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Roald Hoffmann

Publications and source records attributed to Roald Hoffmann.

At least 19 recordsLinked to original sources
PubMed2006

Solid memory: structural preferences in group 2 dihalide monomers, dimers, and solids.

The link between structural preferences in the monomers, dimers, and extended solid-state structures of the group 2 dihalides (MX(2): M = Be, Mg, Ca, Sr, Ba and X = F, Cl, Br, I) is examined theoretically. The question posed is how well are geometric properties of the gas-phase MX(2) monomers and lower order oligomers "remembered" in the corresponding MX(2) solids. Significant links between the bending in the MX(2) monomers and the D(2)(h)()/C(3)(v)() M(2)X(4) dimer structures are identified. At the B3LYP computational level, the monomers that are bent prefer the C(3)(v)() triply bridged geometry, while the rigid linear molecules prefer a D(2)(h)() doubly bridged structure. Quasilinear or floppy monomers show, in general, only a weak preference for either the D(2)(h)() or the C(3)(v)() dimer structure. A frontier orbital perspective, looking at the interaction of monomer units as led by a donor-acceptor interaction, proves to be a useful way to think about the monomer-oligomer relationships. There is also a relationship between the structural trends in these two (MX(2) and M(2)X(4)) series of molecular structures and the prevalent structure types in the group 2 dihalide solids. The most bent monomers condense to form the high coordination number fluorite and PbCl(2) structure types. The rigidly linear monomers condense to form extended solids with low coordination numbers, 4 or 6. The reasons for these correlations are explored.

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PubMed2006

Oxygen interstitials in superconducting La2CuO4: their valence state and role.

The nature of the much debated valence state of an interstitial oxygen atom in oxygen-doped La2CuO4 is the subject of this paper. In model cluster calculations, we studied the position, charge, and spin state of the interstitial oxygen atoms in this superconductor. The models considered allow the interstitial oxygen to move off a symmetrical position, to have varying spin and charge, and to be surrounded by various magnetic environments. UB3LYP calculations show that a model having an interstitial oxygen atom with a total spin of 1 is lowest in energy; the interstitial oxygen atoms here act as stable radicals with a net charge of -1. These results agree with experimental evidence for the paramagnetic behavior for interstitial atoms. The energy associated with a spin flip at a Cu site in our models is lower if interstitial oxygen has a local electron spin density, compared to the case when it does not. We provide a possible explanation for the increase of the doping concentrations of interstitial oxygen with a decrease of the Néel temperature of this system. The relative stability of the models we consider depends on their spin states, accompanied by structural changes; this explains indirectly the experimental change of the slope (from 2 to 1.3) of the linear relationship between the hole concentration and the oxygen content. Our results support a stripe phase in high temperature superconductivity; in our calculations, hole doping to the copper oxide layer comes only through the formation of an oxygen interstitial pair, not from any change of the local structural environment and magnetic field around the single interstitial.

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PubMed2006

Structures and potential superconductivity in at high pressure: en route to "metallic hydrogen".

A way to circumvent the high pressures needed to metallize hydrogen is to "precompress" it in hydrogen-rich molecules, a strategy probed theoretically for silane. We show that phases with tetrahedral SiH4 molecules should undergo phase transitions with sixfold- and eightfold-coordinate Si appearing above 25 GPa. The most stable structure found can be metallized at under a megabar and at a compression close to the prediction of Goldhammer-Herzfeld criterion. According to a BCS-like estimate, metallic silane should be a high-temperature superconductor.

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PubMed2006

Snakes and ladders. The sigmatropic shiftamer concept.

Sigmatropic shiftamers are organic molecules (conceived originally as polymers) in which bonds migrate back and forth along their frameworks. In this Account, we describe the origins of the sigmatropic shiftamer concept, theoretical predictions of molecular architectures that may support shiftamer behavior, and possible future directions for research on this class of molecules.

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PubMed2005

Planar and pyramidal tetracoordinate carbon in organoboron compounds.

Using previously proposed C(BH)2(CH)2 (16, 17) and C(CH)2B2 (22) systems with a central planar tetracoordinate carbon (ptC) atom linking two three-membered rings as building blocks, a series of stable structures containing two and three ptC centers within a molecule have been designed and computationally studied with the DFT (B3LYP/6-311+G) method. Inclusion of a carbon atom ligated with pi-accepting and sigma-donating boron centers into at least one aromatic ring is critical for stabilization of a planar structure. A square pyramidal configuration at tetracoordinate carbon may be achieved in appropriately strained molecules such as [3.3.3.3]tetraborafenestrane 45 and others by surrounding the carbon with boron-centered ligands.

