Modifying electronic communication in dimolybdenum units by linkage isomers of bridged oxamidate dianions

Reactions of Mo(2)(O(2)CCH(3))(DAniF)(3), DAniF = N,N'-di-p-anisylformamidinate, with oxamidate dianions [ArNC(O)C(O)NAr](2-), Ar = C(6)H(5) and p-anisyl, give pairs of isomeric compounds where the [Mo(2)] units are bridged by the oxamidate anions. For the alpha isomers, the C-C unit of the dianion is nearly perpendicular to the Mo-Mo bonds, and these are essentially perpendicular to each other. For the beta isomers, the corresponding C-C unit and the Mo-Mo bonds are essentially parallel to each other. Each type of isomer is stable in solution. The electronic communication as measured by the DeltaE(1/2) for the oxidation of each of the Mo(2) units is significantly better for the beta isomers. This is supported also by the appearance of what is conventionally called an intervalence charge-transfer band in the near infrared region upon oxidation of the beta isomers but not the alpha isomers. Molecular mechanics and DFT calculations help explain the relative conformations in the alpha isomers and the relative energy differences between the alpha and beta isomers.     

Orientational isomers of alpha-cyclodextrin [2]semi-rotaxanes with asymmetric dicationic threads

Two series of novel dicationic threading molecules [Quin(CH2)10R]2+ and [3,5-Lut(CH2)10R]2+, where Quin+ = quinuclidinium, 3,5-Lut+ = 3,5-lutidinium, and R+ = N(CH3)3+ and N(CH3)2CH2CH3+, form [2]semi-rotaxanes with [small alpha]-cyclodextrin (alpha-CD) in aqueous solution. The quinuclidinium and 3,5-lutidinium are sufficiently bulky to prevent threading while the R+ groups allow for slow threading by alpha-CD at 25 degrees C. The resulting [2]semi-rotaxanes exist in two orientational isomers owing to the asymmetry of both the alpha-CD cavity and the threading molecules. Two-dimensional 1H NMR spectroscopy and kinetics experiments reveal that the isomer in which the narrower rim (primary OHs) is positioned near the R+ group is the kinetically preferred isomer, while the other isomer is the thermodynamically preferred product. The kinetics and mechanism of the formation, dissociation, and interconversion of the two isomers have been determined at 25 degrees C.     

A rare dimer of dimers having four hydride linkers joining two quadruply bonded dimolybdenum units

Hydride anions, H-, have been found to cause the assembly of dimolybdenum units [Mo2(cis-DAniF)2]2+, DAniF = N,N'-di(p-anisyl)formamidinate, forming a tetranuclear complex [Mo2(cis-DAniF)2]2(mu-H)4 (1) with an Mo4H4 core that may be described as an elongated tetrahedron in which the H atoms are along the four long edges of such tetrahedron and the Mo2 units are along the short edges. The two quadruply bonded dimolybdenum units, separated by only 2.718 A, are essentially orthogonal. This gives the shortest [Mo2]...[Mo2] distance known for complexes with multiple dimolybdenum units. DFT calculations indicate that the energy of a cuboidal isomer is only 3.8 kcal/mol above that of 1, but such an isomer has not been observed.     

Experimental and theoretical investigations of the sulfite-based polyoxometalate cluster redox series: alpha- and beta-[Mo(18)O(54)(SO(3))(2)](4-/5-/6-)

