Equilibrium partitioning of Ficoll in composite hydrogels

Equilibrium partition coefficients (phi, the concentration in the gel divided by that in free solution) of fluorescein-labeled Ficolls in pure agarose and agarose-dextran composite gels were measured as a function of gel composition and Ficoll size. The four narrow fractions of Ficoll, a spherical polysaccharide, had Stokes-Einstein radii ranging from 2.7 to 5.9 nm. Gels with agarose volume fractions of 0.040 and 0.080 were studied, with dextran volume fractions (calculated as if the chain were a long fiber) up to 0.011. As expected, phi generally decreased as the Ficoll size increased (for a given gel composition) or as the amount of dextran incorporated into the gel increased (for a given agarose concentration and Ficoll size). The decrease in phi that accompanied dextran addition was predicted well by an excluded volume theory in which agarose and dextran were both treated as rigid, straight, randomly positioned and oriented fibers. Modeling dextran as a spherical coil within a fibrous agarose gel produced much less accurate predictions. The diffusional permeabilities of these gels were assessed by combining the current partitioning data with relative diffusivities (Kd, the diffusivity in the gel divided by that in free solution) reported previously. The values of phi Kd for a synthetic gel with 8.0% agarose and 1.1% dextran (by volume) were found to be very similar to those for the glomerular basement membrane, a physiologically important material which also has a total solids content of approximately 10%.     

System size and control parameter effects in reverse perturbation nonequilibrium molecular dynamics

The issue of system size effects in the reverse perturbation nonequilibrium molecular dynamics method for determining transport coefficients of fluids is examined for the case of the Lennard-Jones model. It is found that when adequate precautions are observed in obtaining linear temperature or momentum profiles, a 250 atom system is adequate for determining the thermal conductivity and the shear viscosity. Also, a means of determining the uncertainties in the transport coefficients is described. The conclusion is that this method is computationally competitive with other simulation methods for estimating transport coefficients.     

DNA electrophoresis in confined, periodic geometries: a new lakes-straits model

We present a method to study the dynamics of long DNA molecules inside a cubic array of confining spheres, connected through narrow openings. Our method is based on the coarse-grained, lakes-straits model of Zimm and is therefore much faster than Brownian dynamics simulations. In contrast to Zimm's approach, our method uses a standard stochastic kinetic simulation to account for the mass transfer through the narrow straits and the formation of new lakes. The different rates, or propensities, of the reactions are obtained using first-passage time statistics and a Monte Carlo sampling to compute the total free energy of the chain. The total free energy takes into account the self-avoiding nature of the chain as well as confinement effects from the impenetrable spheres. The mobilities of various chains agree with biased reptation theory at low and high fields. At moderate fields, confinement effects lead to a new regime of reptation where the mobility is a linear function of molecular weight and the dispersion is minimal.     

Changes in molecular properties with changes in molecular geometry: A partitioning into electronic and nuclear components

Most one-electron properties vary with changes in molecular conformation. Although the nuclear component remains constant for some of the one-electron property changes and thus the overall change depends only on the electronic change this result is not general. Often the change in the nuclear component dominates the overall change in a molecular property. An analysis of the changes in a number of one-electron properties with changes in molecular geometry in terms of the changes in the nuclear and the electronic components is presented. The inversion of ammonia and the torsion of ethane were chosen as important examples of conformational changes and the changes in molecular one-electron properties studied.     

Stockholder projector analysis: a Hilbert-space partitioning of the molecular one-electron density matrix with orthogonal projectors

A previously introduced partitioning of the molecular one-electron density matrix over atoms and bonds [D. Vanfleteren et al., J. Chem. Phys. 133, 231103 (2010)] is investigated in detail. Orthogonal projection operators are used to define atomic subspaces, as in Natural Population Analysis. The orthogonal projection operators are constructed with a recursive scheme. These operators are chemically relevant and obey a stockholder principle, familiar from the Hirshfeld-I partitioning of the electron density. The stockholder principle is extended to density matrices, where the orthogonal projectors are considered to be atomic fractions of the summed contributions. All calculations are performed as matrix manipulations in one-electron Hilbert space. Mathematical proofs and numerical evidence concerning this recursive scheme are provided in the present paper. The advantages associated with the use of these stockholder projection operators are examined with respect to covalent bond orders, bond polarization, and transferability.     

