Topological Analysis

We systematically varied conditions of twodimensional (2D) agarose gel electrophoresis to optimize separation of DNA topoisomers that differ either by the extent of knotting, the extent of catenation or the extent of supercoiling. To this aim we compared electrophoretic behavior of three different families of DNA topoisomers: (i) supercoiled DNA molecules, where supercoiling covered the range extending from covalently closed relaxed up to naturally supercoiled DNA molecules; (ii) postreplicative catenanes with catenation number increasing from 1 to ∼15, where both catenated rings were nicked; (iii) knotted but nicked DNA molecules with a naturally arising spectrum of knots. For better comparison, we studied topoisomer families where each member had the same total molecular mass. For knotted and supercoiled molecules, we analyzed dimeric plasmids whereas catenanes were composed of monomeric forms of the same plasmid. We observed that catenated, knotted and supercoiled families of topoisomers showed different reactions to changes of agarose concentration and voltage during electrophoresis. These differences permitted us to optimize conditions for their separation and shed light on physical characteristics of these different types of DNA topoisomers during electrophoresis.

While the primary product of scientific visualization is images and movies, its primary objective is really scientific insight. Too often, the focus of visualization research is on the product, not the mission. This paper presents two case studies, both that appear in previous publications, that focus on using visualization technology to produce insight. The first applies "Query-Driven Visualization" concepts to laser wakefield simulation data to help identify and analyze the process of beam formation. The second uses topological analysis to provide a quantitative basis for (i) understanding the mixing process in hydrodynamic simulations, and (ii) performing comparative analysis of data from two different types of simulations that model hydrodynamic instability.

The synthesis of a novel 1-acyl-thiourea species (C 14 H 17 N 2 O 2 SCl), has been tailored in such a way that two distinct NAHÁ Á ÁO@C intramolecular competing hydrogen bonds are feasible. The X-ray structure analysis as well as the vibrational (FT-IR and FT-Raman) data reveal that the S conformation is preferred, with the C@O and C@S bonds of the acyl-thiourea group pointing in opposite directions. The preference for the intramolecular NAHÁ Á ÁO@C hydrogen bond within the AC(O)NHC(S)NHA core is confirmed. The Natural Bond Orbital and the Atom in Molecule approaches demonstrate that a strong hyperconjugative lpO ? r ⁄ (NAH) remote interaction between the acyl and the thioamide NAH groups is responsible for the stabilization of the S conformation. Intermolecular interactions have been characterized in the periodic system electron density and the topological analysis reveals the presence of an extended intermolecular network in the crystal, including a ClÁ Á ÁN interaction playing a relevant role in crystal packing.

With the increasing diffusion of Internet probing technologies, a large amount of regularly collected traceroutes are available for Internet Service Providers (ISPs) at low cost. We show how it is possible, given solely an arbitrary set of traceroutes, to spot routing paths that change similarly over time and aggregate them into inferred routing events. With respect to previous works, our approach does not require any knowledge of the network, does not need complex integration of several data sources, and exploits the asynchronicity of measurements to accurately position events in time. The formal model at the basis of our methodology revolves around the notion of empathy, a relation that binds similarly behaving traceroutes. The correctness and completeness of our approach are based on structural properties that are easily expressed in terms of empathic measurements. We perform experiments with data from public measurement infrastructures like RIPE Atlas, showing the effectiveness of our algorithm in distilling significant events from a large amount of traceroute data. We also validate the accuracy of the inferred events against ground-truth knowledge of routing changes originating from induced and spontaneous routing events. Given these promising results, we believe our methodology can be an effective aid for troubleshooting at the ISPs level. The source code of our algorithm is publicly available at .

With the increasing diffusion of Internet probing technologies, a large amount of regularly collected traceroutes are available for Internet Service Providers (ISPs) at low cost. We introduce a practically applicable methodology and algorithm that, given solely an arbitrary set of traceroutes, spot routing paths that change similarly over time, aggregate them into inferred events, and report each event along with the impacted observation points and a small set of IP addresses that can help identify its cause. The formal model at the basis of our methodology revolves around the notion of empathy, a relation that binds similarly behaving traceroutes. The correctness and completeness of our approach are based on structural properties that are easily expressed in terms of empathic measurements. We perform experiments with data from public measurement infrastructures like RIPE Atlas, showing the effectiveness of our algorithm in distilling events from a large amount of traceroute data. We also validate the accuracy of the inferred events against ground-truth knowledge of routing changes originating from induced and spontaneous routing events. Given these promising results, we believe our methodology can be an effective aid for ISPs to detect and track routing changes affecting many users (with potentially adverse effects on their connection quality).

