Electronic Structure and Redox Properties of Metal Nitride Endohedral Fullerenes M3N@C2n (M=Sc,Y, La,and Gd; 2n=80, 84, 88, 92, 96)

An extensive study of the redox properties of metal nitride endohedral fullerenes (MNEFs) based on DFT computational calculations has been performed. The electronic structure of the singly oxidized and reduced MNEFs has been thoroughly analyzed and the first anodic and cathodic potentials, as well as the electrochemical gaps, have been predicted for a large number of M₃N@C_2n systems (M=Sc, Y, La, and Gd; 2n=80, 84, 88, 92, and 96). In particular, calculations that include thermal and entropic effects correctly predict the different anodic behavior of the two isomers (I_h and D_5h) of Sc₃N@C₈₀, which is the basis for their electrochemical separation. Important differences were found in the electronic structure of reduced M₃N@C₈₀ when M=Sc or when M is a more electropositive metal, such as Y or Gd. Moreover, the changes in the electrochemical gaps within the Gd₃N@C_2n series (2n=80, 84, and 88) have been rationalized and the use of Y‐based computational models to study the Gd‐based systems has been justified. The redox properties of the largest MNEFs characterized so far, La₃N@C_2n (2n=92 and 96), were also correctly predicted. Finally, the quality of these predictions and their usefulness in distinguishing the carbon cages for MNEFs with unknown structures is discussed.     

Zr(IV)-monosubstituted Keggin-type dimeric polyoxometalates: synthesis, characterization, catalysis of H2O2-based oxidations, and theoretical study

The previously unknown Zr(IV)-monosubstituted Keggin-type polyoxometalates (Zr-POMs), (n-Bu4N)7H[{PW11O39Zr(mu-OH)}2] (1), (n-Bu4N)8[{PW11O39Zr(mu-OH)}2] (2), and (n-Bu4N)9[{PW11O39Zr}2(mu-OH)(mu-O)] (3) differing in their protonation state, have been prepared starting from heteropolyacid H5PW11ZrO40.14H2O. The compounds were characterized by elemental analysis, potentiometric titration, X-ray single-crystal structure, and IR, Raman, and 31P and 183W NMR spectroscopy. The single-crystal X-ray analysis of 2 reveals that two Keggin structural units [PW11O39Zr]3- are linked through two hydroxo bridges Zr-(OH)-Zr with Zr(IV) in 7-fold coordination. The IR spectra of 1 and 2 show a characteristic band at 772 cm(-1), which moves to 767 cm(-1) for 3, reflecting deprotonation of the Zr-(OH)-Zr bond. Potentiometric titration with methanolic Bu4NOH indicates that 1-3 contain 2, 1, and 0 acid protons, respectively. (83W NMR reveals Cs symmetry of 2 and 3 in dry MeCN, while for 1, it discovers nonequivalence of its two subunits and their distortion resulting from localization of the acidic proton on one of the Zr-O-W bridging O atoms. The (31)P NMR spectra of 2 and 3 differ insignificantly in dry MeCN, showing only signals at delta -12.46 and -12.44 ppm, respectively, while the spectrum of 1 displays two resonances at delta -12.3 (narrow) and -13.2 (broad) ppm, indicating slow proton exchange on the (31)P NMR time scale. The theoretical calculations carried out at the density functional theory level on the dimeric species 1-3 propose that protonation at the Zr-O-Zr bridging site is more favorable than protonation at Zr-O-W sites. Calculations also revealed that the doubly bridged hydroxo structure is thermodynamically more stable than the singly bridged oxo structure, in marked contrast with analogous Ti- and Nb-monosubstituted polyoxometalates. The interaction of 1-3 with H(2)O and H(2)O(2) in MeCN has been studied by both (31)P and (183)W NMR. The stability of the [PW(11)O(39)ZrOH](4-) structural unit toward at least 100-fold excess of H2O2 in MeCN was confirmed by both NMR and Raman spectroscopy. The interaction of 1 and 2 with H2O in MeCN produces most likely monomeric species (n-Bu4N)3+n[PW11O39Zr(OH)(n(H2O)(3-n)] (n = 0 and 1) showing a broad 31P NMR signal at delta -13.2 ppm, while interaction with H2O2 leads to the formation of an unstable peroxo species (delta -12.3 ppm), which reacts rapidly with cyclohexene, producing 2-cyclohexen-1-one and trans-cyclohexane-1,2-diol. Both 1 and 2 show a pronounced catalytic activity in H2O2 decomposition and H2O2-based oxidation of organic substrates, including cyclohexene, alpha-pinene, and 2,3,6-trimethylphenol. The oxidation products are consistent with those of a homolytic oxidation mechanism. On the contrary, 3 containing no acid protons reacts with neither H2O nor H2O2 and shows negligible catalytic activity. The Zr-monosubstituted polyoxometalates can be used as tractable homogeneous probes of Zr single-site heterogeneous catalysts in studying mechanisms of H2O2-based oxidations.     

