Особливості реалізації графічного конвеєру при візуалізації тривимірних моделей приміщень університету

В більшості систем комп‘ютерної графіки застосовується графічний конвеєр – логічна група послідовно виконуваних обчислень (етапів), які в результаті дають синтезовану сцену на екрані комп‘ютера. Серед основних – етапи геометричних перетворень та візуалізації. Результат виконання кожного з цих етапів впливає на кінцевий вигляд синтезованої сцени, тому їх коректне завершення є необхідною умовою отримання якісного зображення

Synthesis, Structure, and Magnetic Properties of Regular Alternating μ-bpm/di-μ-X Copper(II) Chains (bpm = 2,2′-bipyrimidine; X = OH, F)

The preparation and X-ray crystal structure of four 2,2′-bipyrimidine (bpm)-containing copper­(II) complexes of formula {[Cu₂(μ-bpm)­(H₂O)₄(μ-OH)₂]­[Mn­(H₂O)₆]­(SO₄)₂}_<i>n</i> (<b>1</b>), {[Cu₂(μ-bpm)­(H₂O)₄(μ-OH)₂]­SiF₆}_<i>n</i> (<b>2</b>), {Cu₂(μ-bpm)­(H₂O)₂(μ-F)₂F₂}_<i>n</i> (<b>3</b>), and [Cu­(bpm)­(H₂O)₂F­(NO₃)]­[Cu­(bpm)­(H₂O)₃F]­NO₃·2H₂O (<b>4</b>) are reported. The structures of <b>1</b>–<b>3</b> consist of chains of copper­(II) ions with regular alternation of bis-bidentate bpm and di-μ-hydroxo (<b>1</b> and <b>2</b>) or di-μ-fluoro (<b>3</b>) groups, the electroneutrality being achieved by either hexaaqua manganese­(II) cations plus uncoordinated sulfate anions (<b>1</b>), uncoordinated hexafluorosilicate anions (<b>2</b>), or terminally bound fluoride ligands (<b>3</b>). Each copper­(II) ion in <b>1</b>–<b>4</b> is six-coordinated in elongated octahedral surroundings. <b>1</b> and <b>2</b> show identical, linear chain motifs with two bpm-nitrogen atoms and two hydroxo groups building the equatorial plane at each copper­(II) ion and the axial position being filled by water molecules. In the case of <b>3</b>, the axial sites at the copper atom are occupied by a bpm-nitrogen atom and a bis-monodentate fluoride anion, producing a “step-like” chain motif. The values of the angle at the hydroxo and fluoro bridges are 94.11(6) (<b>1</b>), 94.75(4) (<b>2</b>), and 101.43(4)° (<b>3</b>). In each case, the copper–copper separation through the bis-bidentate bpm [5.428(1) (<b>1</b>), 5.449(1) (<b>2</b>), and 5.9250(4) Å (<b>3</b>)] is considerably longer than that through the di-μ-hydroxo [2.8320(4) (<b>1</b>) and 2.824(1) Å (<b>2</b>)] or di-μ-fluoro [3.3027(4) Å (<b>3</b>)] bridges. Compound <b>4</b> is a mononuclear species whose structure is made up of neutral [Cu­(bpm)­(H₂O)₂F­(NO₃)] units, [Cu­(bpm)­(H₂O)₃F]⁺ cations, uncoordinated nitrate anions, and crystallization water molecules, giving rise to a <i>pseudo</i>-helical, one-dimensional (1D) supramolecular motif. The magnetic properties of <b>1</b>–<b>3</b> have been investigated in the temperature range 1.9–300 K. Relatively large, alternating antiferro- [<i>J</i> = −149 (<b>1</b>) and −141 cm^–1 (<b>2</b>) across bis-bidentate bpm] and ferromagnetic [α<i>J</i> = +194 (<b>1</b>) and +176 cm^–1 (<b>2</b>) through the dihydroxo bridges] interactions occur in <b>1</b> and <b>2</b> [the Hamiltonian being defined as <i>H</i> = −<i>J</i>∑_<i>i</i>=1^<i>n</i>/2 (<i>S</i>_2<i>i</i>·<i>S</i>_{2<i>i</i>–1} – α<i>S</i>_2<i>i</i>·<i>S</i>_2<i>i</i>+1)]. These values compare well with those previously reported for parent examples. Two weak intrachain antiferromagnetic interactions [<i>J</i> = −0.30 and α<i>J</i> = −8.1 cm^–1 across bpm and the di-μ-fluoro bridges, respectively] whose values were substantiated by density functional theory (DFT)-type calculations occur in <b>3</b>

