Programming the HP 48 Calculator to Control the Lab Works Interface

While the balanced chemical equations for a multireaction system are generally not unique, the minimum number of independent equations, R, is a characteristic property of the system. Deleting one nonspectator species from the system leads to a system with R reduced by one. In this way each system can be reduced to a single-reaction system and ultimately to a no-reaction system. The least number of chemical species that can be deleted to obtain a no-reaction system equals R. Every multireaction system, therefore, can be reduced to a number of single-reaction equations which can be balanced by any one of the standard techniques. Some examples are given where balancing by inspection is employed.     

Variable Coordination Modes Realized with a Dihydroxyalkyldiphosphane as a Hemilabile Ligand: A Combined 103Rh-NMR and Density-Functional Study

Cationic rhodium complexes of (R,R)-1,4-bis(diphenylphosphanyl)butane-2,3-diol and cyclic diolefins exhibit temperature-dependent ³¹P- and ¹⁰³Rh-NMR spectra which are best explained by a hemilabile coordination of one of the hydroxy groups to the rhodium center. A complex with this ligand bound in tridentate fashion is in equilibrium with a species with the common square-planar ligand arrangement. The ¹⁰³Rh-NMR shift of the fivefold coordinated complex is found almost 500 ppm downfield from that of a fourfold coordinated species. This effect is characteristic for an increase in coordination number. At gradient-corrected levels of density-functional theory, a corresponding species with an oxygen-rhodium contact has been located, together with other isomers. The computed trends in energies and ¹⁰³Rh chemical shifts are consistent with the experimental findings.     

Dynamic reduction of a CH4/air chemical mechanism appropriate for investigating vortex–flame interactions

This paper describes two methods, piecewise reusable implementation of solution mapping (PRISM) and dynamic steady‐state approximation (DYSSA), in which chemistry is reduced dynamically to reduce the computational burden in combustion simulations. Each method utilizes the large range in species timescales to reduce the dimensionality to the number of species with slow timescales. The methods are applied within a framework that uses hypercubes to partition multidimensional chemical composition space, where each chemical species concentration, plus temperature, is represented by an axis in space. The dimensionality of the problem is reduced uniquely in each hypercube, but the dimensionality of chemical composition space is not reduced. The dimensionality reduction is dynamic and is different for different hypercubes, thereby escaping the restrictions of global methods in which reductions must be valid for all chemical mixtures. PRISM constructs polynomial equations in each hypercube, replacing the chemical kinetic ordinary differential equation (ODE) system with a set of quadratic polynomials with terms related to the number of species with slow timescales. Earlier versions of PRISM were applied to smaller chemical mechanisms and used all chemical species concentrations as terms. DYSSA is a dynamic treatment of the steady‐state approximation and uses the fast–slow timescale separation to determine the set of steady‐state species in each hypercube. A reduced number of chemical kinetic ODEs are integrated rather than the original full set. PRISM and DYSSA are evaluated for simulations of a pair of counterrotating vortices interacting with a premixed CH₄/air laminar flame. DYSSA is sufficiently accurate for use in combustion simulations, and when relative errors are less than 1.0%, speedups on the order of 3 are observed. PRISM does not perform as well as DYSSA with respect to accuracy and efficiency. Although the polynomial evaluation that replaces the ODE solver is sufficiently fast, polynomials are not reused sufficiently to enable their construction cost to be recovered. © 2007 Wiley Periodicals, Inc. 39: 204–220, 2007     

Biparameter Equations for Calculating Kovats Retention Indices of Hydrocarbons

Abstract

Biparameter equations, in which one parameter is the boiling point of the solutes and the other is any of their physicochemical properties able to account for dispersive solute-stationary phase interactions, are obtained by regression analysis. These equations permit the calculation of Kovats retention index (I_R ) for aliphatic and aromatic hydrocarbons in complex mixtures with standard deviations close to experimental error. The linear change of regression coefficients with the work temperature allow us to obtain equations suitable for calculating I_R at any temperature on a given stationary phase. Furthermore, accurate values for the magnitudes included in the equations can be obtained starting from I_R values.

