Degenerate Rearrangement Research Articles

Formation of Nanotwin Networks during High-Temperature Crystallization of Amorphous Germanium.

Germanium is an extremely important material used for numerous functional applications in many fields of nanotechnology. In this paper, we study the crystallization of amorphous Ge using atomistic simulations of critical nano-metric nuclei at high temperatures. We find that crystallization occurs by the recurrent transfer of atoms via a diffusive process from the amorphous phase into suitably-oriented crystalline layers. We accompany our simulations with a comprehensive thermodynamic and kinetic analysis of the growth process, which explains the energy balance and the interfacial growth velocities governing grain growth. For the 〈111〉 crystallographic orientation, we find a degenerate atomic rearrangement process, with two zero-energy modes corresponding to a perfect crystalline structure and the formation of a Σ3 twin boundary. Continued growth in this direction results in the development a twin network, in contrast with all other growth orientations, where the crystal grows defect-free. This particular mechanism of crystallization from amorphous phases is also observed during solid-phase epitaxial growth of 〈111〉 semiconductor crystals, where growth is restrained to one dimension. We calculate the equivalent X-ray diffraction pattern of the obtained nanotwin networks, providing grounds for experimental validation.

Thermal Isomerization of the Buchwald Seven-Membered Zirconacyclocumulene and Its Interaction with Acetylenes. Synthesis and Structures of Novel Seven-Membered Zirconacyclocumulene Complexes

On prolonged heating of the Buchwald seven-membered zirconacyclocumulene Cp2Zr[η4-Me3SiC4(SiMe3)–C(C2SiMe3)═CSiMe3] (1) in toluene at 100 °C, the isomerization of 1 takes place with the formation of a seven-membered zirconacyclocumulene complex, Cp2Zr[η4-Me3SiC4(SiMe3)–C(SiMe3)═C(C2SiMe3)] (8), containing the Me3SiC≡C group in α-position and the SiMe3 group in β-position with respect to the Zr atom. A remarkable peculiarity of complex 8 is its ability to undergo a rapid degenerate rearrangement at room temperature in toluene solution, as a result of which only two rather than four singlets of the Me3Si groups are observed in the 1H NMR spectrum of 8 under such conditions. At temperatures below 200 K, the rate of this rearrangement decreases and, as a consequence, the 1H NMR spectrum of 8 acquires the normal view. If 1 is heated at 100 °C in the presence of acetylenes such as 1,4-bis(tert-butyl)butadiyne (tBuC≡C–C≡CtBu) and tolane, the corresponding seven-membered zirconacyclocumulenes, viz., Cp2Zr[η4-tBuC4(tBu)–C(C2SiMe3)═CSiMe3] (7) and Cp2Zr[η4-Me3SiC4(SiMe3)–C(Ph)═CPh] (14), are formed along with free Me3SiC≡C–C≡CSiMe3. The interaction of 1 with 1,4-diphenylbutadiyne (PhC≡C–C≡CPh) at 100 °C leads to the formation of a mixture of products, from which a zirconacyclopentadiene metallacycle, Cp2Zr[η2-PhC═C(C2Ph)–C(C2Ph)═CPh] (10), as well as seven-membered zirconacyclocumulenes Cp2Zr[η4-PhC4(Ph)–C(C2SiMe3)═CSiMe3] (11), Cp2Zr[η4-Me3SiC4(SiMe3)–C(C2Ph)═CPh] (12), and Cp2Zr[η4-PhC4(Ph)–C(C2Ph)═CPh] (13) were isolated. The structures of 8, 9, 10, 12, and 14 have been established by X-ray crystallography. The mechanism of the reactions found is discussed.

X-ray imaging of chemically active valence electrons during a pericyclic reaction.

