Effect of cage size on the third‐order optical properties of endohedral metallofullerenes Sc3N@C2n (2n = 68, 70, 78, and 80): A theoretical study

Geometrical structures of the investigated endohedral metallofullerenes Sc₃N@C_2n (2n = 68, 70, 78, and 80) were optimized at the B3LYP/6‐31G* level. The analyses of electronic structures display that the contribution of fullerene cage to the lowest unoccupied molecular orbital decreases as the cage size increases. Based on the optimized structures, the time‐dependent density functional theory combined with the sum‐over‐states method was used to investigate their nonlinear optical properties. Calculated third‐order polarizabilities γ and two‐photon absorption (TPA) cross‐section δ do not present the monotone variation with the size of fullerene cage, with largest γ of 0.48 × 10^?34 esu for Sc₃N@C₇₈ in static state, and largest δ of 12.374 GM for Sc₃N@C₇₀ in the wavelength of 902.5 nm. However, the obtained TPA resonant peaks shift red with the size of fullerene cage. By analyzing the electronic origin of the third‐order optical properties, it is found that the charge transfers from the fullerene cage to the encapsulated Sc₃N cluster make important contributions to the studied properties. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Theoretical studies of structures and stabilities of endohedral fullerenes X0/n+ @C32 (X = H,Li, Na,K, Be,Mg, Ca,B, Al,C, Si,N, P,n = 1–3)

Based on the D₃ C₃₂ fullerene, the equilibrium geometries, electronic structures, and binding energies of the endohedral fullerenes X^0/n+@C₃₂ (X = H, Li, Na, K, Be, Mg, Ca, B, Al, C, Si, N, P, n = 1–3) have been calculated using the DFT/B3LYP/6‐31G(d) method. The results show that the C₃₂ cages are slightly enlarged due to encapsulation, and the sizes of non‐neutral molecules are smaller than the corresponding neutral ones. Cages containing Li, Na, and Ca and most of the cations, except Na⁺ and K⁺, are energetically favorable. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

High Magnetic Moments in Manganese‐Doped Silicon Clusters

We report on the structural, electronic, and magnetic properties of manganese‐doped silicon clusters cations, Si_nMn⁺ with n=6–10, 12–14, and 16, using mass spectrometry and infrared spectroscopy in combination with density functional theory computations. This combined experimental and theoretical study allows several structures to be identified. All the exohedral Si_nMn⁺ (n=6–10) clusters are found to be substitutive derivatives of the bare Si_n+1⁺ cations, while the endohedral Si_nMn⁺ (n=12–14 and 16) clusters adopt fullerene‐like structures. The hybrid B3P86 functional is shown to be appropriate in predicting the ground electronic states of the clusters and in reproducing their infrared spectra. The clusters turn out to have high magnetic moments localized on Mn. In particular the Mn atoms in the exohedral Si_nMn⁺ (n=6–10) clusters have local magnetic moments of 4 μ_B or 6 μ_B and can be considered as magnetic copies of the silicon atoms. Opposed to other 3d transition‐metal dopants, the local magnetic moment of the Mn atom is not completely quenched when encapsulated in a silicon cage.     

Photoelectron Spectroscopy and Density Functional Calculations of TiGen- (n=7-12) Clusters

The growth pattern and electronic properties of TiGe_n^- (n=7-12) clusters were investigated using anion photoelectron spectroscopy and density functional theory calculations. For both anionic and neutral TiGe_n clusters, a half-encapsulated boat-shaped structure appears at n=8, and the boat-shaped structure is gradually covered by the additional Ge atoms to form Ge_n cage at n=9-11. TiGe₁₂^- cluster has a distorted hexagonal prism cage structure. According to the natural population analysis, the electron transfers from the Ge_n framework to the Ti atom for TiGe_n^-/0 clusters at n=8-12, implying that the electron transfer pattern is related to the structural evolution.     

Formation of Dianions in Helium Nanodroplets

The formation of dianions in helium nanodroplets is reported for the first time. The fullerene cluster dianions (C₆₀)_n^2? and (C₇₀)_n^2? were observed by mass spectrometry for n≥5 when helium droplets containing the appropriate fullerene were subjected to electron impact at approximately 22 eV. A new mechanism for dianion formation is described, which involves a two‐electron transfer from the metastable He^? ion. As well as the prospect of studying other dianions at low temperature using helium nanodroplets, this work opens up the possibility of a wider investigation of the chemistry of He^?, a new electron‐donating reagent.     

