scholarly journals Parity symmetry in a number of problems of quantum and structural chemistry

2019 ◽  
Keyword(s):  
Single Molecule ◽  
Electron Correlation ◽  
Quantitative Measure ◽  
High Symmetry ◽  
The Matrix ◽  
Operator Functions ◽  
Symmetry Operators ◽  
Current Context ◽  
Chiral Systems ◽  
Nonnegative Definite

A synthetic review and new results are given of the alternant symmetry theory and its applications within a unified approach. It is based on J–symmetry (parity) operators. Unlike usual commutation rules, these symmetry operators anticommute with Hamiltonians or other relevant quantities. In the J–symmetry terms we treat a variety of problems and topics, mainly related to π-shells of conjugated molecules. In particular, various orbital theories are outlined with a systematic use of block-matrix technique (density matrices, operator functions etc.). Noval π‑models and their J–symmetry are studied within the current context of single-molecule conductance and the relevant problems concerning Green’s function and electron transmission evaluation. We stress on the key importance of account for π-electron correlation for describing correctly transmission π-spectra. We discuss electron-structure peculiarities of alternant radical states and the validity of the Lieb-Ovchinnikov spin rule resulting from the J–symmetry and electron correlation effects. It is shown how the simplified (based on Hückel’s MOs) spin-polarized theory provides a correct number of effectively unpaired electrons in polyradicaloid alternant molecules. Another type of problems is concerned with chirality (generllly, structural asymmetry) problems. By spectral analysys of the previously defined chirality operator we could reinterpret the problem in terms of J–symmetry. It allowed us to construct here the noval chirality operator which is nonnegative definite and vanishes on achiral structures. Its simplest invariant, the matrix trace, surves us as a quantitative measure of the structural (electronic) chirality. Preliminary calculations tell us that the new chirality index behaves reasonably even for the difficult (high-symmetry) chiral systems.

Using crystallographic symmetry in diffraction and contrast analysis

1989 ◽  
Vol 47 ◽  
pp. 504-505
Author(s):  
U. Dahmen ◽  
K.H. Westmacott
Keyword(s):  
Electron Microscopy ◽  
High Symmetry ◽  
Two Phase ◽  
Tem Analysis ◽  
Crystallographic Symmetry ◽  
The Matrix ◽  
Contrast Analysis ◽  
Practical Tool ◽  
Convergent Beam ◽  
Beam Diffraction

Despite the increased use of convergent beam diffraction, symmetry concepts in their more general form are not commonly applied as a practical tool in electron microscopy. Crystal symmetry provides an abundance of information that can be used to facilitate and improve the TEM analysis of crystalline solids. This paper draws attention to some aspects of symmetry that can be put to practical use in the analysis of structures and morphologies of two-phase materials.It has been shown that the symmetry of the matrix that relates different variants of a precipitate can be used to determine the axis of needle- or lath-shaped precipitates or the habit plane of plate-shaped precipitates. By tilting to a special high symmetry orientation of the matrix and by measuring angles between symmetry-related variants of the precipitate it is possible to find their habit from a single micrograph.

scholarly journals Single-molecule imaging of HIV-1 envelope glycoprotein dynamics and Gag lattice association exposes determinants responsible for virus incorporation

2019 ◽  
Vol 116 (50) ◽  
pp. 25269-25277 ◽  
Author(s):  
Nairi Pezeshkian ◽  
Nicholas S. Groves ◽  
Schuyler B. van Engelenburg
Keyword(s):  
Plasma Membrane ◽  
Single Molecule ◽  
Envelope Glycoprotein ◽  
Virus Assembly ◽  
Single Molecule Tracking ◽  
Virus Particles ◽  
Cell Plasma ◽  
The Matrix ◽  
Resolution Single ◽  
Hiv 1

The HIV-1 envelope glycoprotein (Env) is sparsely incorporated onto assembling virus particles on the host cell plasma membrane in order for the virus to balance infectivity and evade the immune response. Env becomes trapped in a nascent particle on encounter with the polymeric viral protein Gag, which forms a dense protein lattice on the inner leaflet of the plasma membrane. While Env incorporation efficiency is readily measured biochemically from released particles, very little is known about the spatiotemporal dynamics of Env trapping events. Herein, we demonstrate, via high-resolution single-molecule tracking, that retention of Env trimers within single virus assembly sites requires the Env cytoplasmic tail (CT) and the L12 residue in the matrix (MA) domain of Gag but does not require curvature of the viral lattice. We further demonstrate that Env trimers are confined to subviral regions of a budding Gag lattice, supporting a model where direct interactions and/or steric corralling between the Env-CT and a lattice of MA trimers promote Env trapping and infectious HIV-1 assembly.

scholarly journals Chemical insights into the electronic structure of Fe(II) porphyrin using FCIQMC, DMRG, and generalized active spaces