Time-resolved imaging of chemically active valence electron densities is a long-sought goal, as these electrons dictate the course of chemical reactions. However, X-ray scattering is always dominated by the core and inert valence electrons, making time-resolved X-ray imaging of chemically active valence electron densities extremely challenging. Here we demonstrate an effective and robust method, which emphasizes the information encoded in weakly scattered photons, to image chemically active valence electron densities. The degenerate Cope rearrangement of semibullvalene, a pericyclic reaction, is used as an example to visually illustrate our approach. Our work also provides experimental access to the long-standing problem of synchronous versus asynchronous bond formation and breaking during pericyclic reactions.

Fragmentation reactions of Si2Cl6+[rad] in the gas phase—A quantum-chemical and mass-spectrometric assessment

The gas-phase ion chemistry of the hexachlorodisilane radical cation Si2Cl6+ has been reinvestigated by a combined electron ionization (EI) mass spectrometry (MS) and high-level quantum chemistry approach. The computational investigation of isomerization and fragmentation pathways of [Si2Cln]+() (n=1–6) species reveals (a) the coexistence of structures of the type Cl3Si–SiClm+1+() and chlorobridged SiCl4–SiClm+() isomers for m=1,2, and (b) a wealth of nearly isoenthalpic structures[Si2Cln]+() for each n with n=2–4, which can result from degenerate rearrangements. This structural diversity appears to be a general feature of the disilicon (radical) cations with low chlorine content. The ionization energy of Si2Cl6 determined by EI-MS (10.1±0.2stat±0.2systeV) with argon (15.759±0.001eV) used as reference, is slightly lower than previously reported experimental values, but in good agreement with the CBS-QB3 (9.87eV) and W1U (9.97eV) adiabatic ionization energy. Measured appearance energies for the lowest two fragmentation channels, which afford SiCl2+ and SiCl3+, are well in line with CBS-QB3 values and with the literature value determined for SiCl3+ in threshold photoelectron–photoion coincidence experiments. Using the experimental heats of formation (ΔfH°298) for SiCl4 and Cl· as anchor points, W1U theory was employed to derive ΔfH°298 values for Si2Cln+() with n=0–6 and for SiClm+() with m=1–4 based on the lowest energy isomer identified in our quantum chemical investigation of reaction pathways for all species investigated. W1U heats of formations obtained for select neutrals lead to a more consistent description of kinetic aspects previously inferred from metastable ion mass spectra.

Electron-Nuclear Motion in the Cope Rearrangement of Semibullvalene: Ever Synchronous?

The effect of nuclear motion on the synchronicity of the pincer motion type electronic rearrangement associated with bond making and bond breaking and vice versa is investigated for the degenerate Cope rearrangement of semibullvalene using a time-independent quantum chemical approach. We find that distinct paths along the potential energy surface corresponding to synchronous nuclear rearrangement involve asynchronous electronic fluxes out of the old and into the new bond while synchronous electronic fluxes entail asynchronous nuclear rearrangement. In order to demonstrate the robustness of the results, various high-level quantum chemical methods including full structure optimizations up to second order multireference perturbation theory using triple-ζ basis sets (RS2/cc-pVTZ), which are subsequently refined at the RS3/cc-pVTZ and MRCI+Dav/cc-pVTZ levels of theory, are used for solving the electronic Schrödinger equation. These benchmark results extend previous quantum chemical data for the degenerate Cope rearrangement of semibullvalene and are tested against lower level methods (e.g., density functional theory calculations using the B3LYP and B3PW91 functionals).

