Analysis topological

A plot of the total electron density for (3- NTO is shown in Fig. 8. The plot has been truncated at the atomic positions to accentuate the bonding features. 

In the case of PDB ligands, only part of the graph information is defined in the PDB file format sepcification bond types and atom hybridization states are missing and will later be derived from the three-dimensional arrangement of connected atoms. Connectivity information, however, is already present and can be used to seperate cyclic from non-cyclic molecule parts. Especially for planar rings, this separation is a prerequisite for geometry interpretation, because of 

Simultaneously extend paths from a starting atom following all neighbors in a breadth-first manner. 

If an atom already has a path, a ring closure is found. If this closure is a valid ring closure (i.e. the intersection of the colliding paths is a one-atom path), the corresponding path will be added to the set of rings. 

The implementation was adapted using reference lists instead of arrays performing the following steps  

Get the first atom a from the queue and remove it from Q. 

In the kinetics of grain growth, the mean boundary is equal to the product of the mobility of the grain boundary and the force applied to it, which is given by 

If it is assumed that the terms on the right-hand side of Eq. (8.41) are constant, integrating Eq. (8.41) yields  

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These fascinating bicontinuous or sponge phases have attracted considerable theoretical interest. Percolation theory [112] is an important component of such models as it can be used to describe conductivity and other physical properties of microemulsions. Topological analysis [113] and geometric models [114] are useful, as are thermodynamic analyses [115-118] balancing curvature elasticity and entropy. Similar elastic modulus considerations enter into models of the properties and stability of droplet phases [119-121] and phase behavior of microemulsions in general [97, 122]. 

Most of the relevant features of the charge density distribution can be elegantly elucidated by means of the topological analysis of the total electron density [43] nevertheless, electron density deformation maps are still a very effective tool in charge density studies. This is especially true for all densities that are not specified via a multipole model and whose topological analysis has to be performed from numerical values on a grid. 

Iversen, B.B., Larsen, F.K., Figgis, B.N. and Reynolds, P.A. (1997) X-N study ofthe electron density distribution in tra s-tetraammine-dinitronickel(II) at 9K transition metal bonding and topological analysis, J. Chem. Soc., Dalton Trans. 2227-2240. 

Topological analysis of X-ray protein relative density maps utilizing the eigenvector following method... 

A topological analysis of the total static density has been carried out. The analysis is not complete, and will not be discussed in any great detail in the present context. It is worth mentioning however that similar results as found for benzoylacetone were obtained. The values of pb and V2pbat the 0(1)-H(X) and 0(3)-H(X) bond critical... 

Petlyuk FB, Kievskii VY and Serafimov LA (1975) Thermodynamic and Topological Analysis of the Phase Diagrams of Polyazeotropic Mixtures II. Algorithm for Construction of Structural Graphs for Azeotropic Ternary Mixtures, Russ J Phys Chem, 49 1836. 

For over a decade, the topological analysis of the ELF has been extensively used for the analysis of chemical bonding and chemical reactivity. Indeed, the Lewis pair concept can be interpreted using the Pauli Exclusion Principle which introduces an effective repulsion between same spin electrons in the wavefunction. Consequently, bonds and lone pairs correspond to area of space where the electron density generated by valence electrons is associated to a weak Pauli repulsion. Such a property was noticed by Becke and Edgecombe [28] who proposed an expression of ELF based on the laplacian of conditional probability of finding one electron of spin a at t2, knowing that another reference same spin electron is present at ri. Such a function... 

It has been recently shown [12] that the ELF topological analysis can also be used in the framework of a distributed moments analysis as was done for Atoms in Molecules (AIM) by Popelier and Bader [32, 33], That way, the Mo( 2) monopole term corresponds to the opposite of the population (denoted N) ... 

Silvi B, Savin A (1994) Classification of chemical bonds based on topological analysis of electron localization functions. Nature 371 683... 

The ELF was proposed by Becke and Edgecombe [7] in 1990 and very soon extensively applied to a variety of systems ranging from atoms to inorganic and organic molecules to solids [9]. In 1994, a topological analysis of the ELF was... 

Recently, quantum calculations and topological analysis using the Quantum Theory of Atoms in Molecules (QTAIM) provide an explanation... 

In this section, we describe a recently proposed approach that aims overcome some of the difficulties [23, 84, 296, 325] Structural Kinetic Modeling (SKM) seeks to provide a bridge between stoichiometric analysis and explicit kinetic models of metabolism and represents an intermediate step on the way from topological analysis to detailed kinetic models of metabolic pathways. Different from approximative kinetics described above, SKM is based on those properties that are a priori independent of the functional form of the rate equation. 

In this equation a c stands for the sensivity of the observed carbon atom within a given parent compound family, and T),. is a reference shift. The R values are obtained by DARC/PELCO topological analysis (416). 

Such analysis sufficiently supplements with topological analysis of the electron density proposed earlier by Bader, where the condition... 

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