Orbital correlation effects: The independent pair-potential approximation with application to the ground state and first ionized state of boron hydride

A new method is proposed for calculating correlation effects in atomic and molecular systems. The basis of the method is the formulation of a set of partial configuration expansions which yield directly variational orbital correlation corrections which are appropriately summed in order to obtain an estimate of the total correlation energy. This method is applied to the ground state of boron hydride and its cation at the equilibrium distance of BH. The results of the method are compared in detail with independent electron pair results and second order CI results. It is further shown that multiple substitutions are approximately accounted for in this method and the extent to which they are included is compared with other approximations. Finally, three methods of increasing accuracy, aimed at reducing the necessary computational effort, are given for determining the vertical ionization potential. The most economical method yields an IP of 9.70 eV or 0.03 eV less than the experimental IP. Completion of the basis is estimated to improve this value to 9.77 eV.     

Ab initio study of Rg2I− (Rg = Ar,Kr, Xe)

The equilibrium geometries, vibrational frequencies, and dissociation energies of rare gas iodine clusters Rg₂I^?(Rg = Ar, Kr, Xe) were calculated at the Hartree–Fock (HF), second‐order Møller–Plesset (MP2), the coupled cluster method with single and double excitation and a noniterative correction for triple excitations method [CCSD(T)] levels. The title species have bent C_2v structure of about 60° angle. The electron correlation effects and relativistic effects on the geometry and stability were investigated at CCSD(T) level. Both effects stabilize title species. The calculated electron affinities are in good agreement with the experimental results available. The effect of high angular momentum functions (g and h) was studied. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

QSPR Modeling of Gibbs Free Energy of Organic Compounds by Weighting of Nearest Neighboring Codes

We examine the encoding of chemical structure of organic compounds by Labeled Hydrogen-Filled Graphs (LHFGs). Quantitative Structure-Property Relationships (QSPR) for a representative set of 150 organic molecules have been derived by means of the optimization of correlation weights of local invariants of the LHFGs. We have tested as local invariants Morgan extended connectivity of zero- and first order, numbers of path of length 2 (P2) and valence shells of distance of 2 (S2) associated with each atom in the molecular structure, and the Nearest Neighboring Codes (NNC). The best statistical characteristics for the Gibbs free energy has been obtained for the NNC weighting. Statistical parameters corresponding to this model are the following n = 100, r² = 0.9974, s = 5.136 kJ/mol, F = 38319 (training set); n = 50, r² = 0.9990, s = 3.405 kJ/mol, F = 48717 (test set). Some possible further developments are pointed out.     

Diffusion Monte Carlo study of correlation in the hydrogen molecule

The diffusion Monte Carlo (DMC) method shows that correlation in H₂ produces a set of three spatial changes: (i) an enhancement in the electron density distribution n( r ) in the left and right anti‐binding regions that include separately the immediate vicinity of each of the two nuclei, (ii) a reduction in n( r ) in the binding region intervening between the two nuclei as a counterbalance, and (iii) a concomitant increase in the equilibrium internuclear separation. It is stressed that the correlation energy E^c (= T^c + V^c) for diatomic molecules be defined by the difference in the total energy between the exact and the Hartree–Fock (HF) variational calculations that are performed at individually optimized internuclear separations. It is this definition that makes it possible to involve a significant contribution from a correlation‐induced change in the equilibrium internuclear separation as part of the correlation energy and to relate (i) and (ii) to (iii) in consistency with the electrostatic theorem. The present calculations fulfill the virial theorem to an accuracy of ?V/T = 2.00 for DMC and ?V^HF/T^HF = 2.000 for HF. The present correlation energy E^c = ?0.0408 hartree is not only in good agreement with the most accurate value previously reported, but also can be analyzed into all its components in accordance with the correlational virial theorem 2T^c + V^c = 0. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

A study for quality evaluation of Taxilli Herba from different hosts based on fingerprint-activity relationship modeling and multivariate statistical analysis

In this study, a fingerprint-activity relationship modeling between chemical fingerprints and antirheumatic activity was established, and multivariate statistical analysis was used to evaluate the quality of Taxilli Herba (TH) from different hosts. Characteristic fingerprints of 20 batches of TH samples were generated by high-performance liquid chromatography coupled with triple quadrupole-time of flight tandem mass spectrometry (HPLC-Triple TOF-MS/MS), and the similarity analysis was calculated based on thirteen common characteristic peaks by hierarchical clustering analysis (HCA). Subsequently, nine efficacy markers were discovered by combining fingerprints and antirheumatic activity through grey correlation analysis (GCA) and bivariate correlation analysis (BCA). Meanwhile, the content of 5 constituents in 9 markers was determined by high-performance liquid chromatography coupled with triple quadrupole-linear ion trap tandem mass spectrometry (HPLC-QTRAP-MS/MS). The comprehensive quality of TH was assessed using multivariate statistical analysis, including principal components analysis (PCA) and technique for order preference by similarity to ideal solution (TOPSIS). The results showed that a high dose of TH extract could markedly ameliorate arthritis damage compared to other doses, with flavonoids playing an important role in the antirheumatic activity. The comprehensive quality of samples from Morus alba L. (SS) was superior to those from Liquidambar formosana Hance (FXS). The present study will demonstrate the markers associated with efficacy, and provide an applicable strategy for more comprehensive quality control and evaluation of TH.     