Quantum chemical study of polycyclic derivatives of cyclohexa-1,3,5-triene

A possibility of the existence of cyclohexa-1,3,5triene derivatives has been proved by the synthesis of compound I [1]. In this work, the quantum chemical calculations of the structural parameters, relative energies, and vibration spectra of similar compounds were performed by PBE0/cc-pVTZ and RHF/3-21G methods using a GAUSSIAN-03 software [2]. The following values were obtained by the PBE0 method. degenerate Cope rearrangements [3,4]. The degenerate Cope rearrangements in the hypothetical isomers III of dedihydrobullvalene C10H8 fragments must be accompanied by oscillations of the bond lengths in the central rings. The relative energy (kcal mol) of the isomers decreases as the alternation of these bond lengths reduces: 33.7 (IIIa) > 22.6 (IIIb) > 7.6 (IIIc) > 0.0 (IIId). Isomer IIId has the smallest bonds alternation in the central ring (1.38 and 1.41 A). For isomer IIIb the obtained bonds lengths are 1.36 and 1.43 A, and for IIIc, 1.37 and 1.42 A. DOI: 10.1134/S1070363213040294

A selection rule for the directions of electronic fluxes during unimolecular pericyclic reactions in the electronic ground state

Unimolecular pericyclic reactions in a non-degenerate electronic ground state proceed under the constraint of zero electronic angular momentum. This restriction engenders a selection rule on the directions of electronic fluxes. Accordingly, clockwise or counter-clockwise fluxes are ‘forbidden’, whereas pincer-like fluxes (which consist of concerted clockwise and counter-clockwise fluxes) are ‘allowed’. The selection rule is illustrated for three reactions: the degenerate Cope rearrangement of hexadiene, hydrogen transfer in malonaldehyde, and double proton transfer in the formic acid dimer.

Electronic Bond‐to‐Bond Fluxes in Pericyclic Reactions: Synchronous or Asynchronous?

One at a time or all at once? Electronic fluxes during a pericyclic reaction in the electronic ground state--exemplified for the degenerate Cope rearrangement of semibullvalene--may proceed either synchronously or asynchronously. Quantum simulations show that the mechanism is determined by the preparation of the reactants, for example, synchronous at cryogenic temperatures (tunneling) but asynchronous when induced by selective laser pulses (with energy over the barrier).

Through-Bond Interactions in the Diradical Intermediates Formed in the Rearrangements of Bicyclo[n.m.0]alkatetraenes

The intermediates and transition structures in the degenerate thermal rearrangements of bicyclo[4.4.0]deca-2,4,7,9-tetraene (1c), bicyclo[5.5.0]dodeca-2,4,8,10-tetraene (11b), and bicyclo[5.4.0]undeca-2,4,8,10-tetraene (14) have been located by (U)B3LYP/6-31G(d) calculations. The singlet-triplet energy differences (ΔE(ST)) in the diradical intermediates (tricyclo[4.4.0.0(2,7)]deca-3,8-dien-5,10-diyl (2c), tricyclo[5.5.0.0(5,11)]dodeca-2,8-dien-4,10-diyl (12b), and tricyclo[5.4.0.0(5,11)]undeca-2,8-dien-4,10-diyl (15)) have been computed, using both UB3LYP and (6/6)CASPT2 calculations. ΔE(ST) in 2c, in which a four-membered ring is anti-bridged by two allylic radicals, is computed to be larger by a factor of 5 than ΔE(ST) in 15, in which the anti-bridged ring is five-membered, and by a factor of 10 than that in 12b, in which the anti-bridged ring is six-membered. The reasons for the much larger interaction between two allylic radicals through the bonds of the four-membered ring in 2c than through the bonds of the five-membered ring in 15 or the six-membered ring in 12b are discussed, and the consequences of the large, through-bond stabilization of the singlet state of 2c are described.

ChemInform Abstract: Dynamic Binuclear Enediolato- and Catecholato-Zirconocene Complexes Relevant to the Structural Problem Associated with Sharpless Oxidation Catalysts.

