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

Ferromagnetic Coupling Through the End-to-End Thiocyanate Bridge in Cobalt(II) and Nickel(II) Chains

The preparation, spectroscopic characterization, and X-ray crystal structure of two novel one-dimensional compounds of formula [M^II(tppz)­(NCS)­(μ-1,3-NCS)]_<i>n</i> [tppz = 2,3,5,6-tetrakis­(2-pyridyl)­pyrazine and M = Co­(<b>1</b>) and Ni (<b>2</b>)] are reported. <b>1</b> and <b>2</b> are isomorphous compounds, and they crystallize in the <i>P</i>2₁/<i>n</i> space group. Their structures are made up of zigzag chains of cobalt­(II) (<b>1</b>) and nickel­(II) ions (<b>2</b>) bridged by single end-to-end thiocyanate groups with a tridentate <i>tppz</i> molecule and a terminally bound thiocyanate-<i>N</i> ligand achieving distorted MN₅S octahedral surroundings around each metal center. The main source of the distortion of the ideal octahedron is due to the geometrical constraints issued from the occurrence of two fused five-member chelate rings of the tridentate <i>tppz</i> ligand, the values of the N–M–N bond angles covering the range 75.58(9)–78.66(9)°. The M–N bond lengths vary in the range 2.025(3)–2.116­(29 (<b>1</b>) and 2.001(2)–2.079(2) Å (<b>2</b>), and they are shorter than the M–S bond distance [2.6395(10) (<b>1</b>) and 2.5225(9) Å (<b>2</b>)]. The values of the intrachain metal–metal separation are 6.4197(7) (<b>1</b>) and 6.3257(5) Å (<b>2</b>). The magnetic properties of <b>1</b> and <b>2</b> have been investigated in the temperature range 1.9–300 K. Both compounds exhibit intrachain ferromagnetic interactions with values of the magnetic coupling (<i>J</i>) of +4.60 (<b>1</b>) and +7.82 cm^–1 (<b>2</b>) [the spin Hamiltonian being defined as <i>Ĥ</i> = −<i>J</i>Σ_{<i>i</i> = 1}^<i>n</i>–1<i>Ŝ</i>_<i>i</i><i>Ŝ</i>_<i>i</i>+1]

Slow Relaxation of the Magnetization in a 4,2-Wavelike Fe^III₂Co^II Heterobimetallic Chain

The reaction of the low-spin iron­(III) complex [Fe­(dmbpy)­(CN)₄]⁻ (<b>1</b>) with fully solvated cobalt­(II) ions affords the cyanide-bridged heterobimetallic chain {[Fe^III(dmbpy)­(CN)₄]₂Co^II(H₂O)₂}<i>_n</i> · 4<i>n</i>H₂O (<b>2</b>), which exhibits intrachain ferromagnetic coupling and double slow relaxation of the magnetization

Self-Assembly of the Hexabromorhenate(IV) Anion with Protonated Benzotriazoles: X‑ray Structure and Magnetic Properties

Two novel Re^IV compounds of formulas [HBTA]₂­[Re^IVBr₆] (<b>1</b>) and [HMEBTA]₂­[Re^IVBr₆] (<b>2</b>) [BTA = 1<i>H</i>-benzotriazole and MEBTA = 1-(methoxy­methyl)-1<i>H</i>-benzotriazole] have been synthesized and magneto-structurally characterized. <b>1</b> and <b>2</b> crystallize in the triclinic system with space group <i>P</i>1̅. In both compounds, the rhenium ion is six-coordinate, bonded to six bromo ligands in a regular octahedral geometry. Short Re^IV–Br···Br–Re^IV contacts, π–π stacking, and H-bonding interactions occur in the crystal lattice of both <b>1</b> and <b>2</b>, generating novel supramolecular structures based on the Re^IV. The different dispositions of the cations and the intermolecular Br···Br contacts in <b>1</b> and <b>2</b> play an important structure–property role, with the magnetic properties of <b>1</b> and <b>2</b> revealing a significant antiferromagnetic coupling between Re^IV ions through intermolecular Br···Br interactions. In <b>1</b>, these interactions account for a maximum in the magnetic susceptibility at ca. 10 K

Homo- and heterometallic complexes constructed from hexafluoroacetylacetonato and Schiff-base complexes as building-blocks