In this article we use a geometric approach to study geometric phases in graphitic cones. The spinor that describes the low energy states near the Fermi energy acquires a phase when transported around the apex of the cone, as found by a holonomy transformation. This topological result can be viewed as an analogue of the Aharonov-Bohm effect. The topological analysis is extended to a system with n cones, whose resulting configuration is described by an effective defect.

Key words: dendritic growth-branching pattern-topological trees-statistical analysis-pyramidal neurons-Kolmogorov goodness-of-fit test-discontinuous probability distributions Statistical analysis of the frequencies of observed branching patterns of neuronal arborescences is an important means of studying neuronal growth and of characterizing axonal or dendritic populations. We recently derived simple formulae for the exact probabilities of occurrence of types of neuronal trees for both segmental and terminal growth. Additionally, the existence of a natural ordering of the neuronal tree types enables the application of the Kolmogorov goodness-of-fit test. In the present report it is illustrated how these facilities can be incorporated in the analysis of neuronal arborizations. Interesting features are that very large neuronal arborizations can be analyzed completely and that only small sample sizes are required for the estimation of the critical level corresponding to the growth hypothesis. Further, it is indicated how populations of neuronal tree structures may be compared with each other without reference to a particular growth theory.

Transmission electron microscopy (TEM) was used to study the precipitation in an 8090 (Al-2.7Li-1.4Cu-1Mg-0.11Zr (wt %)) alloy. TEM diffraction patterns revealed reflections from the orthorhombic S 0 /S (Al 2 CuMg) phase in addition to those of the fcc matrix, the coherent and ordered 0 (Al 3 Li) phase of L1 2 structure and the hexagonal T1 (Al 2 CuLi) phase. The reflections from the T 1 phase were identified and indexed using literature results. Concerning the S 0 /S phase, a theoretical study, based on its orientation relationships with , allowed the construction of transformation matrixes between planes and directions of their reciprocal lattices. The calculation shows that 12 different S 0 /S systems can diffract on a given phase selected area diffraction (SAD) pattern. Theoretically, two diagrams (ð100Þ Ã and ð112Þ Ã) are considered, on which the S 0 /S reflections are indexed. The results obtained for the theoretical patterns are in good agreement with those observed experimentally.

A method, derived from the procedure implemented in the program ORCRIT which was originally developed by C.K. Johnson, is presented for the topological analysis of zeolite electron density maps. This method is an approach to shape analysis of zeolitic frameworks through the location, identification, and linkage of critical points (points where the gradient of the density vanishes) in medium resolution electron density maps. It is observed that, at 3 Å resolution, tetrahedral sites and oxygen atoms generate peaks (density maxima) and passes (saddle points), respectively. The def inition of ellipsoids, built at each peak location from their three local density curvatures, is used to generate a void volume wherein atomic or molecular probes can interact. The energetic behaviour of probes of several sizes interacting with ferrierite and mordenite is qualitatively studied through a pseudo-Lennard-Jones potential approximation.

We study coauthorship networks based on the preprints submitted to the Los Alamos cond-mat database during the period 2000-2005. In our approach two scientists are considered connected if they have coauthored one or more cond-mat preprints together in the same year. We focus on the characterization of the structural properties of the derived graphs and on the time evolution of such properties. The results show that the cond-mat community has grown over the last six years. This is witnessed by an improvement in the connectivity properties of coauthorship graphs over the years, as confirmed by an increasing size of the largest connected component, of the global efficiency and of the clustering coefficient. We have also found that the graphs are characterized by long-tailed degree and betweenness distributions, assortative degree-degree correlations, and a power-law dependence of the clustering coefficient on the node degree.

