A variation principle for energy differences between states of two different Hamiltonians

A modification of a variation principle due to Delves, is derived which permits the direct calculation of energy differences between states of two different Hamiltonians: [Δ ??] = 〈X₀| ??_x – W_x|X₁〉 – 〈Y₀|??_y – W_y|y₁〉 + 〈X₀| Δ ??|Y₀〉 · 〈X₀| Y₀〉^?1. Δ ?? = ??_y – ??_x, |X₀〉 and |Y₀〉 are the wave functions for the X and Y states and |X₁〉 and |Y₁〉 are functions defined in the text. The principle is applied to a few simple examples.     

Does a high UV environment ensure adequate vitamin D status?

This study assesses the Vitamin D status of 126 healthy free-living adults aged 18-87 years, in southeast Queensland, Australia (27 degrees S) at the end of the 2006 winter. Participants provided blood samples for analysis of 25(OH)D (the measure of an individual's Vitamin D status), PTH, Calcium, Phosphate, and Albumin, completed a questionnaire on sun-protective/sun-exposure behaviours, and were assessed for phenotypic characteristics such as skin/hair/eye colour and BMI. We found that 10.2% of the participants had serum 25(OH)D levels below 25 nmol/l (considered deficient) and a further 32.3% had levels between 25 nmol/l and 50 nmol/l (considered insufficient). Our results show that low levels of 25(OH)D can occur in a substantial proportion of the population at the end of winter, even in a sunny climate. 25(OH)D levels were higher amongst those who spent more time in the sun and lower among obese participants (BMI>30) than those who were not obese (BMI<30). 25(OH)D levels were also lower in participants who had black hair, dark/olive skin, or brown eyes, when compared with participants who had brown or fair hair, fair skin, or blue/green eyes. No associations were found between 25(OH)D status and age, gender, smoking status, or the use of sunscreen.     

Magnetism and structure of graphene nanodots with interiors modified by boron, nitrogen, and charge

The properties (geometry, spin, and charge distribution) of a series of flat hexagonal zigzag edged graphene nanodots (GNDs), with interiors modified by centrally located substituent atoms boron and nitrogen and by positive and negative charge, have been calculated using ab initio density functional theory. The doped series X-GND has the stoichiometry C(6m(2)-1)XH(6m), zigzag size index m = 2, 4, 6, 8, 10 and substituent X = B or N. The undoped parents C(6m(2) )H(6m) with m ≤ 8 have spin paired ground states and the parent m = 10 has a spin polarized singlet ground state with edges that alternate α- and β-spin. The spin on the substituent atom decreases to zero with size index m and magnetization builds on the edges of all the X-GND. This demonstrates translocation of substituent spin and a proximity or directional effect for small m as the edges show different degrees of magnetization. For the largest X-GND (m = 10) the magnetization on edges resembles the calculated triplet S = 1(a) configuration of the parent (four edge spins up and two down) and has a higher apparent symmetry than the C(2v) point group of X-GND. For charged (m = 10) GNDs the edge magnetization has strength comparable to the parent on two parallel edges and weak on the other four in a perimeter pattern that resembles the triplet S = 1(b) configuration of the undoped parent and not the ground configuration of the isoelectronic X-GND molecule. Many of the results can be interpreted by simple Kekule? valence bond structures for an unpaired spin on a network where the substituent site group symmetry is not compatible with the perimeter. A deeper understanding is provided by the properties of the Kohn-Sham orbitals. The calculations of the X-doped GNDs reveal limitations in the use of the hex-radical hypothesis of the parent ground state to systems where foreign atoms lower symmetry and perturb the π- and σ-bond manifolds.     

Copper(I) Nitro Complex with an Anionic [HB(3,5-Me(2)Pz)(3)](-) Ligand: A Synthetic Model for the Copper Nitrite Reductase Active Site

