Bounding the extrapolated correlation energy using Padé approximants

We present a rigorous strategy, based on Stieltjes series and Padé approximants, to obtain suitable bounds for extrapolation of the quantum chemical correlation energy. Computational tests are performed for the second‐order Møller–Plesset (MP2) correlation energy, and the bounds obtained are tight enough for practical calculational purposes: The associated error in most cases is much less than 1 kcal/mol. The bounds presented here are also shown to be rigorous for functional forms that represent a wide variety of methods in quantum chemistry and hence may be used in extrapolating a wide range of expressions, some of them yielding significant computational advantages compared to traditional techniques. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 222–234, 2000     

Quadratic Padé approximants and the intruder state problem of multireference perturbation methods

Simple and quadratic Padé resummation methods are applied to high‐order series from multireference many‐body perturbation theory (MR‐MBPT) calculations using various partitioning schemes (Møller–Plesset, Epstein–Nesbet, and forced degeneracy) to determine their efficacy in resumming slowly convergent or divergent series. The calculations are performed for the ground and low‐lying excited states of (i) CH₂, (ii) BeH₂ at three geometries, and (iii) Be, for which full configuration interaction (CI) calculations are available for comparison. The 49 perturbation series that are analyzed include those with oscillatory and monotonic divergence and convergence, including divergences that arise from either frontdoor or backdoor intruder states. Both the simple and quadratic Padé approximations are found to speed the convergence of slowly convergent or divergent series. However, the quadratic Padé method generally outperforms the simple Padé resummation. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Generalized Euler transformation in extracting useful information from divergent (asymptotic) perturbation series and the construction of Padé approximants

Euler transformation for accelerating convergence of a series is considered in the context of handling divergent (asymptotically convergent) perturbation series. A generalized (parametrized) version of this transformation is developed, based on the conjecture of Dalgarno and Stewart, which works better. Viewed from this standpoint, the Padé approximants follow as a special case of the parametrized Euler transformation (PET ), as is the case with the μ transformation procedure of Feenberg in a perturbative context. The PET is shown to serve as a more general method of handling a divergent series and is able to appreciate the construction and convergence behavior of specific sequences of Padé approximants. The role of parametrization in the context of the Z^?1 perturbation theory of atoms is also noted and the workability of the adopted strategy is demonstrated by choosing some specific test cases.     

Fast Padé transform for optimal quantification of time signals from magnetic resonance spectroscopy

The fast Padé transform (FPT) is both a parametric and a nonparametric estimator that is capable of quantifying the input raw time signals without any fitting. The FPT simultaneously interpolates as well as extrapolates, and this is expected to mitigate truncation artifacts. To assess performance, it is necessary to compare the main features of the FPT with the characteristics of other parametric estimators, as well as with the fast Fourier transform (FFT), which can yield only shape spectra. The FPT can also give the shape of a spectrum, but accomplishes this in two totally different ways, with and without computing the spectral parameters (complex frequencies and amplitudes). A number of other parametric estimators used in signal processing are unable to yield shape spectra without prior extraction of the fundamental frequencies and the corresponding amplitudes. The primary goal of the present study is to assess the accuracy, robustness, and efficiency of the FPT for parametric and nonparametric estimations of experimentally measured time signals from in vivo magnetic resonance spectroscopy (MRS). Robustness and steadiness of the FPT are assessed relative to the FFT by monitoring the convergence rates of these two processors through a systematic and gradual decrease of the truncation level of the full signal length. Accuracy of the FPT is verified by performing error analysis of proven validity, using a gold standard, if available. Alternatively, comparison is made between the two complementary variants of the FPT that converge inside and outside the unit circle. Efficiency of the FPT is checked with respect to the FFT for estimation of the shape of a spectrum, as well as relative to other parametric processors, in the case of quantifications. To establish the accuracy, robustness, and efficiency of the FPT within the outlined multi‐level strategy, we use a time signal encoded via MRS at 4T from the brain of a healthy volunteer. We also assess the overall usefulness of the FPT for signal processing of data acquired from patients, in light of the emerging appreciation that spectroscopy of the tissue metabolites offers a number of vital advantages over the corresponding anatomical imaging in diagnostics. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Numerical method to solve chemical differential‐algebraic equations

In this article, the solution of a chemical differential‐algebraic equation model of general type F(y, y′, x) = 0 has been done using MAPLE computer algebra systems. The MAPLE program is given in the Appendix . First we calculate the Power series of the given equations system, then we transform it into Padé series form, which gives an arbitrary order for solving chemical differential‐algebraic equation numerically. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Canted antiferromagnet superimposed on a buckled kagomé network in RbMn4(PO4)3

Rubidium tetramanganese tris(phosphate), RbMn₄(PO₄)₃, has been synthesized as single crystals under hydrothermal conditions. The crystal structure was refined in the space group Pnnm (D_2h¹²). It is argued that the size factor R_M/R_A, i.e. the ratio of the A⁺ ionic radius to the M²⁺ ionic radius, within the morphotropic series AM₄(TO₄)₃ corresponds to a specific type of crystal structure. At low temperatures, the antiferromagnet superimposed on a buckled kagomé network in RbMn₄(PO₄)₃ experiences a transition into a long‐range ordered state with finite spontaneous magnetization. First principles calculations provide the dominant magnetic exchange interactions both within and between the kagomé layers. The analysis of these interactions allows us to suggest a model of alternating ferromagnetic and antiferromagnetic arrangements within chains of Mn3 atoms.     

