A natural scheme for the quantitative analysis of the magnetically induced molecular current density using an oriented flux-weighted stagnation graph. I. A minimal example for LiH

A new natural scheme is introduced to analyze quantitatively the magnetically induced molecular current density vector field, J. The set of zero points of J, which is called its stagnation graph (SG), has been previously used to study the topological features of the current density of various molecules. Here, the line integrals of the induced magnetic field along edges of the connected subset of the SG are calculated. The edges are oriented such that all weights, i.e., flux values become non-negative, thereby, an oriented flux-weighted (current density) stagnation graph (OFW-SG) is obtained. Since in the exact theoretical limit, J is divergence-free and due to the topological characteristics of such vector fields, the flux of all separate vortices (current density domains) and neighbouring connected vortices can be determined exactly by adding the weights of cyclic subsets of edges (i.e., closed loops) of the OFW-SG. The procedure is exemplified by the minimal example of LiH for a weak homogeneous external magnetic field, B, perpendicular to the chemical bond. The OFW-SG exhibits one closed loop (formally decomposed into two edges), and an open line extending to infinity on both of its ends. The method provides the means of accurately determining the strength of the current density even in molecules with a complicated set of distinct vortices.Peer reviewe

Investment in nuclear generation in a restricted electricity market : an analysis of risks and financing options

Thesis (S.M.)--Massachusetts Institute of Technology, Engineering Systems Division, Technology and Policy Program; and, (S.M.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 2006.Includes bibliographical references (p. 222-225).Since the late 1970s, the US electric power industry has been undergoing major changes. The electric utility industry had mainly consisted of highly regulated, vertically integrated, local monopolies, providing customers with all electric services at rates determined by the state regulatory agency. Deregulation and restructuring in the power industry triggered a transition towards competition in electricity generation, due to the formation of competitive markets at the wholesale level - in some states, at the retail level as well. Since utilities can no longer price at cost-of-service rates, investors in electric generation capacity, like nuclear power, will face a different set of financial risks. Moreover, the economic context of volatile coal and gas prices, increasingly stringent NOx, S02 and mercury regulations, and growing support for C02 regulations will likely positively impact the value of nuclear capacity. Conversely, unresolved issues in the nuclear industry inherent to radioactive waste disposal, decommissioning and public opposition related to security concerns will likely penalize the building of new nuclear capacity. More importantly, regulatory delays in construction, mainly caused by the plant approval process by the Nuclear Regulatory Commission, undoubtedly negatively affect nuclear power because of its capital-intensiveness.(cont.) This thesis evaluates the main drivers impacting investments, and especially new investments, in nuclear power technologies to meet the increase in electricity demand in the United States. For that purpose, the ongoing change in the electric power sector and the potential evolution in all regulations concerning nuclear energy are assessed. The new risk factors facing investment in nuclear power, as well as the possible financing options, are examined. The company characteristics that most favor investment in new nuclear power plants in the United States are sketched. The specific issue of plant construction, regulations and licensing is considered with closer attention. An analytic investment model in power generation estimates the impact of the extended construction time caused by regulatory delay in licensing on investment in nuclear power in a context of uncertainty on demand. The case study compares the dynamics of investment in nuclear power plants with gas-fired power plants - which have a much shorter construction time.by Raphael Berger.S.M

Current density and molecular magnetic properties

We give an overview of the molecular response to an external magnetic field perturbing quantum mechanical systems. We present state-of-the-art methods for calculating magnetically-induced current-density susceptibilities. We discuss the essence and properties of current-density susceptibilities and how molecular magnetic properties can be calculated from them. We also review the theory of spin-current densities, how relativity affects current densities and magnetic properties. An overview of the magnetic ring-current criterion for aromaticity is given, which has implications on theoretical and experimental research. The recently reported theory of antiaromaticity and how molecular symmetry affects the magnetic response are discussed and applied to closed-shell paramagnetic molecules. The topology of magnetically induced current densities and its consequences for molecular magnetic properties are also presented with twisted and toroidal molecules as examples.Peer reviewe

Analysis of the magnetically induced current density of molecules consisting of annelated aromatic and antiaromatic hydrocarbon rings

Magnetically induced current susceptibilities and current pathways have been calculated for molecules consisting of two pentalene groups annelated with a benzene (1) or naphthalene (2) moiety. Current strength susceptibilities have been obtained by numerically integrating separately the diatropic and paratropic contributions to the current flow passing planes through chosen bonds of the molecules. The current density calculations provide novel and unambiguous current pathways for the unusual molecules with annelated aromatic and antiaromatic hydrocarbon moieties. The calculations show that the benzene and naphthalene moieties annelated with two pentalene units as in molecules 1 and 2, respectively, are unexpectedly antiaromatic sustaining only a local paratropic ring current around the ring, whereas a weak diatropic current flows around the C-H moiety of the benzene ring. For 1 and 2, the individual five-membered rings of the pentalenes are antiaromatic and a slightly weaker semilocal paratropic current flows around the two pentalene rings. Molecules 1 and 2 do not sustain any net global ring current. The naphthalene moiety of the molecule consisting of a naphthalene annelated with two pentalene units (3) does not sustain any strong ring current that is typical for naphthalene. Instead, half of the diatropic current passing the naphthalene moiety forms a zig-zag pattern along the C-C bonds of the naphthalene moiety that are not shared with the pentalene moieties and one third of the current continues around the whole molecule partially cancelling the very strong paratropic semilocal ring current of the pentalenes. For molecule 3, the pentalene moieties and the individual five-membered rings of the pentalenes are more antiaromatic than for 1 and 2. The calculated current patterns elucidate why the compounds with formally [4n + 2] p-electrons have unusual aromatic properties violating the Huckel pi-electron count rule. The current density calculations also provide valuable information for interpreting the measured H-1 NMR spectra.Peer reviewe

Spatial Contributions to 1H NMR Chemical Shifts of Free-Base Porphyrinoids

A recently developed methodology for calculating, analyzing, and visualizing nuclear magnetic shielding densities is used for studying spatial contributions including ring-current contributions to 1H nuclear magnetic resonance (NMR) chemical shifts of aromatic and anti-aromatic free-base porphyrinoids. Our approach allows a visual inspection of the spatial origin of the positive (shielding) and negative (deshielding) contributions to the nuclear magnetic shielding constants. Diatropic and paratropic current-density fluxes yield both shielding and deshielding contributions implying that not merely the tropicity of the current density determines whether the contribution has a shielding or deshielding character. Instead the shielding or deshielding contribution is determined by the direction of the current-density flux with respect to the studied nucleus

Spatial Contributions to 1H NMR Chemical Shifts of Free-Base Porphyrinoids

A recently developed methodology for calculating, analyzing, and visualizing nuclear magnetic shielding densities is used for studying spatial contributions including ring-current contributions to 1H nuclear magnetic resonance (NMR) chemical shifts of aromatic and anti-aromatic free-base porphyrinoids. Our approach allows a visual inspection of the spatial origin of the positive (shielding) and negative (deshielding) contributions to the nuclear magnetic shielding constants. Diatropic and paratropic current-density fluxes yield both shielding and deshielding contributions implying that not merely the tropicity of the current density determines whether the contribution has a shielding or deshielding character. Instead the shielding or deshielding contribution is determined by the direction of the current-density flux with respect to the studied nucleus