Reviews in Computational Chemistry, Volume 23

1. Linear-Scaling Methods in Quantum Chemistry (Christian Ochsenfeld, Jörg Kussmann, and Daniel S. Lambrecht).

Introduction.

Some Basics of SCF Theory.

Direct SCF Methods and Two-Electron Integral Screening.

Schwarz Integral Estimates.

Multipole-Based Integral Estimates (MBIE).

Calculation of Integrals via Multipole Expansion.

A First Example.

Derivation of the Multipole Expansion.

The Fast Multipole Method: Breaking the Quadratic Wall.

Fast Multipole Methods for Continuous Charge Distributions.

Other Approaches.

Exchange-Type Contractions.

The Exchange-Correlation Matrix of KS-DFT.

Avoiding the Diagonalization Step—Density Matrix-Based SCF.

General Remarks.

Tensor Formalism.

Properties of the One-Particle Density Matrix.

Density Matrix-Based Energy Functional.

‘‘Curvy Steps’’ in Energy Minimization.

Density Matrix-Based Quadratically Convergent SCF (D-QCSCF).

Implications for Linear-Scaling Calculation of SCF Energies.

SCF Energy Gradients.

Molecular Response Properties at the SCF Level.

Vibrational Frequencies.

NMR Chemical Shieldings.

Density Matrix-Based Coupled Perturbed SCF (D-CPSCF).

Outlook on Electron Correlation Methods for Large Systems.

Long-Range Behavior of Correlation Effects.

Rigorous Selection of Transformed Products via Multipole-Based Integral Estimates (MBIE).

Implications.

Conclusions.

References.

2. Conical Intersections in Molecular Systems (Spiridoula Matsika).

Introduction.

General Theory.

The Born–Oppenheimer Approximation and its Breakdown: Nonadiabatic Processes.

Adiabatic-Diabatic Representation.

The Noncrossing Rule.

The Geometric Phase Effect.

Conical Intersections and Symmetry.

The Branching Plane.

Characterizing Conical Intersections: Topography.

Derivative Coupling.

Electronic Structure Methods for Excited States.

Multiconfiguration Self-Consistent Field (MCSCF).

Multireference Configuration Interaction (MRCI).

Complete Active Space Second-Order Perturbation Theory (CASPT2).

Single Reference Methods.

Choosing Electronic Structure Methods for Conical Intersections.

Locating Conical Intersections.

Dynamics.

Applications.

Conical Intersections in Biologically Relevant Systems.

Beyond the Double Cone.

Three-State Conical Intersections.

Spin-Orbit Coupling and Conical Intersections.

Conclusions and Future Directions.

Acknowledgments.

References.

3. Variational Transition State Theory with Multidimensional Tunneling (Antonio Fernandez-Ramos, Benjamin A. Ellingson, Bruce C. Garrett, and Donald G. Truhlar).

Introduction.

Variational Transition State Theory for Gas-Phase Reactions.

Conventional Transition State Theory.

Canonical Variational Transition State Theory.

Other Variational Transition State Theories.

Quantum Effects on the Reaction Coordinate.

Practical Methods for Quantized VTST Calculations.

The Reaction Path.

Evaluation of Partition Functions.

Harmonic and Anharmonic Vibrational Energy Levels.

Calculations of Generalized Transition State Number of States.

Quantum Effects on Reaction Coordinate Motion.

Multidimensional Tunneling Corrections Based on the Adiabatic Approximation.

Large Curvature Transmission Coefficient.

The Microcanonically Optimized Transmission Coefficient.

Building the PES from Electronic Structure Calculation.

Direct Dynamics with Specific Reaction Parameters.

Interpolated VTST.

Dual-Level Dynamics.

Reactions in Liquids.

Ensemble-Averaged Variational Transition State Theory.

Gas-Phase Example: H +CH₄.

Liquid-Phase Example: Menshutkin Reaction.

Concluding Remarks.

Acknowledgments.

References.

4. Coarse-Grain Modeling of Polymers (Roland Faller).

Introduction.

Defining the System.

Choice of Model.

Interaction Sites on the Coarse-Grained Scale.

Static Mapping.

Single-Chain Distribution Potentials.

Simplex.

Iterative Structural Coarse-Graining.

Mapping Onto Simple Models.

Dynamic Mapping.

Mapping by Chain Diffusion.

Mapping through Local Correlation Times.

Direct Mapping of the Lennard-Jones Time.

Coarse-Grained Monte Carlo Simulations.

Reverse Mapping.

A Look Beyond Polymers.

Conclusions.

Acknowledgments.

References.

5. Analysis of Chemical Information Content Using Shannon Entropy (Jeffrey W. Godden and JÜrgen Bajorath).

Introduction.

Shannon Entropy Concept.

Descriptor Comparison.

Influence of Boundary Effects.

Extension of SE Analysis for Profiling of Chemical Libraries.

Information Content of Organic Molecules.

Shannon Entropy in Quantum Mechanics, Molecular Dynamics, and Modeling.

Examples of SE and DSE Analysis.

Conclusions.

References.

6. Applications of Support Vector Machines in Chemistry (Ovidiu Ivanciuc).

Introduction.

A Nonmathematical Introduction to SVM.

Pattern Classification.

The Vapnik–Chervonenkis Dimension.

Pattern Classification with Linear Support Vector Machines.

SVM Classification for Linearly Separable Data.

Linear SVM for the Classification of Linearly Non-Separable Data.

Nonlinear Support Vector Machines.

Mapping Patterns to a Feature Space.

Feature Functions and Kernels.

Kernel Functions for SVM.

Hard Margin Nonlinear SVM Classification.

Soft Margin Nonlinear SVM Classification.

n-SVM Classification.

Weighted SVM for Imbalanced Classification.

Multi-class SVM Classification.

SVM Regression.

Optimizing the SVM Model.

Descriptor Selection.

Support Vectors Selection.

Jury SVM.

Kernels for Biosequences.

Kernels for Molecular Structures.

Practical Aspects of SVM Classification.

Predicting the Mechanism of Action for Polar and Nonpolar Narcotic Compounds.

Predicting the Mechanism of Action for Narcotic and Reactive Compounds.

Predicting the Mechanism of Action from Hydrophobicity and Experimental Toxicity.

Classifying the Carcinogenic Activity of Polycyclic Aromatic Hydrocarbons.

Structure-Odor Relationships for Pyrazines.

Practical Aspects of SVM Regression.

SVM Regression QSAR for the Phenol Toxicity to Tetrahymena pyriformis.

SVM Regression QSAR for Benzodiazepine Receptor Ligands.

SVM Regression QSAR for the Toxicity of Aromatic Compounds to Chlorella vulgaris.

SVM Regression QSAR for Bioconcentration Factors.

Review of SVM Applications in Chemistry.

Recognition of Chemical Classes and Drug Design.

QSAR.

Genotoxicity of Chemical Compounds.

Chemometrics.

Sensors.

Chemical Engineering.

Text Mining for Scientific Information.

SVM Resources on the Web.

SVM Software.

Conclusions.

References.

7. How Computational Chemistry Became Important in the Pharmaceutical Industry (Donald B. Boyd).

Introduction.

Germination: The 1960s.

Gaining a Foothold: The 1970s.

Growth: The 1980s.

Gems Discovered: The 1990s.

Final Observations.

Acknowledgments.

References.

Author Index.

Subject Index.