Can model Hamiltonians describe the electron–electron interaction in π-conjugated systems?: PAH and graphene

Model Hamiltonians have been, and still are, a valuable tool for investigating the electronic structure of systems for which mean field theories work poorly. This review will concentrate on the application of Pariser–Parr–Pople (PPP) and Hubbard Hamiltonians to investigate some relevant properties of polycyclic aromatic hydrocarbons (PAH) and graphene. When presenting these two Hamiltonians we will resort to second quantisation which, although not the way chosen in its original proposal of the former, is much clearer. We will not attempt to be comprehensive, but rather our objective will be to try to provide the reader with information on what kinds of problems they will encounter and what tools they will need to solve them. One of the key issues concerning model Hamiltonians that will be treated in detail is the choice of model parameters. Although model Hamiltonians reduce the complexity of the original Hamiltonian, they cannot be solved in most cases exactly. So, we shall first consider the Hartree–Fock approximation, still the only tool for handling large systems, besides density functional theory (DFT) approaches. We proceed by discussing to what extent one may exactly solve model Hamiltonians and the Lanczos approach. We shall describe the configuration interaction (CI) method, a common technology in quantum chemistry but one rarely used to solve model Hamiltonians. In particular, we propose a variant of the Lanczos method, inspired by CI, that has the novelty of using as the seed of the Lanczos process a mean field (Hartree–Fock) determinant (the method will be named LCI). Two questions of interest related to model Hamiltonians will be discussed: (i) when including long-range interactions, how crucial is including in the Hamiltonian the electronic charge that compensates ion charges? (ii) Is it possible to reduce a Hamiltonian incorporating Coulomb interactions (PPP) to an 'effective' Hamiltonian including only on-site interactions (Hubbard)? The performance of CI will be checked on small molecules. The electronic structure of azulene and fused azulene will be used to illustrate several aspects of the method. As regards graphene, several questions will be considered: (i) paramagnetic versus antiferromagnetic solutions, (ii) forbidden gap versus dot size, (iii) graphene nano-ribbons, and (iv) optical properties.

New Orleans, Louisiana Census tracks and blocks, 1960 (Image 2 of 2) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: New Orleans, Louisiana, by census tracts and blocks: 1960. It was published by The Census Bureau ca. 1960. Scale [ca. 1:17,500]. This layer is image 2 of 2 total images of the two sheet source map. The image inside the map neatline is georeferenced to the surface of the earth and fit to the Louisiana State Plane Coordinate System, South NAD83 (in Feet) (Fipszone 1702). All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, or other information associated with the principal map. This map shows features such as Census block and tract numbers and boundaries, roads, canals, drainage, and more. Includes inset and legend. This layer is part of a selection of digitally scanned and georeferenced historic maps from The Harvard Map Collection as part of the Imaging the Urban Environment project. Maps selected for this project represent major urban areas and cities of the world, at various time periods. These maps typically portray both natural and manmade features at a large scale. The selection represents a range of regions, originators, ground condition dates, scales, and purposes.

New Orleans, Louisiana Census tracks and blocks, 1960 (Image 1 of 2) (Raster Image)

This layer is a georeferenced raster image of the historic paper map entitled: New Orleans, Louisiana, by census tracts and blocks: 1960. It was published by The Census Bureau ca. 1960. Scale [ca. 1:17,500]. This layer is image 1 of 2 total images of the two sheet source map. The image inside the map neatline is georeferenced to the surface of the earth and fit to the Louisiana State Plane Coordinate System, South NAD83 (in Feet) (Fipszone 1702). All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, or other information associated with the principal map. This map shows features such as Census block and tract numbers and boundaries, roads, canals, drainage, and more. Includes inset and legend. This layer is part of a selection of digitally scanned and georeferenced historic maps from The Harvard Map Collection as part of the Imaging the Urban Environment project. Maps selected for this project represent major urban areas and cities of the world, at various time periods. These maps typically portray both natural and manmade features at a large scale. The selection represents a range of regions, originators, ground condition dates, scales, and purposes.

The proteasome inhibitor MLN-273 blocks exoerythrocytic and erythrocytic development of Plasmodium parasites.

Protein degradation is regulated during the cell cycle of all eukaryotic cells and is mediated by the ubiquitin-proteasome pathway. Potent and specific peptide-derived inhibitors of the 20S proteasome have been developed recently as anti-cancer agents, based on their ability to induce apoptosis in rapidly dividing cells. Here, we tested a novel small molecule dipeptidyl boronic acid proteasome inhibitor, named MLN-273 on blood and liver stages of Plasmodium species, both of which undergo active replication, probably requiring extensive proteasome activity. The inhibitor blocked Plasmodium falciparum erythrocytic development at an early ring stage as well as P. berghei exoerythrocytic progression to schizonts. Importantly, neither uninfected erythrocytes nor hepatocytes were affected by the drug. MLN-273 caused an overall reduction in protein degradation in P. falciparum, as demonstrated by immunoblots using anti-ubiquitin antibodies to label ubiquitin-tagged protein conjugates. This led us to conclude that the target of the drug was the parasite proteasome. The fact that proteasome inhibitors are presently used as anti-cancer drugs in humans forms a solid basis for further development and makes them potentially attractive drugs also for malaria chemotherapy.

The private sector, the public sector, and donor assistance in economic development : an interpretive essay /

"PN-AAL-007"--Cover.

Practical concrete-block making; a simple practical treatise for the workman explaining the selection of the materials and the making of substantial concrete blocks and cement brick, together with directions for making molds and remarks on how to obtain the best architectural effects,

Mode of access: Internet.

The manufacture of concrete blocks and their use in building construction /

Includes index.

The Crucifixion with Saints and a Donor

Joos van Cleve and a collaborator; 3 ft. 2 47/64 in.x 2 ft. 5 1/4 in. (center); 3 ft. 3 49/64 in.x 1 ft. 7/8 in. (each wing); oil on wood

New York daguerreotyped : group first, business-streets, mercantile blocks, stores, and banks.

Illustrated with engravings from daguerreotypes.

Square blocks, and other sermons and articles,

Mode of access: Internet.

Specifications for treating and laying creosoted pine paving blocks /

Mode of access: Internet.

G-factor and donor spin-lattice relaxation for electrons in germanium and silicon.

"This group report is based on an article submitted to the Physical review."

A book of the French verbs : wherein the model verbs, and several of the most difficult are conjugated affirmatively, negatively, interrogatively, and negatively and interrogatively, containing also, numerous notes and directions on the different conjugations, not to be found in any other book published for the use of English scholars, to which is added, a complete list of all the irregular verbs /

Author was principal of West Chester Academy.

... Arithmetic on the productive system; accompanied by a key and cubical blocks.

At head of title: Smith's new arithmetic.