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  • 1
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 9 (1988), S. 608-619 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The study of the qualitative and quantitative product distribution in a chemical reaction, in particular regioselectivity, is of fundamental importance. Recently, it has been shown that the regioselectivity of some Diels-Alder cycloadditions can be explained by analyzing the interrelations between electron density contours and molecular electrostatic potentials. This problem is related to a central topic of modern theoretical chemistry and biochemistry: the analysis of molecular shape. This work deals with a rigorous, algebraic method to analyze these surfaces. The procedure is based on the computation of the shape groups (symmetry-independent homology groups of algebraic topology) of the molecular surface, using either a fully analytical algorithm requiring no visual inspection, or a precise method for processing pictorial information if the latter is available. The method provides a concise description of the molecular contour surface, that can replace the usually intuitive, and somewhat subjective, visual characterization of density and electrostatic potential contours. The method is illustrated for the case of Diels-Alder reactions by considering a number of monosubstituted dienes. Extensions of the analysis to dienophiles, as well as other types of reactions are also discussed.
    Additional Material: 5 Ill.
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 8 (1987), S. 462-469 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A group theoretical framework is proposed for a detailed characterization of the shapes of electronic charge distributions of general, asymmetric molecules. The proposed shape groups are the homology and cohomology groups of charge density contour surfaces. These shape groups depend on two real parameters, the charge density value a for the contour and a curvature parameter b. The two-parameter family of various homology groups and cohomology groups of charge density contour surfaces is independent of the symmetry properties of the molecules and gives a concise description of the dominant shape characteristics. For any fixed parameter value b these groups may change only at specific charge density values, characteristic to the given molecule. On the other hand, for a fixed-charge density contour the group changes induced by a change in the curvature parameter b provide a description of the fine details of the shape of the electron density. The changes in the structure of these groups follow strict algebraic relations, that provide a quantitative measure for shape-similarity between various molecules. The two-parameter shape group method is an extension of an earlier method proposed for biochemical applications.
    Additional Material: 5 Ill.
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 14 (1993), S. 1172-1183 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: An algorithm for a detailed 3-D characterization of the shapes of molecular charge distributions is implemented in the form of a comprehensive package of computer programs, GSHAPE, and applied to a series of 10-electron hydrides to critically evaluate the methodology. Attention is paid to the effects of nuclear geometry and the size of basis on the molecular shape. The characterization is performed by computing a number of topological invariants (“shape groups”) associated with a continuum of molecular surfaces: the complete family of all electronic isodensity contours for the given molecules. These shape groups (the homology groups of truncated surfaces derived from isodensity contours) depend on two continuous parameters: a density value defining the density contour and a reference curvature value, to which the local curvatures of the isodensity contours are compared. The electronic charge distribution is calculated at the ab initio level using basis sets ranging from STO-3G to 6-31G**. No visual inspection is required for the characterization and comparison of shapes of molecular charge densities, as these are done algorithmically by the computer. However, visualization of the results is one option of our program using Application Visualization Software (AVS). For a given molecule, in a given nuclear geometry, the technique provides a 2-D shape map, displaying the distribution of the shape gruops as a function of the local curvature and the level set value (the value of the charge density at the contour). The computer program GSHAPE performs the analysis automatically. This feature makes it potentially useful in the context of computer-aided drug design, where unbiased, automated shape characterization methods are valuable tools. As examples, a variety of 2-D shape maps are discussed. © John Wiley & Sons, Inc.
    Additional Material: 6 Ill.
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 16 (1995), S. 1238-1249 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A new method is proposed for the evaluation of numerical similarity measures for large molecules, defined in terms of their electron density (ED) distributions. The technique is based on the Molecular Electron Density Lego Assembler (MEDLA) approach, proposed earlier for the generation of ab initio quality electron densities for proteins and other macromolecules. The reliability of the approach is tested using a family of 13 substituted aromatic systems for which both standard ab initio electron density computations and the MEDLA technique are applicable. These tests also provide additional examples for evaluating the accuracy of the MEDLA technique. Electron densities for a series of 13 substituted benzenes were calculated using the standard ab initio method with STO-3G, 3-21G, and 6-31G** basis sets as well as the MEDLA approach with a 6-31G** database of electron density fragments. For each type of calculation, pairwise similarity measures of these compounds were calculated using a point-by-point numerical comparison of the EDs. From these results, 2D similarity maps were constructed, serving as an aid for quick visual comparisons for the entire molecular family. The MEDLA approach is shown to give virtually equivalent numerical similarity measures and similarity maps as the standard ab initio method using a 6-31G** basis set. By contrast, significant differences are found between the standard ab initio 6-31G** results and the standard ab initio results obtained with smaller STO-3G and 3-21G basis sets. These tests indicate that the MEDLA-based similarity measures faithfully mimic the actual, standard ab initio 6-31G** similarity measures, suggesting the MEDLA method as a reliable technique to assess the shape similarities of proteins and other macromolecules. The speed of the MEDLA computations allows rapid, pairwise comparisons of the actual EDs for a series of molecules, requiring no more computer time than other simplified, less detailed representations of molecular shape. The MEDLA method also reduces the need to store large volumes of numerical density data on disk, as these densities can be quickly recomputed when needed. For these reasons, the proposed MEDLA similarity analysis technique is likely to become a useful tool in computational drug design. © 1995 John Wiley & Sons, Inc.
