Coding of infrared spectra for retrieval purposes by application of information theory

Summary Information contents of the identification by retrieval with binary coded infrared spectra of saturated and unsaturated hydrocarbons, ethers and carbonyl compounds have been calculated, thereby taking into account the correlations between the peaks. Use has been made of spectra that were recorded and coded in a standardised way. As a result the negative influence of the errors on the information contents could be neglected. Information contents appeared to be strongly dependent on the type of compound contained in the library (typical 15–40 bits) and on the intensity threshold used for judging about the presence or absence of a peak in a certain interval (preferably between 3 and 10%). A code based upon a division of the spectral range into 140 equal wavenumber intervals must be preferred to a division into 140 equal wavelength intervals. It has been found that for retrieval two spectral ranges are of particular interest, viz. 3600–2800 cm^–1 and 1300–900 cm^–1.

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Codierung von Infrarotspektren für die Bibliothekssuche unter Anwendung der Informationstheorie

Zusammenfassung Die Informationsgehalte für die Identifizierung durch Vergleich binär codierter Infrarotspektren von gesättigten und ungesättigten Kohlenwasserstoffen, Alkoholen, Äthern und carbonylhaltigen Verbindungen wurden unter Berücksichtigung der Korrelationen zwischen den Banden berechnet. Die benötigten Spektren wurden auf standardisierte Weise registriert und codiert, damit der negative Einfluß der Ungenauigkeiten auf die Informationsgehalte außer Betracht bleiben konnte. Die Informationsgehalte zeigten sich äußerst abhängig vom Typ der in der Bibliothek gesammelten Substanzen (kennzeichnend sind 15–40 Bits) und von der zur Bestimmung der An-oder Abwesenheit einer Bande in einem Wellenlängen-Intervall gewählten Intensitätsgrenze (empfohlen zwischen 3 und 5%). Eine Codierung aufgrund der Aufteilung des Spektralbereichs in 140 gleiche Wellenzahl-Intervalle ist einer Aufteilung in 140 gleiche Wellenlängen-Intervalle vorzuziehen. Für die Bibliothekssuche erwiesen sich zwei Wellenzahlgebiete als besonders wichtig: 3600–2800 cm^–1 und 1300–900 cm^–1.

     

An application of the novel quantum mechanical/molecular mechanical method combined with the theory of energy representation: An ionic dissociation of a water molecule in the supercritical water

A novel quantum chemical approach recently developed has been applied to an ionic dissociation of a water molecule (2H(2)O-->H(3)O(+)+OH(-)) in ambient and supercritical water. The method is based on the quantum mechanical/molecular mechanical (QM/MM) simulations combined with the theory of energy representation (QM/MM-ER), where the energy distribution function of MM solvent molecules around a QM solute serves as a fundamental variable to determine the hydration free energy of the solute according to the rigorous framework of the theory of energy representation. The density dependence of the dissociation free energy in the supercritical water has been investigated for the density range from 0.1 to 0.6 g/cm(3) with the temperature fixed at a constant. It has been found that the product ionic species significantly stabilizes in the high density region as compared with the low density. Consequently, the dissociation free energy decreases monotonically as the density increases. The decomposition of the hydration free energy has revealed that the entropic term (-TDeltaS) strongly depends on the density of the solution and dominates the behavior of the dissociation free energy with respect to the variation of the density. The increase in the entropic term in the low density region can be attributed to the decrease in the translational degrees of freedom brought about by the aggregation of solvent water molecules around the ionic solute.     

Representable reference density matrices induced by information theory

A class of reference full density matrices and their reduced density matrices is presented. These density matrices are designed to be of value as references from which to describe and measure the effects of electron correlation in atoms, molecules, and solids. A given reference full density matrix is constructed to contain the least possible information consistent with having the (recognized) symmetry properties of—and reducing to the 1-matrix of—a given “true” full density matrix (which in a typical application is constructed from a correlated variational wave function). Therefore, the reduced density matrices derived from are representable and depend only upon the 1-matrix of and the (recognized) symmetry properties of for their construction. Furthermore, the property of containing the least possible information consistent with the given constraints makes these reference density matrices ideally suitable as references from which to describe the electron correlation contained in the “true” full density matrix .     