We study coauthorship networks based on the preprints submitted to the Los Alamos cond-mat database during the period 2000-2005. In our approach two scientists are considered connected if they have coauthored one or more cond-mat preprints together in the same year. We focus on the characterization of the structural properties of the derived graphs and on the time evolution of such properties. The results show that the cond-mat community has grown over the last six years. This is witnessed by an improvement in the connectivity properties of coauthorship graphs over the years, as confirmed by an increasing size of the largest connected component, of the global efficiency and of the clustering coefficient. We have also found that the graphs are characterized by long-tailed degree and betweenness distributions, assortative degree-degree correlations, and a power-law dependence of the clustering coefficient on the node degree.

Hartree-Fock calculations with the 6-31G* basis have been performed to investigate the structure and Li + binding energies of the complexes between Li + and pyridine, diazines, triazines and tetrazines. Structures have been fully optimized at the 3-21G level. As for azole-Li + and methyldiazole-Li + complexes, a topological analysis of the Laplacian of the electronic charge density reveals that the azine-Li + is a typical closed-shell interaction and that the stabilization of the complex is mainly electrostatic. BSSE is quite significant, specially for Li+-bridging complexes. The correlation between calculated Li + binding energies and proton affinities follows two different linear relationships, one for those cases where Li + is singly coordinated and a different one for those cases in which an additional three-membered ring is formed. The enhanced stability of these particular conformations explains why while polyazines are less basic than pyridine when the reference acid is a proton; pyridazine and 1,2,4 triazine are more basic than pyridine when the reference acid is Li +. The effect on Li + binding energies of systematic nitrogen substitution roughly follows an additive model.

CHARGE, SPIN AND MOMENTUM DENSITY C423 sets. Therefore, there are only two reports of high-resolution magnetic Compton experiments [2, 3] in this decade. A new setup of the Cauchois-type x-ray spectrometer for Compton scattering experiments installed on BL08W at SPring-8 allows us to perform high-resolution experiments within a reasonable beam time. This spectrometer employs an X-ray image intensifier as a position sensitive detector. Using this spectrometer, a high-resolution magnetic Compton profile of iron single-crystal was measured with a momentum resolution of 0.14 atomic units. The statistical accuracy is approximately 4% at p z =0. The experiment shows a good agreement with the theoretical prediction [1].

Institut National de Recherche en Informatique et en Automatique de RENNES-BRETAGNE ATLANTIQUE Institut de Recherche en Informatique et Systèmes Aléatoires Équipe Dyliss (DYnamics, Logics and Inference for biological Systems and Sequences) CAMPUS DE BEAULIEU 263 AVENUE GENERAL LECLERC 35042 RENNES Vérifications du réseau métabolique entier de Tisochrysis lutea Rapport de stage

Synthetic metalloporphyrin complexes are often used as analogues of natural systems, and they can be used for the preparation of high-dimensional coordination polymers. In this work, a new chiral Fe-TCPP (TCPP is meso-tetra-(4-carboxyphenyl)porphyrin) coordination compound has been synthesised and structurally characterized. The compound is 2D via coordination bonds, and it exhibits strong hydrogen bonds that connect the planar arrays forming the 3D framework. The oxidation of the original Fe II ions to Fe III accounts for the formation of this array, in which the topological analysis reveals a very high connectivity based on a simple extension fashion of the structure. DFT calculations have been also carried out to study the stabilisation of the Fe III-compound. This is the third example of a 2D coordination compound based on TCPP in which the dimensionality refers just to coordination bonds, and no other ligands are present in the structure.