Syntheses, Crystal Structures, and Magnetic Properties of Metal–Organic Hybrid Materials of Mn(II)/Co(II): Three-Fold Interpenetrated α‑Polonium-like Network in One of Them

Three new 1,4-phenylenediacrylate bridged Mn­(II) and Co­(II) complexes of molecular formulas {[Mn₂­(ppda)­(phen)₄­(H₂O)₂]­(ppda)₂­(H₂O)} (<b>1</b>), {[Co­(ppda)­(dpyo)­(H₂O)₃]·4­(H₂O)}<i>_n</i> (<b>2</b>), and {[Co­(ppda)­(bpe)]·(0.5H₂O)}_<i>n</i> (<b>3</b>) [ppda = 1,4-phenylenediacrylate; phen = 1,10-phenanthroline; dpyo = 4,4′-dipyridyl <i>N</i>,<i>N</i>′-dioxide; bpe = 1,2-bis­(4-pyridyl)­ethane] have been synthesized and characterized by elemental analysis, IR spectra, single-crystal X-ray diffraction studies, and low-temperature magnetic measurements. The structural determination reveals that complex <b>1</b> is a discrete dinuclear species, <b>2</b> is a 1D polymeric chain, while <b>3</b> is a three-fold interpenetrated α-polonium network. Hydrogen-bonding interactions, formed by coordinated and/or lattice water molecules with ppda oxygen and π–π stacking interactions of aromatic rings, lead to a 3D supramolecular architecture in both complexes <b>1</b> and <b>2</b>. Low-temperature magnetic study shows antiferromagnetic coupling in all the complexes. In addition, their electronic and fluorescent spectral properties have been investigated

NMR Spectroscopic Characterization and DFT Calculations of Zirconium(IV)-3,3′-Br₂–BINOLate and Related Complexes Used in an Enantioselective Friedel–Crafts Alkylation of Indoles with α,β-Unsaturated Ketones

Experimental and theoretical studies on the structure of several complexes based on (<i>R</i>)-3,3′-Br₂–BINOL ligand and group (IV) metals used as catalysts in an enantioselective Friedel–Crafts alkylation of indoles with α,β-unsaturated ketones have been carried out. NMR spectroscopic studies of these catalysts have been performed, which suggested that at room temperature the catalysts would form a monomeric structure in the case of Ti^IV and a dimeric structure in the cases of Zr^IV and Hf^IV. Density functional theory (DFT) calculations clearly corroborate the conclusions of these experimental spectroscopic studies. The dimeric structure with a doubly bridged motif [Zr^IV₂(μ-(<i>R</i>)-3,3′-Br₂–BINOL)₂] where each binaphthol ligand acts as bridge between the metal centers (Novak’s model) is more stable than the dimeric structure with a doubly bridged motif [Zr^IV₂(μ-O^<i>t</i>Bu)₂] where the <i>tert</i>-butoxide groups act as bridging ligands (Kobayashi’s model). The scope of the Friedel–Crafts alkylation with regard to the indole structure has been studied. Finally a plausible mechanism for the Friedel–Crafts reaction and a stereomodel for the mode of action of the catalyst that explain the observed stereochemistry of the reaction products have been proposed

NMR Spectroscopic Characterization and DFT Calculations of Zirconium(IV)-3,3′-Br₂–BINOLate and Related Complexes Used in an Enantioselective Friedel–Crafts Alkylation of Indoles with α,β-Unsaturated Ketones