The orientation parameter for energy transfer in restricted geometries including block copolymer interfaces: a Monte Carlo study

We describe Monte Carlo simulations of resonance energy transfer (RET) experiments for immobile donor (D) and acceptor (A) dyes confined to planar, cylindrical, and spherical restricted geometries. We compare values of the quantum efficiency (PhiET) evaluated through consideration of individual donor-acceptor pairs, with values calculated assuming a pre-averaged value of the orientation parameter /kappa/2 = 0.476 appropriate for infinite three dimensional (3D) space. For dyes confined to restricted geometries where the length scale of the confining dimension is less than or equal to the F?rster radius R0, the coupling of the orientation parameter and the donor-acceptor distance becomes noticeable. Values of Phi(ET) obtained by proper consideration of the orientation parameter are smaller than those calculated using /kappa/2 = 0.476. We use this Monte Carlo method to reanalyze the fluoresce decay measured from dye-labeled poly(isoprene-b-methyl methacrylate) diblock copolymer with lamellar structure,(1) from which the interface thickness for PI-PMMA lamella can be retrieved. We found the retrieved interface thickness is sensitive to the choice of dipole orientation. If all dipoles in the confined polymer interface have a random orientation, the value of interface thickness was found to be 0.9 +/- 0.2 nm through consideration of individual dipole orientations. Assumption of /kappa/2 = 0.476 in the FRET calculations leads to a larger value of interface thickness (1.3 +/- 0.2 nm) due to the neglect of the coupling between dipole orientation and D-A distance for the dyes confined to lamellar interfaces.     

Communication: Identification of the molecule-metal bonding geometries of molecular nanowires

Molecular nanowires in which a single molecule bonds chemically to two metal electrodes and forms a stable electrically conducting bridge between them have been studied intensively for more than a decade. However, the experimental determination of the bonding geometry between the molecule and electrodes has remained elusive. Here we demonstrate by means of ab initio calculations that inelastic tunneling spectroscopy (IETS) can determine these geometries. We identify the bonding geometries at the gold-sulfur interfaces of propanedithiolate molecules bridging gold electrodes that give rise to the specific IETS signatures that were observed in recent experiments.     

Mass connectivity index,a new molecular parameter for the estimation of ionic liquid properties

A new concept named mass connectivity index (MCI) to encode bond contributions and to allow quantifying the extent of branching in a molecule, especially of ionic liquids, is proposed. The concept is based on the molecular connectivity concept first introduced by Randic in 1975 and modified in different forms by several authors. The proposed concept is much easier to calculate than any of the connectivity indexes available in the literature. Thus the only data required for determining the MCI are the groups forming the molecule and the mass of the groups. The groups forming the molecule are defined as commonly done in group contribution methods. The index is used as a variable in generalized correlations to accurately estimate the density and the heat capacity of ionic liquids.     

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.     

Local and nonlocal contributions to molecular first-order hyperpolarizability: a Hirshfeld partitioning analysis

Based on first-principles calculations, a decomposition scheme is proposed to investigate the molecular site-specific first-order hyperpolarizability (β) responses by means of Hirshfeld population analysis and finite field method. For a molecule, its β is decomposed into local and nonlocal contributions of individual atoms or groups. The former describes the response within the atomic sphere, while the latter describes the contributions from interatomic charge transfer. This scheme is then applied to six prototypical donor-acceptor (D-A) or D-π-A molecules for which the local and nonlocal hyperpolarizabilities are evaluated based on their MP2 density. Both the local and nonlocal parts exhibit site-specific characteristics, but vary differently with molecular structures. The local part depends mainly on the atomic attributes such as electronegativity and charge state, as well as its location in the molecule, while the nonlocal part relates to the ability and distance of charge delocalization within the molecule, increasing rapidly with molecular size. The proposed decomposition scheme provides a way to distinguish atomic or group contributions to molecular hyperpolarizabilities, which is useful in the molecular design for organic nonlinear optical materials.     

