Topological descriptors local

Special cases are discussed in some detail in the literature [112,197,198], where the shape representation P is chosen as a space curve representing a protein backbone and the topological descriptors Fj(s) on the local tangent plane projections are either graphs or knots defined by the crossing pattern on the planar projection at each tangent plane T(s) of the sphere S. 

The local value of the total energy density at a point r, H(r), is another useful topological descriptor that provides supplementary information about the nature of the interaction at r. The total energy density H(r) is the sum of the kinetic energy density G(r), a positive quantity, and the potential energy density F(r), a negative quantity, both densities related with the Laplacian of p(r) through the local expression for the virial theorem [45, 46] ... 

L. F. Pacios, Topological descriptors of the electron density and the electron localization function in hydrogen bond dimers at short intermonomer distances, J. Phys. Chem. A 108, 1177-1188 (2004). 

Des., 1, 115-133 (2002). QSAR Carcinogenic Study of Methylated Polycyclic Aromatic Hydrocarbons Based on Topological Descriptors Derived from Distance Matrices and Correlation Weights of Local Graph Invariants. 

A combination of physicochemical, topological, and geometric information is used to encode the environment of a proton, The geometric information is based on (local) proton radial distribution function (RDF) descriptors and characterizes the 3D environment of the proton. Counterpropagation neural networks established the relationship between protons and their h NMR chemical shifts (for details of neural networks, see Section 9,5). Four different types of protons were... 

Other topological molecular descriptors can be obtained by using suitable functions applied to - local vertex invariants, the most common functions are atom and/or bond additives, resulting in descriptors which give correlation of physico-chemical properties that are atom and/or bond additives themselves. - Zagreb indices and -> ID numbers are derived according to this approach. 

Molecular descriptors calculated as - information content of molecules. Different criteria are used for defining - equivalence classes, i.e. equivalency of atoms in a molecule such as chemical identity, ways of bonding through space, molecular topology and symmetry, - local vertex invariants [Bonchev, 1983]. 

The sums of the local vertex invariants X, and c, over all of the atoms give the corresponding molecular descriptors, called centrocomplexity topological index X and centric topological index C, respectively ... 

These works established the existence of a novel variety of electron pair in DRAs. Extensions of traditional electron pair concepts are clearly needed for these anions. The electron localization function (ELF) 19 is an interesting and robust descriptor of chemical bonding, which has been successfully applied to a wide variety of molecular systems.20-24 This function, which is based on a topological analysis of a quantum function related to Pauli repulsion, describes the degree of localization (or delocalization) of electron pairs within the molecular space. 

In the present article, we report a study concerning the reaction mechanism of a prototype reaction using both static and dynamic approaches to explore a DFT potential surface. The static approach is the standard IRC model, while the dynamic one is based on a Carr-Parrinello method performed with localized (Gaussian) orbitals, the so-called atom-centered density matrix propagation (ADMP) model.25 Our aim is to elucidate the differences, and the common aspects, between the two approaches in the analysis of bond breaking/formation. To this end, we have chosen topological quantities as probe molecular descriptors. 

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