possesses five bound electronic states, including a superatomic state, which is the first superatomic state found for a ring. The nature of these electronic states is discussed. Our calculation reveals a symmetry breaking of the C₂₀ ^- ring anion ground electronic structure occurring upon attaching an electron to the neutral ring. The discussion of the possible symmetry breaking mechanisms indicates that the shrinking and distortion of the ring upon electron attachment, leading to the symmetry breaking, is a result of the interplay between the symmetry breaking and the totally symmetric modes. The discussion enriches the palette of possible symmetry breaking phenomena in carbon clusters.

Distinguishing artificial and essential symmetry breaking in a single determinant: approach and application to the C60, C36, and C20 fullerenes

The existence of a generalized Hartree–Fock solution in C₆₀ has led to controversy on whether C₆₀ is polyradicaloid (or strongly correlated). We attempt to end the controversy with κ-OOMP2 which removes the illusion of this artificial symmetry breaking. We conclude that C₆₀ is not strongly correlated.

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.

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.

Potential energy surfaces of WC6 clusters in different spin states

Stochastic explorations of the structural possibilities of neutral WC6 clusters in several spin states lead to very rich and complex potential energy surfaces, with geometries quite different from those of pure carbon clusters at the PBE0/def2-TZVP level. The global minimum is predicted to be a triplet-state semicyclic C6 conformation having every carbon in direct coordination to the W atom. Interaction energies are comparable to those of C7 clusters, revealing very strong W-C bonding. Our results suggest that C-C interactions in the clusters should be considered as intermediate between single and double bonds.

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.

Calculation of Electron Affinities of Polycyclic Aromatic Hydrocarbons and Solvation Energies of Their Radical Anion

Electron affinities (EAs) and free energies for electron attachment (DeltaGo(a,298K)) have been directly calculated for 45 polynuclear aromatic hydrocarbons (PAHs) and related molecules by a variety of theoretical methods, with standard regression errors of about 0.07 eV (mean unsigned error = 0.05 eV) at the B3LYP/6-31 + G(d,p) level and larger errors with HF or MP2 methods or using Koopmans' Theorem. Comparison of gas-phase free energies with solution-phase reduction potentials provides a measure of solvation energy differences between the radical anion and neutral PAH. A simple Born-charging model approximates the solvation effects on the radical anions, leading to a good correlation with experimental solvation energy differences. This is used to estimate unknown or questionable EAs from reduction potentials. Two independent methods are used to predict DeltaGo(a,298K) values: (1) based upon DFT methods, or (2) based upon reduction potentials and the Born model. They suggest reassignments or a resolution of conflicting experimental EAs for nearly one-half (17 of 38) of the PAH molecules for which experimental EAs have been reported. For the antiaromatic molecules, 1,3,5-tri-tert-butylpentalene and the dithia-substituted cyclobutadiene 1, the reduction potentials lead to estimated EAs close to those expected from DFT calculations and provide a basis for the prediction of the EAs and reduction potentials of pentalene and cyclobutadiene. The Born model has been used to relate the electrostatic solvation energies of PAH and hydrocarbon radical anions, and spherical halide anions, alkali metal cations, and ammonium ions to effective ionic radii from DFT electron-density envelopes. The Born model used for PAHs has been successfully extended here to quantitatively explain the solvation energy of the C60 radical anion.

C20 Carbon Clusters: Fullerene–Boat–Sheet Generation, Mass Selection, Photoelectron Characterization

Electron-impact ionization in a time-of-flight mass spectrometer of C(20)H(0-3)Br(14-12) probes-secured from C(20)H(20) dodecahedrane by a "brute-force" bromination protocol-provided bromine-free C(20)H(0-2(3)) anions in amounts that allowed the clean mass-separation of the hydrogen-free C(20) (-) ions and the photoelectron (PE) spectroscopic characterization as C(20) fullerene (electron affinity (EA)=2.25+/-0.03 eV, vibrational progressions of 730+/-70). The extremely strained C(20) fullerene ions surfaced as kinetically rather stable entities (lifetime of at least the total flight time of 0.4 ms); they only very sluggishly expel a C(2) unit. The HOMO and LUMO are suggested to be almost degenerate (DeltaE=0.27 eV). The assignment as a fullerene was corroborated by the PE characterization of the C(20) bowl (EA=2.17+/-0.03 eV, vibrational progression of 2060+/-50 cm(-1)) analogously generated from C(20)H(10) corannulene (C(20)H(1-3)Br(9-8) samples) and comparably stable. Highly resolved low-temperature PE spectra of the known C(20) ring (EA=2.49+/-0.03 eV, vibrational progressions 2022+/-45 and 455+/-30 cm(-1)), obtained from graphite, display an admixture of, most probably, a bicyclic isomer (EA=3.40+/-0.03 eV, vibrational progression 455+/-30 cm(-1)). The C(20) (+(-)) and C(20)H(2) (+(-)) cluster ions generated from polybrominated perylene (C(20)H(0-2)Br(12-10)) have (most probably) retained the planar perylene-type skeleton (sheet, EA=2.47+/-0.03 eV, vibrational progressions of 2089+/-30 and 492+/-30 cm(-1) and EA=2.18+/-0.03 eV, vibrational progressions of 2105+/-30 and 468+/-30 cm(-1)).

Conversion pathways between a fullerene and a ring among C20 clusters by a sphere contracting walk method: Remarkable difference in local potential energy landscapes around the fullerene and the ring

Conversion pathways from a fullerene to a ring and vice versa among C(20) clusters have been explored. A new technique has been developed for discovering multistep reaction pathways, which can be searched by finding constrained energy minima on spheres whose surfaces are contracting from the starting point to the terminal. Local landscapes that appeared on the pathways were found to be considerably different around the fullerene and the ring, from which one can make a new interpretation for no generation of the C(20) fullerene in laser vaporization of graphite.

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 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.

Structural and electronic properties of metal-encapsulated silicon clusters in a large size range

Structural and electronic properties of metal-doped silicon clusters MSi(n)s (M=W, Zr, Os, Pt, Co, etc.) in a large size range of 8<or=n<or=20 are investigated via ab initio calculations. Different from a recent experimental suggestion that the metal atom is endohedral in MSi(n), we reveal that the formation of endohedral structure strongly depends on the size of the Si(n) cluster. Two novel structures of the chemically stable endohedral species are manifested. The suitable M@Si(n) building blocks of self-assembly materials vary in the range of 10<or=n<or=16. The thermodynamical magic numbers are found to coincide with the chemical magic numbers for five clusters.

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.