Statistical-overlap theory for elliptical zones of high aspect ratio in comprehensive two-dimensional separations

The low prediction by statistical-overlap theory of the numbers of singlets and peaks in two-dimensional separations containing zones represented by either circles of small number or eccentric ellipses of any number is shown to result from use of probability expressions for unbound spaces of infinite extent. An exact theory is derived for the probability of singlet formation in a reduced two-dimensional space of unit length, width, and area. The probability is a weighted sum of the probabilities of singlet formation in the interior, edge, and corner regions of the space, which depend only on saturation. The weighting factors are the fractions of area associated with each region and depend on the number of zones, the aspect ratio, the saturation, and the ellipse's spatial orientation. The average numbers of doublets, triplets, and peaks in the space are approximated by combining these results with Roach's equations describing the clustering of circles in an unbound two-dimensional space. Simulations show that theory predicts the number of singlets, doublets, triplets, and peaks, when the number of zones is 25 or more, the aspect ratio is 100 or less, and the saturation is 2 or less. The relationship is derived between the aspect ratios of ellipses in the reduced space and actual separation space. Calculations are presented for comprehensive two-dimensional gas chromatography.     

The role of the π-bonding network for trigonal level splittings of tris-bidentate Cr(acac)3 and Cr(ox) 3 3−

The varying -bonding contributions in the title compounds caused by the different electronic and molecular structure of the chelate rings are used for explaining the large band splittings in the absorption spectra by trigonal symmetry. It is shown that usual ligand field theory and the angular overlap model are not able to account for the trigonal level splitting of Cr(acac)₃ for which the coordination sphere of oxygen atoms is nearly octahedrally arranged. The experimental finding can, however, be rationalized by an extended angular overlap model which considers the phase coupling of -orbitals in the ligands leading to non-additive contributions to the metal-ligand bond energy.On leave of absence from the Bulgarian Academy of Sciences, Sofia, Bulgaria     

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.     

支化高分子在溶液中的交叠与缠结

溶液中高分子的交叠和缠结与其链结构密切相关。支化聚苯乙烯的临界交叠浓度C和临界缠结浓度C_E比分子量相同的线型聚苯乙烯的大,说明交叠和缠结同分子在溶液中线团的体积有直接关系。     

PP回归方法在预测模型中的应用－用PP回归建立“积累”“消费”模型

本文利用ＰＰ回归方法,建立“积累”“消费”回归模型,并与最小二乘法拟合的线性回归模型相比较,说明用ＰＰ回归建立的模型预测精度较高．     

Spectrochemical Properties of Noncubical Transition Metal Complexes in Solutions. IX. The Mixed Tetragonal Distorted Bis(Salicylato)Cobalt(II) Complex in Various Solvents

Mixed cobalt(II) complexes with the monodentate ligands: 2-hydroxybenzoic acid deprotonated (sal^–, the salicylate ion) and water, have been investigated. The combined results of the spectrophotometric and conductance measurements, as well as known the X-ray structure for solids, were used to determine the structure of the studied complexes in solution. The electronic absorption spectra in aqueous acid (0.01M HClO₄), ethylene glycol (glycol), formamide (FM), N,N-dimethylformamide (DMF), and dimethyl sulfoxide (DMSO) solutions have been recorded. The d-d electronic spectra have been treated by the crystal-field model (CFM) and angular overlap model (AOM). Low-symmetry splittings of the broad asymmetric bands in the experimental spectra (solutions at room temperature) were found by Gaussian analysis. The effect of the and bonding of the monodentate ligands (with oxygen-donor ligators) on the central metal ion was described in the ligand–field framework. A comparison of the stereochemistry of the complex species in various solutions was made.     

The ab initio neglect of differential diatomic overlap method

The ab initio Neglect of Differential Diatomic Overlap (N.D.D.O.) method of Roby is tested numerically for an extensive series of molecules. Agreement with the full ab initio molecular orbital method is poor. Total energies are more negative and dipole moments are overestimated. The failings of the N.D.D.O. method are accounted for using multipole-multipole expansions.     