2020 ◽  
Author(s):  
Oskar Weser ◽  
Leon Freitag ◽  
Kai Guther ◽  
Ali Alavi ◽  
Giovanni Li Manni
Keyword(s):  
Electron Correlation ◽  
Quantitative Measure ◽  
Model System ◽  
Quintet State ◽  
Consistent Field ◽  
Self Consistent ◽  
Stabilizing Effect ◽  
Self Consistent Field ◽  
Preliminary Version

<div>Stochastic-CASSCF and DMRG procedures have been utilized to quantify the role of the electron correlation mechanisms that in a Fe-porphyrin model system are responsible for the differential stabilization of the triplet over the quintet state. Orbital entanglement diagrams and CI-coefficients of the wave function in a localised orbital basis allow for an effective interpretation of the role of charge-transfer configurations. A preliminary version of the <i>Stochastic Generalized Active Space Self-Consistent Field</i> method has been developed and is here introduced to further assess the pi-backdonation stabilizing effect.</div><div>By the new method excitations between metal and ligand orbitals can selectively be removed from the complete CI expansion. It is demonstrated that these excitations are key to the differential stabilization of the triplet, effectively leading to a quantitative measure of the correlation enhanced pi-backdonation.</div><div><br></div>

On Projection of a Positive Definite Matrix on a Cone of Nonnegative Definite Toeplitz Matrices

2018 ◽  
Vol 33 ◽  
pp. 74-82 ◽  
Author(s):  
Katarzyna Filipiak ◽  
Augustyn Markiewicz ◽  
Adam Mieldzioc ◽  
Aneta Sawikowska
Keyword(s):  
Toeplitz Matrices ◽  
Positive Definite Matrix ◽  
Positive Definiteness ◽  
Positive Definite ◽  
Asymptotic Cone ◽  
The Matrix ◽  
Multi Level ◽  
Nonnegative Definite ◽  
Unknown Covariance ◽  
Numer Math

We consider approximation of a given positive definite matrix by nonnegative definite banded Toeplitz matrices. We show that the projection on linear space of Toeplitz matrices does not always preserve nonnegative definiteness. Therefore we characterize a convex cone of nonnegative definite banded Toeplitz matrices which depends on the matrix dimensions, and we show that the condition of positive definiteness given by Parter [{\em Numer. Math. 4}, 293--295, 1962] characterizes the asymptotic cone. In this paper we give methodology and numerical algorithm of the projection basing on the properties of a cone of nonnegative definite Toeplitz matrices. This problem can be applied in statistics, for example in the estimation of unknown covariance structures under the multi-level multivariate models, where positive definiteness is required. We conduct simulation studies to compare statistical properties of the estimators obtained by projection on the cone with a given matrix dimension and on the asymptotic cone.

scholarly journals Quantum anomalous Hall effect from intertwined moiré bands

2021 ◽  
Author(s):  
Kin Fai Mak ◽  
Tingxin Li ◽  
Shengwei Jiang ◽  
Bowen Shen ◽  
Yang Zhang ◽  
...  
Keyword(s):  
Electric Field ◽  
Electron Correlation ◽  
Anomalous Hall Effect ◽  
Mott Insulator ◽  
Zero Magnetic Field ◽  
Hall Resistance ◽  
High Symmetry ◽  
Topological Phase ◽  
Wigner Crystals ◽  
And Topology

Abstract Electron correlation and topology are two central threads of modern condensed matter physics. Semiconductor moiré materials provide a highly tunable platform for studies of electron correlation. Correlation-driven phenomena, including the Mott insulator, generalized Wigner crystals, stripe phases and continuous Mott transition, have been demonstrated. However, nontrivial band topology has remained elusive. Here we report the observation of a quantum anomalous Hall (QAH) effect in AB-stacked MoTe2/WSe2 moiré heterobilayers. Unlike in the AA-stacked structures, an out-of-plane electric field controls not only the bandwidth but also the band topology by intertwining moiré bands centered at different high-symmetry stacking sites. At half band filling, corresponding to one particle per moiré unit cell, we observe quantized Hall resistance, h/e^2 (with h and e denoting the Planck’s constant and electron charge, respectively), and vanishing longitudinal resistance at zero magnetic field. The electric-field-induced topological phase transition from a Mott insulator to a QAH insulator precedes an insulator-to-metal transition; contrary to most known topological phase transitions, it is not accompanied by a bulk charge gap closure. Our study paves the path for discovery of a wealth of emergent phenomena arising from the combined influence of strong correlation and topology in semiconductor moiré materials.

A comparison between high-symmetry Mn12 single-molecule magnets in different ligand/solvent environments

Polyhedron ◽  
2005 ◽  
Vol 24 (16-17) ◽  
pp. 2284-2292 ◽  
Author(s):  
S. Hill ◽  
N. Anderson ◽  
A. Wilson ◽  
S. Takahashi ◽  
K. Petukhov ◽  
...  
Keyword(s):  
Single Molecule ◽  
High Symmetry ◽  
Single Molecule Magnets
Sign in / Sign up

Export Citation Format

Share Document