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PubMed2005

Transition metal complexes of cyclic and open ozone and thiozone.

Cyclic ozone (O3) has not been isolated so far, despite its computed kinetic persistence. Possibilities of "trapping" this molecule (or the valence-isoelectronic cyclic thiozone, S3) in transition metal complexes are investigated in this paper. Candidates were constructed, first using the 18-electron rule as a guide and then optimizing the structures with the DFT-B3LYP method. A variety of structures result: oxo-peroxo species, di-sigma- and pi-bonded open ozone complexes, some eta1 and eta2 cyclic ozone complexes, and a few bona fide eta3 cyclic O3 and S3 complexes. MLn fragments suitable for complex formation would need to contain very strong pi-acceptor ligands. Nitrosyl ligands were chosen to minimize an energy mismatch between the O3 donor orbitals and the MLn acceptor orbitals. On this basis, the existence of the complexes [S3W(NO)3]3+, [O3M(NO)3]3+ (M = Cr, Mo, W, Fe, Ru, Os), and [S3W(NO)2(CO)]2+ containing cyclic O3 and S3 is suggested. In another approach, facing up to the oxidizing power of O3, potential systems were built from late transition metals in high oxidation states, and also d0 early transition metal centers.

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PubMed2004

Planar tetracoordinate carbon in extended systems.

A recently proposed system with a central planar tetracoordinate carbon linking two three-membered rings, C(5)(2-), lends itself to extension in one, two, and three dimensions. Our construction of potential realizations begins with an analysis of the electronic structure of C(5)(2-). Dimers such as C(10)Li(3-), C(10)Li(4), and a trimer C(15)Li(6) are then examined, and their geometries are optimized to find clues for ways the C(5)(2-) unit may polymerize in the presence of countercations. Coordination through the terminal carbons is favored in the oligomers and polymers; several electronically and structurally reasonable systems of the stoichiometry C(5)M(x) (M = Li, x = 2; M = Be, Pt, Zn, x = 1) emerge from band structure calculations and energetic considerations.

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PubMed2004

Dicyclobuta[de,ij]naphthalene and dicyclopenta[cd,gh]pentalene: a theoretical study.

The structures, energetics, and aromatic character of dicyclobuta[de,ij]naphthalene, 1, dicyclopenta[cd,gh]pentalene, 2, dihydrodicyclobuta[de,ij]naphthalene, 3, and dihydrocyclopenta[cd,gh]pentalene, 4, have been examined at the B3LYP/6-311++G//B3LYP/6-31G level of theory. All molecules are bowl-shaped, and the pentalene isomers, 2 and 4, are most stable. A comparison with other C(12)H(6) and C(12)H(8) isomers indicates that 2 is approximately 25 kcal/mol less stable than 1,5,9-tridehydro[12]annulene and 4 is approximately 100 kcal/mol higher in energy than acenaphthylene, both of which are synthetically accessible. The transition state structure for bowl-to-bowl inversion of 1 is planar (D(2)(h)()) and lies 30.9 kcal/mol higher in energy than the ground state; the transition state for inversion of 2 is C(2)(h)() and lies 46.6 kcal/mol higher in energy. Symmetry considerations, bond length alternations, and NICS values (a magnetic criterion) all indicate that the ground states of 1, 3, and 4 are very aromatic; however, HOMA values (a measure of bond delocalization) indicate that 3S and 4S are aromatic but that 1S is less so. NICS values for the ground state of 2 strongly indicate aromaticity; however, bond localization, symmetry, and HOMA values argue otherwise.

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PubMed2004

Electron-deficient bonding in rhomboid rings.

The bonding environment of boron is usually thought about in terms of localized 2c-2e/3c-2e bonding (as in diborane) or completely delocalized polyhedral bonding (as in B(12)H(12)(2)(-)). Recently, a number of boron compounds having a rhomboidal B(4) framework have been synthesized; these show an amazing variation in their skeletal electron count, one that cannot be interpreted in familiar ways. In this report, we systematically explore the origin of the range of electron counts in these compounds. We find that four skeletal MOs are primarily responsible for keeping the B(4) skeleton together. As a subunit in a macropolyhedral environment, termed rhombo-B(4), such an arrangement of B atoms deviates from Wade's rule by three electron pairs (if treated as a distorted arachno system derived from B(6)H(6)(2)(-)). Aided by this analysis, we examine the nature of bonding in Na(3)B(20), where the rhombo-B(4) unit forms linear chains fusing closo-B(7) units. Theory suggests that this structure requires one more electron per formula unit for optimal bonding. Finally, we study the nature of bonding in beta-SiB(3), where silicon atoms also adopt the rhomboid framework.

