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Reviews in Computational Chemistry, Volume 26

ISBN: 978-0-470-38839-6
532 pages
November 2008
Reviews in Computational Chemistry, Volume 26 (0470388390) cover image
Computational chemistry is increasingly used in conjunction with organic, inorganic, medicinal, biological, physical, and analytical chemistry, biotechnology, materials science, and chemical physics. This series is essential in keeping those individuals involved in these fields abreast of recent developments in computational chemistry.
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1. Computations of Noncovalent p Interactions (C. David Sherrill).

Introduction.

Challenges for Computing p Interactions.

Electron Correlation Problem.

Basis Set Problem.

Basis Set Superposition Errors and the Counterpoise Correction.

Additive Basis/Correlation Approximations.

Reducing Computational Cost.

Truncated Basis Sets.

Pauling Points.

Resolution of the Identity and Local Correlation.

Approximations.

Spin-Component-Scaled MP2.

Explicitly Correlated R12 and F12 Methods.

Density Functional Approaches.

Semiempirical Methods and Molecular Mechanics.

Analysis Using Symmetry-Adapted Perturbation Theory.

Concluding Remarks.

Appendix: Extracting Energy Components from the SAPT2006 Program.

Acknowledgments.

References.

2. Reliable Electronic Structure Computations for Weak Noncovalent Interactions in Clusters (Gregory S. Tschumper).

Introduction and Scope.

Clusters and Weak Noncovalent Interactions.

Computational Methods.

Weak Noncovalent Interactions.

Historical Perspective.

Some Notes about Terminology.

Fundamental Concepts: A Tutorial.

Model Systems and Theoretical Methods.

Rigid Monomer Approximation.

Supermolecular Dissociation and Interaction Energies.

Counterpoise Corrections for Basis Set Superposition Error.

Two-Body Approximation and Cooperative/Nonadditive Effects.

Size Consistency and Extensivity of the Energy.

Summary of Steps in Tutorial.

High-Accuracy Computational Strategies.

Primer on Electron Correlation.

Primer on Atomic Orbital Basis Sets.

Scaling Problem.

Estimating Eint at the CCSD(T) CBS Limit: Another Tutorial.

Accurate Potential Energy Surfaces.

Less Demanding Computational Strategies.

Second-Order Møller–Plesset Perturbation Theory.

Density Functional Theory.

Guidelines.

Other Computational Issues.

Basis Set Superposition Error and Counterpoise Corrections.

Beyond Interaction Energies: Geometries and Vibrational Frequencies.

Concluding Remarks.

Acknowledgments.

References.

3. Excited States from Time-Dependent Density Functional Theory (Peter Elliott, Filipp Furche, and Kieron Burke).

Introduction.

Overview.

Ground-State Review.

Formalism.

Approximate Functionals.

Basis Sets.

Time-Dependent Theory.

Runge–Gross Theorem.

Kohn–Sham Equations.

Linear Response.

Approximations.

Implementation and Basis Sets.

Density Matrix Approach.

Basis Sets.

Convergence for Naphthalene.

Double-Zeta Basis Sets.

Polarization Functions.

Triple-Zeta Basis Sets.

Diffuse Functions.

Resolution of the Identity.

Summary.

Performance.

Example: Naphthalene Results.

Influence of the Ground-State Potential.

Analyzing the Influence of the XC Kernel.

Errors in Potential vs. Kernel.

Understanding Linear Response TDDFT.

Atoms as a Test Case.

Quantum Defect.

Testing TDDFT.

Saving Standard Functionals.

Electron Scattering.

Beyond Standard Functionals.

Double Excitations.

Polymers.

Solids.

Charge Transfer.

Other Topics.

Ground-State XC Energy.

Strong Fields.

Electron Transport.

4. Computing Quantum Phase Transitions (Thomas Vojta).

Preamble: Motivation and History.

Phase Transitions and Critical Behavior.

Landau Theory.

Scaling and the Renormalization Group.

Finite-Size Scaling.

Quenched Disorder.

Quantum vs. Classical Phase Transitions.

How Important Is Quantum Mechanics?

Quantum Scaling and Quantum-to-Classical Mapping.

Beyond the Landau–Ginzburg–Wilson Paradigm.

Impurity Quantum Phase Transitions.

Quantum Phase Transitions: Computational Challenges.

Classical Monte Carlo Approaches.

Method: Quantum-to-Classical Mapping and Classical Monte Carlo Methods.

Transverse-Field Ising Model.

Bilayer Heisenberg Quantum Antiferromagnet.