In manufacturing processes like injection molding or die casting, a 2-piece mold is required to be separable, that is, be able to have both pieces of the mold remove in opposite directions while interfering neither with the mold nor with each other. The fundamental problem is to find a viewing (i.e. separating) direction, from which a valid partition line (i.e. the contact curves of the two mold pieces) exists. While previous research work on this problem exists for polyhedral models, verifying and finding such a partition line for general freeform shapes, represented by NURBS surfaces, is still an open question. This paper shows that such a valid partition exists for a compact surface of genus g, if and only if there is a viewing direction from which the silhouette consists of exactly g + 1 non-singular disjoint loops. Hence, the 2-piece mold separability problem is essentially reduced to the topological analysis of silhouettes. In addition we deal with removing almost vertical surface regions from the mold so that the form can more easily be extracted from the mold. It follows that the aspect graph, which gives all topologically distinct silhouettes, allows one to determine the existence of a valid partition as well as to find such a partition when it exists. In this paper, we present an aspect graph computation technique for compact free-form objects represented as NURBS surfaces. All the vision event curves (parabolic curves, flecnodal curves, and bi-tangency curves) relevant to mold separability are computed by symbolic techniques based on the NURBS representation, combined with numerical processing. An image dilation technique is then used for robust aspect graph cell decomposition on the sphere of viewing directions. Thus, an exact solution to the 2-piece mold separability problem is given for such models.

The occurrence of multifurcations in essentially binary trees is investigated with respect to two methods for testing growth models, viz. subtree partition analysis and vertex analysis. It is shown that under certain conditions muhifurcations may be incorporated in the analysis. Although the conditions are more restrictive for subtree partition analysis only minor loss of information occurs if forbidden multifurcations are simply ignored.

In this paper the effects of the occurrence of cut trees in the topological analysis of branching patterns have been studied. It is assumed that branches are removed at random from the trees. We prove that, for both the segmental and terminal growth models, the probability distributions of the cut trees are identical to those of complete trees.

surfaces of the control group, implicating a difference in the corticomedial and basolateral nuclei. In cocaine David N. Kennedy, 2,3,14 Steven E. Hyman, 10,12,14 Bruce R. Rosen, 2,14 and Hans C. Breiter 1,2,4,14, * addicts, amygdala volume did not correlate with any measure of cocaine use. The amygdala symmetry co-1 Motivation and Emotion Neuroscience Collaboration efficient did correlate with baseline but not cocaineprimed craving. These findings argue for a condition Department of Radiology 2 Athinoula A. Martinos Center that predisposes the individual to cocaine dependence by affecting the amygdala, or a primary event early in Department of Radiology 3 Center for Morphometric Analysis the course of cocaine use. Department of Neurology 4 Department of Psychiatry Introduction Massachusetts General Hospital and Harvard Medical School Cocaine use and cocaine addiction are responsible for Boston, Massachusetts 02129 failure in life roles and enormous costs to society in 5 Department of Psychiatry terms of disability and direct health expenditure. Yet Massachusetts Mental Health Center and current treatments remain disappointing, and our under-Harvard Medical School standing of environmental and hereditary risk factors Boston, Massachusetts 02115 and the pathogenesis of addiction (Reich et al., 1999; 6 Department of Psychiatry and Tsuang et al., 2001; Kendler et al., 2003) remains incom-Division of Women's Health plete. Brigham and Women's Hospital and Animal studies of cocaine's action have focused on a Harvard Medical School set of subcortical gray matter structures and paralimbic Boston, Massachusetts 02120 cortices that are involved in the mediation of reward 7 McLean Hospital and reinforcement, most notably the ventral tegmental Belmont, Massachusetts 02478 area of the midbrain, the nucleus accumbens, the amyg-8 Department of Epidemiology dala, and regions of the prefrontal cortex (Dworkin and

The electrophilic/nucleophilic behavior of dimethyl 2,3-dimethylenesuccinate 1, an electron-deficient 2,3disubstituted 1,3-butadiene, in polar Diels-Alder reactions has been studied using DFT methods at the B3LYP/ 6-31G(d) level of theory. The electronic nature of bonding of the transition structures involved in the cycloaddition reactions of the diene 1 toward the nucleophilically activated dienophile 6 and the strong electrophilically activated dienophile 7 has been carefully examined within the natural bond orbital (NBO) and the topological analysis of the electron localization function (ELF) frameworks. Additionally, a study of the global electrophilicity pattern of the reagents at the ground state was performed. This evidence allows us to rationalize the participation of electron-deficient 2-susbtituted and 2,3-disubstituted 1,3-butadienes as nucleophiles in polar Diels-Alder reactions.

The determination of the primary cosmic ray mass composition from the longitudinal development of atmospheric cascades is still an open problem. In this work we propose a new method of the multiparametric topological analysis and show that if both Xmax-the depth of shower maximum and Nmax-the number of charged particles in the shower maximum are used, reliable results can be obtained.