The geometries of molecular complexes: An extended Hückel approach

The extended Hückel scheme of Hoffmann is approximated to allow relatively easy energy cal-calculations as a function of relative intermolecular geometry for a variety of planar charge transfer and charge resonance molecular complex pairs. The Hoffmann scheme is briefly discussed and the pertinent features of the method are illustrated with particular reference to weakly interacting molecular pairs. A dominant experimental structural feature is noted for all the complexes studied, in which a -bond of one molecule is centered over and parallel to two edges of a hexagonal ring of the second molecule; it is basically a bonds-over-bonds arrangement. The calculated structures show good agreement with those observed for systems containing TCNE-like fragments and fair agreement for those in which this dominant structural feature occurs through the projection of two six-membered rings. In general no absolute binding is predicted. However, the agreement of relative minima between calculated and observed geometries coupled with the ease of calculation indicate the simple method may be useful in predicting relative geometries and further elucidating the more complicated structural features which must be involved.

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Zusammenfassung Das erweiterte Hückelschema von Hoffmann wird angenähert und erlaubt damit eine relativ leichte Berechnung der Energie als Funktion der relativen intramolekularen Geometrie einer Anzahl von Molekülpaarkomplexen mit ebener Ladungsübertragung und Ladungsresonanz. Das Hoffmann-Schema wird kurz erörtert und die wesentlichen Züge der Methode beleuchtet mit besonderer Berücksichtigung von Molekülpaaren mit schwacher Wechselwirkung. Ein hervorstechender, experimentell beobachteter, struktureller Grundzug wird für alle untersuchten Komplexe, in denen eine -Bindung eines Moleküls der einen Sorte oberhalb und parallel zweier Seiten eines hexagonalen Ringes liegt, der aus Molekülen der anderen Sorte aufgebaut ist, festgestellt; es ist hauptsächlich eine Bindungen-über-Bindungen-Anordnung. Die berechneten Strukturen zeigen gute Übereinstimmung mit denjenigen, die bei Systemen mit TCNE-artigen Fragmenten beobachtet wurden, und befriedigende Übereinstimmung mit solchen Strukturen, bei denen dieser dominierende Charakter durch die Projektion von zwei sechsgliedrigen Ringen hervorgerufen wird. Allgemein wird keine absolute Bindung vorhergesagt. Die Übereinstimmung der relativen Minima zwischen errechneten und beobachteten Geometrien verbunden mit der Einfachheit der Rechnung deutet jedoch an, daß die einfache Methode nützlich sein kann bei der Vorhersage relativer Geometrien und weiterer Aufklärung komplizierter struktureller Grundzüge, die in Betracht gezogen werden müssen.

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Resumé Le schéma de la méthode de Hückel étendue d'Hoffmann est utilise d'une manière approchée pour permettre des calculs relativement faciles de l'énergie en function de la géometrie intermoléculaire pour des complexes moléculaires plans de type transfert de charge et résonance de charge. Le schéma d'Hoffmann est brièvement discuté et les traits pertinents de la methode sont illustrés avec référence particulière à des paires moléculaires en interaction faible. Les complexes étudiés présentent une caractéristique structurale dominante: une liaison d'une des molécules se trouve parallèlement au dessus de deux côtes d'un cycle hexagonal de l'autre molécule; c'est fondamentalement une disposition liaisons sur liaisons. Les structures calculées sont en bon accord avec celles observées pour des systèmes contenant des fragments du type TCNE et en accord satisfaisant pour des systemes où cette caractéristique structurale dominante intervient par projection de deux cycles hexagonaux. En général on ne prédit pas de liaison absolue. Cependant, l'accord entre les minima relatifs des géométries calculées et observées joint á la facilité du calcul montre que cette méthode simple peut être utile pour prédire des géométries relatives et éclaircir des caractères structuraux plus complexes.

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Supported in Part by the U.S. Army Research Office, Durham, North Carolina.

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Based on work (RWM) submitted in partial fulfillment of the A.M. degree, Duke University, 1968.     