Quantum Chemical Insight of the Dimetallic Sulfide Endohedral Fullerene Sc2S@C70: Does It Possess the Conventional D5h Cage?

Like C₆₀, C₇₀ is one of the most representative fullerenes in fullerene science. Even though there are 8149 C₇₀ isomers, only two of them have been found before: the conventional D_5h and an isolated pentagon rule (IPR)‐violating C_2v(7854). Through the use of quantum chemical methods, we report a new unconventional C₇₀ isomer, C₂(7892), which survives in the form of dimetallic sulfide endohedral fullerene Sc₂S@C₇₀. Compared with the IPR‐obeying C₇₀ and the C_2v(7854) fullerene with three pairs of pentagon adjacencies, the C₂(7892) cage violates the isolated pentagon rule and has two pairs of pentagon adjacencies. In Sc₂S@C₂(7892)‐C₇₀, two scandium atoms coordinate with two pentalene motifs, respectively, presenting two equivalent Sc? S bonds. The strong coordination interaction, along with the electron transfer from the Sc₂S cluster to the fullerene cage, results in the stabilization of the non‐IPR endohedral fullerene. The electronic structure of Sc₂S@C₇₀ can be formally described as [Sc₂S]⁴⁺@[C₇₀]^4?; however, a substantial overlap between the metallic orbitals and cage orbitals has also been found. Electrochemical properties and electronic absorption, infrared, and ¹³C NMR spectra of Sc₂S@C₇₀ have been calculated theoretically.     

Theoretical study of beryllium (II) complexes using CATIVIC: New parametric method

Calculations of several beryllium complexes {[Be(H₂O)_n]²⁺ (n = 1–4), [BeOH(H₂O)_n]⁺ (n = 1–3), and [Be(OH)₂(H₂O)_n] (n = 1, 2)} were carried out to compare different ab initio (density functional theory, MP2) and parametric (PM3(tm), CATIVIC) methods. Results show that the parametric method CATIVIC gives geometries and energies closer to the ab initio geometries than the PM3(tm) method due to the inclusion of the atomic excitation energies of the neutral atoms as well as the ions and to the dependence of the molecular parameters on the system charge. The molecular electronic density analysis of the Be? O bonds shows that the Be–water interaction in the [Be(H₂O)_n]²⁺ complexes can be considered as a closed‐shell interaction with a σ character in the bond while in the [Be(OH)₂(H₂O)_n] complexes the Be? water bond have π character. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Be在富勒烯C74笼内稳定位置的理论研究

为了研究富勒烯金属包合物Be@C74的结构和电子性质,本文采用密度泛函理论B3LYP方法优化了Be@C74的结构,计算了它的势能面、LUMO-HOMO、电子亲和势、电子化能以及Mulliken集居数。结果表明:Be原子位于C74笼中心并且近似保持基态的电子构型;Be原子和C74笼之间是相互排斥作用;Be原子包入C74笼中心后,C74笼只有微小的变形;包合物Be@C74笼的给予和得到电力的能力与C74空笼几乎不变;Be与C74笼之间只有微小的杂化。     

Rapid analysis technique for strontium,thorium, and uranium in urine samples

The electronic properties of the metal atoms encaged in a fullerence cage were investigated using synchrotron X-ray photoelectron spectroscopy. Systematic variations in photoemission of valence band of Gd@C₈₂, Gd@C₈₂(OH)₁₂, and Gd@C₈₂(OH)₂₂ were observed in Gd 5p levels. The results suggest that the electronic properties of the inner metal atom can be efficiently modulated by surface chemistry of the fullerene cage.     