Missense mutations as well as a null allele of the human glycine receptor α1 subunit geneGLRA1result in the neurological disorder hyperekplexia [startle disease, stiff baby syndrome, Mendelian Inheritance in Man (MIM) #149400]. In a pedigree showing dominant transmission of hyperekplexia, we identified a novel point mutation C1128A ofGLRA1. This mutation encodes an amino acid substitution (P250T) in the cytoplasmic loop linking transmembrane regions M1 and M2 of the mature α1 polypeptide. After recombinant expression, homomeric α1P250Tsubunit channels showed a strong reduction of maximum whole-cell chloride currents and an altered desensitization, consistent with a prolonged recovery from desensitization. Apparent glycine binding was less affected, yielding an approximately fivefold increase inKivalues. Topological analysis predicts that the substitution of proline 250 leads to the loss of an angular polypeptide structure, thereby destabilizing open channel conformations. Thus, the ...

The coordination of neutral ligands (L = OC, HCN, NH3, PH3, SH2, HNCO and H2O) to Pb2+ is investigated and analyzed by means of the topological analysis of the Electronic Localization Function (ELF). It is shown that the mean charge density of the V(Pb) basin (〈ρ〉V(Pb)) can reach a ligand‐independent limiting value from n = 6, a coordination number from which the [PbLn]2+ complexes adopt holodirected structures. The investigations performed on anionic series (L = HS−, OH−, CN−, F−, Cl−, and Br−) lead to optimized stable structures in which the coordination number does not exceed n = 4, even in the presence of a model aqueous solvent. This different behavior with respect to the neutral ligand series is interpreted by means of natural populations and electrostatic repulsions. The main result of this contribution is that stable Pb(II) complexes could be those exhibiting reasonable values of 〈ρ〉V(Pb), namely those not exceeding the saturation plateau evidenced in the present piece of wo...

A new improved method for calculation of fault coverage with parallel fault backtracing in combinational circuits is proposed. The method is based on structurally synthesized BDDs (SSBDD) which represent gate-level circuits at higher, macro level where macros represent subnetworks of gates. A topological analysis is carried out to generate an efficient optimized model for backtracing of faults to minimize the repeated calculations because of the reconvergent fanouts. The algorithm is equivalent to exact critical path tracing, however, processing the backtrace in parallel for a group of test patterns. Because of the parallelism, higher abstraction level modeling, and optimization of the topological model, the speed of fault simulation was considerably increased. Compared to the state-of-the-art commercial fault simulators the gain in speed was several times.

Common treatment for venous leg wounds includes topical wound dressings with compression. At each dressing change, wounds are debrided and washed; however, the effect of the washing procedure on the wound microbiome has not been studied. We hypothesized that wound washing may alter the wound microbiome. To characterize microbiome changes with respect to wound washing, swabs from 11 patients with chronic wounds were sampled before and after washing, and patient microbiomes were characterized using 16S rRNA sequencing and culturing. Microbiomes across patient samples prior to washing were typically polymicrobial but varied in the number and type of bacterial genera present.ProteusandPseudomonaswere the dominant genera in the study. We found that washing does not consistently change microbiome diversity but does cause consistent changes in microbiome composition. Specifically, washing caused a decrease in the relative abundance of the most highly represented genera in each patient clus...

Topological analysis was applied for the estimation of stability constants (b 1 and b 2) for sets of copper(II) mono-, ML, and bis-complexes, ML 2 , with bidentate ligands, namely 1,2-diaminoethanes (N = 14), aliphatic amino acids and their N-alkylated derivatives (N = 11), and naturally occurring amino acids (N = 9). A set consisting of 16 mixed (ternary) copper(II) bis-complexes with naturally occurring amino acids was also taken into account. The log b values were correlated on the connectivity index 3 v v of the ligands and their mono-or bis-complexes, with or without water coordination, yielding the best results for the model with two additionally bonded water molecules. An improvement of the method was obtained by proposing an additional ligand coordination in some complexes, especially in the set of mono-(r = 0.888) and bis-complexes (r = 0.786) of naturally occurring amino acids. The error of the estimate is 0.01-0.14 and 0.01-0.33 log b units for mono-and bis-complexes, respectively. The estimation of log b 2 for mixed amino acid complexes (MLA) was performed by bivariate linear regression using composite indices, obtained by addition or subtraction of the 3 v v indices for two chelate rings, ML and MA. This regression gave r = 0.801 and the reproduction of experimental data 0.01-0.33 log b units.