The synthesis, isolation and structural characterization of the sulfite polyoxomolybdate clusters alpha-(D(3h))(C(20)H(44)N)(4){alpha-[Mo(18)O(54)(SO(3))(2)]}CH(3)CN and beta-(D(3d))(C(20)H(44)N)(4){beta-[Mo(18)O(54)(SO(3))(2)]}CH(3)CN is presented. Voltammetric studies in acetonitrile (0.1 M Hx(4)NClO(4), Hx(4)N=tetra-n-hexylammonium) reveal the presence of an extensive series of six one-electron reduction processes for both isomers. Under conditions of bulk electrolysis, the initial [Mo(18)O(54)(SO(3))(2)](4-/5-) and [Mo(18)O(54)(SO(3))(2)](5-/6-) processes produce stable [Mo(18)O(54)(SO(3))(2)](5-) and [Mo(18)O(54)(SO(3))(2)](6-) species, respectively, and the same reduced species may be produced by photochemical reduction. Spectroelectrochemical data imply that retention of structural form results upon reduction, so that both alpha and beta isomers are available at each of the 4-, 5-, and 6-redox levels. However, the alpha isomer is the thermodynamically favored species in both the one- and two-electron-reduced states, with beta-->alpha isomerization being detected in both cases on long time scales (days). EPR spectra also imply that increasing localization of the unpaired electron occurs over the alpha- and beta-[Mo(18)O(54)(SO(3))(2)](5-) frameworks as the temperature approaches 2 K where the EPR spectra show orthorhombic symmetry with different g and hyperfine values for the alpha and beta isomers. Theoretical studies support the observation that it is easier to reduce the alpha cluster than the beta form and also provide insight into the driving force for beta-->alpha isomerization in the reduced state. Data are compared with that obtained for the well studied alpha-[Mo(18)O(54)(SO(4))(2))](4-) sulfate cluster.     

Mechanistic analysis of the electrocatalytic properties of dissolved alpha and beta isomers of [SiW12O40]4- and solid [Ru(bipy)3]2[alpha-SiW12O40] on the reduction of nitrite in acidic aqueous media

Voltammetric studies on the reduction of alpha and beta isomers of the Keggin polyoxometalate anion [SiW12O40]4- reveal a series of electrochemically reversible processes in acidic aqueous media. In the presence of NO2-, catalytic current is detected in the potential region of the [SiW12O40]4-/5- process. Electronic spectroscopy and simulation of voltammetric data undertaken at variable [NO2-] and [H+] allow the following mechanism to be postulated, [SiW12O40]4- + e- <-->[SiW12O40]5-, H+ + HNO2 <--> NO+ + H2O, NO+ + [SiW12O40]5- --> NO + [SiW12O40]4-. The second-order rate constant for the rate-determining step is faster for the alpha isomer than for the beta one. This may be attributed to the different reversible potentials of -0.144 V (alpha isomer) and -0.036 V vs Ag/AgCl (beta isomer) and, hence, smaller driving force for an assumed outer sphere electron-transfer reaction in the case of beta isomer. A stable, water-insoluble, thin-film [Ru(bipy)3]2[alpha-SiW12O40] chemically modified electrode was generated electrochemically via ion-exchange of [Ru(bipy)3]2+ with Bu4N+ in the [Bu4N]4[alpha-SiW12O40] solid. The first reduction process with this modified electrode gives rise to the reaction [Ru(bipy)3]2[alpha-SiW12O40](solid) + H+(soln) + e- <--> H[Ru(bipy)3]2[alpha-SiW12O40](solid). The need to transfer a proton from the solution to the solid phase for charge neutralization purposes introduces a hydrogen-ion concentration dependence into this reaction, which is not found in the solution-phase study. Nevertheless, the voltammetric catalytic activity with respect to nitrite reduction is retained with the chemically modified electrode. However, nitrite catalysis with the [Ru(bipy)3]2[alpha-SiW12O40]-modified electrode is now independent of concentration of H+, rather than exhibiting a first-order dependence, and full mechanistic details for this process are unknown.     

Structural and electronic properties of hetero-transition-metal Keggin anions: a DFT Study of alpha/beta-[XW12O40]n- (X = CrVI, VV, TiIV, FeIII, CoIII, NiIII, CoII, and ZnII) relative stability