Application of reference materials for quality assessment in neutron activation analysis-use of information theory

It is generally accepted that an analytical procedure can be regarded as an information production system yielding information on the composition of the analyzed sample. Thus, information theory can be useful and the quantities characterizing the information properties of an analytical method may be applied not only as evaluation criteria but also as objective functions in the optimization. The usability of information theory is demonstrated on the example of neutron activation analysis. Both precision and bias of NAA results are taken into account together with the possible use of reference materials for quality assessment. The influence of the above-mentioned parameters on information properties such as information gain and profitability of NAA results is discussed in detail. It has been proved that information theory is especially useful in choosing suitable reference materials for the quality assessment of routine analytical procedures not only with respect to matrix and analyte concentration in the sample but also to concentrations and uncertainties of certified values in the CRM used. In the extreme trace analysis, CRMs with relatively large uncertainties and very low certified concentrations can still yield rather high information gain of results.     

Molecular properties and basis set quality: An approach based on information theory

Information theory can be used to evaluate the quality of a wave function by considering its ability to give values for some observables as close as possible to the experimental ones. A new method for improving the quality of a wave function is proposed. This paper deals exclusively with the HF (X ¹∑⁺) molecule.     

Revision of a multiparameter equation of state to improve the representation in the critical region: application to water

We have developed a crossover formalism for the thermodynamic surface of pure fluids, which can be applied to any multiparameter equation of state. This procedure has been used to incorporate scaling law behavior into a representation of the thermodynamic properties of water and steam developed by Pruss and Wagner (PW EOS) and adopted recently by the International Association for the Properties of Water and Steam. Our revision to this equation retains most of the functional form and coefficients of the PW EOS, but replaces two of the terms with a crossover representation of scaling law behavior. In order to develop this model, we first developed a new crossover formulation for steam in the critical region, and second, we have incorporated universal crossover functions into the original PW EOS. In the modified form, the PW equation of state reproduces the scaling laws down to dimensionless temperatures τ=10⁻⁷. Far from the critical point the equations practically coincide.     

Test of the information theory of branching ratios by classical trajectory computations

Extensive classical trajectory calculations are reported for the system F + HD → HF + D or DF + H, over a wide variety of initial conditions. The results of these computations are used to assess the utility of the information theoretic approach to the prediction of the initial-state dependence of the branching ratio, Γ_HF/DF. Two distinct forms for the information theoretic branching ratio are considered, corresponding to two different choices of constraints upon the transition probability matrix. The constraints in question are the “model” constraint employed by Kaplan and Levine, and the “direct” constraint, a generalisation of that introduced by Levine and Kosloff. The two forms of information theory give satisfactory predictions under selected (differing) initial conditions. Neither form is clearly superior. In particular, both fail to predict the observed trend of Γ_HF/DF with initial rotational state J, for the case of thermally averaged initial translational energies. This failure is linked to an important “interbranch constraint” not incorporated in the theory, stemming from the different activation energies for formation of the two products.     

