Comparison of simplex algorithms

A new modification of the super-modified simplex algorithm is described. The performance of this algorithm is compared with that of the super-modified simplex algorithm and the Nelder-Mead, or modified, simplex algorithm, using both mathematical functions and experimental optimization of an inductively coupled plasma spectrometer. The modification added to the super-modified simplex algorithm increases its speed and accuracy over the original super-modified algorithm.     

Simplex optimization of response-time-limited systems : A Study with a Spectrophotometric Determination of Aluminium and Mathematical Test Functions

A two-part modification to the standard simplex optimization is used to speed up the optimization of systems limited by response time. The modications are tested on a slow spectrophotometric procedure for aluminium, and on 2-, 3- and 5-parameter test functions. The modifications are shown to work for the aluminium method, with substantial time-savings, and to be statistically valid when used on the test functions. The best combination of the new modifications and the standard method are discussed.     

QSPR modeling of critical properties of organic binary mixtures

QSPR models for the critical temperatures, critical volumes, and critical pressures of binary organic mixtures are given. The binary organic mixtures have been described in terms of the mixture modification of simplex representation of molecular structure. The accuracy of the obtained models is comparable to the recommended one, the mean error ranging from 6.8 to 14.6%. The models imply that electronic polarizability is the most important factor for the critical volume and that the critical temperature and critical pressure are determined primarily by van der Waals and electrostatic interactions.     

Modulations in restricted amide rotation by steric induced conformational trapping

The rotation around the amide bond in N,N-diethyl-m-toluamide (m-DEET) has been studied extensively and often used in laboratory instructions to demonstrate the phenomenon of chemical exchange. Herein, we show that a simple modification to N,N-diethyl-o-toluamide (o-DEET) significantly alters the dynamics of the restricted rotation around the amide bond due to steric interactions between the ring methyl group and the two N-ethyl groups. This alters the classic two-site exchange due to restricted rotation around the amide bond, to a three-site exchange, with the third conformation trapped at a higher-energy state compared to the other two. This often overlooked phenomenon is elucidated using variable-temperature NMR, two-dimensional exchange spectroscopy and molecular modeling studies.     

Rotational effects in molecular crystals

The Mössbauer spectrum of ferric oxinate exhibits and asymmetric quadrupole doublet. The modification of the dynamic Mössbauer parameters (to the equal values for each line) following the irradiation, was explained by the internal oxine ligands rotation inside of the octahedral coordination.     

Atoms and molecules in cavities: A method for study of spatial confinement effects

A general method for solving the problems of spatially confined quantum mechanical systems is proposed. The method works within the framework of the model space approximation. In the case of atoms and molecules trapped into any-shape microscopic cavity (like molecular sieves or fullerenes), the method reduces to a simple modification of the commonly used basis-set quantum chemical calculations. The modification consists of a particular rotation and projection in the model space, leading to solutions better adapted to the boundary conditions of the spatial confinement than the functions that describe the free systems. To illustrate how this method works, it has been applied to the hydrogen atom confined in a spherical well, near a hard wall and confined in a cubic box. The results are also compared to the exact solutions. © 1995 John Wiley & Sons, Inc.     

Encoded dendrimers with defined chiral composition via'click' reaction of enantiopure building blocks

Dendrimers with end-groups of defined chiral composition have been prepared from alkyne functional enantio-pure building blocks obtained by selective enzymatic (ADH) ketone reductions using click chemistry. Optical rotation and enantioselective enzymatic modification is in agreement with the chiral composition of the dendrimers and permits unique molecular-level encoding of stereoisomeric dendritic libraries.     

Total synthesis of (-)- and (+)-dysibetaine

Glycidamides 6R and 6S were elaborated to (R,R)- and (S,S)-dysibetaines (1R and 1S) by intramolecular alkylation and functional group modification in 23% overall yield. The absolute stereochemistry of natural dysibetaine was established as S,S by comparison of the optical rotation of the natural product with that of the synthetic materials.     

Conformational analysis and rotational barriers of alkyl- and phenyl-substituted urea derivatives