A silver/Coomassie brilliant blue R-250 staining technique that permits a color-coded differentiation of erythrocyte membrane proteins, sialoglycoproteins, and lipids in a single one-dimensional NaDodSO4/polyacrylamide gel has been described. Gels stained first with silver stain and then with Coomassie blue (CB) showed the characteristic blue staining of all conventional CB-sensitive membrane polypeptides, whereas periodic acid-Schiff reagent-sensitive sialoglycoproteins and lipids stained yellow. Several yellow Ag-stained bands corresponding to major and minor sialoglycoproteins were detected at Mr X 10(-3) of 88, 72, 65, 41, 35, 31, 28, 24, and 20. Neuraminidase treatment of intact erythrocytes caused shifts in the electrophoretic mobilities of several yellow-stained bands without affecting the CB-stained polypeptide pattern. These observations afforded evidence that the yellow-staining bands were sialoglycoproteins and lipids. The double-staining technique was used in a topologic...

Gas phase FT-IR spectra of 3-dimethylamino-1-propanol 1 and 3-amino-1-propanol 2 are recorded. It is found that the forms with intramolecular hydrogen bonds strongly predominate up to 1008C in both compounds. The origin of multicompo-Ž. nent structure of n OH bands is discussed on the assumption of conformational equilibria as well as the coupling between Ž. the n OH vibration mode with the low frequency chelate ring deformation modes affecting the N PPP O distance. DFT ab Ž. Ž. Ž. initio calculations are performed at 6-31G d,p and 6-311 qqG 2d,2p levels. It is concluded that the n OH band structure in 1 results from highrlow frequency modes coupling.

We investigate the topology of the new Point Source Catalogue Redshift Survey (PSCz) of IRAS galaxies by means of the genus statistic. The survey maps the local Universe with approximately 15000 galaxies over 84.1 per cent of the sky and provides an unprecedented number of resolution elements for the topological analysis. For comparison with the PSCz data we also examine the genus of large N-body simulations of four variants of the cold dark matter cosmogony. The simulations are part of the Virgo project to simulate the formation of structure in the Universe. We assume that the statistical properties of the galaxy distribution can be identified with those of the dark matter particles in the simulations. We extend the standard genus analysis by examining the influence of sampling noise on the genus curve and introducing a statistic able to quantify the amount of phase correlation present in the density field, the amplitude drop of the genus compared to a Gaussian field with identical power spectrum. The results for PSCz are consistent with the hypothesis of random phase initial conditions. In particular, no strong phase correlation is detected on scales ranging from 10 h −1 Mpc to 32 h −1 Mpc, whereas there is a positive detection of phase correlation at smaller scales. Among the simulations, phase correlations are detected in all models at small scales, albeit with different strengths. When scaled to a common normalization, the amplitude drop primarily depends on the shape of the power spectrum. We find that the constant bias standard CDM model can be ruled out at high significance because the shape of its power spectrum is not consistent with PSCz. The other CDM models with more large-scale power all fit the PSCz data almost equally well, with a slight preference for a high density τ CDM model.

A series of calculations has been performed on the AlF 4 Ϫ and CaAlF 5 species in order to precise their equilibrium geometry as well as to get some insight onto their bonding properties. These species play an important role in electrochemical industrial processes such as the electrowinning of aluminum (i.e. the Héroult-Hall process). The calculations have been performed within the density functional approach using the B3LYP hybrid functional and the 6-311 ϩ ϩ G(3df,2p) all-electron basis sets on all the atomic centres. The optimized geometries and the calculated frequencies of AlF 4 Ϫ are found to be in agreement with those previously obtained at a lower level of calculation and with experiments. The bonding has been investigated by the topological analysis of the electron localization function gradient field. The analysis indicates that the Al-F bond presents a noticeable covalent character testified by the presence of a disynaptic basin between the Al and F cores. The basins' populations and their fluctuations have been calculated indicating an important delocalization between the Al-F bond and the fluorines lone pairs. Moreover, the structural role of the counter cation Ca 2ϩ has been emphasized. A structural and topological analysis of CaAlF 5 has been carried out. This study has clearly established that the CaAlF 5 molecule can be described as purely ionic interactions between the F Ϫ , AlF 3 and Ca 2ϩ species.

