Use of the bond-projected superposition principle in determining the conditional probabilities of orbital events in molecular fragments

The problem of defining and determining the multi-conditional probabilities of many-orbital events in the chemical bond system of a molecule is addressed anew within theoretical framework of the one-determinantal orbital representation of molecular electronic structure. Its solution is vital for determining the information-theoretic indices of bond couplings between molecular fragments or the reactant/product subsystems in chemical reactions. The superposition principle of quantum mechanics, appropriately projected into the occupied subspace of molecular orbitals, is used to condition the atomic orbitals or general basis functions of the self-consistent-field calculations. The conditional probabilities between the subspaces of basis functions (atomic orbitals) are derived from an appropriate generalization of the bond-projected superposition principle. They are then used to define the triply-conditional probabilities, relating one conditional event to another. The resulting expression is shown to satisfy the relevant non-negativity and symmetry requirements. It is applied to probe the π-bond coupling in butadiene and benzene.     

A computational approach to linear conjugacy in a class of power law kinetic systems

This paper studies linear conjugacy of PL-RDK systems, which are kinetic systems with power law rate functions whose kinetic orders are identical for branching reactions, i.e. reactions with the same reactant complex. Mass action kinetics (MAK) systems are the best known examples of such systems with reactant-determined kinetic orders (RDK). We specify their kinetics with their rate vector and T matrix. The T matrix is formed from the kinetic order matrix by replacing the reactions with their reactant complexes as row indices (thus compressing identical rows of branching reactions of a reactant complex to one) and taking the transpose of the resulting matrix. The T matrix is hence the kinetic analogue of the network’s matrix of complexes Y with the latter’s columns of non-reactant complexes truncated away. For MAK systems, the T matrix and the truncated Y matrix are identical. We show that, on non-branching networks, a necessary condition for linear conjugacy of MAK systems and, more generally, of PL-FSK (power law factor span surjective kinetics) systems, i.e. those whose T matrix columns are pairwise different, is \(T = T'\), i.e. equality of their T matrices. This motivated our inclusion of the condition \(T = T'\) in exploring extension of results from MAK to PL-RDK systems. We extend the Johnston–Siegel Criterion for linear conjugacy from MAK to PL-RDK systems satisfying the additional assumption of \(T = T'\) and adapt the MILP algorithms of Johnston et al. and Szederkenyi to search for linear conjugates of such systems. We conclude by illustrating the results with several examples and an outlook on further research.     

Synthesis,crystal structure,and kinetics of thermal decomposition of the Zn(II) complex with vanillin

A complex [Zn(C₈H₇O₃)₂(H₂O)₂] (C₈H₈O₃ is vanillin) has been synthesized and characterized by IR, elemental analysis, and X-ray diffraction single-crystal analysis. The crystals are monoclinic, space group C2/c, a = 22.236(8) Å, b = 10.594(2) Å, c = 7.8190(16) Å, α = 89.90(3)°, β = 106.87(4)°, γ = 89.99(3)°, V = 1762.6(8) ų, Z = 4, F(000) = 832, S = 1.079, ρ _c = 1.521g cm^?3, R = 0.0221, R _w = 0.0604, μ = 1.433 mm^?1. The Zn²⁺ ion is six-coordinated with a distorted octahedron geometry. The complex forms a three-dimensional network through intermolecular hydrogen bonds. The thermal decomposition kinetics of the complex for the second stage was studied under non-isothermal conditions by the TG and DTG methods. The kinetic equation can be expressed as dα/dt = Ae^?E/RT 2(1 ? α)[1 ? ln(1 ? α)]^1/2. The kinetic parameters (E, A), activation entropy ΔS ^≠, and activation free-energy ΔG ^≠ were also gained.     

Spectral and kinetic investigation of interaction of 3,3′-diethyl-9-chlorothiacarbocyanine perchlorate with DNA

Interaction of the meso-substituted carbocyanine dye 3,3′-diethyl-9-chlorothiacarbocyanine (DCTC) perchlorate with DNA in phosphate buffer solutions (pH 7) was studied by spectral and kinetic methods. It was shown that the dye mainly exists in the cis-isomer form in water and aqueous-alcoholic solutions. The interaction with DNA leads to the formation of a trans-DCTC complex, which gradually (over a few tens of minutes) converts into the complex of the dye cis-isomer. It was revealed that the reactant concentration and ionic strength of solution have a considerable effect on the kinetic characteristics of trans-cis-reorganization of DCTC complexes, thus indicating a complex character of the process.     

