Ab initio molecular dynamics: basic theory and advanced methods

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 10
1 Setting the stage: why ab initio molecular dynamics?......Page 13
Part I Basic techniques......Page 21
2.1 Deriving classical molecular dynamics......Page 23
2.2 Ehrenfest molecular dynamics......Page 34
2.3 Born–Oppenheimer molecular dynamics......Page 36
2.4.1 Motivation......Page 39
2.4.2 Car–Parrinello Lagrangian and equations of motion......Page 40
2.4.3 Why does the Car–Parrinello method work?......Page 43
2.4.4 How to control adiabaticity?......Page 48
2.4.5 A mathematical investigation......Page 51
2.4.6 The quantum chemistry viewpoint......Page 52
2.4.7 The simulated annealing and optimization viewpoints......Page 54
2.4.8 The extended Lagrangian viewpoint......Page 56
2.4.9 Analytic and numerical error estimates......Page 57
2.5 What about Hellmann–Feynman forces?......Page 63
2.6 Which method to choose?......Page 68
2.7.1 Introduction......Page 79
2.7.2 Density functional theory......Page 80
2.7.3 Hartree–Fock theory......Page 85
2.7.4 Post Hartree–Fock theories......Page 86
2.8.1 Gaussians and Slater functions......Page 87
2.8.2 Plane waves......Page 89
2.8.3 Generalized plane waves......Page 91
2.8.5 Discrete variable representations......Page 92
2.8.6 Augmented and mixed basis sets......Page 94
2.8.8 Real space grids......Page 95
3.1.1 Supercells and plane wave basis......Page 97
3.1.2 Plane wave expansions......Page 98
3.1.3 Cuto.s and k-points......Page 99
3.1.4 Real space grid and fast Fourier transforms......Page 101
3.1.5 Pseudopotentials......Page 102
3.2.1 General concepts......Page 105
3.2.2 Periodic systems......Page 106
3.2.3 Cluster boundary conditions......Page 107
3.3 Exchange and correlation energy......Page 111
3.4.1 Total energy......Page 116
3.4.3 Gradient for nuclear positions......Page 118
3.4.4 Internal stress tensor......Page 119
3.5 Energy and force calculations in practice......Page 121
3.6 Optimizing the Kohn–Sham orbitals......Page 123
3.6.1 Initial guess......Page 124
3.6.2 Preconditioning......Page 126
3.6.3 Direct methods......Page 127
3.6.4 Fix-point methods......Page 130
3.7.1 Car–Parrinello equations of motion......Page 131
3.7.2 Advanced integration......Page 134
3.7.3 Imposing geometrical constraints......Page 136
3.7.4 Using Car–Parrinello dynamics for optimizations......Page 139
3.8 Program organization and layout......Page 140
3.8.1 Data structures......Page 141
3.8.2 Computational kernels......Page 142
4 Atoms with plane waves: accurate pseudopotentials......Page 148
4.1 Why pseudopotentials?......Page 149
4.2.1 Pseudization of valence wave functions......Page 150
4.2.2 Hamann-Schluter-Chiang conditions......Page 151
4.2.3 Bachelet–Hamann–Schluter pseudopotentials......Page 155
4.2.4 Kerker pseudopotentials......Page 160
4.2.5 Troullier–Martins pseudopotentials......Page 161
4.2.6 Kinetic energy optimized pseudopotentials......Page 163
4.3 Pseudopotentials in the plane wave basis......Page 164
4.3.1 Gauss–Hermite integration......Page 165
4.3.2 Kleinman-Bylander projection......Page 167
4.4 Dual-space Gaussian pseudopotentials......Page 169
4.5 Nonlinear core correction......Page 172
4.6 Pseudopotential transferability......Page 174
4.7 Example: pseudopotentials for carbon......Page 179
Part II Advanced techniques......Page 187
5.1 Introduction......Page 189
5.2.1 Introduction......Page 190
5.2.2 Imposing temperature: thermostats......Page 191
5.2.3 Imposing pressure: barostats......Page 195
