Improved convergence of self-consistence procedures in the MC SCF theory

To obtain optimized orbitals within the MC SCF theory, the energy surface near a chosen point is approximated by a quadratic function of independent matrix elements of a small orthogonal orbital transformation. The method of a second-order one-electron Hamiltonian (OEH) is developed on the basis of this approximation. A procedure is proposed to define step coordinates, insuring a rapid descent along an average-energy surface also in the cases when the matrix of second energy derivatives has eigenvalues negative or close to zero. The results obtained in applying the OEH method for the calculation of ground and triplet states of uracile in the π-electron approximation are discussed. When a complete matrix of the second energy derivatives is used, the self-consistence procedure is quadratically convergent. An exponential, yet rapid enough convergence is provided by a simplified computation scheme neglecting cross derivatives.     

Pairing theorem of graph eigenvalues: Its new proof and a generalization

Each undirected graph has its own adjacency matrix, which is real and symmetric. The negative of the adjacency matrix, also real and symmetric, is a well-defined mathematically elementary concept. By this negative adjacency matrix, the negative of a graph can be defined. Then an orthogonal transformation can be readily found that transforms a negative of an alternant graph to that alternant graph: (?G) → G. Since the procedure does not involve the edge weights, the pairing theorem holds true for all edge-weighted alternant graphs, including the usual “standard” graphs.     

Direct minimization of the energy functional in LCAO-MO density matrix formalism

The general multiconfiguration self-consistent-field method is presented along the density matrix formalism. The proposed optimization procedure for orbitals makes use of an orthogonal transformation in the space spanned by the fixed basis set. Acting on the unconstrained parameters of the transformation a direct minimization of the energy expression is performed using a gradient approach. A similar method may also be applied to the optimization of the expansion coefficients. The method works not only for the ground state of a given system, but also for any excited state, yielding an upper bound to the true energy of the considered state.     

Iterative diagonalization for orbital optimization in natural orbital functional theory

A challenging task in natural orbital functional theory is to find an efficient procedure for doing orbital optimization. Procedures based on diagonalization techniques have confirmed its practical value since the resulting orbitals are automatically orthogonal. In this work, a new procedure is introduced, which yields the natural orbitals by iterative diagonalization of a Hermitian matrix F . The off‐diagonal elements of the latter are determined explicitly from the hermiticity of the matrix of the Lagrange multipliers. An expression for diagonal elements is absent so a generalized Fockian is undefined in the conventional sense, nevertheless, they may be determined from an aufbau principle. Thus, the diagonal elements are obtained iteratively considering as starting values those coming from a single diagonalization of the matrix of the Lagrange multipliers calculated with the Hartree‐Fock orbitals after the occupation numbers have been optimized. The method has been tested on the G2/97 set of molecules for the Piris natural orbital functional. To help the convergence, we have implemented a variable scaling factor which avoids large values of the off‐diagonal elements of F . The elapsed times of the computations required by the proposed procedure are compared with a full sequential quadratic programming optimization, so that the efficiency of the method presented here is demonstrated. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Towards a complete identification of orthogonal variation in multiple regression from a PLS1 modeling point of view: including OPLS by a change of orthogonal basis

It is well known that the predictions of the single response orthogonal projections to latent structures (OPLS) and the single response partial least squares regression (PLS1) regression are identical in the single‐response case. The present paper presents an approach to identification of the complete y ‐orthogonal structure by starting from the viewpoint of standard PLS1 regression. Three alternative non‐deflating OPLS algorithms and a modified principal component analysis (PCA)‐driven method (including MATLAB code) is presented. The first algorithm implements a postprocessing routine of the standard PLS1 solution where QR factorization applied to a shifted version of the non‐orthogonal scores is the key to express the OPLS solution. The second algorithm finds the OPLS model directly by an iterative procedure. By a rigorous mathematical argument, we explain that orthogonal filtering is a ‘built‐in’ property of the traditional PLS1 regression coefficients. Consequently, the capabilities of OPLS with respect to improving the predictions (also for new samples) compared with PLS1 are non‐existing. The PCA‐driven method is based on the fact that truncating off one dimension from the row subspace of X results in a matrix X _orth with y ‐orthogonal columns and a rank of one less than the rank of X . The desired truncation corresponds exactly to the first X deflation step of Martens non‐orthogonal PLS algorithm. The significant y ‐orthogonal structure of X found by PCA of X _orth is split into two fundamental parts: one part that is significantly contributing to correct the first PLS score toward y and one part that is not. The third and final OPLS algorithm presented is a modification of Martens non‐orthogonal algorithm into an efficient dual PLS1–OPLS algorithm. Copyright © 2014 John Wiley & Sons, Ltd.     

