Preface to the first edition ................................... ix
Preface to the second edition .................................. xi
1 Preliminaries ................................................ 1
1.1 Introduction ............................................ 1
1.2 Python .................................................. 2
1.3 Object-oriented programming ............................. 5
1.4 The pDynamo library ..................................... 8
1.5 Notation and units ...................................... 9
2 Chemical models and representations ......................... 14
2 1 Introduction ........................................... 14
2.2 The System class ....................................... 14
2.3 Example 1 .............................................. 17
2.4 Common molecular representations ....................... 18
2.5 Example 2 .............................................. 27
3 Coordinates and coordinate manipulations .................... 31
3.1 Introduction ........................................... 31
3.2 Connectivity ........................................... 31
3.3 Internal coordinates ................................... 35
3.4 Example 3 .............................................. 38
3.5 Miscellaneous transformations .......................... 41
3.6 Superimposing structures ............................... 45
3.7 Example 4 .............................................. 47
4 Quantum chemical models ..................................... 51
4.1 Introduction ........................................... 51
4.2 The Born-Oppenheimer approximation ..................... 51
4.3 Strategies for obtaining energies on a potential
energy surface ......................................... 53
4.4 Molecular orbital methods .............................. 54
4.5 The Hartree-Fock approximation ......................... 56
4.6 Analysis of the charge density ......................... 67
4.7 Example 5 .............................................. 70
4.8 Derivatives of the potential energy .................... 74
4.9 Example 6 .............................................. 78
5 Molecular mechanics ......................................... 81
5.1 Introduction ........................................... 81
5.2 Typical empirical energy functions ..................... 81
5.3 Calculating a molecular mechanics energy ............... 93
5.4 Example 7 ............................................. 101
5.5 Parametrizing potential energy functions .............. 103
5.6 Soft constraints ...................................... 105
6 Hybrid potentials .......................................... 110
6.1 Introduction .......................................... 110
6.2 Combining QC and MM potentials ........................ 110
6.3 Example 8 ............................................. 114
6.4 Covalent bonds between QC and MM atoms ................ 116
6.5 Example 9 ............................................. 120
7 Finding stationary points and reaction paths on potential
energy surfaces ............................................ 122
7.1 Introduction .......................................... 122
7.2 Exploring potential energy surfaces ................... 122
7.3 Locating minima ....................................... 126
7.4 Example 10 ............................................ 129
7.5 Locating saddle points ................................ 130
7.6 Example 11 ............................................ 134
7.7 Following reaction paths .............................. 136
7.8 Example 12 ............................................ 139
7.9 Determining complete reaction paths ................... 140
7.10 Example 13 ............................................ 144
8 Normal mode analysis ....................................... 148
8.1 Introduction .......................................... 148
8.2 Calculation of the normal modes ....................... 148
8.3 Rotational and translational modes .................... 153
8.4 Generating normal mode trajectories ................... 156
8.5 Example 14 ............................................ 158
8.6 Calculation of thermodynamic quantities ............... 161
8.7 Example 15 ............................................ 165
9 Molecular dynamics simulations I ........................... 170
9.1 Introduction .......................................... 170
9.2 Molecular dynamics .................................... 170
9.3 Example 16 ............................................ 178
9.4 Trajectory analysis ................................... 182
9.5 Example 17 ............................................ 184
9.6 Simulated annealing ................................... 186
9.7 Example 18 ............................................ 189
10 More on non-bonding interactions ........................... 195
10.1 Introduction .......................................... 195
10.2 Cutoff methods for the calculation of non-bonding
interactions .......................................... 195
10.3 Example 19 ............................................ 205
10.4 Including an environment .............................. 209
10.5 Periodic boundary conditions .......................... 212
10.6 Example 20 ............................................ 215
10.7 Ewald summation techniques ............................ 217
10.8 Fast methods for the evaluation of non-bonding
interactions .......................................... 223
11 Molecular dynamics simulations II .......................... 225
11.1 Introduction .......................................... 225
11.2 Analysis of molecular dynamics trajectories ........... 225
11.3 Example 21 ............................................ 233
11.4 Temperature and pressure control in molecular
dynamics simulations .................................. 235
11.5 Example 22 ............................................ 244
11.6 Calculating free energies: umbrella sampling .......... 246
11.7 Examples 23 and 24 .................................... 252
11.8 Speeding up simulations ............................... 258
12 Monte Carlo simulations .................................... 262
12.1 Introduction .......................................... 262
12.2 The Metropolis Monte Carlo method ..................... 262
12.3 Monte Carlo simulations of molecules .................. 266
12.4 Example 25 ............................................ 277
12.5 Calculating free energies: statistical perturbation
theory ................................................ 280
12.6 Example 26 ............................................ 286
Appendix 1 The pDynamo library ................................ 294
Appendix 2 Mathematical appendix .............................. 298
A2.1 The eigenvalues and eigenvectors of a matrix .......... 298
A2.2 The method of Lagrange multipliers .................... 300
Appendix 3 Solvent boxes and solvated molecules ............... 302
A3.1 Example 27 ............................................ 302
A3.2 Example 28 ............................................ 305
Bibliography .................................................. 307
Author index .................................................. 326
Subject index ................................................. 330
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