Spectrochemical Properties of Noncubical Transition Metal Complexes in Solution. XII. Angular Overlap Studies of Salicylideneethylenediamine Cu(II) Complex in Various Solvents

As a part of our general interest in the UV-Vis spectroscopy of multidentate mixed-donor ligands, the (salicylideneethylenediamine)Cu(II) complex has been prepared and characterized by elemental analyses, solubility in common solvents, molar conductivities, and ultraviolet (UV), and visible (Vis) spectroscopy. The combined results of spectrophotometric measurements and EPR spectra, as well as known the X-ray structure for solids, were used to determine the structure of the investigated complex in solutions. The spectra of [Cu(salen)] (H₂salen = salicylideneethylenediamine), were measured in various solvents at room temperature, resolved by Gaussian analysis, and angular overlap model (AOM) treated in C _2v symmetry. Because of overparametrization problems, the bis(salicylaldehyde)Cu(II) complex has been characterized and AOM treated. The results of this have been used for AOM studies of [Cu(salen)]. The effect of the solvents upon the - and -bonding ligand abilities is discussed.     

Improving the efficiency and reliability of free energy perturbation calculations using overlap sampling methods

A challenge in free energy calculation for complex molecular systems by computer simulation is to obtain a reliable estimate within feasible computational time. In this study, we suggest an answer to this challenge by exploring a simple method, overlap sampling (OS), for producing reliable free-energy results in an efficient way. The formalism of the OS method is based on ensuring sampling of important overlapping phase space during perturbation calculations. This technique samples both forward and reverse free energy perturbation (FEP) to improve the free-energy calculation. It considers the asymmetry of the FEP calculation and features an ability to optimize both the precision and the accuracy of the measurement without affecting the simulation process itself. The OS method is tested at two optimization levels: no optimization (simple OS), and full optimization (equivalent to Bennett's method), and compared to conventional FEP techniques, including the widely used direct FEP averaging method, on three alchemical mutation systems: (a) an anion transformation in water solution, (b) mutation between methanol and ethane, and (c) alchemical change of an adenosine molecule. It is consistently shown that the reliability of free-energy estimates can be greatly improved using the OS techniques at both optimization levels, while the performance of Bennett's method is particularly striking. In addition, the efficiency of a calculation can be significantly improved because the method is able to (a) converge to the right answer quickly, and (b) work for large perturbations. The basic two-stage OS method can be extended to admit additional stages, if needed. We suggest that the OS method can be used as a general perturbation technique for computing free energy differences in molecular simulations.     

Semiempirical local spin: Theory and implementation of the ZILSH method for predicting Heisenberg exchange constants of polynuclear transition metal complexes

The local spin formalism ( 3 ) for computing expectation values 〈S_A · S_B〉 that appear in the Heisenberg spin model has been extended to semiempirical single determinant wave functions. An alternative derivation of expectation values in restricted and unrestricted cases is given that takes advantage of the zero differential overlap (ZDO) approximation. A formal connection between single determinant wave functions (which are not in general spin eigenfunctions) and the Heisenberg spin model was established by demonstrating that energies of single determinants that are eigenfunctions of the local spin operators with eigenvalues corresponding to high‐spin radical centers are given by the same Heisenberg coupling constants {J_AB} that describe the true spin states of the system. Unrestricted single determinant wave functions for transition metal complexes are good approximations of local spin eigenfunctions when the metal d orbitals are local in character and all unpaired electrons on each metal have the same spin (although spins on different metals might be reversed). Good approximations of the coupling constants can then be extracted from local spin expectation values 〈S_A · S_B〉 energies of the single determinant wave functions. Once the coupling constants are obtained, diagonalization of the Heisenberg spin Hamiltonian provides predictions of the energies and compositions of the spin states. A computational method is presented for obtaining coupling constants and spin‐state energies in this way for polynuclear transition metal complexes using the intermediate neglect of differential overlap Hamiltonian parameterized for optical spectroscopy (INDO/S) in the ZINDO program. This method is referred to as ZILSH, derived from ZINDO, Davidson's local spin formalism, and the Heisenberg spin model. Coupling constants and spin ground states obtained for 10 iron complexes containing from 2 to 6 metals are found to agree well with experimental results in most cases. In the case of the complex [Fe₆O₃(OAc)₉(OEt)₂(bpy)₂]⁺, a priori predictions of the coupling constants yield a ground‐state spin of zero, in agreement with variable‐temperature magnetization data, and corroborate spin alignments proposed earlier on the basis of structural considerations. This demonstrates the potential of the ZILSH method to aid in understanding magnetic interactions in polynuclear transition metal complexes. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003