The new copper(I) nitro complex [(Ph(3)P)(2)N][Cu(HB(3,5-Me(2)Pz)(3))(NO(2))] (2), containing the anionic hydrotris(3,5-dimethylpyrazolyl)borate ligand, was synthesized, and its structural features were probed using X-ray crystallography. Complex 2 was found to cocrystallize with a water molecule, and X-ray crystallographic analysis showed that the resulting molecule had the structure [(Ph(3)P)(2)N][Cu(HB(3,5-Me(2)Pz)(3))(NO(2))]·H(2)O (3), containing a water hydrogen bonded to an oxygen of the nitrite moiety. This complex represents the first example in the solid state of an analogue of the nitrous acid intermediate (CuNO(2)H). A comparison of the nitrite reduction reactivity of the electron-rich ligand containing the CuNO(2) complex 2 with that of the known neutral ligand containing the CuNO(2) complex [Cu(HC(3,5-Me(2)Pz)(3))(NO(2))] (1) shows that reactivity is significantly influenced by the electron density around the copper and nitrite centers. The detailed mechanisms of nitrite reduction reactions of 1 and 2 with acetic acid were explored by using density functional theory calculations. Overall, the results of this effort show that synthetic models, based on neutral HC(3,5-Me(2)Pz)(3) and anionic [HB(3,5-Me(2)Pz)(3)](-) ligands, mimic the electronic influence of (His)(3) ligands in the environment of the type II copper center of copper nitrite reductases (Cu-NIRs).     

Voltage enhancement in dye-sensitized solar cell using (001)-oriented anatase TiO2 nanosheets

A nanocrystalline TiO₂ (anatase) nanosheet exposing mainly the (001) crystal faces was tested as photoanode material in dye-sensitized solar cells. The nanosheets were prepared by hydrothermal growth in HF medium. Good-quality thin films were deposited on F-doped SnO₂ support from the TiO₂ suspension in ethanolic or aqueous media. The anatase (001) face adsorbs a smaller amount of the used dye sensitizer (C101) per unit area than the (101) face which was tested as a reference. The corresponding solar cell with sensitized (001)-nanosheet photoanode exhibits a larger open-circuit voltage than the reference cell with (101)-terminated anatase nanocrystals. The voltage enhancement is attributed to the negative shift of flatband potential for the (001) face. This conclusion rationalizes earlier works on similar systems, and it indicates that careful control of experimental conditions is needed to extract the effect of band energetic on the current/voltage characteristics of dye-sensitized solar cell.     

Synthesis of (−)‐Hebelophyllene E: An Entry to Geminal Dimethyl‐Cyclobutanes by [2+2] Cycloaddition of Alkenes and Allenoates

The first synthesis of hebelophyllene E is presented, along with assignment of its previously unknown relative configuration through synthesis of epi‐ent‐hebelophyllene E. Development of a catalytic enantioselective [2+2] cycloaddition of alkenes and allenoates provides access to the required chiral geminal dimethylcyclobutanes. Key to its success is the identification of a novel oxazaborolidine catalyst which promotes the cycloaddition in high enantioselectivities with good functional‐group tolerance (9 examples, up to 97:3 e.r.). Thus, a late‐stage cycloaddition using a fully functionalized alkene, followed by a diastereoselective reduction allows a concise entry to this class of natural products.     

Unsaturated four-membered N-heterocycles: From synthesis to applications

The ubiquity of strained motifs in drug discovery has recently witnessed a large regain of interest, as such scaffold can be used to modulate the properties of drug candidates. Unsaturated N-containing four-membered heterocycles present unique opportunities to access functionalized azetidines, which play an essential role in pharmacological studies. Even though those unsaturated patterns have been much less reported than the corresponding saturated versions, the consequent impact that those structures could have on molecular design with implementation of strained modules deserves to be summarized. In this review, synthetic accesses to substituted azetes, 1-azetines and 2-azetines are depicted, as well as their involvement in further transformations.     

Die trikline Kristallstruktur von Ag2Bi2S3Cl2: Pseudosymmetrie und Zwillingsbildung

Ruby‐red crystals of Ag₂Bi₂S₃Cl₂ were synthesized from AgCl and Bi₂S₃ by cooling a melt from 770 K to room temperature. X‐ray diffraction on powders and single‐crystals revealed a triclinic crystal structure with special lattice constants (P &1macr; (No. 2), a = 1085.0(2), b = 717.2(1), c = 1137.6(1) pm, α = 89.80(1)?, β = 74.80(1)?, γ = 87.81(1)?). In the structure [Bi^IIIS₃Cl₄] polyhedra form 2[BiS_3/2Cl_4/4]^‐ double‐layers by sharing common faces and edges. The silver(I) cations between the layers are coordinated either octahedrally by sulfide ions or tetrahedrally by sulfide and chloride ions. The deviations from the monoclinic space group P 1 2₁/c 1 are small and induce twinning along [010]. Further pseudosymmetry is based on the stacking of layer packages with the symmetry of the layer group P (2/c) 2₁/c 2/b.