Computing the starting state for Gibbs-Duhem integration

Gibbs-Duhem integration implies the numerical integration of a Clapeyron equation. To start the numerical integration, an initial coexistence point and a corresponding initial slope of the Clapeyron equation are needed. In order to apply Gibbs-Duhem integration to all kinds of systems at diverse physical conditions, one has to investigate and assess the available methods that can be used to compute these initial values. This publication focuses on vapor-liquid equilibria in binary mixtures comprising chain molecules. The initial coexistence point is either computed with the NVbeta Gibbs ensemble or with the Npbeta+test molecule method with overlapping distributions, which is introduced in this publication. Although computationally demanding, the Npbeta+test molecule method with overlapping distributions is applicable at conditions where the NVbeta Gibbs ensemble fails. We investigated three methods that can be employed to compute the initial slope of the Clapeyron equation. The Widom method and the overlapping-distributions difference method provide correct values for the initial slope. The difference method does only provide the correct answer in special cases. The possibility to judge the reliability of the results makes the overlapping-distributions difference method the safest route to the initial slope. Gibbs-Duhem integration requires the frequent computation of the slope of the Clapeyron equation. This slope depends on ensemble averages of the composition. A new bias method for efficient sampling of the composition in a semigrand-canonical simulation of chain molecules is presented. This bias method considerably enhances the composition sampling in systems comprising chain molecules of different sizes.     

An alternative approach to the g-matrix: theory and applications.

Starting from the formula proposed by Gerloch and McMeeking in 1975, the electronic g-matrix is expressed as a sum of two matrices called Lambda and Sigma describing the orbital and spin contributions respectively. This approach is applied on benchmark diatomic and triatomic molecules, and on TiF3 and Cu(NH3)4(2+) using either CASPT2 or CCSD(T) methods to calculate the spin-free states and SO-RASSI to calculate spin-orbit coupling. Results compare very well to experimental data and to previous theoretical work; and, for each molecule, the anisotropy of the g-matrix is modeled by the mean of a few parameters.     

An integration method of enzyme analysis

The application of an integration method of kinetic analysis to first-order and second-order reactions is discussed with particular emphasis on enzyme analyses. Transducer signals or concentrations of products or substrates are integrated for a Fixed time and the net integral of the increased or decreased signal or concentration is related to the initial substrate or enzyme concentration. Equations are developed describing the dependence of the integrals on enzyme and substrate concentrations for first- and second-order reactions, and examples are presented illustrating different cases. The application of this method to complicated enzymatic systems is discussed.     

An accurate numerical multicenter integration for molecular orbital theory

A powerful and accurate numerical three‐dimensional integration scheme was developed especially for molecular orbital calculations. A multicenter integral is decomposed into the sum of single‐center integrals using nuclear weight functions and calculated using Gaussian quadrature rules. The decomposed single‐center integrands show strong anisotropy. With a careful selection of the Gaussian quadrature rule according to the anisotropy, it is possible to obtain an accuracy of 13 digits with a small number of integration points for the overlap integrals, normalization integrals, and molecular integrals for the hydrogen molecule. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 509–523, 1999     

Solvation thermodynamics: theory and applications

Potential distribution and coupling parameter theories are combined to interrelate previous solvation thermodynamic results and derive several new expressions for the solvent reorganization energy at both constant volume and constant pressure. We further demonstrate that the usual decomposition of the chemical potential into noncompensating energetic and entropic contributions may be extended to obtain a Gaussian fluctuation approximation for the chemical potential plus an exact cumulant expansion for the remainder. These exact expressions are further related to approximate first-order thermodynamic perturbation theory predictions and used to obtain a coupling-parameter integral expression for the sum of all higher-order terms in the perturbation series. The results are compared with the experimental global solvation thermodynamic functions for xenon dissolved in n-hexane and water (under ambient conditions). These comparisons imply that the constant-volume solvent reorganization energy has a magnitude of at most approximately kT in both experimental solutions. The results are used to extract numerical values of the solute-solvent mean interaction energy and associated fluctuation entropy directly from experimental solvation thermodynamic measurements.     