High‐Potential Perfluorinated Phthalocyanine–Fullerene Dyads for Generation of High‐Energy Charge‐Separated States: Formation and Photoinduced Electron‐Transfer Studies

High oxidation potential perfluorinated zinc phthalocyanines (ZnF_nPcs) are synthesised and their spectroscopic, redox, and light‐induced electron‐transfer properties investigated systematically by forming donor–acceptor dyads through metal–ligand axial coordination of fullerene (C₆₀) derivatives. Absorption and fluorescence spectral studies reveal efficient binding of the pyridine‐ (Py) and phenylimidazole‐functionalised fullerene (C₆₀Im) derivatives to the zinc centre of the F_nPcs. The determined binding constants, K, in o‐dichlorobenzene for the 1:1 complexes are in the order of 10⁴ to 10⁵ M ^?1; nearly an order of magnitude higher than that observed for the dyad formed from zinc phthalocyanine (ZnPc) lacking fluorine substituents. The geometry and electronic structure of the dyads are determined by using the B3LYP/6‐31G* method. The HOMO and LUMO levels are located on the Pc and C₆₀ entities, respectively; this suggests the formation of ZnF_nPc^.+–C₆₀Im^.? and ZnF_nPc^.+–C₆₀Py^.? (n=0, 8 or 16) intra‐supramolecular charge‐separated states during electron transfer. Electrochemical studies on the ZnPc–C₆₀ dyads enable accurate determination of their oxidation and reduction potentials and the energy of the charge‐separated states. The energy of the charge‐separated state for dyads composed of ZnF_nPc is higher than that of normal ZnPc–C₆₀ dyads and reveals their significance in harvesting higher amounts of light energy. Evidence for charge separation in the dyads is secured from femtosecond transient absorption studies in nonpolar toluene. Kinetic evaluation of the cation and anion radical ion peaks reveals ultrafast charge separation and charge recombination in dyads composed of perfluorinated phthalocyanine and fullerene; this implies their significance in solar‐energy harvesting and optoelectronic device building applications.     

Theoretical Study of the Structures,Properties and Spectroscopies on Fullerene Hydrides C<Subscript>26</Subscript>H<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> (<Emphasis Type="Italic">n</Emphasis> = 2, 4, 6, 8)

The structures, stability patterns of C₂₆H _n (n = 2) formed from the initial D _3h C₂₆ fullerene were investigated by use of second-order-Moller–Plesset perturbation theory. The study of the stability patterns of hydrogenation reaction on C₂₆ cage revealed that type (β) carbons were the active site and the analyses of π-orbital axis vector indicated that the reactivity of C₂₆ was the result of the high strain and the hydrogenation reaction on C₂₆ cage was highly exothermic. The calculated ¹³C NMR spectra of C₂₆H _n (n = 2) predicted that the two sp ³ hybridization carbons in C₂₆H _n (n = 2) obviously moved to high field compare with that in D _3h C₂₆. Hence, the C₂₆H₂ should be obtained and detected experimentally. Similarly, the structures and reaction energies of C₂₆H _n (n = 4, 6, 8) were further studied at HF/6-31G*, B3LPY/6-31G* and MP2/6-31G* level. The results suggested the hydrogenation products of C₂₆, C₂₆H _n (n = 4, 6, 8), were more stable than the C₂₆ cage.     

Searching new structures of beryllium-doped in small-sized magnesium clusters: Be2MgnQ (Q = 0, −1; n = 1–11) clusters DFT study

Using CALYPSO method to search new structures of neutral and anionic beryllium-doped magnesium clusters followed by density functional theory (DFT) calculations, an extensive study of the structures, electronic and spectral properties of Be₂Mg_n^Q (Q = 0, −1; n = 2–11) clusters is performed. Based on the structural optimization, it is found that the Be₂Mg_n^Q (Q = 0, −1) clusters are shown by tetrahedral-based geometries at n = 2–6 and tower-like-based geometries at n = 7–11. The calculations of stability indicate that Be₂Mg₅^Q=0, Be₂Mg₅^Q=−1, and Be₂Mg₈^Q=−1 clusters are “magic” clusters with high stability. The NCP shows that the charges are transferred from Mg atoms to Be atoms. The s- and p-orbitals interactions of Mg and Be atoms are main responsible for their NEC. In particular, chemical bond analysis including molecular orbitals (MOs) and chemical bonding composition for magic clusters to further study their stability. The results confirmed that the high stability of these clusters is due to the interactions between the Be atom and the Mg₅ or Mg₈ host. Finally, theoretical calculations of infrared and Raman spectra of the ground state of Be₂Mg_n^Q (Q = 0, −1; n = 1–11) clusters were performed, which will be absolutely useful for future experiments to identify these clusters.     