LocalSCF method for semiempirical quantum-chemical calculation of ultralarge biomolecules

A linear-scaling semiempirical method, LocalSCF, has been proposed for the quantum-chemical calculations of ultralarge molecular systems by treating the large-scale molecular task as a variational problem. The method resolves the self-consistent field task through the finite atomic expansion of weakly nonorthogonal localized molecular orbitals. The inverse overlap matrix arising from the nonorthogonality of the localized orbitals is approximated by preserving the first-order perturbation term and applying the second-order correction by means of a penalty function. This allows for the separation of the orbital expansion procedure from the self-consistent field optimization of linear coefficients, thereby maintaining the localized molecular orbital size unchanged during the refinement of linear coefficients. Orbital normalization is preserved analytically by the variation of virtual degrees of freedom, which are orthogonal to the initial orbitals. Optimization of linear coefficients of localized orbitals is performed by a gradient procedure. The computer program running on a commodity personal computer was applied to the GroEL-GroES chaperonin complex containing 119,273 atoms.     

Four-level orthogonal array design as a chemometric approach to the optimization of polarographic reaction system for phosphorus determination

It is the purpose of the present work to provide information on the four-level orthogonal array design and data analysis for the optimization of analytical procedures. In the theoretical part, the construction and characteristics of the OA(16)(4(5)) matrix is described in detail, followed by the data analysis strategy, in which the significance of the different factors is quantitatively evaluated by an analysis of variance (ANOVA) method including per cent contribution, and the difference among four levels for each factor is determined by Duncan's multiple F test. Furthermore, a third-order polynomial model representing response surface is established to estimate the effects for the factors with significant influences. In the application part, the proposed four-level orthogonal array design and data analysis method were applied to optimize polarographic reaction system for phosphorus determination. By conducting 16 preplanned experiments that span the maximum working range of the system, the best experimental conditions for achieving the largest response can be obtained. The expected value for each experimental trial calculated by the third-order regression equation established is in good agreement with the corresponding experimental value. To confirm the validity of the optimization procedure, additional experiments using the recommended conditions were performed. The results demonstrate that satisfactory results can be acquired. Therefore, the proposed four-level orthogonal array design as a chemometric approach to optimize the polarographic reaction system for phosphorus determination is rather efficient and effective.     

压力溶弹溶样石墨炉原子吸收法测定硫磺中的砷、硒、碲

建立了硝酸压力溶弹溶样、石墨炉原子吸收法测定硫磺中砷、硒、碲元素的方法。通过正交试验确定样品的溶解条件，选择适当的基体改进剂和最佳的石墨炉升温程序，一次溶样即可实现砷、硒、碲三种元素的检测。该法的回收率为90．0％～110．0％，测定结果的相对标准偏差为2．5％～4．8％。     

Multivariate calibration of near infrared spectra by orthogonal WAVElet correction using a genetic algorithm

Orthogonal WAVElet correction (OWAVEC) is a pre-processing method aimed at simultaneously accomplishing two essential needs in multivariate calibration, signal correction and data compression, by combining the application of an orthogonal signal correction algorithm to remove information unrelated to a certain response with the great potential that wavelet analysis has shown for signal processing. In the previous version of the OWAVEC method, once the wavelet coefficients matrix had been computed from NIR spectra and deflated from irrelevant information in the orthogonalization step, effective data compression was achieved by selecting those largest correlation/variance wavelet coefficients serving as the basis for the development of a reliable regression model. This paper presents an evolution of the OWAVEC method, maintaining the first two stages in its application procedure (wavelet signal decomposition and direct orthogonalization) intact but incorporating genetic algorithms as a wavelet coefficients selection method to perform data compression and to improve the quality of the regression models developed later. Several specific applications dealing with diverse NIR regression problems are analyzed to evaluate the actual performance of the new OWAVEC method. Results provided by OWAVEC are also compared with those obtained with original data and with other orthogonal signal correction methods.     

"Orthogonal" separations for reversed-phase liquid chromatography

A general procedure is proposed for the rapid development of a reversed-phase liquid chromatographic (RP-LC) separation that is "orthogonal" to a pre-existing ("primary") method for the RP-LC separation of a given sample. The procedure involves a change of the mobile-phase organic solvent (B-solvent), the replacement of the primary column by one of very different selectivity, and (only if necessary) a change in mobile phase pH or the use of a third column. Following the selection of the "orthogonal" B-solvent, column and mobile phase pH, further optimization of peak spacing and resolution can be achieved by varying separation temperature and either isocratic %B or gradient time. The relative "orthogonality" of the primary and "orthogonal" RP-LC methods is then evaluated from plots of retention for one method versus the other. The present procedure was used to develop "orthogonal" methods for nine routine RP-LC methods from six pharmaceutical analysis laboratories. The relative success of this approach can be judged from the results reported here.     