<p>Three new homo- and heterotrimetallic complexes have been synthesized and crystallographically characterized: [Cu₂(saldmpn)₂(<i>μ</i>-OCH₃)₂Cu₂(hfac)₂] (<b>1</b>), [Ni₂(valaepy)₂(hfac)₂] (<b>2</b>), [Cu(saldmpn)Co(hfac)₂] (<b>3</b>) [H₂saldmpn is the Schiff-base resulting from condensation of salicylaldehyde with 2,2-dimethyl-1,3-diaminopropane and Hvalaepy results from the reaction of <i>o</i>-vanillin with 2-(2-aminoethyl)pyridine)]. The structure of <b>1</b> consists of a neutral tetranuclear species that can be viewed as resulting from mutual coordination of one {(hfac)Cu(<i>μ</i>-OCH₃)₂(Cu(hfac)} and two {Cu(saldmpn)} building blocks. Compound <b>2</b> is a binuclear complex that results from two {Ni(hfac)(valaepy} fragments, the nickel(II) ions bridged by the two phenoxide-oxygens. The heterobinuclear complex <b>3</b> results from coordination of the [Cu(saldmpn)] metalloligand to cobalt(II) from the {Co(hfac)₂} unit. The magnetic properties of <b>1–3</b> have been investigated from 1.9 to 300 K. An overall ferromagnetic behavior is observed for <b>1</b> and <b>2</b> leading to <i>S</i> = 2 low-lying spin state for each one. In the case of <b>3</b>, a non-magnetic ground state results because of the occurrence of an intramolecular antiferromagnetic coupling between the copper(II) ion and the high-spin cobalt(II) ion, this last one behaving as an effective spin <i>S</i>_eff = ½ at low temperatures where only the ground Kramers doublet of Co(II) is thermally populated. The values of the intramolecular magnetic couplings in <b>1–3</b> are compared with those from the literature on related systems.</p

Homo- and heterometallic complexes constructed from hexafluoroacetylacetonato and Schiff-base complexes as building-blocks

<p>Three new homo- and heterotrimetallic complexes have been synthesized and crystallographically characterized: [Cu₂(saldmpn)₂(<i>μ</i>-OCH₃)₂Cu₂(hfac)₂] (<b>1</b>), [Ni₂(valaepy)₂(hfac)₂] (<b>2</b>), [Cu(saldmpn)Co(hfac)₂] (<b>3</b>) [H₂saldmpn is the Schiff-base resulting from condensation of salicylaldehyde with 2,2-dimethyl-1,3-diaminopropane and Hvalaepy results from the reaction of <i>o</i>-vanillin with 2-(2-aminoethyl)pyridine)]. The structure of <b>1</b> consists of a neutral tetranuclear species that can be viewed as resulting from mutual coordination of one {(hfac)Cu(<i>μ</i>-OCH₃)₂(Cu(hfac)} and two {Cu(saldmpn)} building blocks. Compound <b>2</b> is a binuclear complex that results from two {Ni(hfac)(valaepy} fragments, the nickel(II) ions bridged by the two phenoxide-oxygens. The heterobinuclear complex <b>3</b> results from coordination of the [Cu(saldmpn)] metalloligand to cobalt(II) from the {Co(hfac)₂} unit. The magnetic properties of <b>1–3</b> have been investigated from 1.9 to 300 K. An overall ferromagnetic behavior is observed for <b>1</b> and <b>2</b> leading to <i>S</i> = 2 low-lying spin state for each one. In the case of <b>3</b>, a non-magnetic ground state results because of the occurrence of an intramolecular antiferromagnetic coupling between the copper(II) ion and the high-spin cobalt(II) ion, this last one behaving as an effective spin <i>S</i>_eff = ½ at low temperatures where only the ground Kramers doublet of Co(II) is thermally populated. The values of the intramolecular magnetic couplings in <b>1–3</b> are compared with those from the literature on related systems.</p

Two-Dimensional Coordination Polymers Constructed by [Ni^IILn^III] Nodes and [W^IV(bpy)(CN)₆]^2– Spacers: A Network of [Ni^IIDy^III] Single Molecule Magnets