Potential energy surfaces (PES) for rotation about the N-C(sp(3)) or N-C(aryl) bond and energies of stationary points on PES for rotation about the C(sp(2))-N bond are reported for methylurea, ethylurea, isopropylurea, tert-butylurea, and phenylurea, using the B3LYP/DZVP2 and MP2/aug-cc-pVDZ methods. The analysis of alkylureas reveals cis and (less stable) trans isomers that adopt anti geometries, whereas syn geometries do not correspond to stationary points. In contrast, the analysis of phenylurea reveals that the lowest energy form at the MP2 level is a trans isomer in a syn geometry. The fully optimized geometries are in good agreement with crystal structure data, and PESs are consistent with the experimental dihedral angle distribution. Rotation about the C(sp(2))-N bond in alkylureas and phenylurea is slightly more hindered (8.6-9.4 kcal/mol) than the analogous motion in the unsubstituted molecule (8.2 kcal/mol). At the MP2 level of theory, the maximum barriers to rotation for the methyl, ethyl, isopropyl, tert-butyl, and phenyl groups are predicted to be 0.9, 6.2, 6.0, 4.6, and 2.4 kcal/mol, respectively. The results are used to benchmark the performance of the MMFF94 force field. Systematic discrepancies between MMFF94 and MP2 results were improved by modification of several torsional parameters.     

An optimized direct method for the determination of carboxylic acids in beverages by HPLC

Summary A direct method for the simultaneous determination of tartaric, malic, lactic, acetic, citric, shikimic, fumaric and succinic acids in fruit juices and wines by isocratic reversed phase HPLC is reported.The variables (pH, ionic strength, flow and temperature) have been optimized by a modification of the original simplex method. The separation factor (s) and calibrated resolution product (r^*) have been used as criteria for selectivity optimization. After validation, the method has been applied to the determination of carboxylic acids in apple, orange and lemon juices, white and red wines and musts during the fermenation process.     

Application of a modified simplex method to the multivariable optimization of a new FIA system for the determination of osmium

A methodology based on the coupling of experimental design and a modified simplex method is proposed for the optimization of a new flow injection-kinetic system for the spectrophotometric determination of Os (IV) with m-acetylchlorophosphonazo, which has for the first time been used as chromogenic reagent in the quantitative analysis of this element. An orthogonal array design is utilized to design the experimental protocol, in which six variables are varied simultaneously, and obtain the initial simplex using 25 experiments. A modified simplex method is applied to continuously optimize the data of the orthogonal array design; the search for optimum conditions of ¶6 variables using the modified simplex method required only 25 experiments. The efficiency and simplicity of the coupling of the experimental design and the modified simplex method are attractive for the development of new analytical methods. The method has been applied to the determination of Os (IV) in a refined ore as well as in a secondary alloy and provided satisfactory results.     

Application of a modified simplex method to the multivariable optimization of a new FIA system for the determination of osmium

A methodology based on the coupling of experimental design and a modified simplex method is proposed for the optimization of a new flow injection-kinetic system for the spectrophotometric determination of Os (IV) with m-acetylchlorophosphonazo, which has for the first time been used as chromogenic reagent in the quantitative analysis of this element. An orthogonal array design is utilized to design the experimental protocol, in which six variables are varied simultaneously, and obtain the initial simplex using 25 experiments. A modified simplex method is applied to continuously optimize the data of the orthogonal array design; the search for optimum conditions of 6 variables using the modified simplex method required only 25 experiments. The efficiency and simplicity of the coupling of the experimental design and the modified simplex method are attractive for the development of new analytical methods. The method has been applied to the determination of Os (IV) in a refined ore as well as in a secondary alloy and provided satisfactory results.     

Magneto-optical properties of core-shell magneto-plasmonic Au-Co(x)Fe(3 - x)O4 nanowires

The magneto-optical properties of Au-Co(x)Fe(3?-?x)O(4) core-shell nanowires embedded in porous alumina membranes are studied. The structures were obtained by depositing Co(x)Fe(3?-?x)O(4) on the pore walls of alumina membranes by atomic layer deposition and filling the resulting nanotube with gold by electrodeposition. The effect of plasmon resonance excitation on the magneto-optical activity is clearly observed as a modification of the spectral line shape of the Kerr rotation signal.     

Evaluation of the super-modified simplex for use in chemical pattern recognition

A simplex optimization technique, the super-modified simplex (SMS), is evaluated for use in the pattern recognition analysis of low-resolution mass spectra. For the recognition of eleven functional group categories, the performances of SMS-derived weight vectors are shown to be comparable to those obtained by a previously developed modified simplex method. Data are presented which indicate that the SMS procedure requires fewer simplices and decreased computational time to converge to an optimized solution for the structural analysis problems investigated.     

