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  • 1
    Electronic Resource
    Electronic Resource
    The topology of energy hypersurfaces II. Reaction topology in euclidean spaces (1983)
    Springer
    Theoretical chemistry accounts 63 (1983), S. 9-33 
    Details
    ISSN: 1432-2234
    Keywords: Potential energy surfaces ; Computer-aided synthesis design ; Quantum chemical synthesis design ; Reaction mechanism ; Reaction networks
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract By introducing equivalence classes of critical points of potential energy hypersurfaces a unique topological space, Reaction Topology (3N E, T C ) is defined over an Euclidean nuclear configuration space 3N E for a system of N nuclei and k electrons. Relations between the topological concepts of molecular structure and reaction mechanism are analyzed. Topological equivalences between Euclidean and Riemannian representations of nuclear configuration spaces are exploited for the analysis of quantum mechanical reaction networks of all possible chemical reactions over the given potential energy hypersurface.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00549152
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  • 2
    Electronic Resource
    Electronic Resource
    The topology of energy hypersurfaces III. The fundamental group of reaction mechanisms on potential energy hypersurfaces (1985)
    Springer
    Theoretical chemistry accounts 67 (1985), S. 43-61 
    Details
    ISSN: 1432-2234
    Keywords: Reaction mechanism ; group theory of reaction mechanism ; reaction topology ; potential surfaces ; reaction path ; synthesis planning
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The family of all possible reaction mechanisms on a potential surface has an algebraic structure with potential applications in quantum chemical molecular design and synthesis planning. Transformation properties and equivalence relations of reaction paths on potential energy hypersurfaces lead to a topological definition of reaction mechanisms. The family of all fundamental reaction mechanisms on the hypersurface has a group structure,the fundamental group of an appropriately defined topological space. Isomorphism and homomorphism relations between fundamental groups of reaction mechanisms are used to characterize the chemically important topological properties of various subsets of a hypersurface, or those of different excited state hypersurfaces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00555021
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  • 3
    Electronic Resource
    Electronic Resource
    Topology of energy hypersurfaces (1982)
    Springer
    Theoretical chemistry accounts 62 (1982), S. 133-161 
    Details
    ISSN: 1432-2234
    Keywords: Reaction topology ; Potential energy surfaces ; Reaction path ; Chemical structure ; Reaction mechanism
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Some of the basic notions of chemistry, associated with an energy function of several variables, are shown to be of topological character. Properties of potential energy hypersurfaces, structural relations, models for interconversion processes and transformations between such models suggest a topological theory (reaction topology) for the analysis of potential energy hypersurfaces. By introducing appropriate topologies into the nuclear configuration spaceR and equivalent topologies on the energy hypersurfaceE, rigorous definitions are given for fundamental chemical concepts such asmolecular structure andreaction mechanism. These definitions are based on the properties of the expectation value of energy, a quantum mechanical observable. Topologies based on curvature, structural and energetic relations of the energy hypersurface are proposed for a theoretical interpretation of molecular processes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00581478
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  • 4
    Electronic Resource
    Electronic Resource
    Comparison of potential energy maps and molecular shape invariance maps for two-dimensional conformational problems (1990)
    Springer
    Theoretical chemistry accounts 76 (1990), S. 377-390 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00528878
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  • 5
    Electronic Resource
    Electronic Resource
    A measure of roughness of cross sections of molecular surfaces (1991)
    Springer
    Theoretical chemistry accounts 81 (1991), S. 79-93 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01113379
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  • 6
    Electronic Resource
    Electronic Resource
    Heuristic lipophilicity potential for computer-aided rational drug design (1997)
    Springer
    Journal of computer aided molecular design 11 (1997), S. 503-515 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007949918800
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