Simple correction for perturbations of peak amplitudes in statistical models of overlap

Summary The application of statistical models of overlap (SMOs) to saturated separations is made possible by theory that addresses variable peak amplitudes. These amplitudes cause peak widths to vary, and this variation can be modeled by a random variable whose effect on the probability of overlap is expressed by a convolution integral. Modified probabilities of overlap are derived for both homogeneous and nonhomogeneous one-dimensional separations, and the new probabilities are compared to results determined from published computer simulations. The new theory can describe overlap at saturations that are 3 to 4 times larger than before. Previously reported experimental chromatograms are reinterpreted to show the capabilities of theory. The theoretical extension is an important step towards making SMOs into practical tools for screening analytical separations.     

A practical resolution function

Summary The widely used resolution criterion which is based on the individual base-line widths of two peaks is invalid in practical situations. In this paper, a simple resolution function is presented. All the necessary data for calculating the resolution are directly measurable from the experimental chromatogram. It is shown that this function can be used to characterize the resolution in non-ideal situations where the areas of the two peaks that overlap are different and/or the peaks are non-symmetrical.     

Variable selection using probability density function similarity for support vector machine classification of high-dimensional microarray data

One problem with discriminant analysis of microarray data is representation of each sample by a large number of genes that are possibly irrelevant, insignificant or redundant. Methods of variable selection are, therefore, of great significance in microarray data analysis. To circumvent the problem, a new gene mining approach is proposed based on the similarity between probability density functions on each gene for the class of interest with respect to the others. This method allows the ascertainment of significant genes that are informative for discriminating each individual class rather than maximizing the separability of all classes. Then one can select genes containing important information about the particular subtypes of diseases. Based on the mined significant genes for individual classes, a support vector machine with local kernel transform is constructed for the classification of different diseases. The combination of the gene mining approach with support vector machine is demonstrated for cancer classification using two public data sets. The results reveal that significant genes are identified for each cancer, and the classification model shows satisfactory performance in training and prediction for both data sets.     

Spline wavelet in the resolution of overlapping voltammetric peaks

Spline wavelet transform is used to resolve overlapping voltammetric peaks. A suitable resolving factor is chosen to multiply the filters of spline wavelet and make it a peak resoluter. Simulated overlapping voltammetric peaks are processed by the peak resoluter and satisfactory results are obtained. Base-line separation can be achieved, the relative errors of peak position are less than 3.0%, and the relative errors of peak area are less than 5.0%. The effect of different resolving factors and spline wavelet basis are discussed. To test the procedure, two systems, cadmium (Ⅱ)-indium (Ⅲ) and lead (Ⅱ)-thallium (Ⅰ), are used.     

二维小波变换与子窗口因子分析法结合用于含噪声HPLC-DAD数据的解析

将二维小波变换与子窗口因子分析法相结合,用于模拟的高噪声HPLC-DAD数据的解析.首先应用二维小波变换滤除噪声,然后采用子窗口因子分析法解析重叠峰.结果表明,信噪比为10的高噪声基本被滤除掉.     

An approach for measuring peak area of an overlapped peak pair

Summary Based on the exponentially modified Gaussian (EMG) function, a new approach is presented for the quantitation of a partially overlapped peak pair. This approach can be employed in a wide range of peak area ratio and asymmetry, provided that the relative valley between the two peaks is not greater than 55%. The first peak area is calculated by the use of the ratio of the front half-width at height fraction 0.1 to that at heigt fraction 0.5. The second peak area is calculated by subtracing the first peak area from the total area which is provided by a microprocessor-based integrator. The relative error for the first peak never exceeds ±5%, but this is not always the case for the second peak. The relative error for the second peak depends not only on the accuracy of the total area and that of the first peak area but on area ratio as well.     

