1 Preliminaries

1.1 Introduction

1.2 Python

1.3 Object-oriented programming

1.4 The pDynamo library

1.5 Notation and units

2 Chemical models and representations

2.1 Introduction

2.2 The System class

2.3 Example 1

2.4 Common molecular representations

2.5 Example 2

3 Coordinates and coordinate manipulations

3.1 Introduction

3.2 Connectivity

3.3 Internal coordinates

3.4 Example 3

3.5 Miscellaneous transformations

3.6 Superimposing structures

3.7 Example 4

4 Quantum chemical models

4.1 Introduction

4.2 The Born-Oppenheimer approximation

4.3 Strategies for obtaining energies on a potential energy surface

4.4 Molecular orbital methods

4.5 The Hartree-Fock approximation

4.6 Analysis of the charge density

4.7 Example 5

4.8 Derivatives of the potential energy

4.9 Example 6

5 Molecular mechanics

5.1 Introduction

5.2 Typical empirical energy functions

5.3 Calculating a molecular mechanics energy

5.4 Example 7

5.5 Parametrizing potential energy functions

5.6 Soft constraints

6 Hybrid potentials

6.1 Introduction

6.2 Combining QC and MM potentials

6.3 Example 8

6.4 Covalent bonds between QC and MM atoms

6.5 Example 9

7 Finding stationary points and reaction paths on potential energy surfaces

7.1 Introduction

7.2 Exploring potential energy surfaces

7.3 Locating minima

7.4 Example 10

7.5 Locating saddle points

7.6 Example 11

7.7 Following reaction paths

7.8 Example 12

7.9 Determining complete reaction paths

7.10 Example 13

8 Normal mode analysis

8.1 Introduction

8.2 Calculation of the normal modes

8.3 Rotational and translational modes

8.4 Generating normal mode trajectories

8.5 Example 14

8.6 Calculation of thermodynamic quantities

8.7 Example 15

9 Molecular dynamics simulations Ⅰ

9.1 Introduction

9.2 Molecular dynamics

9.3 Example 16

9.4 Trajectory analysis

9.5 Example 17

9.6 Simulated annealing

9.7 Example 18

10 More on non-bonding interactions

10.1 Introduction

10.2 Cutoff methods for the calculation of non-bonding interactions

10.3 Example 19

10.4 Including an environment

10.5 Periodic boundary conditions

10.6 Example 20

10.7 Ewald summation techniques

10.8 Fast methods for the evaluation of non-bonding interactions

11 Molecular dynamics simulations Ⅱ

11.1 Introduction

11.2 Analysis of molecular dynamics trajectories

11.3 Example 21

11.4 Temperature and pressure control in molecular dynamics simulations

11.5 Example 22

11.6 Calculating free energies:umbrella sampling

11.7 Examples 23 and 24

11.8 Speeding up simulations

12 Monte Carlo simulations

12.1 Introduction

12.2 The Metropolis Monte Carlo method

12.3 Monte Carlo simulations of molecules

12.4 Example 25

12.5 Calculating free energies:statistical perturbation theory

12.6 Example 26

Appendix 1 The pDynamo library

Appendix 2 Mathematical appendix

A2.1 The eigenvalues and eigenvectors of a matrix

A2.2 The method of Lagrange multipliers

Appendix 3 Solvent boxes and solvated molecules

A3.1 Example 27

A3.2 Example 28

Bibliography

Author index

Subject index