Spot Moiré Fringes: Determination of Domain Boundaries and Structural Parameters in Ordered Nanoporous Structures

Spot moiré fringes are generated by the superposition between a nanoporous structure and a digital three‐way grating. The spot moiré fringes are useful for the characterization of the domain boundaries and structural parameters in ordered nanoporous materials. The pitches and the orientations of the nanopore arrays in three directions can be simultaneously determined in a large view field.     

Minimum MD simulation length required to achieve reliable results in free energy perturbation calculations: Case study of relative binding free energies of fructose‐1,6‐bisphosphatase inhibitors

In an attempt to establish the criteria for the length of simulation to achieve the desired convergence of free energy calculations, two studies were carried out on chosen complexes of FBPase‐AMP mimics. Calculations were performed for varied length of simulations and for different starting configurations using both conventional‐ and QM/MM‐FEP methods. The results demonstrate that for small perturbations, 1248 ps simulation time could be regarded a reasonable yardstick to achieve convergence of the results. As the simulation time is extended, the errors associated with free energy calculations also gradually tapers off. Moreover, when starting the simulation from different initial configurations of the systems, the results are not changed significantly, when performed for 1248 ps. This study carried on FBPase‐AMP mimics corroborates well with our previous successful demonstration of requirement of simulation time for solvation studies, both by conventional and ab initio FEP. The establishment of aforementioned criteria of simulation length serves a useful benchmark in drug design efforts using FEP methodologies, to draw a meaningful and unequivocal conclusion. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Simultaneous determination of 9‐dehydro‐17‐hydro‐andrographolide and sodium 9‐dehydro‐17‐hydro‐andrographolide‐19‐yl sulfate in rat plasma by UHPLC‐ESI‐MS/MS after administration of xiyanping injection: application to a pharmacokinetic study

9‐Dehydro‐17‐hydro‐andrographolide (DHA) and sodium 9‐dehydro‐17‐hydro‐andrographolide‐19‐yl sulfate (DHAS) are active ingredients of xiyanping injection in clinical use. A simple, rapid and sensitive UHPLC‐ESI‐MS/MS method was developed for the determination of DHA and DHAS in rat plasma, and the pharmacokinetics of DHA and DHAS after intravenous administration of xiyanping injection was investigated. The plasma samples were treated with methanol to precipitate out protein, and the separation of DHA and DHAS was achieved on a Waters BEH C₁₈ column with a mobile phase consisting of acetonitrile and 10 mmol/L ammonium acetate solution at a flow rate of 0.4 mL/min. DHA, DHAS and the internal standard (internal standard, IS) diethylstilbestrol were detected at negative ion mode. The precursor‐product ion pairs used in multiple reaction monitoring mode were: m/z 349.1 → 286.9 (DHA), m/z 428.9 → 96.0 (DHAS) and m/z 267.1 → 236.9 (IS). Calibration curves offered satisfactory linearity within the test range, and all correlation coefficients were >0.995. The lower limit of detection of DHA and DHAS in plasma samples were determined to be 0.1 ng/mL. The lower limit of quantitation was 0.5 ng/mL for DHA and DHAS. All the recoveries of the quality control samples were in the range of 86.0–102.4%. The ratios of matrix effect were between 89.2 and 105.1%. The method was fully validated and successfully applied to the pharmacokinetic study of DHA and DHAS in rats. The study showed that both DHA and DHAS were distributed and eliminated rapidly in rats. Copyright © 2013 John Wiley & Sons, Ltd.     

Concurrent determination of olanzapine,risperidone and 9‐hydroxyrisperidone in human plasma by ultra performance liquid chromatography with diode array detection method: application to pharmacokinetic study

A simple and sensitive ultra‐performance liquid chromatography (UPLC) method has been developed and validated for simultaneous estimation of olanzapine (OLZ), risperidone (RIS) and 9‐hydroxyrisperidone (9‐OHRIS) in human plasma in vitro. The sample preparation was performed by simple liquid–liquid extraction technique. The analytes were chromatographed on a Waters Acquity H class UPLC system using isocratic mobile phase conditions at a flow rate of 0.3 mL/min and Acquity UPLC BEH shield RP₁₈ column maintained at 40°C. Quantification was performed on a photodiode array detector set at 277 nm and clozapine was used as internal standard (IS). OLZ, RIS, 9‐OHRIS and IS retention times were found to be 0.9, 1.4, .1.8 and 3.1 min, respectively, and the total run time was 4 min. The method was validated for selectivity, specificity, recovery, linearity, accuracy, precision and sample stability. The calibration curve was linear over the concentration range 1–100 ng/mL for OLZ, RIS and 9‐OHRIS. Intra‐ and inter‐day precisions for OLZ, RIS and 9‐OHRIS were found to be good with the coefficient of variation <6.96%, and the accuracy ranging from 97.55 to 105.41%, in human plasma. The validated UPLC method was successfully applied to the pharmacokinetic study of RIS and 9‐OHRIS in human plasma. Copyright © 2015 John Wiley & Sons, Ltd.     

Semi‐analytical description of the S = 9/2 quadrupole nutation NMR experiment: multinuclear application to 113In and 115In in indium phosphide

The density matrix of a spin S = 9/2 excited by a radiofrequency pulse is calculated. The interaction involved during the excitation of the spin system is first‐order quadrupolar. Consequently, the results are valid for any ratio of the quadrupolar coupling ω_Q to the pulse amplitude ω₁. The behavior of the central transition intensities versus the pulse length is discussed. The ¹¹⁵In and ¹¹³In nuclei in a powdered sample of indium phosphide (InP) are used to illustrate the results. It is found that the ratio of the quadrupolar coupling constants determined in this work is in excellent agreement with the ratio of the quadrupole moments of the two nuclei. Copyright © 2015 John Wiley & Sons, Ltd.