Conformational preferences and internal rotation in alkyl- and phenyl-substituted thiourea derivatives

Potential energy surfaces (PES) for rotation about the N-C(sp(3)) or N-C(aryl) bond and energies of stationary points on PES for rotation about the C(sp(2))-N bond are reported for methylthiourea, ethylthiourea, isopropylthiourea, tert-butylthiourea, and phenylurea, using the MP2/aug-cc-pVDZ method. Analysis of alkylthioureas shows that conformations, with alkyl groups cis to the sulfur atom, are more stable (by 0.4-1.5 kcal/mol) than the trans forms. All minima adopt anti configurations with respect to nitrogen pyramidalization, whereas syn configurations are not stationary points on the MP2 potential surface. In contrast, analysis of phenylthiourea reveals that a trans isomer in a syn geometry is the global minimum, whereas a cis isomer in an anti geometry is a local minimum with a relative energy of 2.7 kcal/mol. Rotation about the C(sp(2))-N bond in alkyl and phenyl thioureas is slightly more hindered (9.1-10.2 kcal/mol) than the analogous motion in the unsubstituted molecule (8.6 kcal/mol). The maximum barriers to rotation for the methyl, ethyl, isopropyl, tert-butyl, and phenyl substituents are predicted to be 1.2, 8.9, 8.6, 5.3, and 0.9 kcal/mol, respectively. Corresponding PESs are consistent with the experimental dihedral angle distribution observed in crystal structures. The results of the electronic structure calculations are used to benchmark the performance of the MMFF94 force field. Systematic discrepancies between MMFF94 and MP2 results were improved by modification of selected torsion parameters and one of the van der Waals parameters for sulfur.     

Reassessing the transformation step in factor theory. The case for a non-orthogonal transformation matrix

The existing factor rotational methods (an assortment of orthogonal, oblique and simplex techniques) are assessed for their potential to be generalized for use at higher dimensions (i.e. above threefold factor space). An answer is sought to the problem of why the application of an orthogonal rotation results in mathematical solutions (those containing negative entries) rather than all positive solutions having physical and chemical meaning. Such positive solutions will be within the limits of experimental error if non-perfect data is used. An evaluation of a methodological improvement to an algorithm on factor analysis based on the optimization of them(m - 1) independent variables of a transformation matrix T ofm factors is made, and a case is presented for its introduction as a realistic alternative to the established methods.     

Détermination de la forme la plus stable de l'ortho-dichlorofluorure de benzyle par RMN en phase nématique

The value of direct couplings in o-dichlorobenzylfluoride, obtained from nematic phase NMR, lead to the conclusion that the most stable form is such that the fluorine atom is in a plane perpendicular to the benzene ring. However, the complete intepretation of these couplings in terms of geometrical parameters tends to indicate a modification of orientation with internal rotation of CH₂F.     

单分子微正则系综反应速率常数的理论研究──曲率校准和转动选态速率常数的计算

研究了微正则系综下单分子反应速率常数的理论计算公式,并将曲率因子Ａ引入含振动和转动的隧道几率表达式中,进而得到了反应速率常数表达式。应用该式研究了Ｆ─Ｃ≡Ｃ─Ｈ反应的氢迁移过程的转动选态及曲率因子对反应速率常数的影响。结果表明：在隧道效应区域内,曲率因子对速率常数的影响比较显著,它将引起速率常数的增加;转动选态对速率的影响不太明显。     

Characterization of the restricted rotation of the dimethyl groups in chemically N-terminal 13C-labeled antifreeze glycoproteins: a temperature-dependent study in water to ice through the supercooled state

Site-specific chemical modification, especially with isotopically enriched groups, allows one to study the structure and dynamics of proteins for which uniform enrichment is difficult. When the N-terminal alanine in antifreeze glycoprotein (AFGP) is replaced with an N,N-dimethyl alanine the methyl groups show signatures of slow rotation about the C-N bond. In order to separate the local dynamics of the N-terminus from the overall protein dynamics, we present a complete characterization of this dynamics. Temperature-dependent nuclear magnetic-resonance experiments from room temperature to subzero temperatures, including the supercooled state and in the presence of ice, are presented. Quantum chemical calculations are also performed on a localized N-terminus of the AFGP. Our results show that in the solution state at room temperature and in the super cooled regime, the dimethyl groups undergo a slow, restricted rotation with an unequal distribution of population between two major conformations. At lower temperatures in the presence of ice, the dynamics become much more complex due to freezing out of several conformational states. Based on these results, we conclude that the segmental dynamics of the N-terminus are local to the first residue and do not affect the overall dynamics of the protein.     

Three-dimensional PTx phase diagrams through interactive computer graphics

Interactive computer graphic techniques have been developed for the display of binary mixture phase diagrams. The diagrams are defined in temperature-pressure-composition space, and are portrayed as wireframe objects with depth perception in order to provide a three-dimensional effect. The displays used were vectro refresh workstations whose transformation hardware allows real-time rotation, rescaling, and translation of the diagrams, while software allows the extraction of constant property Px, Tx, PT and x - y plots. The equilibrium surfaces and the critical lines were calculated using the Redlich-Kwong equation of state and its Soave modification.