Polyhedral boranes with exo multiple bonds: three-dimensional inorganic analogues of quinones.
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Biomedical subjects
Roald Hoffmann
Publications and source records attributed to Roald Hoffmann.
Magic electron counts and bonding in tubular boranes.
Ring stacking in some closo-borane dianions and the hypothetical capped borane nanotubes, predicted to be stable earlier, is analyzed in a perturbation theoretic way. A "staggered" building up of rings to form nanotubes is explored for four- and five-membered B(n)H(n) rings. Arguments are given for the stacking of B(5)H(5) rings being energetically more favorable than the stacking of B(4)H(4) rings. Elongated B[bond]B distances in the central rings are predicted for some nanotubes, and the necessity to optimize ring-cap bonding is found to be responsible for this elongation. This effect reaches a maximum in B(17)H(17)(2-); the insertion of additional rings will reduce this elongation. These closo-borane nanotubes obey Wade's n + 1 rule, but the traditional explanation based on a partitioning into radial/tangential molecular orbitals is wanting.
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Prospecting for a 5-center 4-electron (C- - -H- - -C- - -H- - -C)+ bonding array.
Herein we describe our search for a carbocation with a delocalized 5-center 4-electron C- - -H- - -C- - -H- - -C bonding array. Various helical and polycyclic molecular architectures were explored using B3LYP calculations, ultimately leading to cation 8, a remarkable species that possesses two trigonal pyramidal carbons flanking a five-coordinate trigonal bipyramidal carbon.
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A new quasi-one-dimensional ternary chalcogenide: synthesis, crystal structure, and electronic structure of Nb1+xV1-xS5 (x = 0.18).
The new low-dimensional ternary chalcogenide, Nb(1+x)V(1-x)S(5) (x = 0.18), has been prepared and characterized. This compound crystallizes in the monoclinic space group, C2(2h)-P2(1)/m with two formula units in a cell with dimensions a = 9.881(4) A, b = 3.329(1) A, c = 8.775(3) A, and beta = 114.82(3) degrees. The layer is composed of two unique chains of face-sharing Nb-centered bicapped trigonal prisms and edge-sharing M-centered octahedra (M = Nb or V). The electronic structures of the monomeric basic building units, NbS(8) and VS(6), and hypothetical and real one-, two-, and three-dimensional structures making up the compound are examined to understand the nature of inter- and intrachain interactions and orbital overlapping among metals and sulfur atoms. The electronic structure of Nb(1+x)V(1-x)S(5) is essentially given by superimposing those of the individual chains. V d orbitals are found to be crucial for the one-dimensional metallic conductivity along the chain axis.
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Vibronic coupling in molecules and in solids.
We utilize the experience gained in our previous studies on the "chemistry of vibronic coupling" in simple homonuclear and heteronuclear molecules to begin assembling theoretical guidelines for the construction of potentially superconducting solids exhibiting large electron-phonon coupling. For this purpose we analyze similarities between vibronic coupling in isolated molecules and in extended solids. In particular, we study vibronic coupling along the antisymmetric stretch coordinate (Q(as)) in linear symmetric AAA molecules, and along the optical phonon "pairing" mode coordinate (Q(opt)) in corresponding one-dimensional [A]( infinity ) chains built of equidistant A atoms. This is done for a broad range of chemical elements (A). The following similarities between vibronic coupling in molecules and phonon coupling in solids emerge from our calculations: 1) The HOMO/LUMO electronic energy gap in an AAA molecule increases along Q(as), and the highest occupied crystal orbital/lowest unoccupied crystal orbital gap in [A]( infinity ) chain increases along Q(opt). 2) The maximum vibronic instability is invariably obtained for a half-filled, singly occupied molecular orbital in AAA molecules, and for a corresponding half-filled band in [A]( infinity ) chains. 3) The vibronic stability of an AAA molecule increases with a decrease of the AA bond length, as does the vibronic stability of [A]( infinity ) chains (external pressure may lead to a reversal of a Peierls distortion). 4) The high degree of s-p mixing and ionic/covalent forbidden curve crossing dramatically enhance the vibronic instability of both AAA molecules and [A]( infinity ) chains. We also introduce one quantitative relationship: The parameter log(R) (where R is molar refractivity, a parameter used by Herzfeld to prescribe the conditions for the metallization of the elements) correlates with a parameter f(AA) (defined as twice the electronegativity of A, divided by the equilibrium AA bond length), used by two of us previously to describe vibronic coupling in AAA molecules for a broad range of elements (A=halogen, H, or an alkali metal). We hope to illustrate that key chemical aspects of vibronic coupling in simple molecules may thus be profitably transferred to corresponding materials in the solid state.