Exohedral reactivity of trimetallic nitride template (TNT) endohedral metallofullerenes

[structures: see text] Fullerenes containing a trimetallic nitride template (TNT) within the cage are a particularly interesting class of endohedral metallofullerenes. Recently two exohedral derivatives of the Sc3N@C80 fullerene have been synthesized: a Diels-Alder and a fulleropyrrolidine cycloadduct. The successful isolation, purification, and structural elucidation of these metallofullerenes derivatives have encouraged us to understand how the chemical reactivity is affected by TNT encapsulation. First of all, we predicted the most reactive exohedral sites, taking into account the double bond character and the pyramidalization angle of the C-C bonds. For this purpose, a full characterization of all different types of C-C bonds of the following fullerenes was carried out: I(h)-C60:1, D3-C68:6140, D3-Sc3N@C68, D(5h)-C70:1, D(3h')-C78:5, D(3h)-Sc3N@C78, I(h)-C80:7 and several isomers of Sc3N@C80. Finally the exohedral reactivity of these TNT endohedral metallofullerenes, via [4 + 2] cycloaddition reactions of 1,3-butadiene, was corroborated by means of DFT calculations.     

Full exploration of the Diels-Alder cycloaddition on metallofullerenes M3N@C80 (M = Sc, Lu, Gd): the D(5h) versus I(h) isomer and the influence of the metal cluster

In this work a detailed investigation of the exohedral reactivity of the most important and abundant endohedral metallofullerene (EMF) is provided, that is, Sc(3)N@I(h)-C(80) and its D(5h) counterpart Sc(3)N@D(5h)-C(80) , and the (bio)chemically relevant lutetium- and gadolinium-based M(3)N@I(h)/D(5h)-C(80) EMFs (M = Sc, Lu, Gd). In particular, we analyze the thermodynamics and kinetics of the Diels-Alder cycloaddition of s-cis-1,3-butadiene on all the different bonds of the I(h)-C(80) and D(5h)-C(80) cages and their endohedral derivatives. First, we discuss the thermodynamic and kinetic aspects of the cycloaddition reaction on the hollow fullerenes and the two isomers of Sc(3)N@C(80). Afterwards, the effect of the nature of the metal nitride is analyzed in detail. In general, our BP86/TZP//BP86/DZP calculations indicate that [5,6] bonds are more reactive than [6,6] bonds for the two isomers. The [5,6] bond D(5h)-b, which is the most similar to the unique [5,6] bond type in the icosahedral cage, I(h)-a, is the most reactive bond in M(3)N@D(5h)-C(80) regardless of M. Sc(3)N@C(80) and Lu(3)N@C(80) give similar results; the regioselectivity is, however, significantly reduced for the larger and more electropositive M = Gd, as previously found in similar metallofullerenes. Calculations also show that the D(5h) isomer is more reactive from the kinetic point of view than the I(h) one in all cases which is in good agreement with experiments.     

The smallest stable fullerene, M@C28 (m = Ti, Zr, U): stabilization and growth from carbon vapor

The smallest fullerene to form in condensing carbon vapor has received considerable interest since the discovery of Buckminsterfullerene, C(60). Smaller fullerenes remain a largely unexplored class of all-carbon molecules that are predicted to exhibit fascinating properties due to the large degree of curvature and resulting highly pyramidalized carbon atoms in their structures. However, that curvature also renders the smallest fullerenes highly reactive, making them difficult to detect experimentally. Gas-phase attempts to investigate the smallest fullerene by stabilization through cage encapsulation of a metal have been hindered by the complexity of mass spectra that result from vaporization experiments which include non-fullerene clusters, empty cages, and metallofullerenes. We use high-resolution FT-ICR mass spectrometry to overcome that problem and investigate formation of the smallest fullerene by use of a pulsed laser vaporization cluster source. Here, we report that the C(28) fullerene stabilized by encapsulation with an appropriate metal forms directly from carbon vapor as the smallest fullerene under our conditions. Its stabilization is investigated, and we show that M@C(28) is formed by a bottom-up growth mechanism and is a precursor to larger metallofullerenes. In fact, it appears that the encapsulating metal species may catalyze or nucleate endohedral fullerene formation.     