Cages versus Sheets: A Critical Comparison in the Size Range Expected for Methylaluminoxane (MAO)

New cage models (MeAlO)_n(Me₃Al)_m (n=16, m=6 or 7) isomeric with previously reported sheet models for the principle activator found in hydrolytic MAO (h-MAO) are compared at M06-2X and MN15 levels of theory using density functional theory with respect to their thermodynamic stability. Reactivity of the neutrals or corresponding anions with formula [(MeAlO)₁₆(Me₃Al)₆Me]⁻ towards chlorination, and loss of Me₃Al is explored while reactivity of the neutrals towards formation of contact- and outer-sphere ion pairs from Cp₂ZrMe₂ and Cp₂ZrMeCl is examined. The results suggest on balance that a cage model for this activator is less consistent with experiment than an isomeric sheet model, although the latter are more stable based on free energy.     

Encapsulation of the interstellar abundant H3+ in a C60 fullerene

The possible encapsulation of the interstellar abundant H₃⁺ ion inside a C₆₀ fullerene cage has been examined by using the Hartree‐Fock (HF) and the second order Møller‐Plesset perturbation (MP2) methods both with the 6‐31G** basis set. It was found that H₃⁺ forms various stable endohedral complexes inside the cage. Six configurations have been examined among which four were stable compared with the separated initial species, the dissociated H₂ + H⁺ inside the cage being the most stable. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

[6,6]‐Open and [6,6]‐Closed Isomers of C70(CF2): Synthesis,Electrochemical and Quantum Chemical Investigation

Novel difluoromethylenated [70]fullerene derivatives, C₇₀(CF₂)_n (n=1–3), were obtained by the reaction of C₇₀ with sodium difluorochloroacetate. Two major products, isomeric C₇₀(CF₂) mono‐adducts with [6,6]‐open and [6,6]‐closed configurations, were isolated and their homofullerene and methanofullerene structures were reliably determined by a variety of methods that included X‐ray analysis and high‐level spectroscopic techniques. The [6,6]‐open isomer of C₇₀(CF₂) constitutes the first homofullerene example of a non‐hetero [70]fullerene derivative in which functionalisation involves the most reactive bond in the polar region of the cage. Voltammetric estimation of the electron affinity of the C₇₀(CF₂) isomers showed that it is substantially higher for the [6,6]‐open isomer (the 70‐electron π‐conjugated system is retained) than the [6,6]‐closed form, the latter being similar to the electron affinity of pristine C₇₀. In situ ESR spectroelectrochemical investigation of the C₇₀(CF₂) radical anions and DFT calculations of the hyperfine coupling constants provide evidence for the first example of an inter‐conversion between the [6,6]‐closed and [6,6]‐open forms of a cage‐modified fullerene driven by an electrochemical one‐electron transfer. Thus, [6,6]‐closed C₇₀(CF₂) constitutes an interesting example of a redox‐switchable fullerene derivative.     

Quantum chemical calculations of N@Cn endofullerenes (n ≤ 60)

The geometric parameters and energy characteristics of small endofullerenes N@C_n (n = 20, 24, 30, 32, 40, 50) and N@C₆₀ in the quartet ground state were calculated by the B3LYP/6-31G* method. The N atom is located at the center of the carbon cage in all molecules except N@C₃₀, where it is bound to the cage wall. Encapsulation of nitrogen atom has little effect on the fullerene cage geometry for n = 40, 50, and 60. No significant charge transfer from the N endo-atom to the cage was revealed for all the N@C_n endofullerenes studied. The calculated spin density on the nitrogen endo-atom increases as the size (n) of the carbon cage increases. The relative stabilities of C_n fullerenes and corresponding endofullerenes N@C_n are discussed. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 15–20, January, 2006.     

Investigations in the field of higher fullerenes

Halogenation of higher fullerene mixtures or their perfluoroalkylation with R^FI followed by HPLC separation of R^F derivatives and subsequent synchrotron X-ray crystallographic study made it possible to confirm cage connectivities of higher fullerenes and, in addition, to receive information concerning their reactivity in radical addition reactions. The data obtained are compared with theoretical predictions for higher fullerenes. Addition patterns of higher fullerene derivatives are discussed. Skeletal rearrangement of the D ₂-C₇₆ cage during chlorination has been observed for the first time.     