A radial probability density function for analysis of canonical molecular orbitals

A one‐dimensional probability density function, analogous to the atomic radial density for the hydrogen atom, r²R_nl(r), is defined for an arbitrary three‐dimensional density. It is obtained numerically by taking the derivative of a cumulative probability distribution with respect to the cubic root of the volume enclosed by each in a series of isosurfaces. Each point in the function is associated with a unique isosurface, and the isosurface associated with the maximum of the defined function represents the most probable isosurface with respect to the putative radius. This function therefore provides an objective selection criterion for a single isosurface to represent a three‐dimensional density. This technique is applied to set of canonical molecular orbitals. The selected threshold value varies from orbital to orbital, but the enclosed probability falls in the range of 20% to 55% for the reported orbitals. In all cases, the enclosed probability is much smaller than the common choices found in the literature. The concomitant smaller volume often makes possible a more localized interpretation and helps to clarify the conventional delocalized interpretation of molecular orbitals. For example, the isosurface plots selected by this method distinguish the formally bonding orbital in He₂ from the true bonding orbital in H₂. Examples from N₂, F₂, HF, H₂O, C₂H₆, and Ni(CO)₄ are also presented. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 310–321, 2000     

Criteria for judging the quality of separation in chromatograms containing solvent peaks

Summary Formal procedures used for optimizing chromatographic selectivity require objective, numerical functions to assess the quality of each chromatogram obtained during the process. Many of such optimization criteria have been suggested for chromatograms in which all or a number of well-shaped peaks need to be separated. This paper describes a method by which resolution can be measured in chromatograms in which very large, highly non-symmetrical background peaks,e.g. typical solvent peaks, are present. Using this method, various optimization criteria can be calculated. The method is evaluated using a simulation program which constructs chromatograms from the recorded profiles of individual experimental peaks. It is also demonstrated for use in an experimental optimization procedure in reversed-phase liquid chromatography.     

Moment expansion of the linear density‐density response function

We present a low rank moment expansion of the linear density‐density response function. The general interacting (fully nonlocal) density‐density response function is calculated by means of its spectral decomposition via an iterative Lanczos diagonalization technique within linear density functional perturbation theory. We derive a unitary transformation in the space of the eigenfunctions yielding subspaces with well‐defined moments. This transformation generates the irreducible representations of the density‐density response function with respect to rotations within SO(3). This allows to separate the contributions to the electronic response density from different multipole moments of the perturbation. Our representation maximally condenses the physically relevant information of the density‐density response function required for intermolecular interactions, yielding a considerable reduction in dimensionality. We illustrate the performance and accuracy of our scheme by computing the electronic response density of a water molecule to a complex interaction potential. © 2015 Wiley Periodicals, Inc.     

Radial‐template approach for accurate density representation in computational quantum theory

A method for improved representation of electronic charge and spin densities for molecular and solid state systems is presented, based upon extensions of least squares fits to quantum mechanical “true” densities using basis functions of limited support. Attention is given to optimization of radial degrees of fit freedom, and the design of fit functions permitting rapid analytic manipulation and calculation of properties, such as Coulomb potentials. The method is demonstrated for covalent CO and for a large metal‐organic crystalline structure. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Differential density matrix overlap: an index for assessment of electron correlation in atoms and molecules

Summary A new index, called the differential density matrix overlap (DDMO), is proposed for assessment of the electron correlation effects in atoms and molecules. DDMO can be easily calculated as the negative value of the correlation energy derivative with respect to the relative position of the occupied and virtual orbitals. DDMO is transparent to physical interpretation. It can serve as a tool for analyzing the accuracy of approximate electron correlation methods and the validity of the Hartree-Fock wavefunction as the zeroth-order approximation. The properties of DDMO are discussed using test calculations on 11 atoms and molecules as an example.     

SBS/Pani · DBSA mixture plasticized with DOP and NCLS - Effect of the plasticizers on the probability density of volume resistivity measurements

Plasticized mixtures of styrene-butadiene-styrene block copolymer (SBS) and Polyaniline (Pani) were prepared in a Haake internal mixer. Two different plasticizers were used: dioctyl phthalate (DOP) and cashew nut shell liquid (CNSL). Pani and plasticizers were characterized by FTIR and the resistive behavior of plasticized mixtures was investigated along the electrification time. It is shown that obtained experimental data are subject to deterministic dynamic fluctuations that cannot be described by single normal probability distribution functions (PDF) along the time. The PDF analysis shows that obtained PDFs must be described as sums of at least three distinct Gaussian distributions with different areas. It is also shown that the Gaussian component with larger area may provide better representation of the measured volume resistivity values.     