Asymmetric oxidation of verbenone ethylene dithioacetal

Asymmetric oxidation of verbenone ethylene dithioacetal with m-chloroperoxybenzoic acid at different substrate-to-oxidant ratios in methylene chloride at ?10°C gave previously unknown (1S,1′S,2S,3′S,5S)-4,6,6-trimethylspiro[bicyclo[3.1.1]hept-3-ene-2,2′-[1,3]dithiolane] 1′,3′-dioxide, (1S,2S,3′S,5S)-4,6,6-trimethylspiro[bicyclo[3.1.1]hept-3-ene-2,2′-[1,3]dithiolane] 1′,1′,3′-trioxide, and (1S,5S)-4,6,6-trimethylspiro[bicyclo-[3.1.1]hept-3-ene-2,2′-[1,3]dithiolane] 1′,1′,3′,3′-tetraoxide whose structure was determined by X-ray analysis.     

Adjustable crystalline stereocomplexes from enantiopure gradient polycarbonates

Stereoselective interaction was observed in the mixture of enantiopure gradient polycarbonate (denoted as PCOPC-g-PCPC, originated from the enantioselective terpolymerization of CO₂, 3,4-epoxytetrahydrofuran (COPO) and cyclopentene oxide (CPO)) and various isotactic polycarbonates with opposite configuration in chloroform solution. The resultant crystalline stereocomplexes exhibit enhanced thermal stability and new crystalline behaviors, significantly distinct from their parent polymers. It was found that the cocrystallization selectively occurred between (R)-PCOPC (CO₂/COPO copolymer) and (S)-PCOPC-enriched segment in the gradient terpolymer (S)-PCOPC-g-PCPC, while (R)-PCPC (CO₂/CPO copolymer) selectively complexed with (S)-PCPC-enriched segment. No stereocomplexation was observed between (S)-PCOPC-g-PCPC and (S)-PCOPC or (S)-PCPC. This study is beneficial to finding new routes to prepare various semicrystalline materials having a wide variety of physical properties and degradability.     

Effect of donor and acceptor properties of solvents on the kinetics of photoreduction of sterically hindered <Emphasis Type="Italic">о</Emphasis>-benzoquinones

Effect of the solvent nature on the kinetics of photoreduction of 3,6-di-tert-butyl-1,2-benzoquinone and its six derivatives in the presence of N,N-dimethylaniline and 4-(N,N-dimethylamino)benzaldehyde has been investigated. It has been found that for the о-quinone—amine pair, for which the free energy change of electron transfer is ΔG_e > +0.11 eV, the rate constant of о-quinone photoreduction k_H decreases proportionally to the increase in the acceptor number of the solvent. For the о-quinone—amine pair with ΔG_e < +0.11 eV, the k_H value decreases proportionally to the increase in the donor number of the solvent. It has been established that the enhancement of the electron-acceptor properties of the solvent leads to the emergence of kinetic isotope effect for the reactant pairs of 3,6-di-tert-butyl-1,2-benzoquinone and 4,5-dimethoxy-3,6-di-tert-butyl-1,2-benzoquinone with N,N-di-methylaniline (ΔG_e = +0.11 and +0.22 eV, respectively).     

Dual Stereochemical Control in Reaction of Di- and Trialkyl Phosphites with Aldimines

Stereochemistry of addition of di- and trialkyl phosphites to C=N compounds was investigated. Reactions of achiral dialkyl phosphites with chiral aldimines as well as that of chiral di-(1R,2S,5R)-menthyl phosphite with achiral aldimines result in low diastereomeric enrichment of the addition compound. Reaction stereoselectivity increased when supplementary chiral inductor was introduced to the reaction system. Reaction of di-(1R,2S, 5R)-menthyl phosphite with (S)-α-methylbenzylbenzaldimine proceeds as concerted asymmetric induction to form practically one diastereomer of N-substituted aminophosphonic acid. However, reaction of di-(1R,2S, 5R)-menthyl phosphite with (R)-α-methylbenzylbenzaldimine proceeded as not concerted asymmetric induction, and diastereomeric enrichment of the product was low. By chemical extrapolation, absolute configuration of compounds formed was established. Tri-(1R,2S,5R)-menthyl phosphite reacts with C=N compounds in the presence of boron trifluoride etherate to form aminophosphonic acid derivatives with the absolute configuration opposite to that appearing in the reaction of di-(1R,2S,5R)-menthyl phosphite with the same C=N compounds.     

Preparation and characterization of the inclusion complexes of equol with sulfobutylether-β-cyclodextrin: their antioxidant activity and dissolution evaluation

The formation of inclusion complexes between S-(?)-equol (SEq) and cyclodextrins (CDs) was investigated. The binding constant (K_c) of the SEq/sulfobutylether-β-cyclodextrin (SBE-β-CD) inclusion complex was determined to be 1600 L/mol based on UV data. The phenyl ring of the SEq molecule was found to be inserted from the secondary hydroxyl face of the SBE-β-CD as evidenced from ¹H–¹H rotating frame nuclear Overhauser effect spectroscopy (ROESY) NMR. The thermal properties of the solid SEq/SBE-β-CD inclusion complexes prepared by physical mixing, kneading and freeze-drying methods were studied by differential scanning calorimetry. For the solid complex obtained by the freeze-drying method, the endothermic peak corresponding to the melting point of SEq disappeared. The solid SEq/SBE-β-CD complexes exhibited a high score in antioxidant activity evaluation tests compared to SEq alone. Dissolution test revealed that the solid complex obtained by freeze-drying method had improved dissolution of SEq.     

Chromatographic Separation of Bupivacaine Enantiomers by HPLC: Parameters Estimation of Equilibrium and Mass Transfer Under Linear Conditions

Bupivacaine is an amide type local anesthetic widely used in surgery and obstetrics because of its sustained peripheral and central nerve blockade. R-(+)-bupivacaine is more toxic to the central nervous and the cardiovascular systems than S-(?)-bupivacaine. To obtain S-(?)-bupivacaine with high degree of purity using a continuous simulated moving bed (SMB) unity, equilibrium and mass transfer parameters under dilute conditions were obtained by pulse experiments using 0,0′-bis[4-terc-butyl-benzoyl]-N,N′-diallyl-L-tartar diamide immobilized in silica (Kromasil^® CHI-TBB). The linear equilibrium constants were found to be 2.12 and 2.91 for R-(+)-and S-(?)-bupivacaine, respectively. Axial dispersion coefficients were found to be practically the same for both enantiomers. A fast kinetic of mass transfer was observed. The internal resistance to the mass transfer controls all the mass transfer process in this chiral column and the pore diffusion coefficients were of the order 10^?7cm²/s. The equilibrium and mass transfer parameters will be employed in future simulation and design of operating conditions of SMB unity.     

Synthesis and piezoelectric properties of <Emphasis Type="Italic">N</Emphasis>-phthaloylglutamic acid derivatives

The (S,S)- and (R,R)-enantiomers of dimethyl 2,4-diphthalimidoglutarate were synthesized by nucleophilic substitution of bromine in dimethyl (2S,4RS)-4-bromo-N-phthaloyl-glutamate upon treatment with potassium phthalimide, followed by separation. The crystal structure of the obtained compounds was studied by X-ray diffraction. Crystals of enantiomerically pure dimethyl 4-hydroxy- and 4-phthalimido-N-phthaloylglutamates were found to possess a noticeable piezoelectric activity.     

Pyrrolidine synthons for β-lactams

Fused tricyclic aziridines, methyl rel-(2R,2aR,3R,4R,4aR,4bS)- and rel-(2S,2aR,3R,4R,4aR,4bS)-4-hydroxy-2,4a-dimethoxyhexahydro-1-oxa-2b-azacyclopropa[cd]pentalene-3-carboxylates, have been synthesized as possible precursors to β-lactams. The product structure has been determined by two-dimensional NMR techniques in combination with computational methods.     

<Emphasis Type="Italic">S</Emphasis>-functional derivatives of 3,4-dihydro-2<Emphasis Type="Italic">H</Emphasis>-1,4-thiasilines

The first cyclic unsaturated S-functional derivatives of 4,4-diphenyl-3,4-dihydro-2H-1,4-thiasiline, S-oxide, S,S-dioxide, and S-sulfonimide, were prepared. Oxidation of the hydrolytically less stable 4,4-dimethyl-3,4-dihydro-2H-1,4-thiasiline leads to the corresponding sulfoxide and sulfone along with the ring opening products, siloxanes containing the sulfoxide or sulfonyl group.     

Alternate solutions for two particular third order kinetic rate laws

Alternate solutions to third order rate law expressions which are first order in one reactant and second order in another for the generalized reaction \({{aA}+{bB}\mathop \rightarrow \limits^{k_A }{P}}\) with a limiting reactant and for simple cubic autocatalysis \({{A}+{ 2B}\mathop \rightarrow \limits^{k_A }{3B}}\) are presented and discussed. These solutions are expressed in terms of the Lambert function W[x] with argument x(t) = α exp(α ? β t), where α and β are empirical parameters. These expressions permit the concentrations of the reactant species to be explicitly represented as dependent functions of time. For the generalized reaction, the solution involves considering exactly which species is limiting, so that the correct branch of the Lambert function can be determined. For simple cubic autocatalysis, the solution is shown to be consistent with the characteristics associated with clock reactions. An exact expression for the “induction time” associated with a clock reaction described by this mechanism is also derived.     