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Helicoid shiftamers.
We report calculations on the activation barriers for antarafacial [1,7]-hydrogen shifts in various helical polyenes containing saturated substructures. Based on these calculations, we predict that the barrier for analogous hydrogen shifts in the infinite system-a [1,7]-shiftamer-is only approximately 14 kcal/mol if the reactant is preorganized in an appropriate helical conformation.
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Strong electronic consequences of intercalation in cuprate superconductors: the case of a trigonal planar AuI(3) complex stabilized in the Bi(2)Sr(2)CaCu(2)O(y) lattice.
Recently, a molecular AuI(3) complex was stabilized in the interlayer space of the Bi(2)Sr(2)CaCu(2)O(y) (Bi2212) high-T(c) superconducting phase, adopting an exceptional D(3)(h) structure (Choy, J.-H.; et al. J. Phys.Chem. B 2000, 104, 7273). If the gold were formally Au(III), a strong Jahn-Teller distortion to T- and Y-shaped structures would be expected. In this work, we try to understand the structural preferences of AuI(3) in both the gas phase and the Bi2212 lattice, as well as the influence of the AuI(3) intercalation on the superconductor lattice. What we think actually happens is that there is an effective electron transfer from the s-type Bi lone pair to the gold, increasing the formal oxidation state of Bi from +3 to +5 and decreasing that of Au from +3 to +1. A trigonal Au(I) trihalide is just fine. The DFT results confirm in the Bi-rich regions the same kind of electron transfer as encountered on the EHT level of theory, but they reveal additional complexities of the problem. The effect of the Bi to intercalating molecule electron transfer on the cuprate layer may be important, quite apart from this specific example, in tuning superconductivity in the cuprates.
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Electron-rich three-center bonding: role of s,p interactions across the p-block.
This paper analyzes the importance of s,p mixing-a necessary addition to the simplest Rundle-Pimentel picture-and periodic and group trends in electron-rich three-center bonding. Our analysis proceeds through a detailed quantum chemical study of the stability of electron-rich three-center bonding in triatomic 22-valence electron anions. To provide interpretations, a perturbational molecular orbital (MO) analysis of s,p mixing is carried out. This analysis of the orbitals and the overlap populations is then tested by density functional calculations for a number of linear trihalides, trichalcogenides, and tripnictides. The most important effect of s,p mixing on the in-line bonding is in destabilization of the 3sigma(g) orbital and is determined by the overlap between the s orbital of the central atom and the p orbital of the terminal atom. Further destabilization arises from the repulsion of p(pi) lone pairs. Both of these antibonding effects increase with increasing negative charge of the system. The stability of isoelectronic X(3) systems thus decreases when moving from right to left in the periodic table. Interesting group trends are discerned; for instance, for the electron-rich tripnictides, the ability to accommodate a hypervalent electron count is the largest in the middle rather at the end of the group. Particularly strong s,p mixing can reverse the bonding/antibonding character of MOs: thus MO 2sigma(u) that is responsible for bonding for trihalides and trichalcogenides is actually antibonding in N(3)(7)(-).
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Bcc and Fcc transition metals and alloys: a central role for the Jahn-Teller effect in explaining their ideal and distorted structures.
Transition metal elements, alloys, and intermetallic compounds often adopt the body centered cubic (bcc) and face centered cubic (fcc) structures. By comparing quantitative density functional with qualitative tight-binding calculations, we analyze the electronic factors which make the bcc and fcc structures energetically favorable. To do so, we develop a tight-binding function, DeltaE(star), a function that measures the energetic effects of transferring electrons within wave vector stars. This function allows one to connect distortions in solids to the Jahn-Teller effect in molecules and to provide an orbital perspective on structure determining deformations in alloys. We illustrate its use by considering first a two-dimensional square net. We then turn to three-dimensional fcc and bcc structures, and distortions of these. Using DeltaE(star), we rationalize the differences in energy of these structures. We are able to deduce which orbitals are responsible for instabilities in seven to nine valence electron per atom (e(-)/a) bcc systems and five and six e(-)/a fcc structures. Finally we demonstrate that these results account for the bcc and fcc type structures found in both the elements and binary intermetallic compounds of group 4 through 9 transition metal atoms. The outline of a theory of metal structure deformations based on loss of point group operation rather than translational symmetry is presented.