Some results on the behavior and estimation of the fractal dimensions of distributions on attractors

The strong interest in recent years in analyzing chaotic dynamical systems according to their asymptotic behavior has led to various definitions of fractal dimension and corresponding methods of statistical estimation. In this paper we first provide a rigorous mathematical framework for the study of dimension, focusing on pointwise dimension(x) and the generalized Renyi dimensionsD(q), and give a rigorous proof of inequalities first derived by Grassberger and Procaccia and Hentschel and Procaccia. We then specialize to the problem of statistical estimation of the correlation dimension and information dimension. It has been recognized for some time that the error estimates accompanying the usual procedures (which generally involve least squares methods and nearest neighbor calculations) grossly underestimate the true statistical error involved. In least squares analyses of and we identify sources of error not previously discussed in the literature and address the problem of obtaining accurate error estimates. We then develop an estimation procedure for which corrects for an important bias term (the local measure density) and provides confidence intervals for. The general applicability of this method is illustrated with various numerical examples.     

Metastable systems driven by colored noise: The stationary state

The influence of the Bardeen-Herring back-jump correlations on the Fermi-Dirac statistics of the one-dimensional nonhomogeneous fermionic lattice gas is studied by the Monte Carlo simulation technique and semianalytically. The resulting distribution is obtained, exhibiting increased population of the lower levels in comparison to the Fermi-Dirac statistics.     

硬脂酸晶体压力效应的FT-IR光谱研究

 本文在0~4 GPa范围内研究了预压力对硬脂酸晶体的相关场劈裂和固态-熔融态相变过程的影响。通过γCH₂面内摇摆振动模和γ'CH₂相关场模的强度和频率变化,发现预压力对晶体内的相关场合分子链取向有明显的影响。预压力对硬脂酸的熔点虽然没有影响,但对γ'CH₂模有“硬化”作用。并且由此出发,对硬脂酸的预熔过程作了讨论。     

Substituent dependence of the d-d transition band in the electronic absorption spectra of arylferrocenes and the corresponding arylferricenium salts

The electronic absorption spectra of 22 arylferrocenes and their arylferricenium salts with pentacyanopropenide (PCNP) were recorded. The attemptedHammett correlation of _max of the d-d transition bands of arylferrocenes revealed that this band is substituent dependent only for strong electron-withdrawing substituents. Excellent correlation of _max of the d-d transition bands with ⁺ constants was found in the case of arylferricenium cations. Good correlations of _max was also found with theE _1/2 oxidation potentials measured by cyclic voltametry.

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Substituentenabhängigkeit des d-d-Überganges in den Elektronenabsorptions-Spektren von Arylferrocenen und entsprechenden Arylferricenium-Salzen

Zusammenfassung Elektronenabsorptions-Spektren von 22 Arylferrocenen und ihren Arylferricenium-Pentacyanopropenid-Salzen wurden gemessen. VersuchteHammett-Korrelationen des längstwelligen d-d-Überganges (_max) zeigten, daß diese Bande nur von stark elektronenanziehende Substituenten abhängig ist. Im Fall der Arylferricenium-Kationen wurde eine ausgezeichnete Korrelation zwischen _max der d-d-Bande und den ⁺-Konstanten festgestellt. Eine gute Korrelation der _max-Werte wurde auch mit denE _1/2 Oxidationspotentialen gefunden, die durch cyclische Voltametrie meßbar sind.

     

Perturbational approach to the electron correlation cusp applied to helium‐like atoms

A recently proposed perturbational approach to the electron correlation cusp problem 1 is tested in the context of three spherically symmetrical two‐electron systems: helium atom, hydride anion, and a solvable model system. The interelectronic interaction is partitioned into long‐ and short‐range components. The long‐range interaction, lacking the singularities responsible for the electron correlation cusp, is included in the reference Hamiltonian. Accelerated convergence of orbital‐based methods for this smooth reference Hamiltonian is shown by a detailed partial wave analysis. Contracted orbital basis sets constructed from atomic natural orbitals are shown to be significantly better for the new Hamiltonian than standard basis sets of the same size. The short‐range component becomes the perturbation. The low‐order perturbation equations are solved variationally using basis sets of correlated Gaussian geminals. Variational energies and low‐order perturbation wave functions for the model system are shown to be in excellent agreement with highly accurate numerical solutions for that system. Approximations of the reference wave functions, described by fewer basis functions, are tested for use in the perturbation equations and shown to provide significant computational advantages with tolerable loss of accuracy. Lower bounds for the radius of convergence of the resulting perturbation expansions are estimated. The proposed method is capable of achieving sub‐μHartree accuracy for all systems considered here. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003