An accurate analytic representation of the water pair potential

The ab initio water dimer interaction energies obtained from coupled cluster calculations and used in the CC-pol water pair potential (Bukowski et al., Science, 2007, 315, 1249) have been refitted to a site-site form containing eight symmetry-independent sites in each monomer and denoted as CC-pol-8s. Initially, the site-site functions were assumed in a B-spline form, which allowed a precise optimization of the positions of the sites. Next, these functions were assumed in the standard exponential plus inverse powers form. The root mean square error of the CC-pol-8s fit with respect to the 2510 ab initio points is 0.10 kcal mol(-1), compared to 0.42 kcal mol(-1) of the CC-pol fit (0.010 kcal mol(-1) compared to 0.089 kcal mol(-1) for points with negative interaction energies). The energies of the stationary points in the CC-pol-8s potential are considerably more accurate than in the case of CC-pol. The water dimer vibration-rotation-tunneling spectrum predicted by the CC-pol-8s potential agrees substantially and systematically better with experiment than the already very accurate spectrum predicted by CC-pol, while specific features that could not be accurately predicted previously now agree very well with experiment. This shows that the uncertainties of the fit were the largest source of error in the previous predictions and that the present potential sets a new standard of accuracy in investigations of the water dimer.     

Classical density functional theory of orientational order at interfaces: application to water

A classical density functional formalism has been developed to predict the position-orientation number density of structured fluids. It is applied to the liquid-vapor interface of pure water, where it consists of a classical term, a gradient correction, and an anisotropic term that yields order through density gradients. The model is calibrated to predict that water molecules have their dipole moments almost parallel to a planar interface, while the molecular plane is parallel to it on the liquid side and perpendicular to it on the vapor side. For a planar interface, the surface tension obtained is twice its experimental value, while the surface potential is in qualitative agreement with that calculated by others. The model is also used to predict the orientation of water molecules near the surface of droplets, as well as the dependence of equilibrium vapor pressure around them on their size.     

Improvement of quality of epoxide materials by modification with ethylsilicates

The influence of ethylsilicate additive on the properties of epoxide compositions and cured films on their basis was investigated. It was shown that the introduction of ES-32 ethylsilicate to epoxide composition formulation reduces their viscosity and favors the significant improvement of the physicomechanical properties of cured polymers.     

Novel quantum mechanical/molecular mechanical method combined with the theory of energy representation: free energy calculation for the Beckmann rearrangement promoted by proton transfers in the supercritical water

The Beckmann rearrangement of acetone oxime promoted by proton transfers in the supercritical water has been investigated by means of the hybrid quantum mechanical/molecular mechanical approach combined with the theory of energy representation (QM/MM-ER) recently developed. The transition state (TS) structures have been explored by ab initio calculations for the reaction of hydrated acetone oxime on the assumption that the reaction is catalyzed by proton transfers along the hydrogen bonds connecting the solute and the solvent water molecules. Up to two water molecules have been considered as reactants that take part in the proton transfers. As a result of the density functional theory calculations with B3LYP functional and aug-cc-pVDZ basis set, it has been found that participation of two water molecules in the reaction reduces the activation free energy by -12.3 kcal/mol. Furthermore, the QM/MM-ER simulations have revealed that the TS is more stabilized than the reactant state in the supercritical water by 2.7 kcal/mol when two water molecules are involved in the reaction. Solvation free energies of the reactant and the TS have been decomposed into terms due to the electronic polarization of the solute, electron density fluctuation, and others to elucidate the origin of the stabilization of the TS as compared with the reactant. It has been revealed that the promotion of the chemical reaction due to the hydration mainly originates from the interaction between the nonpolarized solute and the solvent water molecules at the supercritical state.     

Ab initio molecular dynamics with discrete variable representation basis sets: techniques and application to liquid water

Finite temperature ab initio molecular dynamics (AIMD), in which forces are obtained from "on-the-fly" electronic structure calculations, is a widely used technique for studying structural and dynamical properties of chemically active systems. Recently, we introduced an AIMD scheme based on discrete variable representation (DVR) basis sets, which was shown to have improved convergence properties over the conventional plane wave (PW) basis set [Liu,Y.; et al. Phys. Rev. B 2003, 68, 125110]. In the present work, the numerical algorithms for the DVR based AIMD scheme (DVR/AIMD) are provided in detail, and the latest developments of the approach are presented. The accuracy and stability of the current implementation of the DVR/AIMD scheme are tested by performing a simulation of liquid water at ambient conditions. The structural information obtained from the present work is in good agreement with the result of recent AIMD simulations with a PW basis set (PW/AIMD). Advantages of using the DVR/AIMD scheme over the PW/AIMD method are discussed. In particular, it is shown that a DVR/AIMD simulation of liquid water in the complete basis set limit is possible with a relatively small number of grid points.     