New chiral block for cyclopentanoids synthesis

Hydroxymethylation of bicyclic allylsilane, (3aR,6R,6aS)-3,3a,6,6a-tetrahydro-6-(trimethylsilyl)-cyclopenta[c]furan-1-one with formaldehyde by Prins reaction proceeds via S_E2' mechanism with the formation of anti-addition product. Some reactions of obtained (3aS,4S,6aR)-4-(hydroxymethyl)-3,3a,4,6a-tetrahydro-1H-cyclopenta[c]furan-1-one were investigated.     

Phase equilibria in the BaS–Ga<Subscript>2</Subscript>S<Subscript>3</Subscript> system

In the BaS–Ga₂S₃ system, the following compounds form: congruently melting compound BaGa₄S₇ (rhombic system, space group Pmn2₁, a = 1.477 nm, b = 0.624 nm, c = 0.593 nm, and T_melt = 1490 K) and incongruently melting compounds BaGa₂S₄ (cubic system, space group Pa3, a = 1.2661 nm, and Tmelt = 1370 K), Ba₂Ga₂S₅ (monoclinic system, space group C2/c, a = 1.529, b = 1.479, c = 0.858 nm, ß = 106.04°, and T_melt = 1150 K), Ba₃Ga₂S₆ (monoclinic system, space group C2/c, a = 0.909 nm, b = 1.448 nm, c = 0.903 nm, ß = 91.81°, and T_melt = 1190 K), Ba₄Ga₂S₇ (monoclinic system, space group P2₁/m, a = 1.177 nm, b = 0.716 nm, c = 0.903 nm, ß = 108.32°, and T_melt = 1230 K), and Ba₅Ga₂S₈ (rhombic system, space group Cmca, a = 2.249 nm, b = 1.215 nm, c = 1.189 nm, and T_melt = 1480 K). The compositions of eutectics are 38 and 72 mol % Ga₂S₃, and their melting points are 1120 and 1160 K, respectively. The BaS solubility in γ-Ga₂S₃ at 1070 K reaches 3 mol %.     

Synthesis of <Emphasis Type="Italic">ortho</Emphasis>-carboranyl derivatives of (<Emphasis Type="Italic">S</Emphasis>)-asparagine and (<Emphasis Type="Italic">S</Emphasis>)-glutamine

(S)-Asparagine and (S)-glutamine ortho-carboranyl derivatives with free amino and carboxy groups in the α-position were synthesized. By an example of N ^γ-(1,2-dicarba-closo-dodecarboran-3-yl)-(S)-glutamine it was demonstrated that the developed synthetic approach carboranyl derivatives of amino acids allowed the preparation of optically pure isomers.     

Percolation in the model of random successive adhesion of anisotropic particles

Numerical studies of random successive adsorption (the RSA model) of rectangular particles on a flat substrate are performed and the dependences of saturation concentration and the percolation threshold on the parameters of a model are determined. The dependences of saturation concentration φ _j∞ on the particle diameter-to-length ratio r and the parameter of orientational order S are found. Correlations between the ? _j∞(r) function and excluded surface area are discussed. It is revealed that for highly ordered systems (S ≈ 1), the saturation concentration φ _j∞ is equal to 0.557 ± 0.005 and is virtually independent of r. For partially ordered systems, the ? _j∞ value decreases with an increase in r and in the r → ∞, ? _j∞ → 0. Percolation transition and electrical connectivity for the systems studied can take place only under the assumption of the tunnel mechanism of conductivity through gaps with finite thicknesses. The minimum thickness of tunnel gaps, at which percolation can occur, rises with increasing r and decreasing S.     

The internal rotation potential functions of the methacryloyl chloride molecule in the ground and excited electronic states

The systems of torsional vibration levels of the trans and cis methacryloyl chloride isomers in the ground (S ₀) and excited (S ₁) electronic states obtained by analyzing the vibrational structure of the gas-phase UV spectrum were used to reproduce the internal rotation potential functions of the molecule in both electronic states. The kinematic F factor in the S ₀ and S ₁ electronic states was calculated taking into account the relaxation of geometric parameters depending on the internal rotation angle. The internal rotation potential function parameters in the S ₀ state are substantially different from the parameters obtained using the torsional levels of the IR Fourier transform spectrum; at the same time, they are substantiated by quantum-mechanical calculations.     

2,6-Disubstituted 4-azidopyrimidines: synthesis,kinetic and thermodynamic studies of azide-tetrazole rearrangement by NMR spectroscopy

Thermodynamic and kinetic parameters of the tautomeric tetrazole-azide rearrangement for a series of 2,6-disubstituted 4-azidopyrimidines are determined by NOESY/EXSY and DNMR: ΔH = 15—28 kJ mol^–1; ΔS = 47—65 J mol^–1 К–1; Е _a = 93—117 kJ mol^–1; lgA = 15.1—18.9. They are dependent on electronic properties of the substituents and the polarity of solvent.