The topological analysis of the gradient field of the electron localization function provides a convenient theoretical framework for the partition of the molecular space into basins of attractors having a clear chemical meaning. The basin populations are evaluated by integrating the one-electron density over the basins. The variance of the basin population provides a measure of the delocalization. The behavior of the core C(X) and protonated valence basins V(X, H) populations have been investigated. The analysis of the population variance in terms of cross-contributions is presented for aromatic and antiaromatic systems, hypervalent molecules and hydrogen-bonded complexes. For hypervalent molecules this analysis emphasizes the importance of the ionic resonance structures. ᭧ 1998 Elsevier Science B.V.

The bonding in KgInll and RbgInl1 has been investigated at the SCF level with the periodic Hartree-Fock method. Comparison is made with In11 clusters with formal charges 7and 8calculated at the same level. The structure of the 7cluster has been optimized; it significantly differs from the structure observed in the condensed phase. The second anion (8-) is found to be dissociative. Moreover, the indium Mulliken populations in clusters are dramatically different from those calculated for the solid phase. This indicates that the reliability of the cluster approach is highly questionable. The stability of the solid phases is mostly due to the electrostatic interactions between the anionic clusters and the alkali counterions. The integrated charge density in the cation region is consistent with a picture in which an electron is delocalized over the potassium layers. The band structure and density of states of the solid phases are discussed. Both &Inll and Rb81nl1 are found to be weak electronic conductors. At the present state of the art, it is not possible to assess the charge borne by the indium cluster and, therefore, to decide whether one or more electrons are delocalized over potassium layers. The bonding in these systems has been investigated from the topological analysis of the electron localization function point of view. The bonding in the In11 anionic clusters is characterized by a network of attractors lying 1 A outward from the indium centers.

Neutral rare-gas containing molecules HRgCN ͑RgϭKr, Xe͒, HXeSH and HXeOH are investigated by means of topological analysis of the electron localization function ͑ELF͒. This analysis explains the type of bonding and delocalization of electron density in chemical systems based on the indirect probability of finding two electrons with the opposite spins. The calculations reveals that all studied species are charge-transfer systems with the approximate formulas: ͓HKr͔ ϩ0.65 ͓CN͔ Ϫ0.65 , ͓HXe͔ ϩ0.66 ͓CN͔ Ϫ0.66 , ͓HXe͔ ϩ0.45 ͓SH͔ Ϫ0.45 , and ͓HXe͔ ϩ0.57 ͓OH͔ Ϫ0.57. The isomerization process from HRgCN to HRgNC increases the charge separation to 0.72e for Kr and 0.74e for Xe containing molecules. It is shown that the Rg-C, Rg-N, Xe-S, and Xe-O bonds belong to the unshared electron type and are mainly of the electrostatic origin. The minimum of ELF in the Kr-C and Kr-N linkage, studied at the B3LYP/6-311ϩϩG(2d,2p) computational level, yields relatively high values of about 0.4 and 0.3, respectively. There is a correlation between larger stability of HRgCN isomers and an increased exchange of the electron density between the lone electron pair of carbon and the nonbonding electron density of xenon: V(C)↔V(Xe) as compared to smaller V(N)↔V(Xe) delocalization in less stable HRgNC isomers. The analysis of the CN group reveals the covalent character of the carbon-nitrogen bond, which is confirmed on the basis of presence of the disynaptic valence V(C,N) attractor positioned near to nitrogen. The HRgCN→HRgNC isomerization results in depletion of the carbon-nitrogen bond V(C,N) and a large saturation of the valence nitrogen basin V(N).