Experimental and theoretical studies on the structure of several complexes based on (<i>R</i>)-3,3′-Br₂–BINOL ligand and group (IV) metals used as catalysts in an enantioselective Friedel–Crafts alkylation of indoles with α,β-unsaturated ketones have been carried out. NMR spectroscopic studies of these catalysts have been performed, which suggested that at room temperature the catalysts would form a monomeric structure in the case of Ti^IV and a dimeric structure in the cases of Zr^IV and Hf^IV. Density functional theory (DFT) calculations clearly corroborate the conclusions of these experimental spectroscopic studies. The dimeric structure with a doubly bridged motif [Zr^IV₂(μ-(<i>R</i>)-3,3′-Br₂–BINOL)₂] where each binaphthol ligand acts as bridge between the metal centers (Novak’s model) is more stable than the dimeric structure with a doubly bridged motif [Zr^IV₂(μ-O^<i>t</i>Bu)₂] where the <i>tert</i>-butoxide groups act as bridging ligands (Kobayashi’s model). The scope of the Friedel–Crafts alkylation with regard to the indole structure has been studied. Finally a plausible mechanism for the Friedel–Crafts reaction and a stereomodel for the mode of action of the catalyst that explain the observed stereochemistry of the reaction products have been proposed

Delivery Modulation in Silica Mesoporous Supports via Alkyl Chain Pore Outlet Decoration

This article focuses on the study of the release rate in a family of modified silica mesoporous supports. A collection of solids containing ethyl, butyl, hexyl, octyl, decyl, octadecyl, docosyl, and triacontyl groups anchored on the pore outlets of mesoporous MCM-41 has been prepared and characterized. Controlled release from pore voids has been studied through the delivery of the dye complex tris­(2,2′-bipyridyl)­ruthenium­(II). Delivery rates were found to be dependent on the alkyl chain length anchored on the pore outlets of the mesoporous scaffolding. Moreover, release rates follow a Higuchi diffusion model, and Higuchi constants for the different hybrid solids have been calculated. A decrease of the Higuchi constants was observed as the alkyl chain used to tune the release profile is longer, confirming the effect that the different alkyl chains anchored into the pore mouths exerted on the delivery of the cargo. Furthermore, to better understand the relation between pore outlets decoration and release rate, studies using molecular dynamics simulations employing force-field methods have been carried out. A good agreement between the calculations and the experimental observations was observed

Analysis of Mexican Spotted Owl Diet in the Canyonlands of Southern Utah

While diets of Mexican Spotted Owls within forested habitat have been studied, little research has been published on the diet of owls that occupy canyon habitats (see Willey In Press). Since the Mexican Spotted Owl is federally listed as a threatened species, it is important to identify primary prey of Utah’s canyon dwelling owls to better understand their dietary needs (U.S. Fish and Wildlife Service 1993). We hope that the findings from this research can better inform state and federal managers on spotted owl prey use and aid in future management of small mammal populations in canyon habitats. We intend to compare our results with the findings of Willey (In Press) to determine whether any differences in diet exist. We will determine the time of day owls were foraging. A complete list of prey species will be compiled and the mean dietary composition will be computed for each owl territory. Mean biomass and frequency of prey captured at each site will also be calculated. Lastly, the evenness of the owl’s diet between study areas will be compared using the Simpson’s Index. Understanding the Mexican spotted owl’s prey base in canyon habitats will provide insights into potential population limiting factors

Topological Versatility of Oxalate-Based Bimetallic One-Dimensional (1D) Compounds Associated with Ammonium Cations

