Computer Simulations of Molecules and Condensed Matter

From Electronic Structures to Molecular Dynamics

This book provides a relatively complete introduction to the methods used in computational condensed matter. A wide range of electronic structure theories are introduced, including traditional quantum chemistry methods, density functional theory, many-body perturbation theory, and more. Molecular dynamics simulations are also discussed, with extensions to enhanced sampling and free-energy calculation techniques including umbrella sampling, meta-dynamics, integrated tempering sampling, etc. As a further extension beyond the standard Born-Oppenheimer molecular dynamics, some simulation techniques for the description of quantum nuclear effects are also covered, based on Feynman's path-integral representation of quantum mechanics. The book aims to help beginning graduate students to set up a framework of the concepts they should know before tackling the physical/chemical problems they will face in their research.

Contents:

• Introduction to Computer Simulations of Molecules and Condensed Matter

• Quantum Chemistry Methods and Density-Functional Theory

• Pseudopotentials, Full Potential, and Basis Sets

• Many-Body Green's Function Theory and the GW Approximation

• Molecular Dynamics

• Extension of Molecular Dynamics, Enhanced Sampling and the Free-Energy Calculations

• Quantum Nuclear Effects

• Appendices:

  • Useful Mathematical Relations
  • Expansion of a Non-Local Function
  • The Brillouin-Zone Integration
  • The Frequency Integration

• References

• Acknowledgements

Readership: Researchers in computational condensed matter physics.
Key Features:

• Elaboration on a framework of concepts based on the authors' research experiences
• Illustrations of methods ranging from electronic structures to molecular dynamics
• Detailed explanation of the path-integral method