Reviews in Computational Chemistry, Volume 26ISBN: 9780470388396
532 pages
November 2008

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.
SpinComponentScaled MP2.
Explicitly Correlated R12 and F12 Methods.
Density Functional Approaches.
Semiempirical Methods and Molecular Mechanics.
Analysis Using SymmetryAdapted 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.
TwoBody Approximation and Cooperative/Nonadditive Effects.
Size Consistency and Extensivity of the Energy.
Summary of Steps in Tutorial.
HighAccuracy 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.
SecondOrder 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 TimeDependent Density Functional Theory (Peter Elliott, Filipp Furche, and Kieron Burke).
Introduction.
Overview.
GroundState Review.
Formalism.
Approximate Functionals.
Basis Sets.
TimeDependent Theory.
Runge–Gross Theorem.
Kohn–Sham Equations.
Linear Response.
Approximations.
Implementation and Basis Sets.
Density Matrix Approach.
Basis Sets.
Convergence for Naphthalene.
DoubleZeta Basis Sets.
Polarization Functions.
TripleZeta Basis Sets.
Diffuse Functions.
Resolution of the Identity.
Summary.
Performance.
Example: Naphthalene Results.
Influence of the GroundState 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.
GroundState 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.
FiniteSize Scaling.
Quenched Disorder.
Quantum vs. Classical Phase Transitions.
How Important Is Quantum Mechanics?
Quantum Scaling and QuantumtoClassical Mapping.
Beyond the Landau–Ginzburg–Wilson Paradigm.
Impurity Quantum Phase Transitions.
Quantum Phase Transitions: Computational Challenges.
Classical Monte Carlo Approaches.
Method: QuantumtoClassical Mapping and Classical Monte Carlo Methods.
TransverseField Ising Model.
Bilayer Heisenberg Quantum Antiferromagnet.
Dissipative TransverseField Ising Chain.
Diluted Bilayer Quantum Antiferromagnet.
Random TransverseField Ising Model.
Dirty Bosons in Two Dimensions.
Quantum Monte Carlo Approaches.
WorldLine 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. RealSpace and Multigrid Methods in Computational Chemistry (Thomas L. Beck).
Introduction.
Physical Systems: Why Do We Need Multiscale Methods?
Why Real Space?
RealSpace Basics.
Equations to Be Solved.
FiniteDifference Representations.
FiniteElement Representations.
Iterative Updates of the Functions, or Relaxation.
What Are the Limitations of RealSpace 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.
SelfConsistency.
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 RealSpace 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 AtomicLevel Simulations Spanning Multiple–Length Scales in the Solid State (Francesca Tavazza, Lyle E. Levine, and Anne M. Chaka).
Introduction.
General Remarks about Hybrid Methods.
CompleteSpectrum Hybrid Methods.
About this Review.
Atomistic/Continuum Coupling.
ZeroTemperature Equilibrium Methods.
FiniteTemperature 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 TimeStep 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 SelfDiffusivities, Viscosities, Electrical Conductivities, and Thermal Conductivities for Ionic Liquids.
Nonequilibrium Methods for Computing Transport Properties.
CoarseGrained 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.