The proton transfer mechanism in malonaldehyde has been investigated from the points of view of the topological analysis of the electron localization function and of the catastrophe theory. The calculations were carried out at the B3LYP hybrid functional level with the ccp-VTZ basis set. Complementary calculations were performed at the HF, MP2, BLYP, and B3LYP levels with the STO-3G, 6-31G, and 6-31G** basis sets in order to discuss the stability of the method. The mechanism of the reaction does not involve any reorganization of the skeleton: it is localized in the hydrogen bond region and involves three chemical structures corresponding to the reactant, the transition state, and the product. It is shown that the proton detachment is in fact the covalent breaking of the OH bond, and by symmetry its attachment on the other oxygen is also a covalent process. The analysis of the catastrophe shows that the reaction is driven by two active coordinates related to the OH and OO distance and provides a method for the determination of the limiting paths.

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The topological analysis of the electron localization function has been applied to complexes representative of the weak, medium and strong hydrogen bond. For both the weak and the medium hydrogen bonds, the number of basins in the complexes is the sum of those of the moieties. In this case, the formation of a weak or a medium hydrogen-bonded complex does not involve a chemical reaction. In the weak hydrogen bond case, the reduction of the localization domain yields two domains in the ®rst step, which can be partitioned afterwards into valence and core domains. In contrast, for medium complexes the core±valence separation is the ®rst event which occurs during the reduction process and therefore the complex should be considered as a single molecular species. Moreover, the analysis of the basin population variance indicates in this case a noticeable delocalization between the V(A, H) and V(B) basins. Finally, the symmetrical strong hydrogen bond has a protonated basin V(H) at the bond midpoint. Such a topology corresponds to an incomplete proton transfer and to a rather covalent bond.

A series of calculations has been performed on the AlF 4 Ϫ and CaAlF 5 species in order to precise their equilibrium geometry as well as to get some insight onto their bonding properties. These species play an important role in electrochemical industrial processes such as the electrowinning of aluminum (i.e. the He ´roult-Hall process). The calculations have been performed within the density functional approach using the B3LYP hybrid functional and the 6-311 ϩ ϩ G(3df,2p) all-electron basis sets on all the atomic centres. The optimized geometries and the calculated frequencies of AlF 4 Ϫ are found to be in agreement with those previously obtained at a lower level of calculation and with experiments. The bonding has been investigated by the topological analysis of the electron localization function gradient field. The analysis indicates that the Al-F bond presents a noticeable covalent character testified by the presence of a disynaptic basin between the Al and F cores. The basins' populations and their fluctuations have been calculated indicating an important delocalization between the Al-F bond and the fluorines lone pairs. Moreover, the structural role of the counter cation Ca 2ϩ has been emphasized. A structural and topological analysis of CaAlF 5 has been carried out. This study has clearly established that the CaAlF 5 molecule can be described as purely ionic interactions between the F Ϫ , AlF 3 and Ca 2ϩ species.

This contribution explains how the topological methods of analysis of the electron density and related functions such as the electron localization function (ELF) and the electron localizability indicator (ELI-D) enable the theoretical characterization of various metal-metal (M-M) bonds (multiple MM bonds, dative MM bonds). Examples are taken in both bulk metals, alloys and molecular complexes. Metallic bonds as well as weak partially covalent MM interactions, are described and characterized unambiguously combining AIM (atoms in molecules) and ELF/ELI-D topological analysis.

The topological analysis of the electron localization function has been applied to complexes representative of the weak, medium and strong hydrogen bond. For both the weak and the medium hydrogen bonds, the number of basins in the complexes is the sum of those of the moieties. In this case, the formation of a weak or a medium hydrogen-bonded complex does not involve a chemical reaction. In the weak hydrogen bond case, the reduction of the localization domain yields two domains in the ®rst step, which can be partitioned afterwards into valence and core domains. In contrast, for medium complexes the core±valence separation is the ®rst event which occurs during the reduction process and therefore the complex should be considered as a single molecular species. Moreover, the analysis of the basin population variance indicates in this case a noticeable delocalization between the V(A, H) and V(B) basins. Finally, the symmetrical strong hydrogen bond has a protonated basin V(H) at the bond midpoint. Such a topology corresponds to an incomplete proton transfer and to a rather covalent bond.