Micro free-flow electrophoresis: theory and applications

Free-flow electrophoresis (FFE) is a technique that performs an electrophoretic separation on a continuous stream of analyte as it flows through a planar flow channel. The electric field is applied perpendicularly to the flow to deflect analytes laterally according to their mobility as they flow through the separation channel. Miniaturization of FFE (μFFE) over the past 15 years has allowed analytical and preparative separation of small volume samples. Advances in chip design have improved separations by reducing interference from bubbles generated by electrolysis. Mechanisms of band broadening have been examined theoretically and experimentally to improve resolution in μFFE. Separations using various modes such as zone electrophoresis, isoelectric focusing, isotachophoresis, and field-step electrophoresis have been demonstrated.

Pulsed discharge detector: theory and applications

The pulsed discharge detector (PDD) is a significant advancement in gas chromatography (GC) detector design which can be operated in three different modes: pulsed discharge helium ionization (He-PDPID), pulsed discharge electron capture (PDECD) and helium ionization emission (PDED). The He-PDPID can detect permanent gases, volatile inorganics and other compounds which give little or no response with the flame ionization detector (FID) and has significantly better limits of detection (minimum detectable quantities (MDQs) in low picogram range) than can be achieved with a thermal conductivity detector (typically not lower than 1 ng). The PDECD has similar or better sensitivity (MDQs of 10(-15) to 10(-12) g) than radioactive source ECD but does not require licensing, wipe tests and other administrative or safety requirements which have increased over security concerns. The PDED shows promise as an extremely selective and sensitive elemental detector but a commercial unit is not presently available. In this report, the theory of operation, applications of the PDD and the practical aspects of using this novel detector are presented.     

An overview of coupled cluster theory and its applications in physics

Summary What has since become known as the normal coupled cluster method (NCCM) was invented about thirty years ago to calculate ground-state energies of closed-shell atomic nuclei. Coupled cluster (CC) techniques have since been developed to calculate excited states, energies of open-shell systems, density matrices and hence other properties, sum rules, and the sub-sum-rules that follow from imbedding linear response theory within the NCCM. Further extensions deal both with systems at nonzero temperature and with general dynamical behaviour. More recently, a new version of CC theory, the so-called extended coupled cluster method (ECCM) has been introduced. It has the potential to describe such global phenomena as phase transitions, spontaneous symmetry breaking, states of topological excitation, and nonequilibrium behaviour. CC techniques are now widely recognized as providing one of the most universally applicable, most powerful, and most accurate of all microscopicab initio methods in quantum many-body theory. The number of successful applications within physics is now impressively large. In most such cases the numerical results are either the best or among the best available. A typical case is the electron gas, where the CC results for the correlation energy agree over the entire metallic density range to within less than 1 millihartree (or <1%) with the essentially exact Green's function Monte Carlo results. The role of CC theory within modern quantum many-body theory is first surveyed, by a comparison with other techniques. Its full range of applications in physics is then reviewed. These include problems in nuclear physics, both for finite nuclei and infinite nuclear matter; the electron gas; various integrable and nonintegrable models; various relativistic quantum field theories; and quantum spin chain and lattice models. Particular applications of the ECCM include the quantum hydrodynamics of a zero-temperature, strongly-interacting condensed Bose fluid; a charged impurity in a polarizable medium (e.g., positron annihilation in metals); and various anharmonic oscillator and spin systems.     

Statistical rate theory and kinetic energy-resolved ion chemistry: theory and applications

Ion chemistry, first discovered 100 years ago, has profitably been coupled with statistical rate theories, developed about 80 years ago and refined since. In this overview, the application of statistical rate theory to the analysis of kinetic-energy-dependent collision-induced dissociation (CID) reactions is reviewed. This procedure accounts for and quantifies the kinetic shifts that are observed as systems increase in size. The statistical approach developed allows straightforward extension to systems undergoing competitive or sequential dissociations. Such methods can also be applied to the reverse of the CID process, association reactions, as well as to quantitative analysis of ligand exchange processes. Examples of each of these types of reactions are provided and the literature surveyed for successful applications of this statistical approach to provide quantitative thermochemical information. Such applications include metal-ligand complexes, metal clusters, proton-bound complexes, organic intermediates, biological systems, saturated organometallic complexes, and hydrated and solvated species.     