Density functional theory calculations have been carried out to investigate the electronic structures and the alpha/beta relative stability of Keggin-typed [XW(12)O(40)]n- anions with transition metal as heteroatom X (X = Cr(VI), V(V), Ti(IV), Fe(III), Co(III), Ni(III), Co(II) and Zn(II)). Nice agreement in geometries between computation and experiment has been obtained, and the higher stability of the alpha isomer over the beta one has been confirmed. Structural parameter analysis reveals that the {M(3)O(13)} triads in both alpha and beta isomers contract considerably with the increase of the negative anionic charge, while the overall size of both isomers shrinks only slightly. Fragment molecular orbital analysis shows that except alpha/beta-[TiW(12)O(40)]4-, the electronic structures of Keggin anions can be described by the insertion of the e and/or t2 orbital of XO4n- into the frontier orbitals of W(12)O(36) cage, and this leads to the specific redox property, which is different from that of the Keggin anions with main-group elements as heteroatoms. Energy decomposition analysis shows that the enhanced intrinsic stability of the alpha isomer in Td arrangement of W(12)O(36) shell and the larger deformation of the alpha over the beta isomer are two dominating factors and contribute oppositely to the alpha/beta relative stability.     

Relative stability in alpha- and beta-Wells-Dawson heteropolyanions: a DFT study of [P2M18O62]n- (M = W and Mo) and [P2W15V3O62]n-

To determine the relative stability of alpha and beta rotational isomers of the Wells-Dawson structure, the energies of some fully oxidized, single- and 2-fold-reduced systems were calculated by means of DFT calculations. The thermodynamics of the alpha/beta equilibrium for P(2)M(18) Wells-Dawson anions is slightly shifted toward the alpha structure, but the difference in stability is smaller than in the Keggin anions. Tungstates (2:18) and vanadotungstates (2:3:15) show minimal redox differences between isomers, as the electronic structure of the frontier orbitals appears to be nearly the same. In addition, an alternative arrangement is proposed that have long and short Mo-O bonds in beta-P(2)Mo(18) with an idealized C(3) symmetry. This arrangement was computed to be about 8.2 kcal mol(-1) more stable than the nonalternate framework of C(3)(v)() symmetry. The P(2)Mo(18) is the Wells-Dawson anion for which the alpha/beta equilibrium most resembles that of the Keggin anions.     

Stabilization of reduced molybdenum-iron-sulfur single- and double-cubane clusters by cyanide ligation

Recent work has shown that cyanide ligation increases the redox potentials of Fe(4)S(4) clusters, enabling the isolation of [Fe(4)S(4)(CN)4]4-, the first synthetic Fe(4)S(4) cluster obtained in the all-ferrous oxidation state (Scott, T. A.; Berlinguette, C. P.; Holm, R. H.; Zhou, H.-C. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 9741). The generality of reduced cluster stabilization has been examined with MoFe(3)S(4) clusters. Reaction of single-cubane [(Tp)MoFe(3)S(4)(PEt(3))3]1+ and edge-bridged double-cubane [(Tp)2Mo(2)Fe(6)S(8)(PEt(3))4] with cyanide in acetonitrile affords [(Tp)MoFe(3)S(4)(CN)3]2- (2) and [(Tp)2Mo(2)Fe(6)S(8)(CN)4]4- (5), respectively. Reduction of 2 with KC(14)H(10) yields [(Tp)MoFe(3)S(4)(CN)3]3- (3). Clusters were isolated in approximately 70-90% yields as Et(4)N+ or Bu(4)N+ salts; clusters 3 and 5 contain all-ferrous cores, and 3 is the first [MoFe(3)S(4)]1+ cluster isolated in substance. The structures of 2 and 3 are very similar; the volume of the reduced cluster core is slightly larger (2.5%), a usual effect upon reduction of cubane-type Fe(4)S(4) and MFe(3)S(4) clusters. Redox potentials and 57Fe isomer shifts of [(Tp)MoFe(3)S(4)L3]2-,3- and [(Tp)2Mo(2)Fe(6)S(8)L(4)]4-,3- clusters with L = CN-, PhS-, halide, and PEt3 are compared. Clusters with pi-donor ligands (L = halide, PhS) exhibit larger isomer shifts and lower (more negative) redox potentials, while pi-acceptor ligands (L = CN, PEt3) induce smaller isomer shifts and higher (less-negative) redox potentials. When the potentials of 3/2 and [(Tp)MoFe(3)S(4)(SPh)3]3-/2- are compared, cyanide stabilizes 3 by 270 mV versus the reduced thiolate cluster, commensurate with the 310 mV stabilization of [Fe(4)S(4)(CN)4]4- versus [Fe(4)S(4)(SPh)4]4- where four ligands differ. These results demonstrate the efficacy of cyanide stabilization of lower cluster oxidation states. (Tp = hydrotris(pyrazolyl)borate(1-)).     