Dimethylzirconocene complexes [ZrMe2(C5H4R)2](R = H or CH3) were treated with catechol to give the (catecholato)zirconocene complexes. Low-temperature NMR spectra indicated dimeric metallatricyclic structures for these complexes and the corresponding (ethene-1,2-diolato)- and (but-2-ene-2,3-diolato)-zirconocenes. Dynamic temperature-dependent NMR spectroscopy revealed that all these complexes underwent a thermally induced degenerate rearrangement process, similar to the reorganization reaction of some Sharpless catalyst precursors, with Gibbs activation energies close to 50 kJ mol–1. A labelling experiment showed the intramolecular nature of this automerization. (4-tert-Butylcatecholato)zirconocene formed two diastereoisomeric dimers which did not interconvert on the NMR time-scale (ΔG‡inter >90 kJ mol–1) although the intramolecular rearrangement was observed [ΔG‡intra(241 K)= 52 ± 2 kJ mol–1]. The intermolecular equilibration process probably proceeding via monomeric (catecholato)zirconocene was monitored in the case of the bulky (4-tert-butyl-catecholato)bis(tert-butylcyclopentadienyl)zirconium system by dynamic NMR spectroscopy at high temperature [ΔG‡inter(364 K)= 78 ± 5 kJ mol–1].

ChemInform Abstract: Kinetics of Cyclopentene Isomerization at 1200 K

This study was conducted to determine the rate of intramolecular degenerate rearrangement of cyclopentene (CP), presumably via reversible conversion to vinylcyclopropane (VCP). Cyclopentene-3-{sup 13}C was synthesized and heated to 1,200 K in a single-pulse shock tube and then analyzed by {sup 13}C NMR to ascertain the extent of migration of the {sup 13}C label to the 4-position. The very small amounts of migration observed were consistent with log k(CP {yields} VCP) = 15.7 {minus} (16,000/T). This rate constant for CP {yields} VCP is too small to account for the previously reported evidence of multiple channels for H{sub 2} elimination from CP.

Calculations Predict That Carbon Tunneling Allows the Degenerate Cope Rearrangement of Semibullvalene to Occur Rapidly at Cryogenic Temperatures

Calculations on the role of tunneling in the degenerate Cope rearrangements of semibullvalene (1) and barbaralane (3) predict that, at temperatures below 40 K, tunneling from the lowest vibrational level should make the temperature-independent rate constants k = 1.43 x 10(-3) s(-1) and k = 7.28 x 10(-9) s(-1), respectively. An experiment, using semibullvalene-2(4)-d(1), is proposed to test the prediction of rapid tunneling by 1 at cryogenic temperatures.

Degenerate rearrangement of long-lived 9-cyclopropyl-9,10-dimethyl-9,10-dihydrophenanthren-9-ylium: Migration of cyclopropyl group

Dynamic NMR study showed that long-lived 9-cyclopropyl-9,10-dimethyl-9,10-dihydrophenanthren-9-yl cation generated from 9-cyclopropyl-9,10-dimethyl-9,10-dihydrophenanthren-9-ol in HSO3F-SO2ClF-CD2Cl2 at −100 to −75°C undergoes fast degenerate 1,2-shift of the cyclopropyl group. The Arrhenius parameters for this process were determined: E a = 33.7 kJ/mol, log A = 13.0.

Synthesis and fluxional behaviour of new “heavy fluorous” cyclopentadienes

The new “heavy fluorous” cyclopentadienes C 5H 6− n [M(C 2H 4C 6F 13) 3] n (M = Si, n = 1 ( 3); n = 2 ( 4) and M = Sn, n = 1 ( 10)) were synthesized by reaction of cyclopentadienyl lithium with BrSi(C 2H 4C 6F 13) 3 ( 2) or commercial BrSn(C 2H 4C 6F 13) 3. Fluorous cyclopentadienes prepared in this manner contain three or six C 6F 13 groups, which significantly increase their solubility in perfluorinated solvents. They also provide intermediates for titanium complexes suitable for fluorous biphase catalysis. All three isomers of silylcyclopentadienes 3 and 4 were identified and fully characterized by two dimensional NMR spectroscopy, which was performed at low temperature. The allylic isomers 3a and 4a undergo degenerate metallotropic rearrangement. This fluxional behaviour was compared with the behaviour of previously prepared cyclopentadienes 6 and 7 (C 5H 6− n [SiMe 2(C 2H 4C 8F 17)] n where n = 1, 2, respectively). The presence of allylic isomers 6a and 7a was further confirmed by Diels-Alder cycloaddition of the strong dienophile tetracyanoethylene (TCNE), providing compounds 8 and 9.