    Additional Material: 7 Ill.
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  • 5
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The shape group method (SGM) and the associated (a,b)-parameter maps provide a detailed shape characterization of molecular charge distributions. This method is applied to the study of the variations of shape and conjugation of conformers of 2-phenyl pyrimidine in their electronic ground state. Within the SGM framework, the method of (a,b)-parameter maps provides a concise, nonvisual, algorithmic technique for shape characterization of molecules with fixed nuclear geometries. Moreover, shape codes derived from the (a,b)-parameter maps afford a practical means for efficiently storing the shape properties of molecules in an electronic database. The shape codes of two or more charge distributions can be compared directly, and numerical measures of molecular shape similarity can be computed using a technique that is simple, fast, and inexpensive, especially in relation to direct, pairwise comparisons of electronic charge densities. The quantitative and automated nature of the method suggests applications in the field of computer-aided molecular design. In this study, the method is used for the first time to determine detailed numerical shape codes and shape similarity measures for a nontrivial conformational problem involving changes in energy and in conjugation. Numerical shape similarity measures of eight conformers of 2-phenyl pyrimidine are determined and correlated with variations in conformational energy and conjugation. The competing effects of steric repulsion and conjugation lead to important correlations between conformational energy and shape. © 1995 John Wiley & Sons, Inc.
    Additional Material: 4 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 1 (1980), S. 134-140 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Several “core-deficient” small Gaussian basis sets were constructed and analyzed in terms of the balance requirements of functions that contribute predominantly to the core. Variations in the conformational energy barriers and geometrical parameters for ammonia and ethane, calculated with these basis sets, were analyzed with a gradient technique. A scheme for the reduction of the size of molecular basis sets is proposed.
    Additional Material: 4 Tab.
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  • 7
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Basis-set balance parameters, defined in terms of various projections of an abstract force vector in the space spanned by the logarithms of orbital exponents, are evaluated for a sample of 100 Gaussian basis sets. These basis sets are taken from a random Gaussian distribution of bases, centered on the best energy, fully variational uniform quality (UQ) atomic orbital (AO) basis sets. With each basis geometry optimization has been carried out for model molecule dimethyl sulfoxide, the wavefunction of which molecule is exceptionally sensitive to basis-set errors. Correlations between the balance of basis sets and calculated molecular properties are analyzed.
    Additional Material: 1 Tab.
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  • 8
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 5 (1984), S. 190-196 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Ab initio self-consistent-field molecular orbital calculations have been carried out for the CnH2n (n = 3 to 6) cycloalkanes and various conformers of their protonated forms. The calculated protonation energies for the sequence of conformers of the protonated forms follow the experimentally observed trend. Correlations between optimum C—C—C bond angles at the protonation site and the calculated protonation energies have been observed, and these correlations may be of some use in estimating protonation energy-bond angle relations in other (strained) cyclic compounds when the central carbon atom of a C—C—C moiety is protonated.
    Additional Material: 4 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 9 (1988), S. 554-563 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: An algebraic method is proposed to represent and to characterize in a concise way the shape of an arbitrarily asymmetrical surface composed from spherical pieces. These surfaces include, among others, the well-known van der Waals surfaces. The procedure is based on the computation of a hierarchy of homology groups (“shape groups”) of algebraic topology, for a family of objects defined by the original surface. The technique uses the same input information as that necessary to produce a graphical display of the molecular surface. However, the actual figure is not necessary for the computation of the shape groups. Only a classification of the points on the surface, according to their position with respect to the intersection of two or more spheres, is needed. The result is a purely algebraic characterization that can be obtained and stored by a computer, and that may prove to be useful when comparing shapes of different molecules. Illustrative examples are provided for different molecules, as well as for different conformations of the same molecule.
    Additional Material: 4 Ill.
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  • 10
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The molecular electrostatic potential is an important property for characterizing chemical reactivity and the interactions between biomolecules. A joint description of the molecular electrostatics and the molecular shape in 3-space is more complete than the one provided by only the electrostatics. The characterization of the interrelations between the shape features of a formal “molecular surface” and electrostatic potential is of importance in assessing the degree of similarity within a family of molecules. In this work, we have applied a recently developed topological technique to characterize these aspects of the molecular shape. The approach allows one to calculate simple and concise shape codes which can be used for rationalizing structure-activity correlations. These shape codes are related to topological invariants which characterize the topological structure given to the molecular surface by the electrostatic potential. In this work the molecules of interest are a series of four agonists of the H2-receptor of histamine with very different pharmacological activities. We have analyzed the electrostatics on the fused-sphere (van der Waals) surfaces of these compounds for a number of conformations. Some structural properties and the shape descriptions have been found to correlate with the activity. The results are discussed in the context of the current H2-receptor models.
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