Synthesis and redox characterization of the polyoxo anion, gamma*-[S2W18O62]4-: a unique fast oxidation pathway determines the characteristic reversible electrochemical behavior of polyoxometalate anions in acidic media

The synthesis and characterization of (Bu4N)4[S2W18O62].1.23MeCN.0.27H2O are reported. It crystallizes in the monoclinic space group C2/c with a = 22.389(6) A, b = 22.104(3) A, c = 25.505(5) A, beta = 95.690(15) degrees, V = 12560(5) A3, and Z = 4. The anion exists as the gamma* isomer, the second example of this isomer type to be characterized structurally. The equivalent molybdenum salt occurs as the alpha isomer. gamma*-[S2W18O62]4- in MeCN solution displayed four electrochemically reversible one-electron redox processes at E1/2 values of -0.24, -0.62, -1.18, and -1.57 V versus the Fc+/Fc couple. Upon addition of acid in MeCN/H2O (95/5 v/v), the two most cathodic processes converted to an overall two-electron process at -0.71 V. The total data suggested that this process actually comprises two one-electron transfer processes, occurring at different potentials, with associated proton-transfer reactions. The interpretation is supported by simulation of the effect of acid titration upon the cyclic voltammetry. While multiple pathways for correlated reduction and protonation are present in both the molybdenum and tungsten systems, only a single fast oxidation pathway is available. As the reduced forms of [S2W18O62]4- are much weaker bases than those of [S2Mo18O62]4-, the individual oxidation pathways are not the same. However, their existence determines the highly reversible electrochemical behavior that is characteristic of these anions, and that of polyoxometalate systems in general.     

Electronic localization versus delocalization determined by the binding of the linker in an isomer pair

By using stoichiometric amounts of (C5H5)2FePF6, the isomeric neutral diamidate-bridged molecules, alpha- and beta-(DAniF)3Mo2(ArN(O)CC(O)NAr)Mo2(DAniF)3, with Ar = p-MeOC6H4, have been oxidized to give the PF6 salts of the four cations alpha1+, alpha2+, beta1+, and beta2+. All four structures have been accurately determined and, together with supporting evidence from near-IR, EPR, NMR and magnetic susceptibility measurements, it clearly establishes that in the mixed-valent alpha+ species the unpaired electron is localized over only one of the Mo2 units while the alpha2+ cation behaves as a diradical having two Mo25+ units that are essentially uncoupled. However, the beta+ species is fully delocalized, in the time scale of the experiments, with the unpaired electron being equally shared by the two Mo2 units. It displays a HOMO-1 --> SOMO transition at 4700 cm-1 (Deltanu1/2 = 2300 cm-1). Because of strong coupling, the beta2+ species is diamagnetic.     

An unusual trigonal D3 assembly composed of molybdate anions and multiply bonded dimolybdenum units

Oxidation of the molybdate-linked pair having two quadruply bonded Mo(2)(4+) units, [Mo(2)(DAniF)(3)](2)(micro(2)-MoO(4)), (DAniF = N,N'-di-(p-anisyl)formamidinate) leads to the formation of a species consisting of three oxidized Mo(2)(5+) units connected by two micro(3)-MoO(4)(2-) dianions, {[Mo(2)(DAniF)(3)](3)(micro(3)-MoO(4))(2)}(2+). This cation displays overall D(3) point group symmetry due to a slight twisting of the three Mo(2)(5+) units about the threefold symmetry axis. This distortion removes all mirror symmetry but preserves all C(2) axes orthogonal to the unique C(3) axis. Cyclic voltammetry of {[Mo(2)(DAniF)(3)](3)(micro(3)-MoO(4))(2)}(2+) in CH(2)Cl(2) reveals three reversible one-electron redox processes, corresponding to successive reduction of each of the three Mo(2)(5+) units, with DeltaE(1/2) separations of 0.36 V and 0.41 V.     

