理想化抽象在数学建模中的作用

理想化抽象是以抽象的理想形态表现研究对象的性质,以理想实验和理想模型为表现形式,是数学研究中采用的重要抽象方法,特别是在建立数学理论模型和数学应用模型时起到重要的作用。     

Second hydrogen atom abstraction by molecular ions

We report the observation of a new physical phenomenon of the addition of 2 hydrogen atoms to molecular ions thus forming [M + 2H]⁺ ions. We demonstrate such second hydrogen atom abstraction onto the molecular ions of pentaerythritol and trinitrotoluene (TNT). We used both gas chromatography mass spectrometry (GC‐MS) with supersonic molecular beam (SMB) with methanol added into its make‐up gas and electron ionization (EI) liquid chromatography mass spectrometry (LC‐MS) with SMB with methanol as the LC solvent. We found that the formation of methanol clusters resulted upon EI in the formation of dominant protonated pentaerythritol ion at m/z = 137 plus about 70% relative abundance of pentaerythritol molecular ion with 2 additional hydrogen atoms at m/z = 138 which is well above the 5.7% natural C¹³ isotope abundance of protonated pentaerythritol. Similarly, we found an abundant protonated TNT ion at m/z = 228 and a similar abundance of TNT molecular ion with 2 additional hydrogen atoms at m/z = 229. Upon the use of deuterated methanol (CD₃OD) as the solvent, we observed an abundant m/z = 231 (M + 2D)⁺ of TNT with 2 deuterium atoms. We found such abundant second hydrogen atom abstraction with butylglycolate and at low abundances in dioctylphthalate, Vitamin K3, phenazine, and RDX. At this time, we are unable to report the magnitude and frequency of occurrence of this phenomenon in standard electrospray LC‐MS. This observation could have important implications on the provision of elemental formula from mass spectra that are involved with protonated molecules. Accordingly, while accurate mass measurements can serve for the generation of elemental formula, their further support and improvement via isotope abundance analysis are questionable. Consequently, if a given compound can be analyzed by both GC‐MS and LC‐MS, its GC‐MS analysis can be superior for the provision of accurate elemental formulae if its EI mass spectrum exhibits abundant molecular ions such as with GC‐MS with SMB (also known as cold EI).     

A study of β-hydride abstraction from alkanediyl homobimetallic complexes [{Cp(CO)2Fe}2{μ-(CnH2n)}] (n = 4-10, Cp = η-C5H5)

The alkyl-bridged iron(II) complexes [{Cp(CO)₂Fe}₂{μ-(C_nH_2n)}] (n = 6-10, Cp = η⁵-C₅H₅) undergo both single and double hydride abstraction when reacted with one equivalent of Ph₃CPF₆ to give both the monocationic complexes, [{Cp(CO)₂Fe}₂{μ-(C_nH_2n−1)}]PF₆, and the dicationic complexes, [{Cp(CO)₂Fe}₂{μ-(C_nH_2n−2)}](PF₆)₂. The ratios of monocationic to dicationic complexes decrease with the increase in the value of n. The complexes where n = 4 and 5 undergo only single hydride abstraction under similar conditions. When reacted with two equivalents of Ph₃CPF₆, the complexes where n = 6-10 undergo double hydride abstraction to give dicationic complexes only. In contrast, the complex where n = 5 gives equal amounts of the monocationic and the dicationic complexes, while the complex where n = 4 only gives the monocationic complex. ¹H and ¹³C NMR data show that in the monocationic complexes one metal is σ-bonded to the carbenium ion moiety while the other is bonded in a η²-fashion forming a chiral metallacylopropane type structure. In the dicationic complexes both metals are bonded in the η²-fashion. The monocationic complexes where n = 4-6, react with methanol to give η¹-alkenyl complexes[Cp(CO)₂Fe(CH₂)_nCHCH₂] (n = 2-4) as the major products and σ-bonded ether products [{Cp(CO)₂Fe}₂{μ-(CH₂)_nCH(OCH₃)CH₂}] as the minor products. The complex where n = 8 reacted with iso-propanol to give the η¹-alkenyl complex [Cp(CO)₂Fe(CH₂)₆CHCH₂]. The dicationic complexes where n = 5, 8 and 9 were reacted with NaI to give the respective α, ω-dienes and [Cp(CO)₂FeI].     

Electrochemically Driven C−H Hydrogen Abstraction Processes with the Tetrachloro‐Phthalimido‐N‐Oxyl (Cl4PINO) Catalyst

The radical redox mediator tetrachloro‐phthalimido‐N‐oxyl (Cl₄PINO) is generated at a glassy carbon electrode and investigated for the model oxidation of primary and secondary alcohols with particular attention to reaction rates and mechanism. The two‐electron oxidation reactions of a range of primary, secondary, and cyclic alcohols are dissected into an initial step based on C−H hydrogen abstraction (rate constant k₁, confirmed by kinetic isotope effect) and a fast radical‐radical coupling of the resulting alcohol radical with Cl₄PINO to give a ketal that only slowly releases the aldehyde/ketone and redox mediator precursor back into solution (rate constant k₂). In situ electrochemical EPR reveals Cl₄PINO sensitivity towards moisture. DFT methods are applied to confirm and predict C−H hydrogen abstraction reactivity.     