Determination of Organotin Compounds in Wine by Microwave-Assisted Extraction and High Performance Liquid Chromatography–Inductively Coupled Plasma Mass Spectrometry

A new analytical procedure for the determination of five organotin compounds in several matrix wine samples is reported. The organotin compounds were extracted by microwave-assisted extraction with n-hexane. Extraction conditions, such as volume of n-hexane required, extraction temperature, and extraction time, were investigated and optimized by an orthogonal array experimental design. The determination of organotin compounds in the final extracts was carried out by liquid chromatography–inductively coupled plasma mass spectrometry. The procedure showed limits of detection between 0.029–0.049 µg · L^?1. The linearity was in the range of 0.5 to 100 µg · L^?1. The precision expressed as relative standard deviation (RSD) was below 9.43%. The developed method was successfully employed to analyze different matrix wine samples, and some analytes were detected at the level of 0.053 to 1.14 µg · L^?1.     

Communication: Hilbert-space partitioning of the molecular one-electron density matrix with orthogonal projectors

A double-atom partitioning of the molecular one-electron density matrix is used to describe atoms and bonds. All calculations are performed in Hilbert space. The concept of atomic weight functions (familiar from Hirshfeld analysis of the electron density) is extended to atomic weight matrices. These are constructed to be orthogonal projection operators on atomic subspaces, which has significant advantages in the interpretation of the bond contributions. In close analogy to the iterative Hirshfeld procedure, self-consistency is built in at the level of atomic charges and occupancies. The method is applied to a test set of about 67 molecules, representing various types of chemical binding. A close correlation is observed between the atomic charges and the Hirshfeld-I atomic charges.     

段式正交信号校正方法及在小麦近红外光谱数据分析中的应用

针对光谱数据峰宽、局部效应显著、含有噪音、变量个数多及彼此间常存在严重的复共线性等问题,改进和设计一种光谱数据局部校正方法:基于窗口平滑的段式正交信号校正方法,并将之结合偏最小二乘回归,以实现光谱数据的预处理及定量分析。通过NIPALS算法初始化将滤去的正交成分,以近邻分段方式进行逐个波长点的正交信号校正。而后将去噪后的光谱矩阵作为新的自变量阵,通过偏最小二乘回归构建其与性质参变量间的校正模型。通过小麦近红外漫反射光谱数据的应用实验结果表明,本方法正交成分估计稳定,去噪明显,模型的预报性能优于其它方法,PLS成分数减少,模型更加简洁。     

On spin wavefunctions and young orthogonal matrices

Electron spin wavefunctions are expressed in the Young orthogonal representation. The normalization factor is calculated. An explicit expression for the first column elements of the Young orthogonal matrices is obtained by a comparison to the branching diagram wavefunctions. These matrix elements are used in a multideterminant representation of the total wavefunction. © 2012 Wiley Periodicals, Inc.     

New ultraviolet signal actuated switching valve for the measurement of low level impurities by liquid chromatography/mass spectrometry

A new ultraviolet (UV) signal actuated switching valve for diverting the main matrix compound to waste, preventing it entering the ion source of the mass spectrometer is described. Sensitivity for trace impurities eluting after the drug substance cimetidine or related compounds could be enhanced by a factor of 4-5. The increase in sensitivity was dependent on the type of ion source which interfaced the mass spectrometer. The benefit of the switching valve was greater with a line of sight type source than with an orthogonal one. The detection limit for a trace compound in a matrix compound was improved by up to a factor of 10 with the line of sight type source but only by a factor of 5 with the orthogonal source.     

Linear scaling density matrix perturbation theory for basis-set-dependent quantum response calculations: an orthogonal formulation

Linear scaling density matrix perturbation theory [A. M. N. Niklasson and M. Challacombe, Phys. Rev. Lett. 92, 193001 (2004)] is extended to basis-set-dependent quantum response calculations for a nonorthogonal basis set representation. The generalization is achieved by a perturbation-dependent congruence transform, derived from the factorization of the inverse overlap matrix, which transforms the generalized eigenvalue problem to an orthogonal, standard form. With this orthogonalization transform the basis-set-dependent perturbation in the overlap matrix is included in the orthogonalized Hamiltonian, which is expanded in orders of the perturbation. In this way density matrix perturbation theory developed for an orthogonal representation can be applied also to basis-set-dependent response calculations. The method offers an alternative to the previous solution of the basis-set-dependent response problem, based on a nonorthogonal generalization of the density matrix perturbation theory, where the calculations are performed within a purely nonorthogonal setting [A. M. N. Niklasson et al., J. Chem. Phys. 123, 44107 (2005)].     