Production,isolation and structural characterization of [92]fullerene isomers

High-resolution 13C NMR has been used to structurally characterize a single isomer possessing C2 molecular symmetry as well as an inseparable mixture of other isomers of [92]fullerene, produced from dysprosium arc-burned soot, separated and isolated via multi-stage recycling HPLC.     

Organotin derivatives of alpha-[XIIIW9O33]9- (X = As,Sb) heteropolytungstates. Solution- and solid-state characterization of [[C6H5Sn)2O]2H(alpha-AsW9O33)2]9- and [(C6H5Sn)3Na3(alpha-SbW9O33)2]6-

The tris(phenyltin)-substituted tungstoantimonate(III) Cs6[(PhSn)3Na3(alpha-SbW9O33)2].20H2O (1) and the tetrakis-(phenyltin)-substituted tungstoarsenate(III) Na9[[(PhSn)2O]2H(alpha-AsW9O33)2].20H2O (2) have been prepared by reaction of phenyltin trichloride with Na9[alpha-SbW9O33].19.5H2O and Na9[alpha-AsW9O33].19.5H2O, respectively, in aqueous solution. The products were characterized by elemental analysis, X-ray crystallography, multinuclear NMR, and infrared spectroscopy. Crystals of 1 are monoclinic, space group P2(1)/n, with a = 13.7952(1) A, b = 22.3133(2) A, c = 34.4493(2) A, beta = 90.933(1) degrees, and Z = 4. Anion 1 has nominal D3h symmetry and contains three PhSn3+ groups and three sodium ions sandwiched between [alpha-SbW9O33]9- units. Crystals of 2 are triclinic, space group P1, with a = 15.272(6) A, b = 15.303(6) A, c = 16.760(7) A, alpha = 93.59(3) degrees, beta = 106.187(19) degrees, gamma = 112.23(3) degrees, and Z = 1. Anion 2 has nominal C2h symmetry and contains four PhSn3+ groups sandwiched between two [alpha-AsW9O33]9- units.     

DFT study on the five isomers of PW(12)O(40)(3)(-): relative stabilization upon reduction

The electronic characteristics and the redox properties of each isomer of PW(12)O(40)(3)(-) depend on the arrangement adopted by the metal-oxide framework. At the DFT/BP86 level, we computed the structures of the five isomers of PW(12)O(40)(3)(-) in oxidized form. The energy scale fits the experimental findings as well as the number of rotated triads of the metal-oxide core since the energy grows as follows: alpha < beta < gamma < delta < epsilon. The reduced clusters behave differently as long as the beta form becomes the most stable isomer after the second reduction. The gamma isomer also gains stability upon reduction, but not enough to be competitive with beta. For the 4-fold reduced PW(12) cluster, the energy difference computed between beta and gamma in solution is 11 kcal mol(-)(1). This large difference proves that the beta --> gamma isomerization is not favored upon simple reduction. The other isomers, delta and epsilon, are much more unstable than alpha or beta in any reduction state.     

Assembly and autochirogenesis of a chiral inorganic polythioanion Möbius strip via symmetry breaking

Using [Mo(2)S(2)O(2)(H(2)O)(6)](2+) and squarate dianion, we synthesized the thiometalate ring compounds [(Mo(2)S(2)O(2))(x)(OH)(y)(C(4)O(4))(z)(Mo(2)O(8))(o)(H(2)O)(p)](n-), where [x,y,z,o,p,n] = [7,14,2,0,2,4] for 1, [6,8,2,2,4,8] for 2, and [4,6,1,1,0,4] for both 3a and 3b, which are chiral and nonchiral isomers, respectively. Not only do the four thiometalate clusters show decreasing symmetry at the molecular level across the series, but the incorporation of the "addendum" {Mo(2)O(8)}(o) unit also allows the thiometalate ring to twist. The reaction initially yields the chiral molecule 3a with a twisted ring, which undergoes spontaneous resolution upon crystallization; the reaction mixture later yields the intrinsically nonchiral isomer 3b with a nontwisted ring. In addition, the compounds are able to promote the electrocatalytic evolution of hydrogen.     

