Roald Hoffmann

An Extended Hückel Theory. I. Hydrocarbons

The Huckel theory, with an extended basis set consisting of 2s and 2p carbon and 1s hydrogen orbitals, with inclusion of overlap and all interactions, yields a good qualitative solution of most hydrocarbon conformational problems. Calculations have been performed within the same parametrization for nearly all simple saturated and unsaturated compounds, testing a variety of geometries for each. Barriers to internal rotation, ring conformations, and geometrical isomerism are among the topics treated. Consistent σ and π charge distributions and overlap populations are obtained for aromatics and their relative roles discussed. For alkanes and alkenes charge distributions are also presented. Failures include overemphasis on steric factors, which leads to some incorrect isomerization energies; also the failure to predict strain energies. It is stressed that the geometry of a molecule appears to be its most predictable quality.

Theory of Polyhedral Molecules. I. Physical Factorizations of the Secular Equation

An LCAO—MO systematization of polyhedral molecules such as BNHN is undertaken. Peculiarities of polyhedral systems, such as inapplicability of nearest‐neighbor assumption and increased number of parameters are discussed within the framework of a Huckel type of theory. It is found that inclusion of hydrogen atoms does not affect predictions of closed shells, but is important in determining electronic transitions. Various physical factorizations of the secular equations, such as the in‐surface, apex‐equatorial, and ring‐polar separations are critically examined. A computer program for calculations on molecules of up to 15 atoms is described and used to obtain the energy levels of a variety of polyhedral molecules.

Boron Hydrides: LCAO—MO and Resonance Studies

The results of an LCAO—MO calculation for the boron hydrides and hydride ions B2H6, B4H10, B5H9, B5H11, B6H10, B9H15, B10H14, B10H16, BH4—, B3H8—, B9H14—, B10H10—2, B10H14—2, B12H12—2 are reported. Charge distributions and overlap populations are calculated from the wavefunctions for real distances and for idealized molecules with all distances equal. The three‐center bond theory is extended to incorporate unsymmetric equivalent structures with concomitant improvement in charge distributions. These are compared with the presumably better LCAO—MO charges. The valence structure of a new boron hydride, B18H22, is discussed.

Conjugated one and two dimensional polymers

The band structures of some existing and hypothetical one and two dimensional conjugated polymers are examined in this work. The aim is to explore how the band gap sizes and the occurrence of partially filled bands are related to unit cell constitution and the geometrical disposition of the atoms in the unit cell. Among the polymers explored are poly-acetylene, polydiacetylene, polyphenylene, polyacene, graphite, boron nitride, polynitrile, polycyanonitrile, polypyridinopyridine, paracyanogen, the C3N net, (SN)x, (XCNSN)x, and C2S3N6 net.

Theory of Polyhedral Molecules. III. Population Analyses and Reactivities for the Carboranes

Population analyses of the molecular orbitals of the polyhedral carboranes, BN—2C2HN, are computed. All the geometrical isomers of the trigonal, tetragonal, pentagonal bipyramid, and the icosahedron geometries are analyzed, and predictions made of the reactivities of these compounds and their derivatives. A comparison is also made between an LCAO‐MO charge distribution and one derived from the three‐center bond formalism.

Extended Hückel Theory. III. Compounds of Boron and Nitrogen

The extended Huckel theory is applied to compounds of boron and nitrogen, with emphasis placed upon similarities and differences with isoelectronic and isosteric carbon analogs. The barrier to internal rotation in borazane is predicted to be ∼1.5 kcal/mole and the torsional barrier in aminoborane∼10 kcal/mole. The internal charge‐transfer nature of the expected electronic transitions is stressed. The highest occupied orbitals in aminoborane and borazine are computed to be σ type, with important consequences for the reactions of these molecules. It is proposed that the accepted valence picture of borazine is incorrect and that in all B–N molecules N is more negative. Stabilization due to nonbonded electrostatic interactions is studied. Predictions are made regarding the geometry of B–N analogs of cyclobutadiene and cyclooctatetraene. Borazine is calculated to be inefficient in transmitting electronic effects. Computations of the relative stabilities of heteroaromatic B–N compounds are made.

Extended hückel theory—v : Cumulenes, polyenes, polyacetylenes and cn

Abstract Approximate calculations of the extended Huckel type are reported for ground and excited states of cumulenes, polyenes, polyacetylenes and Cn. Bond length variation in these molecules is studied by an iterative method which relates bond distance to Mulliken overlap population. For the cumulenes, simple aninons and cations as well as the first excited state prefer some twisting of the terminal CH2 groups from the ground state geometry. In the case of allene skeletal bending is also indicated in the excited state. An alternation of torsional barriers in the cumulene series is predicted. For the ground state of butadiene, one calculates a potential curve to twisting around the central single bond which has the s-cis form as a potential maximum, and which shows no activation energy to cis-trans interconversion. The first excited state of butadiene prefers a geometry with one CH2 group twisted out of plane. Distinct cis and trans bending tendencies in various excited acetylene states are obtained. Bond alternation is found for polyacetylenes, polyenes, essentially none for cumulenes. For linear Cn an intermediate situation occurs; bond alternation appears in short chains, is not expected to persist for large n, but a large “end effect” is predicted. Cn rings with n = 4q + 2 become more stable than the corresponding linear chains for n≥10.