A DFT quantum‐chemical study on the structures and active sites of polymethylaluminoxane

The electronic structure and geometry of polymethylaluminoxane (MAO) [—Al(CH₃)O—]_n with different size (n = 4–12) have been studied using quantum‐chemical DFT (density functional theory) calculations. It has been found: 1) Starting from n = 6, the three‐dimensional oxo‐bridged (cage) structure of MAO is more stable than the cyclic structure. 2) Both for cage structure and for cyclic structure the Lewis acidity of Al atoms characterized by their net positive charge amplifies with increasing size of MAO (n). 3) Trimethylaluminium (AlMe₃) reacts with the cage structure of MAO with cleavage of an Al‐O dative bond and formation of acidic tri‐coordinated Al^v and basic di‐coordinated O^v atoms in the MAO molecule. Two molecules AlMe₃ are associated with acidic Al^v and basic O^v centers. As the MAO increases in size, the acidity of Al^v centers amplifies and the distance Al^v‐(AlMe₃) shortens; on the contrary, interaction of AlMe₃ with O^v centers weakens and the distance O^v‐(AlMe₃) increases with increasing n value. The total heat of Al₂Me₆ interaction with MAO (sum interaction of Al^v‐(AlMe₃) and O^v‐(AlMe₃)) noticeably decreases as the size of MAO increases (from 50.9 kcal/mol for n = 4 to 20.2 kcal/mol for n = 12). It is proposed that acidic Al^v and basic O^v centers formed in the cage structure of MAO interact with zirconocene yielding ‘cation‐like’ zirconium active centers.     

Activation of the Unreactive Bond in C70 Fullerene toward Diels‐Alder Reaction by Encapsulation of a Lithium Atom

Diels‐Alder cycloaddition reaction is useful for generation of covalent derivatives of fullerenes. Diels‐Alder reactions of C₇₀ and dienes usually take place at the carbon‐carbon bond that has a short bond length in C₇₀, while the bonds with long lengths are generally unreactive. In this paper, we investigated the reactivities of Li⁺@C₇₀ and Li@C₇₀ toward Diels‐Alder reactions with cyclohexadiene by means of density functional theory calculations. We found that the thermodynamic and kinetic reactivities of the fullerene cage are changed significantly after the encapsulation of the lithium ion or atom. The encapsulated lithium ion causes a remarkable decrease of the activation barrier for the cycloaddition reaction, which can be ascribed to the enhanced orbital interaction between cyclohexadiene and the fullerene cage. The unreactive bond with a long length in C₇₀ is activated efficiently after the encapsulation of the lithium atom. According to the activation‐strain model analysis, the improved reactivity of the long bond is associated with the small deformation energy and large interaction energy of the reactants. Unlike conventional Diels‐Alder reactions that proceed through concerted mechanism, the reaction of Li@C₇₀ and cyclohexadiene undergoes an unusual stepwise mechanism because of the open‐shell electronic structure of Li@C₇₀.     

Electronic Communication between S=1/2 Spins in Negatively‐charged Double‐caged Fullerene C60 Derivative Bonded by Two Single Bonds and Pyrrolizidine Bridge

Radical anion salt {cryptand[2.2.2] (K⁺)}₂(bispheroid)^2??3.5C₆H₄Cl₂ ( 1 ) of the double‐caged fullerene C₆₀ derivative, in which fullerene cages are linked by a cyclobutane bridging cycle and additionally by a pyrrolizidine moiety, was obtained. Each fullerene cage in this derivative accepts one electron on reduction, thus forming the (bispheroid)^2? dianions with two interacting S=1/2 spins on the neighboring cages. Low‐temperature magnetic measurements reveal a singlet ground state of the bispheroid dianions whereas triplet contributions prevail at increased temperature. An estimated exchange interaction between two spins J/k_B=?78 K in 1 indicates strong magnetic coupling between them, nearly two times higher than that (J/k_B=?44.7 K) in previously studied (C₆₀^?)₂ dimers linked via a cyclobutane bridge only. The enhancement of magnetic coupling in 1 can be explained by a shorter distance between the fullerene cages and, possibly, an additional channel for the magnetic exchange provided by a pyrrolizidine bridge. Quantum‐chemical calculations of the lowest electronic state of the dianions by means of multi‐configuration quasi‐degenerate perturbation theory support the experimental findings.