Density-functional theory calculation of the nuclear magnetic resonance indirect nuclear spin—spin coupling constants in C60

Density-functional theory is used to study the nuclear magnetic resonance (NMR) indirect nuclear spin-spin coupling constants in C₆₀. Knowledge of these coupling constants may help in the analysis of future experimental NMR studies of ¹³C-enriched C₆₀. At the Becke 3-parameter Lee-Yang-Parr (B3LYP) Kohn-Sham level, the one-bond couplings within pentagons and between pentagons are 62 Hz and 77 Hz, respectively; the corresponding geminal couplings are 7 Hz and 1 Hz, respectively. Except for the vicinal couplings (about 4 Hz), the long-range couplings are all 1 Hz or smaller. This is the largest theoretical calculation to date of the complete set of indirect nuclear spin-spin coupling constants of a molecular system; it has been made possible by solving the response equations only for the perturbing operators related to one nuclear magnetic moment, making the calculation feasible.     

NONRENEWABLE RESOURCE EXTRACTIONS WITH A POLLUTION SIDE EFFECT: A COMPARATIVE DYNAMIC ANALYSIS

ABSTRACT. In this paper, we present a nonrenewable resource model including environmental pollution as a state variable. The model is analyzed to identify some of the characteristics of the optimal paths. In addition, we present a numerical example on the basis of the algebraic solutions of our qualitative model, and identify some of characteristics of the optimal time paths for two sets of social costs of the pollutant. These results are consistent with the proposition of the previous literature that levying the shadow cost of the pollution stock reduces the consumption of resource; hence, it slows the accumulation of the pollutant in the atmosphere. One quirk in the results, however, is that extractions will persist longer in the higher pollution cost scenario. The costate variable for the resource stock is decomposed into a scarcity effect and a cost effect; and the costate variable for the pollution stock is decomposed into an undesirable abundance effect and a cost effect. Both of these, however, are cost effects.     

Assessing isomeric structures of pincer-ligated ruthenium and osmium polyhydrides using density functional calculations

DFT calculations on a [N(SiH₂CH₂PH₂)₂]MH₃ model (M = Ru and Os) of experimentally known compounds show that the three H have different bonding modes for Ru (H + H₂) and for Os (three independent H). Calculation shows that the Ru(H)(H₂) compound adds H₂ to give an RuH(H₂)₂ substructure; the Os(H)₂ species adds H₂ to give the Os(H)₃(H₂) substructure. The impact of these intramolecular redox processes on bond lengths is discussed, as are attempts to provide an improved computational model of P(alkyl) _n without the introduction of additional alkyl atoms.     

THE TRANSMISSION OF COMBINED NEUTRAL DENSITY FILTERS

Abstract— Stacking of neutral density filters to decrease transmission causes various problems, depending on the type of filters used. Combining reflective filters results in a higher total transmission than the product of the individual transmissions suggests. The error increases dramatically with increasing reflection of the filters due to multiple reflection between the filters. Equations are presented which allow the calculation of combinations of reflective filters and those combining both reflection and absorption.     

Unleashing a Microcomputer in the Laboratory, Part II Second in a series of three articles

This is the second article in a series discussing the use of the microcomputer in the laboratory. Part I examined the features of the PET* microcomputer which make it a useful partner in the laboratory. It showed how the microcomputer can be used to control four types of devices: (1) the devices which only require control signals, (2) the devices which talk only, (3) the devices which listen only, and (4) the devices which both talk and listen.     

EXCITATION TRANSFER BY CHLOROPHYLL a IN MONOLAYERS AND THE INTERACTION WITH CHLOROPLAST GLYCOLIPIDS*

In mixed monolayers with purified chloroplast glycolipids and other colorless lipids, chlorophyll a fluorescence exhibits a decrease in quantum efficiency with increasing chlorophyll concentration. The fluorescence, which is strongly polarized in dilute films, becomes progressively depolarized as the area fraction of chlorophyll increases, and it is completely depolarized in a pure chlorophyll a monolayer. The observed behavior is consistent with an inductive resonance mechanism of energy transfer among the chlorophyll molecules with a critical transfer distance of 20–90 Å, depending on the model chosen for the energy transfer mechanism. The purified glycolipids–mono-and digalactosyl diglycerides and sulfoquinovodiglyceride–separately form stable, compressible monolayers of the liquid-expanded type on an aqueous subphase and in an atompshere of nitrogen. At maximum compression the three glycolipids occupy areas of 55, 80 and 47 A²-molecule^-1, respectively, in the monolayer. Mixed monolayers of chlorophyll a with, separately, the monogalactolipid and the sulfolipid behave upon compression as two-dimensional solutions. The fluorescence polarization at high chlorophyll concentrations in mixed monolayers indicates that several of the lipid diluents facilitate local ordering of the pigment molecules.