Second row molecular orbital calculations: III. Semi-empirical calculations of geometries

The ability of four semi-empirical methods to predict geometries of molecules containing atoms in the second row of the periodic table is investigated for about 80 molecules. Non-empirical, minimal basis set calculations, with and without optimization of valence orbital exponents, are carried out for a number of diatomic molecules. While none of the methods are capable of predicting geometries with an accuracy comparable to the first row parametrization, the SPD' method of Santry and the related INDO method of Benson and Hudson appear to be the most consistent. The ab initio calculations do not suffer from the drawbacks exhibited by the latter two semi-empirical methods. From this it is concluded that the failure of such methods lies in the parametrization rather than in the use of a minimal basis set.     

Absorption and emission spectroscopy of molecular trimers: Cyclic versus linear geometries

The spectroscopic properties of molecular trimers are studied within a model where three degenerate electronically excited states are coupled via dipole–dipole interactions. Taking a single vibrational degree of freedom for each monomer into account, this results in a non-adiabatic nuclear dynamic which determines features of the spectra. The cases of a cyclic and a linear coupling scheme are regarded and it is investigated how these different geometries influence the absorption and emission spectra.     

A new partitioning scheme for molecular interacting systems within a multiconfigurational or monoconfigurational Hartree–Fock formalism

A new method, based on the spatial decomposition of the reduced‐density and pair‐density matrices and the indistinguishable integrals formalism, is introduced to partition the molecular and stabilization energies into meaningful fragments. These are defined as entirely flexible variable‐size entities, for example, atoms, group of atoms, ions, and interacting monomers. This new partitioning scheme is especially appropriated to study systems in which a directly bonded group‐transfer process occurs. In these cases, the stabilization energies are partitioned into an intrafragment component, associated with the difference of intrinsic affinity to the transferred group between the involved fragments, and an interfragment component, associated with the difference of the magnitude of the interaction between the fragments in the initial and final binding complexes. This method was applied to the study of the arginine–carboxylate interactions, allowing us to have insight into what really happens in this system. Two (zwitterionic and neutral) binding complexes can be considered. The main effects accountable for the preferential stabilizations of the binding complexes are determined to be basis‐set independent. The zwitterionic complex is favored by the interfragment component, while the neutral complex is favored by the larger intrinsic proton affinity of the acetate relatively to the methylguanidium. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 157–176, 1999     

Substituent effects on aromatic ring: Theoretical studies of molecular geometries of alkylphenols

Molecular mechanics calculations have been carried out for a series of alkylphenols in order to assess the effects of substituents on bond angles. The results are in good agreement with crystallographic data.     

吡啶甲酸分子平衡构型的ab initio理论研究

本文用能量梯度法TEXAS从头计算程序,选取4-21G(,N原子含极化d轨道)基组,对α-,β-吡啶甲酸分子的平衡几何构型进行了全优化计算,二套基组的理论优化表明,三个吡啶甲酸分子都具有平面的平衡构型,其计算键长经4-21G 基组的标准经验校正值校正后,所得的理论预测平衡几何构型与X射线单晶衍射实验结果有很好的一致性.对部分键长以及羧基与吡啶华平面的二面角中出现的差异进行了讨论.     

Multiblock variance partitioning: a new approach for comparing variation in multiple data blocks

More than one multi-informative analytical technique is often applied when describing the condition of a set of samples. Often a part of the information found in these data blocks is redundant and can be extracted from more blocks. This study puts forward a method (multiblock variance partitioning—MVP) to compare the information/variation in different data blocks using simple quantitative measures. These measures are the unique part of the variation only found in one data block and the common part that can be found in more data blocks. These different parts are found using PLS models between predictor blocks and a common response. MVP provides a different view on the information in different blocks than normal multiblock analysis. It will be shown that this has many applications in very diverse fields such as process control, assessor performance in sensory analysis, efficiency of preprocessing methods and as complementary information to an interval PLS analysis. Here the ideas of the MVP approach are presented in detail using a study of red wines from different regions measured with GC-MS and FT-IR instruments providing different kinds of data representations.