Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach

A generalized quantum master equation theory that governs the exact, nonperturbative quantum dissipation and quantum transport is formulated in terms of hierarchically coupled equations of motion for an arbitrary electronic system in contact with electrodes under either a stationary or a nonstationary electrochemical potential bias. The theoretical construction starts with the influence functional in path integral, in which the electron creation and annihilation operators are Grassmann variables. Time derivatives on the influence functionals are then performed in a hierarchical manner. Both the multiple-frequency dispersion and the non-Markovian reservoir parametrization schemes are considered for the desired hierarchy construction. The resulting hierarchical equations of motion formalism is in principle exact and applicable to arbitrary electronic systems, including Coulomb interactions, under the influence of arbitrary time-dependent applied bias voltage and external fields. Both the conventional quantum master equation and the real-time diagrammatic formalism of Schon and co-workers can be readily obtained at well defined limits of the present theory. We also show that for a noninteracting electron system, the present hierarchical equations of motion formalism terminates at the second tier exactly, and the Landuer-Buttiker transport current expression is recovered. The present theory renders an exact and numerically tractable tool to evaluate various transient and stationary quantum transport properties of many-electron systems, together with the involving nonperturbative dissipative dynamics.     

On the generalized approach to the structure count

A generalized approach to the structure count of n-radical-m-cation systems based on the properties of the acyclic polynomial is presented. The mathematical proof for the expression relating the structure count to the coefficients of the acyclic polynomial is given. The connection between the structure count of biradical structures and the number of Dewar structures is discussed and tested on some examples.     

Exact relation between the spectrum and the eigenfunctions of a generalized Jahn-Teller hamiltonian for different parameter values

A generalized E ? ? Jahn-Teller hamiltonian with a parameter δ (δ = ?1/4 in the JT case) is studied. As in the Jahn-Teller case, the angular momentum is a constant of the motion with the eigenvaluesj + 1/2 where j is a non-negative integer. For j fixed, consider two values δ₁ = ?j/2 ?1/2 and δ₂ = ?gd₁ ?1/2. The spectrum and the eigenfunctions for δ₂ are completely determined by the spectrum and the eigenfunctions for δ₁.     

Nonadiabatic treatment of molecular systems by the wavepackets method

We have already developed the many-electron wavepackets (MEWP) method in order to study the dynamics and electronic structure of molecular systems. We extended the MEWP method to study the nonadiabatic effects and formulated a nonadiabatic molecular theory, where both electron and nucleus are treated equivalently. Then we applied our method to the isotope series of hydrogen molecule i.e., H₂, HD, and D₂, and calculated the total energy and the average distance between nucleus-nucleus, electron-electron, and nucleus-electron in order to analyze numerically the nonadiabatic effect in the molecule. Finally we calculated the real-time evolution of the polarization by means of Chebyshev scheme; and by Fourier transforming this, we found out the excitation spectrum of the system, which corresponds to the electronic excitation and the nuclear vibrational frequency. © 1996 John Wiley & Sons, Inc.     

Exploring the optimal site for modifications of pyranmycins with the extended arm approach

[reaction: see text] Continuing from the syntheses and the antibacterial studies of a library of pyranmycins, we further probed the proximity around ring III of pyranmycin by introducing an "extended arm" that has hydroxyethyl or aminoethyl groups at the O-2' ', O-3' ', or O-4' ' positions. The results from the antibacterial studies reveal the optimal structural motif is the attachment of an extended arm with a terminal hydroxyl group at the O-3' ' position.     

Divergent approach for synthesis and terminal modifications of dendritic polyphenylazomethines

In the past, dendritic polyphenylazomethines (DPA) have been synthesized via the convergent method. However, the convergent method has problems such as difficult terminal-group modifications and an increased number of steps. Therefore, we synthesized the terminal-protected DPA to construct the dendritic structure via the divergent method. The combination of the convergent method and the divergent method easily achieved the rapid synthesis of a higher generation dendrimer. Furthermore, we succeeded in the synthesis of the water-soluble PEG-DPA via the divergent method using the ester-DPA.     

Characterization of zinc hydroxynitrates by diffuse reflectance infrared spectroscopy--structural modifications during thermal treatment

Four zinc hydroxynitrates are known, but only the Infrared spectrum of Zn5(OH)8(NO3)2.2H2O is reported in the literature. Here, we report the IR spectra of the other three zinc hydroxynitrates, namely Zn(OH)(NO3).H2O, Zn3(OH)4(NO3)2 and Zn5(OH)8(NO3)2. The positions of the bands of the nitrate groups between 1000 and 1600 cm(-1) are discussed in relation to the structure of these compounds. The modifications of these IR spectra with temperature are consistent with previous studies on the thermal decomposition of these compounds.     

Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas-Kroll-Hess transformation up to arbitrary order

In order to achieve exact decoupling of the Dirac Hamiltonian within a unitary transformation scheme, we have discussed in part I of this series that either a purely numerical iterative technique (the Barysz-Sadlej-Snijders method) or a stepwise analytic approach (the Douglas-Kroll-Hess method) are possible. For the evaluation of Douglas-Kroll-Hess Hamiltonians up to a pre-defined order it was shown that a symbolic scheme has to be employed. In this work, an algorithm for this analytic derivation of Douglas-Kroll-Hess Hamiltonians up to any arbitrary order in the external potential is presented. We discuss how an estimate for the necessary order for exact decoupling (within machine precision) for a given system can be determined from the convergence behavior of the Douglas-Kroll-Hess expansion prior to a quantum chemical calculation. Once this maximum order has been accomplished, the spectrum of the positive-energy part of the decoupled Hamiltonian, e.g., for electronic bound states, cannot be distinguished from the corresponding part of the spectrum of the Dirac operator. An efficient scalar-relativistic implementation of the symbolic operations for the evaluation of the positive-energy part of the block-diagonal Hamiltonian is presented, and its accuracy is tested for ground-state energies of one-electron ions over the whole periodic table. Furthermore, the first many-electron calculations employing sixth up to fourteenth order DKH Hamiltonians are presented.     

A chemoenzymatic approach toward the rapid and sensitive detection of O-GlcNAc posttranslational modifications

We report a new chemoenzymatic strategy for the rapid and sensitive detection of O-GlcNAc posttranslational modifications. The approach exploits the ability of an engineered mutant of beta-1,4-galactosyltransferase to selectively transfer an unnatural ketone functionality onto O-GlcNAc glycosylated proteins. Once transferred, the ketone moiety serves as a versatile handle for the attachment of biotin, thereby enabling chemiluminescent detection of the modified protein. Importantly, this approach permits the rapid visualization of proteins that are at the limits of detection using traditional methods. Moreover, it bypasses the need for radioactive precursors and captures the glycosylated species without perturbing metabolic pathways. We anticipate that this general chemoenzymatic strategy will have broad application to the study of posttranslational modifications.     

Spin alignment in organic high-spin molecules as studied by ESR and the generalized Hubbard Hamiltonian approach

In order to examine the role of topological symmetry in spin alignment of organic high-spin molecules, a novel hydrocarbon, 3,4′-diphenylmethylenebis(phenylmethylene) (3,4′-DPBPM), has beeen synthesized and characterized by single-crystal ESR. This molecule has a triplet ground state with a closely located quintet excited state in contrast to its topological isomer, 3,3′-DPBPM, with a non-degenerate septet ground state. UHF SCF calculation of the generalized Hubbard Hamiltonian satisfactorily predicts these results.     

Mo approach to the aromaticity of transition states of the generalized pericyclic reactions

The aromaticity of transition states of generalised pericyclic reaction has been examined by the HMO method. Established thereby is a secular equation from which all the specific secular equations for different types of pericyclic reactions can be derived and with which the generalistion of Woodward and Hoffman can be substantiated.     

Upper and lower bounds and the generalized variation-perturbation approach of many-electron theory

The theory of upper and lower bounds is used in conjunction with the “varied-portions approach” (VPA ) of the “many-electron theory of atoms and molecules” (MET ). Upper and lower bounds equations are derived. It is recognized that if a very natural portion of the full variational expression is made stationary, according to (VPA ), a for of Löwdin's lower bound wave equation results. By using the bracketing theorem it is also possible to give lower bounds to the quantities arising from the (VPA ) of (MET ). This will be useful to study in the future the (MET ) pair correlations and to supplement the computational methods currently available with lower bound estimates as well.     

A generalized approach to the fluid dynamics of particulate systems part III: General correlation for the pressure drop through fixed beds of spherical particles

A general correlation for pressure drop through fixed beds of spherical particles, based upon a discrete particle model corrected for particle interaction, is presented in this paper. The standard C_D versus Re curve for single spheres is extended to multiparticle systems by incorporating proper functions of the volumetric particle concentration. The resulting correlation is compared with others and with data from eleven independent sources. A good fit is obtained in the creeping flow and intermediate regions as well as for distended bed data in the highly turbulent range. However, a certain deviation is noticed in the turbulent range with normal packed bed data.This paper, together with the others in this series, allows the prediction of pressure drop or drag in single particle and multiparticle systems by a single curve. Systems correlated with this curve include fluidization and sedimentation with either solid or fluid particles, minimum fluidization and, now, fixed beds.     

Investigation of the chemical modifications of beech wood lignin during heat treatment

Holocellulose, Klason lignin and milled wood lignin (MWL) of beech wood were extracted before and after heat treatment and analysed using CP MAS ¹³C NMR, ¹³C NMR, ³¹P NMR and size exclusion chromatography (SEC). Experimental results showed that the thermal treatment degrades hemicelluloses and affects lignin polymer through depolymerisation due mainly to cleavage of β-aryl-ether linkages and recondensation reactions. The spectroscopic analysis of MWL demonstrated that these recondensation reactions involved mainly guaiacyl units through formation of 5,5′-biphenolic and diarylmethane structures.Analysis of molecular weight distribution of MWL by SEC indicated that average molecular weights of heat treated milled wood lignin were lower than those of native milled wood lignin.     

Exact Kohn-Sham versus Hartree-Fock in momentum space: Examples of two-fermion systems

The question of how density functional theory (DFT) compares with Hartree-Fock (HF) for the computation of momentum-space properties is addressed in relation to systems for which (near) exact Kohn-Sham (KS) and HF one-electron matrices are known. This makes it possible to objectively compare HF and exact KS and hence to assess the potential of DFT for momentum-space studies. The systems considered are the Moshinsky [Am. J. Phys. 36, 52 (1968)] atom, Hooke's atom, and light two-electron ions, for which expressions for correlated density matrices or momentum densities have been derived in closed form. The results obtained show that it is necessary to make a distinction between true and approximate DFTs.