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  • 1
    ISSN: 1432-2234
    Keywords: Molecular shape ; Conformational energy maps ; Shape invariance maps ; van der Waals surfaces
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary It is well known that many molecular properties are strongly dependent on internal nuclear arrangements. Two possible, independent approaches can be followed while studying changes in molecular characteristics as functions of the nuclear geometry. These are the analysis of potential energy surfaces and the analysis of molecular shape. In this work, we seek to establish relationships between potential energy maps and shape invariance region maps, where each point of these maps represents a nuclear configuration. The study is performed by analyzing the occurrence and lack of certain symmetries in both types of maps. As illustrative examples, we consider the three structural isomers of the dihydroxybenzene molecule. Potential energy is computed at the STO-3G ab initio level, while the shape is described by the shape group method as applied to fused-sphere van der Waals surfaces. It is shown that the symmetry of the shape invariance maps follows closely, but not exactly, the symmetry of potential energy surfaces. The molecular surface is thus “blind” to some small changes of the potential (a feature to be expected to hold also for molecular surfaces defined in terms of electronic charge density). Our findings suggest that a crude fused-sphere model may suffice to describe some of the structural changes in molecular surfaces, as well as their relationships to the electronic energy.
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 81 (1991), S. 79-93 
    ISSN: 1432-2234
    Keywords: Molecular shape ; Cross sections of molecular surfaces ; Roughness measures ; Shape descriptors ; Roughness spectrum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary It is possible to describe some aspects of the 3D shape features of molecules by characterizing a selection of 2D cross sections (planar curves) of a formal molecular surface. In this work we propose a new method to analyze the complexity of the shape of planar curves, in particular, to recognize and measure their roughness. Our approach provides a discrete “roughness spectrum” of the curve, which, in turn, can be characterized by other, simpler shape descriptors. The procedure is applied to cross sections of molecular electronic isodensity contours, which are classified and compared in terms of their roughness measures.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of computer aided molecular design 11 (1997), S. 503-515 
    ISSN: 1573-4951
    Keywords: Molecular shape ; Lipophilicity potential ; Electrostatic potential ; Molecular modeling ; Drug design
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract In this contribution we suggest a heuristic molecular lipophilicitypotential (HMLP), which is a structure-based technique requiring noempirical indices of atomic lipophilicity. The input data used in thisapproach are molecular geometries and molecular surfaces. The HMLP is amodified electrostatic potential, combined with the averaged influences fromthe molecular environment. Quantum mechanics is used to calculate theelectron density function ρ(r) and the electrostatic potential V(r), andfrom this information a lipophilicity potential L(r) is generated. The HMLPis a unified lipophilicity and hydrophilicity potential. The interactions ofdipole and multipole moments, hydrogen bonds, and charged atoms in amolecule are included in the hydrophilic interactions in this model. TheHMLP is used to study hydrogen bonds and water–octanol partitioncoefficients in several examples. The calculated results show that the HMLPgives qualitatively and quantitatively correct, as well as chemicallyreasonable, results in cases where comparisons are available. Thesecomparisons indicate that the HMLP has advantages over the empiricallipophilicity potential in many aspects. The HMLP is a three-dimensional andeasily visualizable representation of molecular lipophilicity, suggested asa potential tool in computer-aided three-dimensional drug design.
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Chirality 10 (1998), S. 173-179 
    ISSN: 0899-0042
    Keywords: chirality at low and high resolution ; functional groups ; fuzzy density fragments ; continuum models ; fuzzy sets ; Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Mislow's Label Paradox and the chirality preserving or abandoning properties of deformation paths of polyhedral models are extended to simple representations of electron density continua of molecules. Chirality 10:173-179, 1998. © 1998 Wiley-Liss, Inc.