A new family of oxalate-bridged chains of formula (C₁)­[Mn­(H₂O)₃Cr­(ox)₃]·H₂O (<b>1</b>), (C₂)₄[Mn₂(H₂O)₃ClCr₂(ox)₆]­Cl·H₂O·2C₂H₆O (<b>2a</b>), (C₂)₄[Co₂(H₂O)₃ClCr₂(ox)₆]­Cl·2H₂O·2C₂H₆O (<b>2b</b>), [Mn­(C₃)­(H₂O)₂Cr­(ox)₃]·H₂O (<b>3</b>), and (C₄)₄[Mn­(H₂O)­{Cr­(ox)₃}₂]·H₂O (<b>4</b>) [C₁⁺ = tetramethylammonium, C₂⁺ = 4-<i>N,N</i>-dimethylaminopyridinium, C₃⁺ = 1-hydroxyethyl-4-<i>N,N</i>-dimethylamino-pyridinium, C₄⁺ = 1-hydroxyethyl-4-(4′-dimethylamino-α-styryl)-pyridinium, ox^2– = oxalate] have been synthesized by self-assembly of the (C_<i>n</i>)₃[Cr­(ox)₃] (<i>n</i> = 1–4) mononuclear compound and the chloride salts of the corresponding metal­(II) ions. The crystal structures of the five chain compounds have been determined by single-crystal X-ray diffraction. Compounds <b>1</b> and <b>2</b> crystallize in the <i>Pc</i> and <i>P</i>2₁/<i>c</i> centrosymmetrical space groups, respectively, whereas <b>3</b> and <b>4</b> crystallize in the <i>C</i>2<i>cb</i> and <i>P</i>1 noncentrosymmetrical space groups, respectively. Compounds <b>1</b>, <b>2</b>, and <b>3</b> adopt a zigzag chain structure while <b>4</b> exhibits a comb-like chain structure consisting of the repetition of the [Mn­(H₂O)­{Cr­(μ-ox)­(ox)₂}­{Cr­(μ-ox)₂(ox)}]^4– entities. Compound <b>3</b> displays large second-order optical nonlinearity. The magnetic properties of <b>1</b>–<b>4</b> have been investigated in the temperature range 2–300 K. Monte Carlo simulations on <b>1</b>, <b>2a</b>, <b>2b</b>, and <b>3</b> provide a quantitative description of the magnetic properties indicating ferromagnetic interactions through the bis­(bidentate) oxalate bridges [<i>J</i> = +0.55 cm^–1 (<b>1</b>), <i>J</i> = +1.02 cm^–1 (<b>2a</b>), <i>J</i> = +3.83 cm^–1 (<b>2b</b>), and <i>J</i> = +0.75 cm^–1 (<b>3</b>) using Hamiltonian <i>Ĥ</i> = −<i>J</i>(<i>Ŝ</i>_<i>i</i>·<i>Ŝ</i>_<i>j</i>)]. On the other side, the fit of the magnetic susceptibility data of <b>4</b> by full-matrix diagonalization agrees with a ferromagnetic exchange interaction within the [Mn­(H₂O)­{Cr­(μ-ox)­(ox)₂}­{Cr­(μ-ox)₂(ox)}]^4– trinuclear units (<i>J</i> = +2.07 cm^–1) antiferromagnetically coupled along the chain. Compound <b>2b</b> exhibits a metamagnetic behavior, the value of the critical field being <i>H</i>_C = 1000 G, due to the occurrence of weak interchain antiferromagnetic interactions

Cytosine Nucleobase Ligand: A Suitable Choice for Modulating Magnetic Anisotropy in Tetrahedrally Coordinated Mononuclear Co^II Compounds

A family of tetrahedral mononuclear Co^II complexes with the cytosine nucleobase ligand is used as the playground for an in-depth study of the effects that the nature of the ligand, as well as their noninnocent distortions on the Co­(II) environment, may have on the slow magnetic relaxation effects. Hence, those compounds with greater distortion from the ideal tetrahedral geometry showed a larger-magnitude axial magnetic anisotropy (<i>D</i>) together with a high rhombicity factor (<i>E</i>/<i>D</i>), and thus, slow magnetic relaxation effects also appear. In turn, the more symmetric compound possesses a much smaller value of the <i>D</i> parameter and, consequently, lacks single-ion magnet behavior

Theoretical Insights into the Ferromagnetic Coupling in Oxalato-Bridged Chromium(III)-Cobalt(II) and Chromium(III)-Manganese(II) Dinuclear Complexes with Aromatic Diimine Ligands