Molybdenum-iron-sulfur clusters of nuclearities eight and sixteen, including a topological analogue of the P-cluster of nitrogenase

Transformations of the edge-bridged double cubane cluster [(Cl4cat)2(Et3P)2Mo2Fe6S8(PEt3)4] (1) under reducing conditions have been investigated as synthetic approaches to the clusters of nitrogenase. Cluster 1 is a versatile precursor to different Mo-Fe-S cluster types. The reaction system 1/K(C14H10) in THF yields the reduced cluster [(Cl4cat)2(Et3P)2Mo2Fe6S8(PEt3)4]1- (2), which as its crystalline Et4N+ salt retains the edge-bridged structure of 1. X-ray structural and M?ssbauer spectroscopic results indicate an unsymmetrical electron distribution with localized [MoFe3S4]2+,1+ cubane-type units. The system 1/2K(C14H10)/2HS- in THF/acetonitrile affords [(Cl4cat)4(Et3P)4Mo4Fe12S20K3(DMF)]5- (3), whose structure was determined as the Ph3PMe+ salt. The cluster consists of two isostructural Mo2Fe6S9 fragments connected by two mu 2-S bridges. Three potassium ions are bound between the two fragments. In each fragment, the iron atoms are present in tetrahedral FeS4 and the molybdenum atoms in octahedral MoO2PS3 coordination units, and two MoFe3(mu 3-S)3 cuboidal units are bridged by a common mu 6-S atom. The fragments have idealized mirror symmetry and are isostructural with two of the fragments present in the previously reported high-nuclearity cluster [(Cl4cat)6(Et3P)6Mo6Fe20S30]8- (4) (Osterloh, F.; Sanakis, Y.; Staples, R. J.; Münck, E.; Holm, R. H. Angew. Chem., Int. Ed. Engl. 1999, 38, 2066). On the basis of overall shape, atom connectivities, and metric features, the Mo2Fe6S9 fragment is a topological analogue of the P-cluster of nitrogenase in the PN (reduced) state. A third cluster type, formed as a minor byproduct in the reaction system leading to 2, was crystallographically identified as [(Cl4cat)2(Et3P)2Mo2Fe6S8(PEt3)4]4-, whose core is made up of two MoFe3(mu 3-S)3 cuboidal units bridged by two mu 2-S atoms and connected by a direct Fe-Fe bond. Full structural details and the redox properties of 2 and 3 are reported.     

Preparation and crystal structures of formato complexes of the [MIV3O4]4+ and [MIV3S4]4+ (M = Mo,W) clusters. Convenient precursors to the corresponding aqua complexes

In the aqueous chemistry of molybdenum(IV) and tungsten(IV), trinuclear, incomplete cubane-like, oxo and sulfido clusters of the type [M3E4]4+ (M = Mo, W; E = O, S) play a central role. We here describe how formato complexes of all these cluster cores can be prepared in high yields by crystallization from methanol-water or ethanol-water mixtures. Since potassium and ammonium formate are very soluble in these alcohol-water mixtures, high formate concentrations could be accomplished in the solutions from which the corresponding salts of cluster formato complexes crystallized. The [Mo3O4]4+ compounds could be synthesized without requiring the use of noncomplexing acids in the process. Some [M3E4]4+ compounds were characterized by single-crystal structure determinations. [NH4]3.20[K]0.80[H3O][Mo3O4(HCO2)8][HCO2].H2O was triclinic, space group P1 (No. 2) with a = 11.011(2) A, b = 13.310(2) A, c = 9.993(1) A, alpha = 106.817(7) degrees, beta = 91.651(9) degrees, gamma = 88.340(9) degrees, and two formula units per cell. [K]6[W3S4(HCO2)9][HCO2].2.27H2O.0.73CH3OH was monoclinic, space group C2/m (No. 12) with a = 19.605(6) A, b = 14.458(7) A, c = 13.627(5) A, beta = 118.94(2) degrees, and four formula units per cell. Generally, the nine coordination sites of [M3E4]4+ were occupied either by a mixture of monodentate and mu 2-bridging formato ligands or by monodentate formato ligands only. By dissolution in noncomplexing strong acid, all the formato complexes immediately hydrolyzed to form [M3E4(H2O)9]4+ aqua complexes. This allows, for example, high concentrations of [Mo3S4(H2O)9]4+ in CF3SO3H to be obtained and these solutions to be used for the synthesis of bimetallic clusters containing the cubane-like motif Mo3M'S4.     