When alkylbenzenes are separated on polar phases, such as Carbowax 20M, it is necessary to add a new parameter accounting for inductive interactions. Once again, regression coefficients, except that of the boiling point which remains constant, change linearly with the polarity of the phase (Tarjan's scale) enabling the obtaining of an equation for calculating I_R on any stationary phase at a given work temperature, although constant deviations between calculated and experimental I_R , on polymeric stationary phases, are found.     

A model investigation of ab initio geometries for identity and nonidentity substitution with three‐center four‐ and three‐electron transition states

With the van't Hoff model derived from the dynamics of a regular tetrahedron in which the interstitial carbon changes its position from tetrahedral into a trigonal (bi)pyramidal configuration, the introduction of dimensionless ratio numbers (R) can serve to localize significant points on the principal reaction coordinate. These numbers are expressed as R(d) and R(n) based on transition state geometries and the number of electrons involved in the three‐center bonding, respectively. Using this concept, we obtain a model for the evaluation of different ab initio calculations based on identity and nonidentity substitution reactions for three‐center four‐ and three‐electron bonding transition states. Similar ratio numbers have been derived for proton exchange reactions. The reactions under investigation show clearly that in spite of the differences in chemical outcome the transition steps reduced to the first principles of chemical bonding are similar. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Comparative study of characteristic compounds of three species of truffle

The Panxi area in Sichuan Province is the main area for the production of truffles in China, and several species of truffle are known to exist in this region. Nevertheless, it is unclear what the differences in chemical composition between the truffles are. Using an ultra-high-performance liquid chromatography quadrupole/orbitrap high-resolution mass spectrometry coupled with Compound Discoverer 3.0, we identified chemical components in three mainly known truffles from the Panxi region. Further analysis of chemical composition differences was conducted using principal component analysis, and orthogonal partial least squares discriminant analysis. Note that, 78.9% of the variance was uncovered by the principal component analysis model. As a result of the orthogonal partial least squares discriminant analysis model, the three species of truffles (Tuber pesudohimalayense, Tuber indicum, and Tuber sinense) from Panxi were better discriminated, with R²X, R²Y, and Q² being 0.821, 0.993, and 0.947, respectively. In this study, 87 components were identified. T. pesudohimalayense contained significantly higher levels of nine different compounds than the other two species. Hence, it was possible to identify similarities and differences between three species of truffles from Panxi in terms of chemical composition. This can be used as a basis for quality control.     

Topologically entangled polymers

Summary The statistical mechanics of a ring polymer confined to a plane and entangled with many randomly placed thin rods perpendicular to the plane are considered. The entanglements are characterized by the Gauss linking number. If the statistics of the random distribution of the rods is given by only the second cumulant then it is shown that the resulting entanglement problem can be solved formally exactly. For this special case the exact solution becomes possible because the problem can be reduced to one involving the winding of the polymer around one infinitely thin rod. The exact solution can be obtained for both the annealed and the quenched random distribution of obstacles. The entanglement of the ring polymer around the obstacles leads to a repulsive topological potential which is an effective interaction between the polymer and the rods. The origin of this potential is solely due to the constraint that the winding number be conserved. It is shown that forR ²/Lll (R is the location of the polymer segment,L is the total length of the polymer, andl is the length of the monomer) the topological potential for the annealed random case goes asN ln ln(Ll/R ²) whereN is the number of obstacles whereas for the quenched random case the potential is given byC lnLl/R ², whereC is a numerical constant that depends onN.     

Copper(I)-Catalyzed Conjugate Addition/Enantioselective Protonation with Selenols and α-Substituted α,β-Unsaturated Thioamides

Herein, a copper(I)-catalyzed asymmetric conjugate addition/protonation with selenols and α-substituted α,β-unsaturated thioamides is disclosed, which affords a series of chiral selenides in high to excellent enantioselectivity. As for both selenols and α-substituted α,β-unsaturated thioamides, the reaction enjoys broad substrate scopes. The present catalytic system is also successfully applied to asymmetric selenation of β-substituted α,β-unsaturated thioamides. A [Cu-(R,R_P)-TANIAPHOS]-SePh species is characterized by its ⁷⁷Se NMR spectra, which gives a chemical shift at δ 462 ppm. Moreover, a {[Cu-(R)-TOL-BINAP]-SePh}₂ species is characterized by X-ray analysis, which confirms the formation of Cu−Se bond in the reaction. Finally, the transformations of the thioamide group to amine and thioester are demonstrated to be straightforward.     

