Molecular Simulations – Fundamentals and Practice

Saman Alavi, PhD, is Adjunct Professor at the Department of Chemical and Biological Engineering at the University of British Columbia (Vancouver, Canada) and acts as a Scientific Evaluator at Health Canada. After obtaining his PhD from the University of British Columbia, he spent research periods in the National Research Council of Canada, at Oklahoma State University (USA) and the University of Ottawa (Canada). Saman Alavi has authored over 120 scientific publications on molecular simulations of different classes of materials.

1. INTRODUCTION

Motivation: Relating Microscopic Molecular Properties to Macroscopic /

Thermodynamic Behavior of Bulk Systems

Molecular Dynamics and Monte Carlo Simulations for Modeling Macroscopic Scale Experiment

Scope of the Book and Background Needed



2. CLASSICAL MECHANICS FOR MANY-MOLECULE SYSTEMS

Newton's Equations of Motion for Many-Molecule Systems

Analytical Solution of Newton's Equations for Simple Systems

The Concept of Trajectory and Phase Space

Numerical Solution of Newton's Equations, Finite-Difference Method

The Verlet and Leapfrog Time Progression Algorithms

The Trajectory for a Many-Particle System



3. FORCE FIELD MODELS IN CLASSICAL MOLECULAR SIMULATIONS

Summary of the Quantum Mechanics of Molecular Force Fields

Modeling the Potential Energy Surface of Non-Reactive Systems

Inter- and Intra-Molecular Force Fields

Design and Choice of Force Fields

Calculation of the Force Field Parameters Using Quantum Chemistry, Spectroscopy, and Modeling



4. INTRODUCTION TO PROBABILITY CONCEPTS

Basic Concepts of Probability Theory: Single and Multiple Variable Probabilities, Discrete and Continuous Probabilities, the Central Limit Theorem

Maxwell-Boltzmann Probability Distribution for Molecular Velocity, Speed

Maxwell-Boltzmann Energy Distribution for Single Molecules and Collections of Molecules

Probability Distributions of Large Collections of Molecules

Assigning Molecular Velocities in Molecular Simulations from the Maxwell-Boltzmann Probability Distribution



5. INTRODUCTION TO STATISTICAL MECHANICS

Statistical Mechanics in Classical Mechanics Language

The Concept of Partition Function and Ensembles in Statistical Mechanics:

Canonical (Isothermal Isochoric), Isothermal Isobaric, Grand-Canonical and Other Ensembles

Thermodynamic Properties: Energy, Temperature, Pressure, Entropy, Free Energy, Fluctuations in These Quantities in Microscopic Systems

The Quantum Mechanical Approach to Statistical Mechanics



6. MOLECULAR DYNAMICS (MD) SIMULATIONS 1

Periodic Boundary Conditions: Simulating "Infinite" Bulk Systems with a Finite Number of Molecules

Simulating Bulk Phases, Surfaces, and Nanoparticles;

Short-Range Van Der Waals Forces: Truncation of Potentials

Long-Range Electrostatic Forces: Ewald Summations



7. MOLECULAR DYNAMICS (MD) SIMULATIONS 2

Including the Effect of the Environment in Molecular Simulations: Thermostats and Barostats

Determining Thermodynamic Averages from Molecular Dynamics Trajectories: Multiple Time Origins and Maximizing Sample Size and Statistical Averaging



8. ANALYZING MOLECULAR DYNAMICS SIMULATIONS

Characterizing the Microscopic Structure of Phases

Radial Distribution Functions, Order Parameters

Dynamics of Molecules from MD

Mean-Square Displacements, Velocity Autocorrelations, Diffusion Coefficients



9. MONTE CARLO (MC) SIMULATION METHODS AND APPLICATIONS

Principles of Monte Carlo Methods, Sampling from the Ensemble Probability Distribution

Importance Sampling, Microscopic Reversibility

Advantage and Disadvantages of Monte Carlos Simulations in Comparison to MD Simulations

Simulations in Different Ensembles with MC



10. ADVANCED MOLECULAR SIMULATION TECHNIQUES

Free Energy from Molecular Simulations

Replica Exchange and Improving Phase Space Sampling

Course-Graining of Potentials



11. OTHER BACKGROUND KNOWLEDGE REQUIRED FOR RUNNING MOLECULAR SIMULATIONS

Setting Up the Initial Geometry: Solids, Space Groups and Symmetry, Liquids and Gases

Selecting and Setting Up the Force Field for a Molecular Simulation

Simulations of Proteins, DNA, and RNA

Simulations of Biological Membranes

The PDB Format for Initial Geometry