Three isomorphous two-dimensional (2D) coordination polymers of general formula {[Ni^II(valpn)­Ln^III­(NO₃)­(H₂O)­(μ-NC)₄W^IV­(bipy)­(CN)₂]­·<i>x</i>H₂O­·<i>y</i>CH₃CN}_<i>n</i> have been synthesized by reacting Ph₄P­[W^V(CN)₆­(bipy)] with the heterodinuclear [Ni^IILn^III(valpn)­(O₂NO)₃] complexes [H₂valpn = 1,3-propanediyl-bis­(2-iminomethylene-6-methoxyphenol), bipy = 2,2′-bipyridine, and Ln = Gd (<b>1</b>), Dy (<b>2</b>), and Tb (<b>3</b>) with <i>x</i> = 2 (<b>1</b>), 3.9 (<b>2</b>), and 3.35 (<b>3</b>) and <i>y</i> = 2.50 (<b>1</b>), 2 (<b>2</b>), and 1.8 (<b>3</b>)]. Their crystal structures consist of [Ni^IILn^III] 3d-4f nodes which are connected by [W^IV(bipy)­(CN)₆]^2– diamagnetic linkers resulting from the reduction of W^V to W^IV during the reaction process. The Ni­(II) and Ln­(III) ions occupy the inner and outer coordination sites of the dideprotonated valpn ligand, respectively, and they are doubly bridged by the phenoxo oxygen atoms of such a ligand. The value of Ni­(II)···Ln­(III) separation through this bridge is 3.4919(10) (<b>1</b>), 3.4760(10) (<b>2</b>), and 3.4799(9) (<b>3</b>) Å, and those of the angles at the bridgehead phenoxo atoms are 106.6(2) and 107.3(2) (<b>1</b>), 106.9(2), and 107.8(2) (<b>2</b>) and 106.5(2)–106.8(2)° (<b>3</b>). Each W­(IV) is eight-coordinated with a bidentate bipy molecule and six cyanide-carbon atoms building a somewhat distorted square antiprism environment. The rare-earth cations are nine-coordinated, the donor atoms describing a monocapped square antiprism for <b>1</b> and <b>3</b> and a tricapped trigonal prism for <b>2</b>. Magnetic susceptibility measurements in the temperature range 1.9–300 K show the occurrence of ferromagnetic interactions between the Ni­(II) and Ln­(III) ions in <b>1</b>–<b>3</b>. Frequency-dependent alternating susceptibility signals were observed for the Dy^III derivative below 8.0 K under an applied dc field of 2500 G indicating the presence of slow magnetic relaxation with values of the pre-exponential factor (τ₀) and energy barrier (<i>E</i>^#) of ca. 5.7 × 10^–8 s and 15.9 cm^–1, respectively. Complex <b>2</b> constitutes the first example of a 2D 3d-4f heterobimetallic single molecule magnet (SMM)

Effect of Protonated Organic Cations and Anion−π Interactions on the Magnetic Behavior of Hexabromorhenate(IV) Salts

Two novel Re^IV compounds of formula (Hbpym)₂[Re^IVBr₆]·4H₂O (<b>1</b>) and (H₄biim)­[Re^IVBr₆]·4H₂O (<b>2</b>) [Hbpym⁺ = 2,2′-bipyrimidinium cation and H₄biim²⁺ = 2,2′-biimidazolium dication] have been prepared and magnetostructurally characterized. <b>1</b> and <b>2</b> exhibit distinct crystal packing, and the presence of weak intermolecular contacts, such as Re–Br···Br–Re (<b>1</b> and <b>2</b>), Re–Br···(H₂O)···Br–Re (<b>1</b> and <b>2</b>), and Re–Br···π···Br–Re (<b>2</b>), lead to different magnetic behaviors. While <b>1</b> is antiferromagnetic, <b>2</b> is a ferromagnetic compound and indeed the first example of ferromagnetic salt based on the hexabromorhenate­(IV) anion. These results suggest a straightforward synthetic route to the preparation of new ferromagnetically coupled Re^IV compounds

Oxotris(oxalate)niobate(V): An oxalate delivery agent in the design of building blocks

<p>This work concerns the oxalate delivery process that occurs when using (NH₄)₃[NbO(C₂O₄)₃]·6H₂O as a suitable oxalate source in the synthesis of two compounds, [Cu(dmphen)(C₂O₄)(H₂O)] (<b>1</b>) and [{Cu(dmphen)(CH₃OH)}₂(μ-C₂O₄)](ClO₄)₂ (<b>2</b>) (dmphen = 2,9-dimethyl-1,10-phenanthroline). {[Fe{HB(pz)₃}(CN)₂(μ-CN)]₂[{Cu(dmphen)}₂(μ-C₂O₄)]}∙<i>x</i>CH₃OH (<b>3</b>) (2.0 ≤ <i>x</i> ≤ 2.4) was obtained by reacting <b>2</b> and PPh₄[Fe{HB(pz)₃}(CN)₃]∙H₂O [ = tetraphenylphosphonium and  = tris(pyrazolyl)borate]. Crystal structures of <b>1</b>–<b>3</b> have been determined by single-crystal X-ray diffraction experiments: <b>1</b> is a mononuclear trigonal bipyramidal copper(II) species, <b>2</b> is a centrosymmetric oxalato-bridged dicopper(II) complex, and <b>3</b> consists of centrosymmetric tetranuclear units with intramolecular iron–copper and copper–copper distances around 5.010(1) and 5.1833(9) Å, respectively. Variable-temperature magnetic measurements of <b>2</b> and <b>3</b> were carried out from 50 to 350 (<b>1</b>) and 1.9 to 300 K (<b>3</b>). A strong antiferromagnetic interaction between copper(II) ions occurs in <b>2</b> (<i>J</i> = −340 cm⁻¹, the spin Hamiltonian being defined as ). Analysis of the magnetic data of <b>3</b> shows magnetic interactions across the oxalate (<i>J</i>₁ = −341 cm⁻¹) and single cyanide (<i>J</i>₂ = +12.9 cm⁻¹) … (<i>J</i>₂ = +12.9 cm⁻¹) bridges . Simple symmetry considerations of the interacting magnetic orbitals in <b>2</b> and <b>3</b> provide a clear picture of the exchange pathways involved in these complexes.</p

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>