Electrosynthesis of a Sc3N@I(h)-C80 methano derivative from trianionic Sc3N@I(h)-C80

The electrosynthetic method has been used for the selective synthesis of fullerene derivatives that are otherwise not accessible by other procedures. Recent attempts to electrosynthesize Sc(3)N@I(h)-C(80) derivatives using the Sc(3)N@I(h)-C(80) dianion were unsuccessful because of its low nucleophilicity. Those results prompted us to prepare the Sc(3)N@C(80) trianion, which should be more nucleophilic and reactive with electrophilic reagents. The reaction between Sc(3)N@C(80) trianions and benzal bromide (PhCHBr(2)) was successful and yielded a methano derivative, Sc(3)N@I(h)-C(80)(CHPh) (1), in which the >CHPh addend is selectively attached to a [6,6] ring junction, as characterized by MALDI-TOF mass spectrometry and NMR and UV-vis-NIR spectroscopy. The electrochemistry of 1 was studied using cyclic voltammetry, which showed that 1 exhibits the typical irreversible cathodic behavior of pristine Sc(3)N@I(h)-C(80), resembling the behavior of other methano adducts of Sc(3)N@I(h)-C(80). The successful synthesis of endohedral metallofullerene derivatives using trianionic Sc(3)N@I(h)-C(80) and dianionic Lu(3)N@I(h)-C(80), but not dianionic Sc(3)N@I(h)-C(80), prompted us to probe the causes using theoretical calculations. The Sc(3)N@I(h)-C(80) trianion has a singly occupied molecular orbital with high spin density localized on the fullerene cage, in contrast to the highest occupied molecular orbital of the Sc(3)N@I(h)-C(80) dianion, which is mainly localized on the inside cluster. The calculations provide a clear explanation for the different reactivities observed for the dianions and trianions of these endohedral fullerenes.     

连续波锁模Pr3+:YLF激光器

本文报导了采用氩离子激光器来泵浦Pr³⁺:YLF晶体,应用声光调制器实现了主动锁模;同时应用振动─高反射平面镜也实现了被动锁模,两种锁模均得到了ps光脉冲.据作者了解这是这种晶体材料的第一次锁模运转.     

Solution of sparse quasi-square rectangular systems by Gaussian elimination

We present a general method for the linear least-squares solutionof overdetermined and underdetermined systems. The method isparticularly efficient when the coefficient matrix is quasi-square,that is when the number of rows and number of columns is almostthe same. The numerical methods for linear least-squares problemsand minimum-norm solutions do not generally take account ofthis special characteristic. The proposed method is based onLU factorization of the original quasi-square matrix A, assumingthat A has full rank. In the overdetermined case, the LU factorsare used to compute a basis for the null space of A^T. The right-handside vector b is then projected onto this subspace and the least-squaressolution is obtained from the solution of this reduced problem.In the case of underdetermined systems, the desired solutionis again obtained through the solution of a reduced system.The use of this method may lead to important savings in computationaltime for both dense and sparse matrices. It is also shown inthe paper that, even in cases where the matrices are quite small,sparse solvers perform better than dense solvers. Some practicalexamples that illustrate the use of the method are included.     

Ab initio and DFT modelling of complex materials: towards the understanding of electronic and magnetic properties of polyoxometalates

In this review we summarise the quantum chemistry studies carried out by several groups over the last ten years on polyoxometalates, or polyoxoanions. This is an immense family of compounds made up of transition metal ions in their highest oxidation state and oxo ligands. The continuous progress of computers in general, and quantum chemistry software in particular, has enabled a number of topics in polyoxometalate chemistry to be studied from the electronic structure of the most representative polyoxometalate, the so-called Keggin anion, to the factors governing the inclusion complexes and the magnetism in reduced complexes.