The far-infrared absorption of a periodic 2DEG in the transition regime between weak and strong modulation

We study the optical absorption of arrays of quantum dots and antidots in a perpendicular homogeneous magnetic field. The electronic system is described quantum mechanically using a Hartree approximation for the mutual Coulomb interaction of the electrons. The evolution of the absorption is traced from the homogeneous to the strongly modulated case identifying the ensuing collective modes, the magnetoplasmons, and their correlations with inherent length scales of the system.     

Symmetric excitation and de-excitation of a cavity QED system

We calculate the time evolution of a cavity-QED system subject to a time dependentsinusoidal drive. The drive is modulated by an envelope function with the shape of apulse. The system consists of electrons embedded in a semiconductor nanostructure which iscoupled to a single mode quantized electromagnetic field. The electron-electron as well asphoton-electron interaction is treated exactly using “exact numerical diagonalization” andthe time evolution is calculated by numerically solving the equation of motion for thesystem’s density matrix. We find that the drive causes symmetric excitation andde-excitation where the system climbs up the Jaynes-Cummings ladder and descends back downsymmetrically into its original state. This effect is known at low electron-photoncoupling strengths but our main finding is how robust the effect is even at ultra-strongcoupling strength where the JC-model does not give qualitatively correct results. Weinvestigate the robustness of this symmetric behavior with respect to the drive de-tuningand pulse duration.     

An investigation of the quantum chemical description of the ethylenic double bond in reactions: II. Insertion of ethylene into a titanium–carbon bond

Insertion of ethylene into the Ti–methyl bond in TiH₂CH⁺₃ is chosen as a model reaction for investigating the performance of a range of contemporary quantum chemical models in polymerization studies. Basis set effects are investigated at the self-consistent-field level, covering Hartree–Fock, pure DFT, and hybrid DFT. In agreement with findings in part I of this study, the basis set sensitivity of ethylene is shown to introduce a bias in computed energetics, amounting to 2–3 kcal/mol when DZP bases are used to compute the overall heat of monomer insertion. The geometry of stationary points relevant to the insertion reaction is determined using hybrid density functional theory. Based on these structures, the energy profile of the insertion reaction is computed using a range of popular quantum chemical approximations. The methods include Hartree–Fock and Møller–Plesset (MP) perturbation theory up through the fourth order in spin-restricted, spin-unrestricted, and spin-projected formalisms. Furthermore, configuration-interaction-based methods are included, of which the top level method is singly and doubly excited coupled clusters with a perturbative estimate of the contribution from triply excited configurations added [CCSD(T)]. The performance of the methods just mentioned, as well as three pure density functional and three hybrid density functional methods, are compared with respect to “best” relative energies, defined through extrapolation of CCSD(T) correlation energies according to the PCI scheme of Siegbahn and coworkers. Even though the MP series show poor convergence, spin-projected MP2, as well as two pure DFT methods (BPW91, BP86) and PCI-78 based on the MCPF method, show similar and very good agreement with best relative energies for the insertion reaction. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 947–960, 1998     

Effects of photon field on heat transport through a quantum wire attached to leads

We theoretically investigate photo-thermoelectric transport through a quantum wire in a photon cavity coupled to electron reservoirs with different temperatures. Our approach, based on a quantum master equation, allows us to investigate the influence of a quantized photon field on the heat current and thermoelectric transport in the system. We find that the heat current through the quantum wire is influenced by the photon field resulting in a negative heat current in certain cases. The characteristics of the transport are studied by tuning the ratio, $?{\omega }_{\gamma }/k_{\mathrm{B}}\mathrm{\Delta }T$, between the photon energy, $?{\omega }_{\gamma }$, and the thermal energy, $k_{\mathrm{B}}\mathrm{\Delta }T$. The thermoelectric transport is enhanced by the cavity photons when $k_{\mathrm{B}}\mathrm{\Delta }T>?{\omega }_{\gamma }$. By contrast, if $k_{\mathrm{B}}\mathrm{\Delta }T<?{\omega }_{\gamma }$, the photon field is dominant and a suppression in the thermoelectric transport can be found in the case when the cavity-photon field is close to a resonance with the two lowest one-electron states in the system. Our approach points to a new technique to amplify thermoelectric current in nano-devices.     

Time discretization via Laplace transformation of an integro-differential equation of parabolic type

We consider the discretization in time of an inhomogeneous parabolic integro-differential equation, with a memory term of convolution type, in a Banach space setting. The method is based on representing the solution as an integral along a smooth curve in the complex plane which is evaluated to high accuracy by quadrature, using the approach in recent work of López-Fernández and Palencia. This reduces the problem to a finite set of elliptic equations with complex coefficients, which may be solved in parallel. The method is combined with finite element discretization in the spatial variables to yield a fully discrete method. The paper is a further development of earlier work by the authors, which on the one hand treated purely parabolic equations and, on the other, an evolution equation with a positive type memory term. The authors acknowledge the support of the Australian Research Council.     

Site epimerization in ansa-zirconocene polymerization catalysts

Metallocene alkyl cations for polymerization of olefins possess two active sites involved in migratory insertion. Site epimerization, with an inversion at the metal atom, is considered to be one of the major causes for break-down of the alternating propagation model, resulting in stereoerrors whenever the two catalytic sites have substantially different enantioface selectivities. Density functional theory has been used to determine the intrinsic reaction coordinate that connects the optimized minima and transition states of inversion in the parent ansa-zirconocene [{H₂C(Cp)₂}Zr-Pr]⁺ (Pr = n-propyl). These calculations yield a three-step reaction path for site epimerization. Starting from the pyramidal β-agostic complex, an activated rotation around the Zr-Pr bond first produces an α-agostic conformation. Continued rotation leads to an equivalent second α-agostic intermediate and then finally to the inverted β-agostic complex. The second step is rate-determining and proceeds through a planar three-coordinate transition state. In the case of [{H₂C(Cp)₂}Zr-ⁱBu]⁺ (ⁱBu = iso-butyl), the situation is more complicated, because there are several interconvertible α-, β- and γ-agostic intermediates, but the rate-limiting step is again an inversion process connecting two different α-agostic conformers with the alkyl group on opposite enantiosides. For both ansa-zirconocene catalysts, the computed free-energy barriers for epimerization are around 11-12 kcal/mol and almost independent of temperature, while those for insertion increase with temperature due to the entropic cost of association. According to the computational results for the isolated catalysts, insertion remains favored over epimerization for the experimentally relevant temperature range in the n-propyl case, whereas both processes are competitive in the iso-butyl case. Inclusion of bulk solvent effects by a continuum solvation model does not affect the results much, while explicit consideration of a coordinating counterion causes larger changes. The present model calculations on the role of site epimerization should thus be most relevant for propene polymerization with non-coordinating counterions.     

A Facile Formal Synthesis of Volicitin

A short and concise synthesis of volicitin is presented. The synthesis is based on repeated chemoselective copper salt cross coupling reactions of alkynes and propargylic halides.