Chlorine-atom abstraction and cluster fragmentation in the reaction of H3Re3(CO)10(MeCN)2 with the diphosphine ligand 4,5-bis(diphenylphosphino)-4-cyclopenten-1,3-dione (bpcd): X-ray diffraction structure of fac-ClRe(CO)3(bpcd)

Treatment of the activated trirhenium cluster H₃Re₃(CO)₁₀(MeCN)₂ with the diphosphine ligand 4,5-bis(diphenylphosphino)-4-cyclopenten-1,3-dione (bpcd) in CH₂Cl₂ does not afford the expected cluster product H₃Re₃(CO)₁₀(bpcd) but rather the mononuclear complex fac-ClRe(CO)₃(bpcd). The identity of fac-ClRe(CO)₃(bpcd) was determined in solution by IR and NMR (¹H and ³¹P) spectroscopies and the solid-state structure was established by X-ray diffraction analysis. fac-ClRe(CO)₃(bpcd) crystallizes in the triclinic space P-1, a = 9.958(2) Å, b = 11.991(3) Å, c = 13.676(3) Å, α = 73.230(4)°, β = 73.806(4)°, γ = 77.409(4)°, V = 1484.6(6) ų, Z = 2, and d _calc = 1.723 Mg/m³; R = 0.0367, R _w  = 0.0857 for 4253 reflections with I > 2σ(l).     

Reactions of mono- and bimolecular hydrogen transfer in alkyl radicals: analysis using the parabolic model and density functional calculations

Experimental data on monomolecular hydrogen transfer in the reactions of the type RC^·H(CH₂)_nCH₂R¹ RCH₂(CH₂)_nC^·HR¹ (n = 2—4, R and R¹ are alkyl substituents) were analyzed using the parabolic model (PM). The parameters characterizing this class of reactions were calculated. Isomerization of alkyl radicals via cyclic transition states (TS) is characterized by the following energy barriers to thermoneutral reaction E _e0: 53.5, 65.4, and 63.2 kJ mol^–1 for the six-, five-, and seven-membered TS, respectively. The E _e0 energy and the strain energy change in parallel in the series of cycloparaffins C_nH_2n. Density functional calculations of intramolecular hydrogen transfer in the n-butyl and n-pentyl radicals and of the bimolecular hydrogen abstraction from the ethane molecule by the ethyl radical were performed. The activation energies of the intra- and intermolecular hydrogen transfer were compared. The parameters of the PM were compared with the interatomic distances in the reaction center of the TS calculated by the density functional method.     

酯-二苯酮光化夺氢反应活泼自由基的ESR研究

自旋捕捉技术与ESR相结合,为检测反应过程中产生的自由基活泼中间体提供一个方便且有效的方法。近年来,国内外研究工作者利用这一方法,对固相,液相和气相中产生的活泼自由基已进行了广泛的研究^[1-12]。     

Protonation and Hydrogen Atom Abstraction Reactions in the Synthesis of the [HP7M(CO)3]2– Ions (M = Cr,W)

Ethylenediamine (en) solutions of [P₇M(CO)₃]^3– (M = Cr, W) react with weak acids to give [HP₇M(CO)₃]^2– ions where M = Cr ( 4 a ) and W ( 4 b ) in high yields. Competition studies with known acids revealed a pK_a range for 4 b in DMSO of 17.9 to 22.6. The [P₇M(CO)₃]^3– complexes also react with one-half equivalent of I₂ to give 4 through an oxidation/hydrogen atom abstraction process. Labeling studies show that the abstracted hydrogen originates from the [K(2,2,2-crypt)]⁺ ions or from the solvent (DMSO-d₆) in the absence of [K(2,2,2-crypt)]⁺ or other good hydrogen atom donors. In the solid state, the ions have no crystallographic symmetry but in solution they show virtual C_s symmetry (³¹P NMR spectroscopy) due to an intramolecular wagging process. Crystallographic data for [K(2,2,2-crypt)]₂[HP₇W(CO)₃]: triclinic, P 1, a = 10.9709(8) Å, b = 13.9116(10) Å, c = 19.6400(14) Å, α = 92.435(6)°, β = 93.856(6)°, γ = 108.413(6)°, V = 2831.2(4) ų, Z = 2, R(F) = 7.65%, R(wF²) = 14.17% for all 7400 reflections. For [K(2,2,2-crypt)]₂[HP₇Cr(CO)₃]: triclinic, P 1, a = 12.000(3) Å, b = 14.795(3) Å, c = 17.421(4) Å, α = 93.01(2)°, β = 93.79(2)°, γ = 110.72(2)°, V = 2877(2) ų, Z = 2.     

PERFORMANCE AND INITIATION MECHANISM OF ISOPROPYLTHIOXANTHONE IN SURFACE PHOTOGRAFTING

In a polymerization model with low density polyethylene (LDPE) as the substrate and acrylic acid (AA) as themonomer, the performance of isopropylthioxanthone (ITX) in initiating surface photografting polymerization was evaluated.The results show that the reactivity of photopolymerization and photografting of ITX locate between benzophenone (BP) andbenzildimethylketal (BDK) for polymerization, BDK> ITX> BP; for surface grafting polymerization, BP> ITX>BDK.These results can be explained by a reaction mechanism of the inter-molecular or intra-molecular hydrogen abstractionreaction of ITX.     

Photoinduced hydrogen abstraction‐coupling reaction mechanism of Δ5‐steroids with substituted 1, 4‐benzoquinones via electron transfer pathways

The photochemical reaction between three A⁵‐steroids (1–3) and a series of substituted 1,4‐benzoquinones and their mechanistic study were reported. The reaction in nitrogen atmosphere led to the formation of three products including the steroid‐quinone coupling compound (A), 7‐hydroxy derivatives of Δ⁵‐steroids (B) and substituted 1, 4‐hydroquinone (C). Both chemical and spectrometric evidences such as UV‐Visible spectra, ESR, chemically induced dynamic nuclear polarization (CIDNP) and cyclic voltammetry (CV) verified that the title reaction underwent a predominant photoinduced electron transfer pathway via the triplet quinone.