Dissipative Transverse-Field Ising Chain.

Diluted Bilayer Quantum Antiferromagnet.

Random Transverse-Field Ising Model.

Dirty Bosons in Two Dimensions.

Quantum Monte Carlo Approaches.

World-Line Monte Carlo.

Stochastic Series Expansion.

Bilayer Heisenberg Quantum Antiferromagnet.

Diluted Heisenberg Magnets.

Superfluid–Insulator Transition in an Optical Lattice.

Fermions.

Other Methods and Techniques.

Summary and Conclusions.

5. Real-Space and Multigrid Methods in Computational Chemistry (Thomas L. Beck).

Introduction.

Physical Systems: Why Do We Need Multiscale Methods?

Why Real Space?

Real-Space Basics.

Equations to Be Solved.

Finite-Difference Representations.

Finite-Element Representations.

Iterative Updates of the Functions, or Relaxation.

What Are the Limitations of Real-Space Methods on a Single Fine Grid?

Multigrid Methods.

How Does Multigrid Overcome Critical Slowing Down?

Full Approximations Scheme (FAS) Multigrid, and Full Multigrid (FMG).

Eigenvalue Problems.

Multigrid for the Eigenvalue Problem.

Self-Consistency.

Linear Scaling for Electronic Structure?

Other Nonlinear Problems: The Poisson—Boltzmann and Poisson—Nernst—Planck Equations.

Poisson–Boltzmann Equation.

Poisson–Nernst–Planck (PNP) Equations for Ion Transport.

Some Advice on Writing Multigrid Solvers.

Applications of Multigrid Methods in Chemistry, Biophysics, and Materials Nanoscience.

Electronic Structure.

Electrostatics.

Transport Problems.

Existing Real-Space and Multigrid Codes.

Electronic Structure.

Electrostatics.

Transport.

Some Speculations on the Future.

Chemistry and Physics: When Shall the Twain Meet?

Elimination of Molecular Orbitals?

Larger Scale DFT, Electrostatics, and Transport.

Reiteration of ‘‘Why Real Space?’’

6. Hybrid Methods for Atomic-Level Simulations Spanning Multiple–Length Scales in the Solid State (Francesca Tavazza, Lyle E. Levine, and Anne M. Chaka).

Introduction.

General Remarks about Hybrid Methods.

Complete-Spectrum Hybrid Methods.

About this Review.

Atomistic/Continuum Coupling.

Zero-Temperature Equilibrium Methods.

Finite-Temperature Equilibrium Methods.

Dynamical Methods.

Classical/Quantum Coupling.

Static and Semistatic Methods.

Dynamics Methodologies.

7. Extending the Time Scale in Atomically Detailed Simulations (Alfredo E. Ca´rdenas and Eric Barth).

Introduction.

The Verlet Method.

Molecular Dynamics Potential.

Multiple Time Steps.

Reaction Paths.

Multiple Time-Step Methods.

Splitting the Force.

Numerical Integration with Force Splitting: Extrapolation vs. Impulse.

Fundamental Limitation on Size of MTS Methods.

Langevin Stabilization.

Further Challenges and Recent Advances.

An MTS Tutorial.

Extending the Time Scale: Path Methodologies.

Transition Path Sampling.

Maximization of the Diffusive Flux (MaxFlux).

Discrete Path Sampling and String Method.

Optimization of Action.

Boundary Value Formulation in Length.

Use of SDEL to Compute Reactive Trajectories: Input Parameters, Initial Guess, and Parallelization Protocol.

Applications of the Stochastic Difference Equation in Length.

Recent Advances and Challenges.

8. Atomistic Simulation of Ionic Liquids (Edward J. Maginn).

Introduction.

Short (Pre)History of Ionic Liquid Simulations.

Earliest Ionic Liquid Simulations.

More Systems and Refined Models.

Force Fields and Properties of Ionic Liquids Having Dialkylimidazolium Cations.

Force Fields and Properties of Other Ionic Liquids.

Solutes in Ionic Liquids.

Implications of Slow Dynamics when Computing Transport Properties.

Computing Self-Diffusivities, Viscosities, Electrical Conductivities, and Thermal Conductivities for Ionic Liquids.

Nonequilibrium Methods for Computing Transport Properties.

Coarse-Grained Models.

Ab Initio Molecular Dynamics.

How to Carry Out Your Own Ionic Liquid Simulations.

What Code?

Force Fields.

Data Analysis.

Operating Systems and Parallel Computing.

Summary and Outlook.

Acknowledgments.

References.

Author Index.

Subject Index.

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