Molecular Quantum Similarity in QSAR and Drug Design [Paperback]

1 Introduction.- 1.1 Origins and evolution of QSAR.- 1.2 Molecular similarity in QSAR.- 1.3 Scope and contents of the book.- 2 Quantum objects, density functions and quantum similarity measures.- 2.1 Tagged sets and molecular description.- 2.1.1 Boolean tagged sets.- 2.1.2 Functional tagged sets.- 2.1.3 Vector semispaces.- 2.2 Density functions.- 2.3 Quantum objects.- 2.4 Expectation values in Quantum Mechanics.- 2.5 Molecular Quantum Similarity.- 2.6 General definition of molecular quantum similarity measures (MQSM).- 2.6.1 Overlap MQSM.- 2.6.2 Coulomb MQSM.- 2.7 Quantum self-similarity measures.- 2.8 MQSM as discrete matrix representations of the quantum objects..- 2.9 Molecular quantum similarity indices (MQSI).- 2.9.1 The Carb? index.- 2.10 The Atomic Shell Approximation (ASA).- 2.10.1 Promolecular ASA.- 2.10.2 ASA parameters optimization procedure.- 2.10.3 Example of ASA fitting: adjustment to ab initio atomic densities using a 6-31 IG basis set.- 2.10.4 Descriptive capacity of ASA.- 2.11 The molecular alignment problem.- 2.11.1 Dependence of MQSM with the relative orientation between two molecules.- 2.11.2 Maximal similarity superposition algorithm.- 2.11.3 Common skeleton recognition: the topo-geometrical superposition algorithm.- 2.11.4 Other molecular alignment methods.- 3 Application of Quantum Similarity to QSAR.- 3.1 Theoretical connection between QS and QSAR.- 3.1.1 Beyond the expectation value.- 3.2 Construction of the predictive model.- 3.2.1 Multilinear regression.- 3.3 Possible alternatives to the multilinear regression.- 3.3.1 Partial least squares (PLS) regression.- 3.3.2 Neural Network algorithms.- 3.4 Parameters to assess the goodness-of-fit.- 3.4.1 The multiple determination coefficient r2.- 3.4.2 The standard deviation coefficient ?N.- 3.5 Robustness of the model.- 3.5.1 Cross-validation by leave-one-out.- 3.5.2 The prediction coefficient q2.- 3.5.3 Influence on the regression results.- 3.6 Study of chance correlations.- 3.6.1 The randomizatiol3(