Treatment on the electronic energy bands of the helix-symmetrical polymers (n1) by LCAO/TO-LCTO/HO-LCHO/PO

Helix-Symmetrical polymer possesses not only translation symmetry but also rotation symmetry. On the basis of this kind of symmetry, a new linear combination method named as LCAO/TO-LCTO/HO-LCHO/PO has been established to derive the secular equation for this kind of polymers. In such a manner, the order of secular equations can be reduced from n × P to P (where n is the number of atomic Orbitals in each translational unit, and P is the same number but in each helical unit), thus obtaining the maximum factorization of the secular equations and favoring the symmetrical analysis of the results. The computational program corresponding to the EHMO scheme was edited for calculating the helix-symmetrical polymers. In principle, this treatment can be applied to the other quantum chemistry computation. Take polyethylene and polyacetylene as examples, the energy bands with 2₁, 3₁ and 4₁ helical comformations were calculated by the computional program. The discussions on the influence of the variation of comformations to energy bands and the related. physical and chemical properties were given.     

Analytical-numerical solution for turbulent jet diffusion flames of hydrogen

The hydrogen fuel seems to be a good candidate to replace the energy obtained from some fossil fuels. Therefore this work explains the process of obtaining a two-step reduced chemical kinetic mechanism for the hydrogen combustion. The development of a reduced mechanism consists in eliminating reactions that produce negligible influence on the combustion process. Moreover, for this mechanism, we obtain an analytical-numerical solution for a turbulent jet diffusion flame. To quantify the intermediate species, the mixture fraction is decomposed into three parts, each part directly related to the mass fraction of a species. The governing equations are discretized using the second order finite-difference approach and are integrated in time using the second order simplified three-step Runge-Kutta scheme. Obtained results compare favorably with data in the literature for a 50/50 % volume H ₂?N ₂ jet diffusion flame. The main advantage of this strategy is the decrease of the work needed to solve the system of governing equations, by one order of magnitude for the hydrogen.     

Relationship between radical polymerization rate and initiator concentration in various solvents

Methyl methacrylate and styrene were polymerized by using 2,2′-azobis(2,4-dimethyl valeronitrile) as initiator in various solvents. When a poor solvent is used, the dependence of polymerization rate R_p on initiator concentration [C] is small and can be treated by equations for the analysis of the polymerization with primary radical termination. With a good solvent, the dependence of R_p on [C] is so large that such equations are not applicable. Thus, the [C] dependence in a good solvent is explained qualitatively through the molecular weight dependence of rate for termination between polymer radicals, based on the excluded volume effect.     

A hiperbolic sine procedure for the spectrophotometric evaluation of acidity constants for two-step overlapping equilibria

An equation relating the absorbance of the solute to the acidity constants (pK _a1 and pK _a2) and pH is derived for weak diprotic acids (diprotic bases and zwitterions). The equation is applicable in those cases in which the limiting absorbance of the species HR is intermediate between that of R and H ₂ R. The evaluation of acidity constants for two-step overlapping equilibria from spectrophotometric measurements may be carried out in this way by linear plotting. The task is solving via a hyperbolic sine linearization of the absorbance versus pH graph. The procedure has been tested with the benzidine system and found to give good results. The equation derived could also be applied to other additive properties such as chromatographic retention factors, electrophoretic mobilities, NMR chemical shifts, fluorescence measurements, or hyperpolarizability.     

Synthesis of Epigoitrin from (R)‐(+)‐4‐Hydroxy‐γ‐butyrolactone

Epigoitrin is one of the major components of several natural species, including Isatis indigotica Fort, turnip, and cabbage. It presents antithyroid and antivirus activities. Here, we report an efficient and practical method for the chemical synthesis of epigoitrin from commercially available (R)‐(+)‐4‐hydroxy‐γ‐butyrolactone.     