Study on Separation Method of Overlapped Peaks in Differential Thermal Analysis with Computer Simulation

With the computer simulations, it has been found that in Differential Thermal Analysis (DTA) the overlapped peaks do not satisfy the linear overlapping principle, and the relationship between the overlapped peaks is rather complex that is a function of sample thermal conductivity, specific heat, quantity and latent heats, etc. If the first point where the two peaks begin to overlap is at the posterior half of the first peak curve and the two overlapped peaks can be identified by two different peaks, from the curve of overlapped peaks we can know that the temperature corresponding to the first point deviating from the sample's first phase change curve is the sample's second phase change temperature. This revised version was published online in August 2006 with corrections to the Cover Date.     

Study on electronic density topology of various cluster models of Mg/Al hydrotalcite by density functional theory

The geometry and electronic topology properties of Mg/Al hydrotalcite cluster models were comparatively investigated by means of density functional theory at GGA/DND levels. The results suggested that cluster model containing seven octahedral cations was the smallest size to be employed to simulate other properties. The fact that the n+ charge of cluster models containing n aluminum atoms can reflect electronic properties of anionic clay layer sheet. The bond lengths of clusters can be modified by terminating with or without OH~-/H_2O groups in terms of principle of bond order conservation.     

Experimental determination of adsorption energies, adsorption isotherms, probability density functions, and lateral molecular interactions on CXHY/CaO systems

Reversed-flow gas chromatography (RF-GC) is extended to the measurements of the probability density function for the adsorption energies as well as the differential energies of adsorption due to lateral interactions of molecules adsorbed on different heterogeneous solid surfaces. All these calculations are based on a non-linear adsorption isotherm model as it is well accepted that the linear one is inadequate for substances such as these used in this work. Thus, some new important physicochemical parameters have been obtained for the characterization of the heterogeneous systems studied. The adsorbent used in this study was calcium oxide. The adsorption of many significant hydrocarbons was investigated. With these systematic experiments under conditions which are similar to the atmospheric ones, an extrapolation of the results obtained to "real" atmospheres with a high degree of confidence is possible.     

联用色谱数据的双窗口因子分析

利用组分光谱的特征信息,发展了一种能直接对联用色谱重叠峰中组分进行定性定量分析的新方法──双窗口因子分析（dualwindowfactoranalysis,DWPA）。该法可从多组分重叠峰中定性目标组分,且在未经其它组分的分辨下可直接对目标组分的光谱、色谱进行分辨。因此更适应于联用色谱对复杂体系中待测组分的定性定量分析。用该法成功地对4组分重叠峰进行了分析,实验结果令人满意。     

氢化可的松的热力学函数和晶体结构——密度泛函理论分析

采用密度泛函理论B3LYP/6-31G和B3LYP/6-311G*方法优化了气相状态氢化可的松的几何结构,利用优化的结构得到了氢化可的松各原子净电荷及前沿轨道分布;基于简谐振动分析求得氢化可的松的红外光谱频率和热力学函数;并计算了环己烷、乙酸丁酯、二氯乙烷、异丙醇、甲醇、水六种不同极性的溶剂对氢化可的松几何构型、电荷分布及能量的影响.结果表明,由理论计算得到的氢化可的松的晶体结构与实测的晶体结构接近.     

Comparison of some representative density functional theory and wave function theory methods for the studies of amino acids

Energies of different conformers of 22 amino acid molecules and their protonated and deprotonated species were calculated by some density functional theory (DFT; SVWN, B3LYP, B3PW91, MPWB1K, BHandHLYP) and wave function theory (WFT; HF, MP2) methods with the 6-311++G(d,p) basis set to obtain the relative conformer energies, vertical electron detachment energies, deprotonation energies, and proton affinities. Taking the CCSD/6-311++G(d,p) results as the references, the performances of the tested DFT and WFT methods for amino acids with various intramolecular hydrogen bonds were determined. The BHandHLYP method was the best overall performer among the tested DFT methods, and its accuracy was even better than that of the more expensive MP2 method. The computational dependencies of the five DFT methods and the HF and MP2 methods on the basis sets were further examined with the 6-31G(d,p), 6-311++G(d,p), aug-cc-pVDZ, 6-311++G(2df,p), and aug-cc-pVTZ basis sets. The differences between the small and large basis set results have decreased quickly for the hybrid generalized gradient approximation (GGA) methods. The basis set convergence of the MP2 results has been, however, very slow. Considering both the cost and the accuracy, the BHandHLYP functional with the 6-311++G(d,p) basis set is the best choice for the amino acid systems that are rich in hydrogen bonds.