Data evaluation in high-performance liquid chromatography-diode-array detection-fluorescence detection by information theory

The concepts of information theory were applied to the high-performance liquid chromatography (HPLC) technique, with diode-array (DAD) and/or fluorescence (FLD) detections. The information amount for a complete analysis can be computed as a function of analytical parameters, such as the number of analytes, level of concentration, and standard deviation of determinations. By means of the proposed method, the information content of a qualitative and quantitative analysis accomplished by HPLC-DAD-FLD was estimated, and sensitivity was optimized taking into account a maximum information content, while the detection limit was estimated considering that at this level of concentration the information content approaches zero.     

The quality control chart principle: application to the routine analysis of pesticide residues in water

Summary In the routine analysis of pesticide residues in drinking water, a quality control chart (qcc) for every pesticide recorded the recovery from the fortification experiment which accompanied every series. The starting period included the first 10 recoveries and displayed the intra-laboratory performance in terms of the mean and of the ±3 standard deviations (sdv) confidence band. With every new recovery obtained, the starting period was moved on. So the qcc always displayed the latest state of performance. In general the ±3 sdv band width was less than 50–150% with several herbicides at the 0.1 g/l level, and it often contracted in the course of time. Typically, the mean moved around 100%. The fortification concentration for organochlorine compounds being reduced from 0.1 to 0.02 g/l, the confidence band broadened to ca. 10–200%. The qccs allowed a detailed knowledge on the whole palette of pesticides analysed and on the changes in the course of time.     

Self consistent field theory of solvent effects representation by continuum models: Introduction of desolvation contribution

We examine the representation of solvent effects by continuum models in the frame of the Reaction Field Theory. Particular attention is devoted to the problem raised by the adaptation of the current methods of Quantum Chemistry in the Self Consistent Field approximation especially at a semiempirical level. A critical examination of the literature in the field shows that, for the main part, the proposed methods suffer from theoretical internal incoherence. As an illustration of this study, we propose an extension of the generalized Born formula which is able to account for the desolvation effects produced by the specific neighborhood of each center of the solvated species. This work has been presented by one of us (R. Contreras) for partial fulfilment of a 3e Cycle Doctoral Thesis at the University P. and M. Curie (Paris VI)     

Application of many-body perturbation theory in the localized representation for the all-trans conjugated polyenes

Ab initio self-consistent field (SCF ) calculations are performed with the standard 6-31G* basis set for all-trans conjugated oligomers C_2n+2H_2n+4. The canonical occupied and virtual molecular orbitals (MO s) are separately localized by unitary transformations. Due to the localization, the perturbation operator is partitioned into two-particle and into single-particle terms; the MBPT is, therefore, a double-perturbation expansion in this case. By using the localized representation of the MBPT , the correlation energy contributions can be partitioned into local and nonlocal effects. It can be shown that the local effects are very important and well transferable, which makes possible the calculation of the correlation energy of larger molecules if the localized molecular orbitals (occupied and virtual) of smaller related molecules are known. © 1994 John Wiley & Sons, Inc.     

Application of the many-body perturbation theory to normal saturated hydrocarbons in the localized representation

The second-order energy corrections are calculated for some normal saturated hydrocarbons by using the many body-perturbation theory (MBPT) based on localized orbitals. The correlation energies are expressed as the sum of contributions from virtual orbital pairs. We have found that these contributions are transferable and have interesting structural features: the trans-coplanar effects are relatively large. Partitioning the correlation energies according to the order of neighbourhood we have found that the zero order effects are the largest but the first and second neighbour contributions are also important.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday