Reviews in Computational Chemistry Volume 18

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overlap between the libraries. Two very dissimilar libraries formed two distinct clusters with little overlap, whereas two very similar libraries showed no distinction. The use of mixture-model or density-based clustering has not yet been reported for processing chemical data sets. An interesting application of these techniques is their use to group the compound descriptors so as to obtain a set of orthogonal descriptors. Up to this point, the clustering that we have discussed has been applied to the patterns (fingerprints or dataprints) characterizing each compound; this is the ‘‘Q-mode clustering’’ referred to by Sneath and Sokal. 1 One can also cluster the features (the descriptors used in the fingerprints or dataprints) to highlight groups of similar descriptors. Sneath and Sokal call this ‘‘R-mode clustering.’’ The similar property principle, upon which structure–property relationships depend, assumes that the compound descriptors are independent of each other. Reducing the number of descriptors can thus help in subsequent Q-mode clustering by reducing the dimensionality. Clustering the descriptors, so that a subset of orthogonal descriptors can be extracted, is an alternative to factor analysis and principal components analysis. Using an orthogonal subset of descriptors has the benefit that the result is a set of individual descriptors rather than composite descriptors. Taraviras, Ivanciuc, and Cabrol-Bass 65 applied the single-link, group-average, completelink, and Ward hierarchical methods, along with Jarvis–Patrick, variablelength Jarvis–Patrick, and k-means nonhierarchical methods to a set of 240 topological indices in an attempt to reveal any ‘‘natural’’ clusters of the descriptors. Descriptors that were found to exist in the same clusters across all seven methods were regarded as being strongly clustered. Reducing the number of methods that needed to be in agreement revealed progressively weaker clusters. Overall, it was found that the strategy of using multiple clustering methods for R-mode clustering could be used to provide representative sets of orthogonal descriptors for use in QSAR analysis. CONCLUSIONS Conclusions 33 Clustering methodology has been developed over many decades. The application of clustering to chemical data sets began in the 1980s, coinciding with the increasing size of in-house compound collections having their information contained in structural databases and with advances made by the information retrieval community to analyze large document collections. In the 1990s the advent of high-throughput screening, combinatorial libraries, and commercially available external chemical inventories placed a greater emphasis on rational compound selection. The demands of clustering data sets of several million compounds with high-dimensional representations led to the widespread adoption of a few inherently efficient and optimally implemented methods, namely, the Jarvis–Patrick, Ward, and k-means methods.
34 Clustering Methods and Their Uses in Computational Chemistry Acceptance of these methods—and inclusion of them as routine operations within such applications as lead-finding strategies, QSAR analyses, and compound acquisition—has been a gradual process rather than an abrupt revolution. The current decade should see this process continue as the methodologies are refined. The push for such advancement appears to be coming again from the information retrieval community but also from the data mining community, which has made significant progress. The emphasis of current research is turning toward the quality of the resultant clusters. It has been shown that, using representatives selected from clusters for lead-finding can increase the active hit rate significantly and consistently. The results so far in chemistry are promising, but research in other areas outside of chemistry suggests that clustering is still a blunt instrument that can be sharpened by refinements. An example of this refinement is to be able to handle mixed or nonnumerical data, and another example is to take more consideration of cluster sizes, shapes, and distribution. The existing methods and implementations used to analyze chemical data sets do an impressive job when compared with the situation a decade ago. What is exciting is the number of new ideas that are being generated that should result in significant advances in the next decade. REFERENCES 1. P. H. A. Sneath and R. R. Sokal, Numerical Taxonomy, W. H. Freeman, San Francisco, CA, 1973. 2. L. Kaufman and P. J. Rousseeuw, Finding Groups in Data: An Introduction to Cluster Analysis, Wiley-Interscience, New York, 1990. 3. B. S. Everitt, Cluster Analysis, 3rd ed., Edward Arnold, London, 1993. 4. A. D. Gordon, Classification, 2nd ed., Chapman and Hall, London, 1999. 5. P. Willett, Similarity and Clustering in Chemical Information Systems, Research Studies Press, Letchworth, UK, 1987. 6. N. Bratchell, Chemom. Intell. Lab. Systems, 6, 105 (1989). Cluster Analysis. 7. J. M. Barnard and G. M. Downs, J. Chem. Inf. Comput. Sci., 32 (6), 644 (1992). Clustering of Chemical Structures on the Basis of Two-Dimensional Similarity Measures. 8. G. M. Downs and P. Willett, in Advanced Computer-Assisted Techniques in Drug Discovery, H. van de Waterbeemd, Ed., VCH Publishers, Weinheim, 1994, pp. 111–130. Clustering of Chemical Structure Databases for Compound Selection. 9. R. A. Lewis, S. D. Pickett, and D. E. Clark, in Reviews in Computational Chemistry, K. B. Lipkowitz and D. B. Boyd, Eds., Wiley-VCH, New York, 2000, Vol. 16, pp. 1–51. Computer-Aided Molecular Diversity Analysis and Combinatorial Library Design. 10. Clustan Ltd., 16 Kingsburgh Road, Edinburgh, UK. http://www.clustan.com. 11. SAS Institute Inc., SAS Campus Drive, Cary, NC 27513, USA. http://www.sas.com. 12. Barnard Chemical Information Ltd., 46 Uppergate Road, Stannington, Sheffield S6 6BX, UK. http://www.bci.gb.com. 13. Chemical Computing Group Inc., 1010 Sherbrooke Street West, Suite 910, Montreal, Quebec H3A 2R7, Canada. http://www.chemcomp.com.
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Reviews in Computational Chemistry
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Kenny B. Lipkowitz Department of Ch
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vi Preface three-dimensional struct
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viii Preface some descriptors and i
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Epilogue and Dedication My associat
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84 The Use of Scoring Functions in
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86 The Use of Scoring Functions in
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CHAPTER 3 Potentials and Algorithms
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Vn (1 + cos(nω + γ)) 2 K θ (θ
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are modified by their environment w
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Table 1 Polarizability Parameters f
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The polarizable point dipole models
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two to three orders of magnitude sl
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M i z i + q i d i k i and shell cha
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Shell Models 103 on estimates of sh
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minimization can be replaced by mor
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The energy required to create a cha
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for all i ði:e:; 8 iÞ: @U @qi l
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where we have used q Cl ¼ qNa. The
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Electronegativity Equalization Mode
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Electronegativity Equalization Mode
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of N molecules is taken as a Hartre
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is treated using variable charges.
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water have been developed, includin
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Applications 123 classical and rigi
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developing polarizable models. A va
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Comparison of the Polarization Mode
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negligible errors in such propertie
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ecome significant at field strength
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noteworthy in this regard because t
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References 135 9. P. Cieplak and P.
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References 137 48. E. L. Pollock an
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References 139 Computational Chemis
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References 141 139. J. Hinze and H.
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References 143 178. J. J. P. Stewar
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References 145 216. M. W. Mahoney a
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CHAPTER 4 New Developments in the T
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Introduction 149 applications). For
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FCWD(∆E ) FCWD(0) ∆E = 0 ∆E
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Introduction 153 Equations [6]-[12]
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Paradigm of Free Energy Surfaces 15
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Paradigm of Free Energy Surfaces 15
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In Eqs. [18] and [19], F0i is the e
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where ‘‘þ’’ and ‘‘ ’
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is, however, small for the usual co
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solute-solvent coupling through the
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where Z is the electrode overpotent
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energy surfaces of ET. 33,50-56 It
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This result indicates a fundamental
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βF i (X ) 40 20 0 −20 1 2 βλ 1
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Table 1 Main Features of the Two-Pa
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and Hss ¼ U rep ss 1 2 X j;k ðmj
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λ i /eV 4 3 2 1 0 0 10 20 30 40 Bo
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the width/Stokes shift relation (Eq
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Table 3 Mapping of the Q Model on S
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This situation is of course not sat
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F ± (Y ad )/λ I 0.8 0.4 0 −0.4
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it by choosing the GMH basis set 7
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Anharmonic higher order terms gain
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of the radiation is the perturbatio
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individual vibrational excitations
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m 12 /D 6 5.5 5 4.5 4 3.5 17 18 19
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In Eq. [144], the coordinates Y km
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ε/M −1 cm −1 4000 2000 0 analy
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βσ 2 /10 3 cm −1 14 12 10 8 Opt
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0.2 0.1 0 12 16 20 24 28 32 The app
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References 207 7. M. D. Newton, Adv
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References 209 59. R. Kubo and Y. T
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