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Electronic properties of the silver-silver chloride cluster interface.
The objective of this study was to gain insight into the electronic structure of silver-silver chloride cluster composites and especially into the metal-semiconductor interface. For this purpose a theoretical study of (AgCl)(n) (n=4, 32, 108, 192, and 256), of Ag(m) (m=1-9, 30, 115, 276, and 409), and of the cluster composites Ag(115)-(AgCl)(192) and Ag(409)-(AgCl)(192) has been carried out. Density of levels (DOL), local density of levels (l-DOL), and projection of surface states, as well as projection of properties of individual atoms or groups of atoms obtained in molecular orbital calculations, are shown to be powerful tools for gaining deep insight into the properties of these large systems. The Ag(115)-(AgCl)(192) aggregate, consisting of a cubic Ag(115) cluster without corner atoms on top of a cubic (AgCl)(192) cluster, was found to be remarkably stable with a cluster-to-cluster distance of about 280 pm, and a geometry in which the number of bonding interactions between the silver atoms of Ag(115) and the chloride ions of (AgCl)(192) is at its maximum. A sharp jump in charge distribution occurs at the Ag(115)-(AgCl)(192) composite interface. The first AgCl slab picks up negative charge from the two adjacent silver slabs, so that in total the silver cluster is positively charged. In addition, the core of the silver cluster is positively charged with respect to its outermost layer. The main reason for the charge transfer from the silver cluster to the silver chloride is the newly formed MIGS (metal induced gap states) in the energy-gap range of the silver chloride and the MIdS (metal induced d states) in the d-orbital region. Their wave functions mix with orbitals of the silver cluster and with both the orbitals of the silver and the chloride ions of the silver chloride. The MIGS and the MIdS are of a quite localized nature. In them, nearest neighbor interactions dominate, with the exception of close-lying silver chloride surface states-which mix in to a large extent. We conclude that especially the MIGS not only influence the photochemical properties of silver chloride, but that their existence might be probed by appropriate spectroscopic measurements.
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Sigmatropic shiftamers: fluxionality in broken ladderane polymers.
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Fickle hexadienes. Manipulating the relative energies of chairlike and boatlike transition structures for the cope rearrangement.
We report calculations on various hexadienes that can assume both chairlike and boatlike conformations, yet turn out (theoretically) to have transition structures for boatlike Cope rearrangement that are equal to or lower in energy than those of alternative chairlike structures. Pathways connecting boatlike and chairlike transition states in these systems also allow for unusual and facile isomerization pathways of certain strained alkenes.
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Coping with Fritz Haber's Somber Literary Shadow We are grateful to the reviewers of this paper for their provocative comments.
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Not a Library I am grateful to Albert Eschenmoser, Sylvie Coyaud, and Henning Hopf for their comments.
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Real and Hypothetical Intermediate-Valence Ag(II)/Ag(III) and Ag(II)/Ag(I) Fluoride Systems as Potential Superconductors.