Structure, Stability and Vibrational Spectra of LaC_5~n(n=-1,0,+1) Clusters

用密度泛含方法研究了ＬａＣ５ｎ（ｎ＝－１，０，＋１）分子簇的结构和稳定性及振动光谱，对这个六原子体系提出了三种可能构型，点群结构为Ｃ２ｖ对称性．第一个构型为Ｌａ接在弯曲的Ｃ５链上，第二个是Ｌａ通过二个键与Ｃ５环相连第三个是Ｌａ通过一个键与Ｃ５环相连；结果表明，第一个构型即当Ｌａ接在弯曲的Ｃ５链上时能量最低．振动光谱分析指出，当ｎ＝－１时，第二个构型为局域极小值；当ｎ＝＋１时，第一个和第二个构型为局域极小值；对ｎ＝０，局域极小值没有找到．     

Ab initio calculation of carbon clusters. II. Relative stabilities of fullerene and nonfullerene C24

Chemical stabilities of six low-energy isomers of C24 derived from global-minimum search are investigated. The six isomers include one classical fullerene (isomer 1) whose cage is composed of only five- and six-membered rings (56-MRs), three nonclassical fullerene structures whose cages contain at least one four-membered ring (4-MR), one plate, and one monocyclic ring. Chemical and electronic properties of the six C24 isomers are calculated based on a density-functional theory method (hybrid PBE1PBE functional and cc-pVTZ basis set). The properties include the nucleus-independent chemical shifts (NICS), singlet-triplet splitting, electron affinity, ionization potential, and gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO-LUMO) gap. The calculation suggests that the neutral isomer 2, a nonclassical fullerene with two 4-MRs, may be more chemically stable than the classical fullerene (isomer 1). Analyses of molecular orbital NICS show that the incorporations of 4-MRs into the cage considerably reduce paratropic contributions from HOMO, HOMO-1, and HOMO-2, which are mainly responsible for the sign change in NICS from positive for isomer 1 (42) to negative (-19) for isomer 2, although C24 clusters satisfy neither 4N+2 nor 2(N+1)2 aromaticity rule. Anion photoelectron spectra of four cage isomers, one plate, one monocyclic ring, and one tadpole isomer, as well as three bicyclic ring isomers are calculated. The simulated photoelectron spectra of mono- and bicyclic rings (with C1 symmetry) appear to match the measured HOMO-LUMO gap (between the first and second band in the experimental spectra) [S. Yang et al., Chem. Phys. Lett. 144, 431 (1988)]. Nevertheless, the nonclassical fullerene isomers 3 and 4 apparently also match the measured vertical detachment energy (2.90 eV) reasonably well. These results suggest possible coexistence of nonclassical fullerene isomers with the mono- and bicyclic ring isomers of C24(-) under the experimental conditions.     

On the bond-stretch isomerism in the benzo[1,2:4,5]dicyclobutadiene system--an ab initio MR-AQCC study.

Bond-stretch isomerism in benzo[1,2:4,5]dicyclobutadienle (BDCB) has been investigated using the MR-AQCC/6-31G(d) method, a high-level multireference ab initio approach including size-extensivity corrections. The applied theoretical approach includes both nondynamical and dynamical electron correlation effects. Full MR-AQCC geometry optimizations of localized (1) and delocalized (3) isomers as well as the transition structure (TS) have been determined using D2h, symmetry restriction. The calculations show that both isomers are approximately of equal stability separated by a barrier with a height of about 5 kcal mol(-1). Thus, the present results strongly indicate that benzof[1,3:4,5]dicyclobutadiene is a very good candidate for an organic compound exhibiting bond-stretch isomerism, since isomers 1 and 3 correspond to true minima on the double-well potential energy surface, which are separated by a sufficiently high barrier. It is particularly important to emphasize that isomer 3 represents a realization of the highly elusive quasi-[10]annulene.