Group theory and reaction mechanisms: An extension of the mciver-stanton rules

McIver and Stanton's rules concerning the symmetry of transition states have a counterpart in rules concerning the permutation symmetry of single steps in degenerate rearrangements, derivable with the aid of Longuet-Higgins group theory. Examples in organometallic fluxional systems and carbonium ions illustrate the rules; the analysis leads to prediction of hitherto unexplored pathways for rearrangements in ethyl and homotetrahedryl cations.

On the structure of 3‐acetylamino‐5‐methyl‐1,2,4‐oxadiazole and on the fully degenerate rearrangements (FDR) of its anion: a stimulating comparison between the results of ‘in‐silicon chemistry’ and ‘laboratory chemistry’

AbstractAn accurate crystal structure determination has provided evidence for a planar conformation for 3‐acetylamino‐5‐methyl‐1,2,4‐oxadiazole (5), in agreement with quantum‐mechanical calculations in the gas phase. In the crystal, a series of strong intermolecular N7H7….O9 hydrogen bonds link the amido groups of different molecules, causing the formation of infinite parallel ordered chains. The effect of the DMSO solvent on the energy and charge distribution of compound 5 and on its relevant 5− anion, involved in a fully degenerate rearrangement (FDR), has been deepened by quantum‐mechanical DFT calculations. The calculated energy barrier for the FDR increases in going from in vacuo to DMSO, in agreement with previsions based on the Hughes and Ingold rules concerning the nucleophilic substitution of an anionic reagent (the deprotonated amido group in the side chain) on a neutral substrate (the 1,2,4‐oxadiazole ring). Copyright © 2009 John Wiley & Sons, Ltd.

Effect of Intramolecular Paternò−Büchi Reaction on the Thermodynamics and Kinetics of Nearly Degenerate [3,3]-Sigmatropic Shift in Fluxional Polycycles

In reactions with weak dienophiles, cyclooctatetraene (COT) often yields 2:1 adducts possessing the fluxional bicyclo[5.1.0]octadiene moiety. They undergo fast, nearly degenerate Cope rearrangement with an activation barrier similar to that of the parent dihydrobullvalene. Irradiation to excite the carbonyl moiety induces an intramolecular Paterno-Buchi cyclization yielding endo-oxetanes and significantly changing the Cope-averaged NMR spectra. In this paper we examine the effect of skeletal distortion caused by intramolecular [2 + 2]-photoaddition on thermodynamics and the activation barrier of the [3,3]-sigmatropic tautomerism. Our finding is that such a distortion lifts the energetic degeneracy of the two valence tautomers, while not affecting the activation barrier.

QTAIM Study on the Degenerate Cope Rearrangements of 1,5-Hexadiene and Semibullvalene

Using the homotropylium cation (1) as an archetypal example of a homoaromatic molecule, we carried out a quantum theory of atoms-in-molecules (QTAIM) computational study--at DFT (density functional theory), CCSD (coupled cluster with singles and doubles), and CASSCF (complete active space self-consistent field) levels--on 1 and the degenerate Cope rearrangements of 1,5-hexadiene (2) and semibullvalene (3) including the evaluation of delocalization indexes and a visualization of atomic basins. This study yielded new insights into the factors determining the reaction barriers and the bonding of the ground and transitions states of 2 and 3. Contrary to conclusions reached in earlier studies, we found that the transition state for the degenerate rearrangement of 2 is not aromatic and that the driving force for the very facile Cope rearrangement of semibullvalene is caused by the stabilization of individual atoms as well as electronic delocalization, not by the release of strain in the three-membered ring.

