Three properties of relative shape envelopes of molecular electron density contours

Mezey, Paul G.

doi:10.1007/bf01114847

Cited by 10 publications

(6 citation statements)

References 5 publications

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“…Thus usually nothing happens. An alternative topological approach based on the density has been proposed by Mezey and co-workers, − who consider the change of the shape of bonding isosurfaces. This enables one to recognize formal species along the path that characterize the steps of the reaction.…”

Section: Theorymentioning

confidence: 99%

Characterization of Elementary Chemical Processes by Catastrophe Theory

1997

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The topological analysis of the electron localization function (ELF) provides a convenient theoretical framework to characterize chemical bonds. This method does not rely on the particular approximations that are made in actual quantum chemical calculations of the electronic structure. In principle, it can be applied to exact wave functions as well as to experimental electron densities. Introduction of a control space, such as a set of reaction pathways, allows extension of the analysis to chemical reactions. The study of the bifurcations occurring during such processes is of particular interest for their classification and their qualitative description. This is achieved with the help of René Thom's catastrophe theory. The following examples are discussed: the ammonia inversion, the breaking of the ethane C−C bond, and the breaking of the dative bond in NH3BH3. The types of catastrophe and their unfolding have been determined for each of these processes. As by-products, nonempirical definitions of covalent and dative bonds are proposed.

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Section: Theorymentioning

confidence: 99%

Characterization of Elementary Chemical Processes by Catastrophe Theory

1997

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“…Proof: For the two T-plaster sets A and B, there exist some sets S and S‘ such that A = 〈S〉 T and B = 〈S‘〉 T . We know that the T-hull of the T-hull is the T-hull, hence and The first statement of the theorem is proven in two parts, (a) and (b).…”

Section: External T-plasters and Interior T-aggregatesmentioning

confidence: 94%

“…Besides their role as generalizations of convexity, T-hulls have been shown to provide novel tools for molecular shape analysis. In particular, T-hulls provide intuitively transparent representations of various shape constraints for solvent−solute interactions, for solvent accessible surfaces, for biomolecular shape-complementarity, and for union surfaces in drug design. − Exterior plaster sets and interior aggregate sets represent a natural extension of the T-hull approach, suitable to study the shape-modifying role of solvation shells and the inner cavities of supramolecular structures filled with solvent molecules.…”

Section: Closing Commentsmentioning

confidence: 99%

“…T-Hulls are designed for relative shape characterization of molecules, offering a family of tools for molecular shape and similarity analysis. , Using local comparisons between the shapes of the actual object S and the reference object T and applying this method to molecules, the electron density T-hulls have been suggested for the analysis of various shape constraints in biomolecular complementarity and in solvent−solute interactions. − Earlier applications of T-hulls include a new description of union surfaces in drug design and a geometrical-topological treatment of solvent accessible surfaces 1 Illustration of the concept of T-hull 〈S〉 T using the examples of a rectangle as set S and an ellipse as reference shape T. See text for detail. …”

Section: Introductionmentioning

confidence: 99%

“…In 3D chemical shape analysis, T is usually chosen as a molecular density domain or the relative complement of a suitable molecular fragment. Usually, a version T v of the reference object T is any set obtained from T by 3D translations and rotations. , Alternatively, various constrained motions as well as additional freedoms can be considered. , …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Theorems on Molecular Shape-Similarity Descriptors: External T-Plasters and Interior T-Aggregates

Mezey

1996

J. Chem. Inf. Comput. Sci.

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Exterior T-plasters and interior T-aggregates, two new families of tools of molecular similarity analysis, provide shape comparisons between molecular bodies represented by electron density contours. Two theorems are proven, and some fundamental properties of T-plasters and T-aggregates are discussed, relevant to the shape-modifying effects of solvation layers and to the study of inner cavities filled with solvent molecules, such as water clusters in proteins.

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Molecular geometry and symmetry from a differential geometry viewpoint

Zimpel

Mezey

1997

Int. J. Quant. Chem.

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ABSTRACT:Relations between an earlier generalization of molecular symmetry called symmorphy and a molecular equivalence based on diffeomorphisms of electron Ž density functional graphs the so-called DFG equivalence introduced in our previous . work are analyzed. Any two DFG-equivalent electron density functions can be derived from one another by a suitable transformation of the spatial coordinates and the electronic charge density scale; the classes of DFG equivalence are the orbits of a group of linear operators operating in the space of electron density functions. Within the symmorphy framework, the symmetry group is derived from the symmorphy group by taking an intersection of a subgroup of the symmorphy group and the group of isometries for a natural choice of the Riemannian metric tensor. The Riemannian metric properties provide a choice for a suitable reference electron density function for each class of equivalent densities. Such reference densities serve as tools for a systematic classification of the infinite family of electron densities of molecular conformations.

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Three properties of relative shape envelopes of molecular electron density contours

Cited by 10 publications

References 5 publications

Characterization of Elementary Chemical Processes by Catastrophe Theory

Characterization of Elementary Chemical Processes by Catastrophe Theory

Theorems on Molecular Shape-Similarity Descriptors: External T-Plasters and Interior T-Aggregates

Molecular geometry and symmetry from a differential geometry viewpoint

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