    Additional Material: 1 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 64 (1997), S. 669-678 
    ISSN: 0020-7608
    Keywords: Molecular geometry ; symmetry ; symmorphy ; topology ; electron density ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Relations between an earlier generalization of molecular symmetry called symmorphy and a molecular equivalence based on diffeomorphisms of electron 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.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64: 669-678, 1997
    Additional Material: 1 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 19 (1998), S. 1337-1344 
    ISSN: 0192-8651
    Keywords: density averaging ; average conformation ; molecular deformations ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The concepts of averaged electron densities and averaged nuclear arrangements are discussed with reference to small nuclear distortions and an electron density transformation based on the inverse Löwdin transform.   © 1998 John Wiley & Sons, Inc.   J Comput Chem 19: 1337-1344, 1998
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  • 7
    Electronic Resource
    Electronic Resource
    New York : Wiley-Blackwell
    Biopolymers 32 (1992), S. 1609-1621 
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In this work we present a new method to characterize the shape of flexible chain molecules. The procedure associates a sphere and a spherical shape map with each given molecular backbone. Each point on the sphere is classified according to the crossing pattern obtained when the backbone is looked at along a direction defined by the center of the sphere and the chosen point. The approach is simple to implement. It consists of the following steps: (a) enclosing the backbone by a sphere, whose center is the geometrical center of the backbone; (b) projecting the backbone onto a plane tangent to the sphere at the given point; and (c) characterizing the resulting planar curve by a vector specifying the number and handedness type of the crossings. When the procedure is repeated for all points on the spherical surface, the latter is divided into regions that are equivalence classes of points, corresponding to directions from where the backbone has the same overcrossing pattern. The computation of these equivalence classes is performed automatically by the computer, by determining the boundary of the regions characterized by different crossing vectors. The characterization provided is thus direction independent since it takes into account all possible directions from where a backbone can be analyzed. The procedure is illustrated for a number of supersecondary protein structures and small proteins. We find that a characterization of substructures can be obtained in terms of the arrangement of the equivalence region for the viewing directions from where the backbone shows no crossings. For instance, an α-helix is represented by a spherical map with a small “band” region of no crossings perpendicular to the helical axis. Other supersecondary structural features are described in a similar fashion. A number of refinements of the method, based on the distances between crossings, are also given for the case of irregular backbones. © 1992 John Wiley & Sons, Inc.
    Additional Material: 11 Ill.
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  • 8
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 66 (1998), S. 99-105 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The distribution of the essential functional groups within biomolecules is described by a series of polyhedral models. As a function of a threshold of the electronic density of the biomolecule, the combinatorial types of these polyhedra are threshold-dependent within each series, resulting in a characteristic sequence of combinatorial types for each biomolecule. A comparison of combinatorial types is the basis for the introduction of new measures of shape similarity and shape complementarity between biomolecules.   © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66: 99-105, 1998
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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 353-361 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A family of related techniques for the reduction of square-cell configurations (“animals”) to simpler ones by cell-shedding processes provide physically motivated, novel approaches for shape characterization and similarity criteria as well as similarity measures based on equivalence relations. The two main algorithms, csk, k = 1, 2, involve the simultaneous “shedding” of all cells having precisely k sides exposed on the periphery of the animal; the shedding steps are repeated as long as the resulting structure is an animal. Since the termination criteria of these two algorithms are different, they can be combined sequentially into composite algorithms, leading to various alternative shape characterizations and equivalence relations. The third main algorithm, cs32, involves incomplete elimination of peripheral cells of a given type, thus retaining some additional local shape features inherited from the original animal. Following the introduction of these transformations, some of their properties are derived and several examples are discussed. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 353-361, 1997
    Additional Material: 4 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 63 (1997), S. 39-48 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The relations between the general form of Carbó's quantum similarity measure and the similarity measure based on the Löwdin transform of approximate density matrices are discussed. These relations provide the basis for the study of macromolecular forces and small deformations of electron densities induced by limited changes of nuclear configurations of both small and large molecules. © 1997 John Wiley & Sons, Inc.
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