Intramolecular Methylacridan–Methylacridinium Complexes with a Phenanthrene‐4,5‐diyl or Related Skeleton: Geometry–Property Relationships in Isolable CH Bridged Carbocations

Bridging the gap: Snapshots of 1,6-H-shift precursors indicate that a narrower C-HC(+) separation (D in the ORTEP diagram) in the title complexes induces faster degenerate rearrangement of 1(+). A contact distance of less than 2.7 A is necessary to realize the organic three-center two-electron bond of [C-H-C](+), as indicated by extrapolation of the X-ray data.The isolation and low-temperature X-ray analyses of a series of intramolecular methylacridan-methylacridinium complexes have been achieved. The two chromophores are in close proximity due to an arylene spacer, such as a phenanthrene-4,5-diyl or biphenyl-2,2'-diyl unit. These bridged carbocations prefer the C-H localized structure both in solution and in the solid state. The bridging hydrogen atom undergoes a facile intramolecular hydride shift from one carbon atom to another in solution, and the energy barrier is linearly correlated with the intramolecular CC(+) distance in the solid-state geometry, as determined by single-crystal X-ray analyses. By extrapolation from the data, the delocalized three-center bond of [C-H-C](+) would be formed when the CC(+) distance is less than 2.7 A.

William von Eggers Doering’s Many Research Achievements during the First 65 Years of his Career in Chemistry

This Account highlights William von Eggers Doering's important discoveries in many fields of chemistry. His synthetic and mechanistic studies have contributed to areas including non-benzenoid aromatics, carbenes, pericyclic reactions, and diradical intermediates. Doering's synthesis with L. H. Knox of the highly stable tropylium ion and their investigation of its reactivity were the starting point for the development of the field of non-benzenoid aromatics. Working with A. K. Hoffmann, Doering demonstrated the synthesis of dichloro- and dibromocarbene by base-induced alpha elimination of HCl or HBr from CHCl3 or CHBr3 under anhydrous conditions. These results allowed for the synthesis of a variety of cyclopropanes and derivatives including allenes. Using 14C labeling experiments, Doering and Prinzbach showed that the mechanism of insertion of singlet methylene into a C-H bond was a concerted process.In their work on the Cope rearrangement, Doering and Roth's outstanding stereochemical analysis showed that the rearrangement of acyclic 1,5-hexadienes proceeds concertedly, passing over a chairlike transition state. This work has had an enormous impact on the understanding of stereochemical control in synthetic organic chemistry, and many fruitful applications in synthesis have stemmed directly from this finding. Transition-state resonance structures analogous to those for ground-state aromatics can qualitatively explain the relatively large substituent effects on the rate of the Cope rearrangement. However, quantum chemical calculations have quantitatively described these effects. The rapid degenerate Cope rearrangements in the cis-divinylcyclopropane units of 3,4-homotropilidene, barbaralone, and bullvalene establish these molecules as having fluxional structures. The unique molecule bullvalene has more than 1.2 million possible structures interconnected by degenerate Cope rearrangements, which average all H and all C atoms. Doering has also examined stepwise thermal reorganizations that pass through intermediary 1,3- or 1,4-diradicals and do not show conformational equilibration as would be expected for classical intermediates. Doering calls these processes "not-obviously concerted". He discusses "continuous diradicals" as transition states and rationalizes the course of these reactions through the concept of a "caldera" (a flat surface with small energy wells as found on the top of volcanoes).The understanding of fundamental chemical reactions remains the focus of Doering's research. In his terms, "understanding" means not only gaining deep insight but also the intellectual control that allows researchers to predict a reaction's course. Because the interplay between theory and experiment has led to great progress in this predictive ability, Doering's experimental work has provided an important input for computational chemistry and to the essential understanding of chemical reactions.