Large-scale soft colloidal template synthesis of 1.4 nm thick CdSe nanosheets.

Two-dimensional (2D) nanocrystals have attracted tremendous attention from many researchers in various disciplines because of their unique properties. Since ways of making graphene were devised, there have been significant research efforts to synthesize free-standing 2D nanocrystals of various materials, including metals, oxides, and chalcogenides. Many of these 2D nanocrystals have been generated from exfoliation of materials with layered structures, and tiny amounts of products are generally produced. CdSe nanocrystals are among the most intensively studied nanostructured materials, owing to their many size-dependent optical and electrical characteristics and resulting exciting applications. Herein, we report on the large-scale synthesis of single-layered and lamellar-structured 2D CdSe nanocrystals with wurtzite crystal structure as thin as 1.4 nm by a soft colloidal template method. These free-standing 2D nanocrystals with insulating organic layers at the interface could find many interesting electronic and optoelectronic applications, including in quantum cascade lasers and resonant tunneling diodes utilizing their multiple quantum well structures. Compared to materials with layered crystal structures such as graphite, the synthesis of free-standing 2D nanocrystals of nonlayered materials such as CdSe is extremely challenging, because selective growth along one specific facet among several with similar energies is required. For example, in CdSe with a hexagonal wurtzite crystal structure, a (0001) facet has significantly higher surface energy than other facets, which leads to the formation of many one-dimensional nanostructures. Although there is a slight difference in the surface energies of (1120) and (1100) facets, quantum-confined thin CdSe 2D nanocrystals could not be synthesized using a conventional colloidal chemical route that employs thermal decomposition of precursors at high temperature, because the small difference in the surface energies of these two facets is negated by the high reaction temperature. Consequently, there have been only a few reports on the successful chemical synthesis of 2D CdSe nanocrystals. For example, CdSe inorganic–organic hybrid lamellar structures and CdSe nanoplatelets with zinc-blende structure were synthesized using colloidal chemical routes. However, their 2D growth mechanism has not been clearly elucidated. Furthermore, nanostructural control to form single-layered or multiple-layered nanosheets has not been demonstrated. In the current approach to creating 2D CdSe nanocrystals, we employed a soft template method, and we were able to synthesize not only free-standing single-layered CdSe nanosheets but also lamellar-structured nanosheets by controlling the interaction between organic layers in 2D templates of cadmium chloride alkyl amine complexes. It has been reported that the complex of cadmium halide and diamine can form a cadmium halide /diamine alternating layered structure through diamine bridging and hydrogen bonding between hydrogen atoms of the amine and halogen atoms. Likewise, a [CdCl2(RNH2)2] lamellar complex, which is used herein as a soft template, is expected to form lamellar structures composed of 2D arrays of CdCl2 and alkyl amine by van der Waals attraction between hydrocarbon sidechains of the alkyl amine. The small-angle X-ray scattering (SAXS) patterns of [CdCl2(RNH2)2] complexes with butylamine (BA), octylamine (OA), and dodecylamine (DA) show 00l orders of reflection, which confirms that the complexes formed typical lamellar structures (Supporting Information, Figure S1). A [CdCl2(OA)2] lamellar complex was chosen as the soft template for the synthesis of lamellarstructured CdSe nanosheets because of its optimum reactivity. [*] J. S. Son, Dr. J. Joo, K. Park, Dr. J. H. Kim, Dr. K. An, J. H. Yu, S. G. Kwon, Dr. S.-H. Choi, Prof. T. Hyeon National Creative Research Initiative Center for Oxide Nanocrystalline Materials and School of Chemical and Biological Engineering Seoul National University Seoul 151-744 (Korea) Fax: (+82)2-886-8457 E-mail: thyeon@snu.ac.kr

Predicting molecules--more realism, please!

The body of computations of molecules for which there is as yet no experimental evidence is growing very rapidly. This is simply wonderful—as a marker of the reliability of theory, and, sociologically, in creating a tense and fruitful balance between theory and synthesis in chemistry. Claims of “stability,” implicit and explicit, are made for the calculated molecules; we have been as guilty of this as others. We would like to suggest that literature reports of these claims be qualified, and that the computations performed be described in a circumspect way.

M3L9(ligand) complexes

The frontier orbitals of an M3(C0)9 unit are constructed from three M(CO)3 pieces or by removing three ligands from a M3(CO),2. They consist of a relatively low-lying Walsh-like set la, + le and a higher cyclopropenium-like 2ai + 2e. The latter are empty for a d8 M. These orbitals are used to analyze the electronic and geometrical structure of M3Ly(li- gand) complexes where the ligand is CO, S, (CO)2, S2, CR, CCH>+, ethylene, acetylene, or acyclic and cyclic polyenes. In the case of (CO)~CO~CCH~+ the symmetrically topped structure is not a local energy minimum, but instead there are three equiv- alent unsymmetrical structures of a complexed ethylidene type The rich and beautiful chemistry of metal clusters is un- folding only now.I,* Perhaps its most highly developed aspect is the reactivity of trinuclear compounds. Both structural data and reactivity studies cover a wide range of such complexes including systems with both bridging and terminal carbonyls or hydrides or highly complicated molecules where the ligand no longer can be separated from the cluster unit.