Analysis of native milk oligosaccharides directly from thin-layer chromatography plates by matrix-assisted laser desorption/ionization orthogonal-time-of-flight mass spectrometry with a glycerol matrix

We have recently presented a new method for direct coupling of high-performance thin-layer chromatography (HPTLC) with matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS), illustrated by the analysis of a complex ganglioside mixture. In the current communication, an adaptation of this procedure to mixtures of native oligosaccharides from human and from elephant milk is described. The key features in this method are (1) glycerol as a liquid matrix, to provide a homogeneous wetting of the silica gel and a simple and fast MALDI preparation protocol, (2) an infrared (IR) laser for volume material ablation and particular soft desorption/ionization conditions, and (3) an orthogonal time-of-flight mass spectrometer for a high mass accuracy, independent of any irregularity of the silica gel surface. Chromatographic "mobility profiles" were determined by scanning the laser beam across the analyte bands. The current limit of detection for the MS analysis was determined to approximately 10 pmol of individual oligosaccharides spotted for chromatography. A liquid composite matrix, containing glycerol and the ultraviolet (UV-)MALDI matrix alpha-cyano-4-hydroxycinnamic acid, allows a direct HPTLC-MALDI-MS analysis with a 337 nm-UV laser as well. Compared to the IR-MALDI mode, the analytical sensitivity in UV-MALDI was found to be lower by one order of magnitude, whereas unspecific analyte ion fragmentation as well as adduct formation was found to be more extensive.     

Magnetic nanoparticles as an orthogonal support of polymer resins: applications to solid-phase suzuki cross-coupling reactions

[reaction: see text] Most of the reactants immobilized on conventional solid-phase resins are buried inside the interiors of lightly cross-linked polystyrene beads. An orthogonal support of solid-phase resins needs to be small enough to penetrate the interpolymeric chain spaces of a swollen resin to reach reaction sites. In this paper, we report the use of magnetic nanoparticles ( approximately 4 nm) as an orthogonal matrix to assist solid-phase reactions. A magnetic nanoparticle-supported homogeneous Pd catalyst was employed for promoting the Suzuki cross-coupling of an aryl halide on resins and an excessive arylboronic acid in solution. The workup separating three components (the catalyst, product, and remaining arylborate) is a chromatography-free process. The Pd catalyst was magnetically isolated and recycled from the reaction mixture by applying an external magnetic field. Then, a filtration process was followed to recover the excess borate reagent from the resins/product. Our work here presents the first example of an orthogonal matrix of solid-phase resins and shows the promise of employing nanomaterials in organic synthesis.     

A high throughput approach for determination of dermorphin in human urine using liquid chromatography–mass spectrometry for doping control purposes

Dermorphin is a peptide with analgesic actions similar to morphine, but with greater effect and less potential to cause tolerance. The use of dermorphin has been documented in race horses, and its use in humans has already been reported. Considering the potential advantages from the use of dermorphin over morphine, a method to monitor it, and its main metabolite dermorphin (1‐4) in humans becomes necessary for doping control. Here, we present two orthogonal methods for this purpose: a high‐throughput liquid chromatography coupled to high‐resolution mass spectrometry (HRMS) as an initial testing procedure and liquid chromatography–tandem mass spectrometry (MS/MS) in the selected reaction monitoring (SRM) acquisition mode for a confirmation procedure. For urine samples, pretreatment through a mixed‐mode weak cation‐exchange solid‐phase extraction emerged as an effective approach to extract peptides from the biological sample. For the HRMS analysis, a full‐MS scan acquisition mode was selected to detect the exact masses of dermorphin and dermorphin (1‐4) at m/z 803.37226 and 457.20816, respectively. The SRM method used in the MS/MS confirmation protocol presented high specificity and sensitivity. The selected product ions for dermorphin were 602.2, 202.1 and 574.3 and for dermorphin (1‐4) were 207.1, 223.1, and 235.1. Both methods were evaluated for specificity, repeatability, carryover, matrix effects, and recovery. No carryover and matrix effects were detected. The limit of detection for initial testing procedure and the limit of identification for confirmation procedure was 2.5 ng/ml. Also, specificity and robustness were acceptable for the application. Together, the developed methods proved to be efficient for the analysis of dermorphin and metabolite for human doping control purpose.