With the aim of gauging their potential as conducting or superconducting materials, we examine the crystal structures and magnetic properties of the roughly one hundred binary, ternary, and quaternary Ag(II) and Ag(III) fluorides in the solid state reported up to date. The Ag(II) cation appears in these species usually in a distorted octahedral environment, either in an [AgF](+) infinite chain or as [AgF(2)] sheets. Sometimes one finds discrete square-planar [AgF(4)](2-) ions. The Ag(III) cation occurs usually in the form of isolated square-planar [AgF(4)](-) ions. Systems containing Ag(III) (d(8)) centers are typically diamagnetic. On the other hand, the rich spectrum of Ag(II) (d(9)) environments in binary and ternary fluorides leads to most diverse magnetic properties, ranging from paramagnetism, through temperature-independent paramagnetism (characteristic for half-filled band and metallic behavior) and antiferromagnetism, to weak ferromagnetism. Ag(II) and Ag(III) have the same d-electron count as Cu(II) (d(9)) and Cu(III) (d(8)), respectively. F(-) and O(2-) ions are isoelectronic, closed-shell (s(2)p(6)) species; both are weak-field ligands. Led by these similarities, and by some experimental evidence, we examine analogies between the superconducting cuprates (Cu(II)/Cu(III)-O(2-) and Cu(II)/Cu(I)-O(2-) systems) and the formally mixed-valence Ag(II)/Ag(III)-F(-) and Ag(II)/Ag(I)-F(-) phases. For this purpose we perform electronic-structure computations for a number of structurally characterized binary and ternary Ag(I), Ag(II), and Ag(III) fluorides and compare the results with similar calculations for oxocuprate superconductors. Electronic levels in the vicinity of the Fermi level (x(2)-y(2) or z(2)) have usually strongly mixed Ag(d)/F(p) character and are Ag-F antibonding, thus providing the potential of efficient vibronic coupling (typical for d(9) systems with substantially covalent bonds). According to our computations this is the result not only of a coincidence in orbital energies; surprisingly the Ag-F bonding is substantially covalent in Ag(II) and Ag(III) fluorides. The electron density of state at the Fermi level (DOS(F)) for silver fluoride materials and frequencies of the metal-ligand stretching modes have values close to those for copper oxides. The above features suggest that properly hole- or electron-doped Ag(II) fluorides might be good BCS-type superconductors. We analyze a comproportionation/disproportionation equilibrium in the hole-doped Ag(II) fluorides, and the possible appearance of holes in the F(p) band. It seems that there is a chance of generating an Ag(III)-F(-)/Ag(II)-F(0) "ionic/covalent" curve crossing in the hole-doped Ag(II)-F(-) fluorides, significantly increasing vibronic coupling.
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Origin of the Metal-to-Insulator Transition in H(0.33)MoO(3).
The electronic structure of the double octahedral layers present in H(0.33)MoO(3) has been studied. It is shown that, depending on structural details, three bands, two of them having a two-dimensional character and one having a one-dimensional character, can be in competition at the bottom of the t(2g)-block band structure. Both qualitative arguments and detailed computations show that the Fermi surface of the double octahedral layers has a two-dimensional character and does not exhibit nesting vectors. Consequently, the metal-to-insulator transition exhibited by H(0.33)MoO(3) cannot be a Fermi surface driven electronic instability, as recently proposed. An order-disorder transition of the protons is suggested as a more likely origin of this resistivity anomaly.
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The Four-Connected Net in the CeCu(2) Structure and Its Ternary Derivatives. Its Electronic and Structural Properties.
The crystallochemistry of and the bonding in the orthorhombic four-connected nets of BaIn(2) (CeCu(2) structure) and of CaPtSn (TiNiSi structure, a derivative of the CeCu(2) structure) are analyzed with approximate molecular orbital calculations. Following the Zintl concept, in BaIn(2) the In(-) ions are isoelectronic with group IV tin and should adopt a four-connected structure. In contrast to alpha-tin, which has a cubic diamond structure, the indium ions in BaIn(2) build up an orthorhombic three-dimensional four-connected net containing distorted tetrahedra and ladder polymers of four-membered rings. In the CeCu(2) structure (space group Imma) two bond angles in these distorted tetrahedra are fixed at 90 degrees. The four-connected net in the CeCu(2) structure is topologically related to the layers in black phosphorus (space group Cmca). In CaPtSn (TiNiSi structure) the orthorhombic four-connected net is formed by (PtSn)(2)(-) ions in an ordered arrangement. Calculations on BaIn(2) and CaPtSn show that the four-connected nets are increasingly stabilized as the valence electron count is increased from 16 to 30 valence electrons per 4 formula units. For more than 30e, the nets are destabilized due to filling of M-E antibonding states. Structural data obtained by precise single crystal investigations for the TiNiSi series CaPdIn (20e), CaPdSn (24e), CaPdSb (28e), and CaAgSb (32e), confirm the results of the extended Hückel calculations. We find an interesting and understandable angular asymmetry of the tetrahedral sites in these ternary compounds.
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