Microbial Transformation of Isolongifolen‐4‐one

The microbial transformation of (+)‐isolongifolen‐4‐one ( 4 ) by a number of fungi by means of a standard two‐stage fermentation technique afforded (7R)‐12‐hydroxyisolongifolen‐4‐one ( 5 ), (7S)‐13‐hydroxyisolongifolen‐4‐one ( 6 ), (11R)‐11‐hydroxyisolongifolen‐4‐one ( 7 ), (10R)‐10‐hydroxyisolongifolen‐4‐one ( 8 ), and (9R)‐9‐hydroxyisolongifolen‐4‐one ( 9 ) (Scheme). All five metabolites were found to be new, and metabolites 6 and 9 showed potent tyrosinase inhibitory activity (Table 1). The metabolites and their derivatives were characterized on the basis of spectroscopic and single‐crystal X‐ray‐diffraction techniques.     

An effective calculation procedure for two-phase equilibria in multireaction systems

In this work, we present a method for the calculation of two-phase equilibria in multireaction systems. The procedure uses a transformed composition variable in the orthogonal derivatives of the Gibbs function and the tangent plane equation to form a system of non-linear equations. We solve this system with a Newton–Raphson method and our initialization procedure uses results from the reactive stability analysis and the reactive equal area rule. With this initialization strategy, convergence occurs with only a few iterations in the numerical method. Several examples with multiple chemical reactions demonstrate the performance of our approach.     

Study of the Lipophilic Character of Xanthine and Adenosine Derivatives: II. Relationships Between Log K', RM and Log P Values

Abstract

The log k' values of a series of xanthine and adenosine derivatives were measured by means of a reversed-phase HPLC. The HPLC data were shown to be well correlated with previously reported R_M and R_MC18 values. The equations describing the relationships log k'/R_M and log k'/R_MC18 allowed the calculation of the log k' values of some compounds, which were not tested in the HPLC system. Since the relationship log k'/log P is very close to the previously described relationships R_M/log P and R_MC18/log P one can conclude that reversed-phase TLC and HPLC are very similar in describing the lipophilicity of the compounds.     

Chiral terpenes in different phases: <Emphasis Type="Italic">R</Emphasis>-(−)-camphorquinone studied by IR–Raman–VCD spectroscopies and theoretical calculations

R-(−)-camphorquinone is a bicyclical terpenoid with many usages and application in different fields. Different experimental and theoretical works reveal that there is only one stable conformer of this chiral chemical species in agreement to the sterical restriction that the bicycle introduces. In the current work, from a complete assignment of the vibrational IR and Raman spectra, we are able to explain the VCD spectrum of the title compound. The recorded spectra of R-(−)-camphorquinone in different phases have been analyzed and compared: the first one in CCl₄ solution, the second one using Nujol and Fluorolube suspensions and the third one using thin films. Finally, to study the coupling between the two C=O stretching normal modes, a NBO analysis is performed. The present work reveals that IR, Raman and VCD, combined with quantum chemical calculations, are helpful complementary techniques to characterize chiral systems, as terpenes, in different phases.     

An inverse problem in reaction kinetics

In this paper we investigate the problem of extracting information about chemical reactions involving multiple species from the time history of the concentration of each species. The mathematical model of the kinetic system leads to a system of ordinary differential equations. Our focus is to examine whether the species’ concentrations as functions of time are sufficient to determine what chemical reactions, and at what reaction rates, have occurred. We show that within the limitation of our model, there may be many candidate reaction systems that could explain the data. Using the notion of sparsity, we provide a quantitative assessment of the question of distinguishability. We further demonstrate that sparsity enforcing approaches, such as minimizing the ℓ ₁ or the ℓ ₀ norms are not reliable. Our conclusion is that additional knowledge about the kinetic system will be necessary to reliably solve this inverse problem.     

Enantioselective Syntheses of Lignin Models: An Efficient Synthesis of β‐O‐4 Dimers and Trimers by Using the Evans Chiral Auxiliary

We describe an efficient five‐step, enantioselective synthesis of (R,R)‐ and (S,S)‐lignin dimer models possessing a β‐O‐4 linkage, by using the Evans chiral aldol reaction as a key step. Mitsunobu inversion of the (R,R)‐ or (S,S)‐isomers generates the corresponding (R,S)‐ and (S,R)‐diastereomers. We further extend this approach to the enantioselective synthesis of a lignin trimer model. These lignin models are synthesized with excellent ee (>99 %) and high overall yields. The lignin dimer models can be scaled up to provide multigram quantities that are not attainable by using previous methodologies. These lignin models will be useful in degradation studies probing the selectivity of enzymatic, microbial, and chemical processes that deconstruct lignin.