Silica nanowires: Growth,integration, and sensing applications

This review (with 129 refs.) gives an overview on how the integration of silica nanowires (NWs) into micro-scale devices has resulted, in recent years, in simple yet robust nano-instrumentation with improved performance in targeted application areas such as sensing. This has been achieved by the use of appropriate techniques such as di-electrophoresis and direct vapor-liquid-growth phenomena, to restrict the growth of NWs to site-specific locations. This also has eliminated the need for post-growth processing and enables nanostructures to be placed on pre-patterned substrates. Various kinds of NWs have been investigated to determine how their physical and chemical properties can be tuned for integration into sensing structures. NWs integrated onto interdigitated micro-electrodes have been applied to the determination of gases and biomarkers. The technique of directly growing NWs eliminates the need for their physical transfer and thus preserves their structure and performance, and further reduces the costs of fabrication. The biocompatibility of NWs also has been studied with respect to possible biological applications. This review addresses the challenges in growth and integration of NWs to understand related mechanism on biological contact or gas exposure and sensing performance for personalized health and environmental monitoring. Figure

Silica nanowires decorated micro-electrodes for sensing application     

Silica nanowires: Growth,integration, and sensing applications

This review (with 129 refs.) gives an overview on how the integration of silica nanowires (NWs) into micro-scale devices has resulted, in recent years, in simple yet robust nano-instrumentation with improved performance in targeted application areas such as sensing. This has been achieved by the use of appropriate techniques such as di-electrophoresis and direct vapor-liquid-growth phenomena, to restrict the growth of NWs to site-specific locations. This also has eliminated the need for post-growth processing and enables nanostructures to be placed on pre-patterned substrates. Various kinds of NWs have been investigated to determine how their physical and chemical properties can be tuned for integration into sensing structures. NWs integrated onto interdigitated micro-electrodes have been applied to the determination of gases and biomarkers. The technique of directly growing NWs eliminates the need for their physical transfer and thus preserves their structure and performance, and further reduces the costs of fabrication. The biocompatibility of NWs also has been studied with respect to possible biological applications. This review addresses the challenges in growth and integration of NWs to understand related mechanism on biological contact or gas exposure and sensing performance for personalized health and environmental monitoring.

Silica nanowires decorated micro-electrodes for sensing application

     

Extremely localized molecular orbitals: theory and applications

Orbitals that are extremely localized on molecular fragments represent a powerful tool for a number of purposes: to cite a few examples, they allow to reduce strongly the complexity of calculations on large systems and are easily transferable from one molecule to another, providing a suitable and efficient way to build up the electronic structure of large molecules. Recently, we have developed efficient algorithms to determine extremely localized molecular orbitals (ELMOs), which will be reviewed in this paper. As a rigorous localization is strictly connected to a reduction in the number of variational parameters, which reflects into an increased value of the associated energy with respect to the Hartree Fock value, we have developed a number of strategies to relax the wavefunction built up using transferred localized orbitals. The extreme localization has also been exploited in connection with the “Divide and Conquer” technique to determine the electron densities of large polypeptides assembled from orbitals computed on small model molecules. Moreover, we will discuss the recent application of the ELMOs in the framework of the hybrid QM/MM methods to describe the frontier region. We will also show that the ELMOs can be used to extract chemical interpretations from numerical results. A variety of applications will be presented.     

Comprehensive multidimensional liquid chromatography: theory and applications

Comprehensive two-dimensional (2D) liquid chromatographic (LC x LC) techniques can be considered innovative methods only recently developed and adopted in many configurations. The revolutionary aspect of comprehensive two-dimensional techniques, with respect to classical multidimensional (MD) chromatography, is that the entire sample is subjected to the 2D advantage. The major benefit is that the separation capacities of each dimension are multiplied, offering a high peak capacity to resolve samples of great complexity. The first part of the present review briefly describes the theoretical and practical aspects related to the development of a multidimensional comprehensive liquid chromatographic method. Applicational experiences in comprehensive liquid chromatography are then described, divided into four groups, according to the HPLC modes used in the two dimensions and to the nature of the samples analyzed.     

Gas chromatographic headspace analysis: its theory and applications

Gas chromatographic headspace analysis is concerned predominantly with the determination of traces of volatile compounds in samples which are difficult to analyse by conventional gas chromatography.     

An explicitly correlated Mukherjee's state specific coupled cluster method: development and pilot applications

This paper reports development of the explicitly correlated variant of Mukherjee's state specific multireference coupled cluster method (MkCC-F12). The current implementation is restricted to conventional single and double excitations and to pseudo-double excitations related to the Slater Type Geminal (STG) correlation factor using the SP ansatz. The performance of the MkCCSD-F12 was tested on calculations of singlet methylene, dissociation curve of the fluorine molecule, and the BeH(2) insertion pathway. As expected, the results of the newly developed method reconfirm the significantly faster convergence with respect to the basis set limit compared to the traditional expansion in Slater determinants. Results prove that treating the correlation factor separately for each reference is appropriate.     

Multiresolution quantum chemistry: basic theory and initial applications

We describe a multiresolution solver for the all-electron local density approximation Kohn-Sham equations for general polyatomic molecules. The resulting solutions are obtained to a user-specified precision and the computational cost of applying all operators scales linearly with the number of parameters. The construction and use of separated forms for operators (here, the Green's functions for the Poisson and bound-state Helmholtz equations) enable practical computation in three and higher dimensions. Initial applications include the alkali-earth atoms down to strontium and the water and benzene molecules.     

pH gradient high-performance liquid chromatography: theory and applications

pH gradient high-performance liquid chromatography (HPLC) is a method of reversed-phase high-performance liquid chromatography suitable for ionogenic substances. It consists in programmed increase during the chromatographic process of the eluting strength of eluent with respect to the analytes separated. On the analogy of the conventional organic modifier gradient reversed-phase HPLC, in the pH gradient approach the eluting strength of the mobile phase increases due to its changing pH: increasing in case of acids or decreasing in case of bases. At the same time the content of organic modifier remains constant. A theory of the pH gradient HPLC has been elaborated. The resulting mathematical model is easily manageable. Its ability to predict changes in retention and separation of analytes following the changes in chromatographic conditions is demonstrated. The pH gradient method is uniquely suitable to determine pKa values of analytes. An equation is presented allowing to calculate pKa values basing on appropriate retention data. The effects on pKa are discussed of the concentration of methanol in the mobile phase. The RP HPLC-derived pKa data correlate to the reference pKa values (w(w)pKa) but are not identical. That may be explained by the effects on the chromatographically determined pKa of the specific interactions of analytes with stationary phases. The proposed pH gradient RP HPLC procedure offers a fast and convenient means to get comparable acidity parameters for larger series of compounds, like drug candidates, also when the analytes are available only in minute amounts and/or as complex mixtures.     

Microfluidic integration for electrochemical biosensor applications

Electrochemical biosensors are particularly suitable for miniaturization and integration in microfluidic devices. Applications include the detection of whole cells, cell components, proteins, and small molecules to address tasks in the fields of diagnostics and food and environmental control. Microfluidic setups range from simple channels for sample transport to channels with integrated sensing electrodes to highly sophisticated platforms with additional elements for sample preparation. The design of the microfluidics depends on both the type of detection and on the application and sample material. This review summarizes recent work on electrochemical biosensors with integrated microfluidics with the focus on developments for real sample applications, particularly those including measurements with real sample media.     

The Gibbs-Duhem type relation for ionic/nonionic mixed micelles--an alternative approach to Hall's method

The micellar Gibbs-Duhem relation for two-component ionic/nonionic mixed micelles is presented in terms of the apparent bound amount to micelles. For simplicity, the ionic surfactant and a salt are both uni-uni valent electrolytes and have a common counterion species. Compared to the theory by D.G. Hall on the basis of a consideration on the Donnan equilibrium [D.G. Hall, J. Chem. Soc. Faraday Trans. 87 (1991) 3529], the present approach is simple and unambiguous. Considering changes at constant temperature and pressure, the two approaches provide nearly identical results.