Two novel heterobimetallic complexes of formula [Cr­(bpy)­(ox)₂Co­(Me₂phen)­(H₂O)₂]­[Cr­(bpy)­(ox)₂]·4H₂O (<b>1</b>) and [Cr­(phen)­(ox)₂Mn­(phen)­(H₂O)₂]­[Cr­(phen)­(ox)₂]·H₂O (<b>2</b>) (bpy = 2,2′-bipyridine, phen = 1,10-phenanthroline, and Me₂phen = 2,9-dimethyl-1,10-phenanthroline) have been obtained through the “complex-as-ligand/complex-as-metal” strategy by using Ph₄P­[CrL­(ox)₂]·H₂O (L = bpy and phen) and [ML′(H₂O)₄]­(NO₃)₂ (M = Co and Mn; L′ = phen and Me₂phen) as precursors. The X-ray crystal structures of <b>1</b> and <b>2</b> consist of bis­(oxalato)­chromate­(III) mononuclear anions, [Cr^IIIL­(ox)₂]⁻, and oxalato-bridged chromium­(III)-cobalt­(II) and chromium­(III)-manganese­(II) dinuclear cations, [Cr^IIIL­(ox)­(μ-ox)­M^IIL′(H₂O)₂]⁺ [M = Co, L = bpy, and L′ = Me₂phen (<b>1</b>); M = Mn and L = L′ = phen (<b>2</b>)]. These oxalato-bridged Cr^IIIM^II dinuclear cationic entities of <b>1</b> and <b>2</b> result from the coordination of a [Cr^IIIL­(ox)₂]⁻ unit through one of its two oxalato groups toward a [M^IIL′(H₂O)₂]²⁺ moiety with either a <i>trans-</i> (M = Co) or a <i>cis</i>-diaqua (M = Mn) configuration. The two distinct Cr^III ions in <b>1</b> and <b>2</b> adopt a similar trigonally compressed octahedral geometry, while the high-spin M^II ions exhibit an axially (M = Co) or trigonally compressed (M = Mn) octahedral geometry in <b>1</b> and <b>2</b>, respectively. Variable temperature (2.0–300 K) magnetic susceptibility and variable-field (0–5.0 T) magnetization measurements for <b>1</b> and <b>2</b> reveal the presence of weak intramolecular ferromagnetic interactions between the Cr^III (<i>S</i>_Cr = 3/2) ion and the high-spin Co^II (<i>S</i>_Co = 3/2) or Mn^II (<i>S</i>_Mn = 5/2) ions across the oxalato bridge within the Cr^IIIM^II dinuclear cationic entities (M = Co and Mn) [<i>J</i> = +2.2 (<b>1</b>) and +1.2 cm^–1 (<b>2</b>); <b>H</b> = –<i>J</i> <b>S</b>_<b>Cr</b>·<b>S</b>_<b>M</b>]. Density functional electronic structure calculations for <b>1</b> and <b>2</b> support the occurrence of <i>S</i> = 3 Cr^IIICo^II and <i>S</i> = 4 Cr^IIIMn^II ground spin states, respectively. A simple molecular orbital analysis of the electron exchange mechanism suggests a subtle competition between individual ferro- and antiferromagnetic contributions through the σ- and/or π-type pathways of the oxalato bridge, mainly involving the d_<i>yz</i>(Cr)/d_<i>xy</i>(M), d_<i>xz</i>(Cr)/d_<i>xy</i>(M), d_{<i>x</i>²–<i>y</i>²}(Cr)/d_<i>xy</i>(M), d_<i>yz</i>(Cr)/d_<i>xz</i>(M), and d_<i>xz</i>(Cr)/d_<i>yz</i>(M) pairs of orthogonal magnetic orbitals and the d_{<i>x</i>²–<i>y</i>²}(Cr)/d_{<i>x</i>²–<i>y</i>²}(M), d_<i>xz</i>(Cr)/d_<i>xz</i>(M), and d_<i>yz</i>(Cr)/d_<i>yz</i>(M) pairs of nonorthogonal magnetic orbitals, which would be ultimately responsible for the relative magnitude of the overall ferromagnetic coupling in <b>1</b> and <b>2</b>