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PubMed2004

The Nowotny chimney ladder phases: following the c(pseudo) clue toward an explanation of the 14 electron rule.

We account for two empirical rules of the Nowotny chimney ladder phases (NCLs, intermetallic compounds of the form T(t)E(m); T, groups 4-9; E, groups 13-15). The first rule is that for late transition metal NCLs the total number of valence electrons per T atom is 14. The second is the appearance of a pseudoperiodicity with a spacing, c(pseudo), which is directly related to the stoichiometry, T(t)E(m), by (2t - m) c(pseudo)= c. Both rules are accounted for by viewing the NCLs as twinned structures constructed from blocks of the parent compound, RuGa(2) of thickness c(pseudo)/2, with the successive layers rotated relative to each other by 90 degrees. Sterically encumbered E atoms are then deleted at the interfaces between layers, followed by relaxation.

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PubMed2004

The Nowotny chimney ladder phases: whence the 14 electron rule?

The late transition metal Nowotny chimney ladder phases (NCLs, T(t)E(m); T, groups 7-9; E, groups 13 and 14) follow a 14 electron rule: the total number of valence electrons per T atom is 14. In this paper, we extract a chemical explanation for this rule from extended Hückel calculations; we focus on RuGa(2), the parent NCL structure. A gap between filled and unfilled bands arises from the occupation of two Ga-Ga bonding/Ru-Ga nonbonding orbitals per RuGa(2), independent of k-point. In addition, the five Ru d levels are filled. Together this makes for 7 filled bands at each k-point, or 14 electrons per Ru. We discuss the connections between this 14 electron rule and the 18 electron rule of organometallic complexes.

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PubMed2004

Main group element nets to a T.

T-shaped nets (three-coordinated nets with an angular metric, bond angles near 90 degrees, 90 degrees, 180 degrees) are found in a number of extended structures. We explore in this paper the geometrical and electronic consequences of a stricter T-shape metric, where the distances between the vertices of the net are approximately equal and in the range of a chemical bond. Every atom in such a net has a T-shaped environment. One can think of these nets as extensions of BrF(3) or of substructures of various extended tellurium compounds. Several construction principles are found which allow an enumeration of a variety of one-, two-, and three-dimensional T-shape nets; not every three-coordinated net lends itself to the stricter geometrical and distance metric. Not everything is possible; there are no zero-dimensional T-nets, and none made entirely of three atom segments. Previous ideas on electron-rich multicenter bonding lead to a simple way of calculating the magic electron counts for each net; these lie in the range of 6 to 6.67.

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PubMed2004

Extended barbaralanes: sigmatropic shiftamers or sigma-polyacenes?

Starting from fused barbaralanes, we come (theoretically) to a new class of delocalized molecules in which two polyenyl radical chains interact with each other through space in a bonding way, but do not form full sigma-bonds. These molecules resemble sigma-homologues of polyacenes and are bishomoaromatic.

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PubMed2004

Exohedral multiple bonding in polyhedra. 2. Skeletal distortions in ring-stacked boranes.

Ring-stacked boranes of the B(10)H(10)(2)(-) and B(12)H(12)(2)(-) type, when substituted with lone pair bearing groups such as -O, -NH, and -S at the para positions, are theoretically shown to exhibit exopolyhedral multiple bonding on oxidation. Successive removal of two and four electrons from the parent B(n)H(n)(-)(2)X(2) results in highly varied and intriguing skeletal deformations that are explained using fragment molecular theory.

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PubMed2003

Unusual geometries and questions of oxidation state in potential Sn(III) chemistry.

A mixed-valence compound (Sn2I3(NPPh3)3) with nonequivalent Sn atoms in characteristic 2+ and 4+ Sn geometries, raised the idea of an average Sn3+ structure. The extended structures of Sr4Sn2Se9 and Sr4Sn2Se10 contain an unusual Sn2Se6 subunit, which has two equal Se-Sn-Se angles close to 160 degrees. This was suggestive of a Sn3+/Sn3+ compound, similar to the putative transition state for the valence state interchange in the molecular compound. These interesting geometrical features of two quite different molecules prompt a series of computations, a detective story of geometries and oxidation states, which concludes tentatively that the Sn with the abnormal angle in the extended structure is still likely to be formally Sn4+.

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