5.2.4 Sampling rare events and free energies: metadynamics......Page 201
5.3.1 Introduction......Page 206
5.3.2 A single excited state: ROKS dynamics......Page 208
5.3.3 A few excited states: explicit nonadiabatic dynamics......Page 215
5.3.4 Many excited states: free energy functionals......Page 222
5.3.5 RT-TDDFT: explicit real-time propagation......Page 229
5.3.6.1 Time-dependent linear response method......Page 233
5.3.6.2 Tamm–Danco. approximation......Page 236
5.3.6.3 Dynamical polarizability and oscillator strengths in extended systems......Page 237
5.3.6.4 Derivatives and LR-TDDFT molecular dynamics......Page 241
5.3.6.5 Analysis of electronic excitations......Page 244
5.4.1 Introduction......Page 245
5.4.2 Ab initio path integrals: statics......Page 247
5.4.3 Ab initio path centroids: dynamics......Page 261
5.4.4 Ab initio path integrals: spectroscopy......Page 267
5.4.5 Quantum corrections of classical susceptibilities: infrared spectra......Page 272
5.4.6 Related ab initio quantum approaches......Page 277
5.5 Mixed quantum/classical hybrid molecular dynamics 5.5.1 Introduction......Page 279
5.5.2.1 CP-PAW/AMBER interface......Page 283
5.5.2.2 CPMD/GROMOS interface......Page 286
5.5.2.3 EGO/CPMD interface......Page 290
5.5.3 Embedding in continuum environments......Page 293
5.5.4 QM/MM molecular dynamics involving excited states......Page 295
6.1 Introduction......Page 298
6.2 The PAW transformation......Page 299
6.3 Expectation values......Page 302
6.4 Ultrasoft pseudopotentials......Page 304
6.5 PAW energy expression......Page 308
6.6 Integrating the Car–Parrinello equations......Page 309
7.1.1 Introduction......Page 321
7.1.2 Coupled perturbed Kohn–Sham equations......Page 322
7.1.3 Nuclear Hessian......Page 327
7.1.3.1 Selected eigenmodes of the Hessian......Page 328
7.1.4 Polarizability......Page 329
7.1.5 NMR chemical shifts......Page 330
7.1.5.1 Chemical shifts and susceptibilities......Page 331
7.1.5.2 The gauge origin problem......Page 333
7.1.5.3 The position operator problem......Page 335
7.1.5.4 Density functional perturbation theory......Page 337
7.1.5.5 Pseudopotential correction......Page 338
7.2.2 Position operator in periodic systems......Page 339
7.2.3 Localization functionals......Page 343
7.2.4.1 Generalized localization procedure......Page 347
7.2.4.2 Orbital rotations......Page 349
7.2.4.3 Exponential representation......Page 350
7.2.5 Wannier functions in Car–Parrinello simulations......Page 351
7.2.6 Applications: dipole moments, infrared spectra, and atomic charges......Page 355
7.2.6.1 Molecular dipole moments......Page 356
7.2.6.2 Solute infrared absorption spectra......Page 358
7.2.6.3 Atomic charges......Page 359
8.1 Introduction......Page 362
8.2 Data structures......Page 364
8.3 Computational kernels......Page 366
8.4 Massively parallel processing......Page 371
Part III Applications......Page 381
9.1 Introduction......Page 383
9.2 Solids, minerals, materials, and polymers......Page 384
9.3 Surfaces, interfaces, and heterogeneous catalysis......Page 388
9.4 Mechanochemistry and molecular electronics......Page 392
9.5 Water and aqueous solutions......Page 394
9.6 Non-aqueous liquids and solutions......Page 397
9.7 Glasses and amorphous systems......Page 401
9.8 Matter at extreme conditions......Page 402
9.9 Clusters, fullerenes, and nanotubes......Page 404
9.10 Complex and .uxional molecules......Page 406
9.11 Chemical reactions and transformations......Page 408
9.12 Homogeneous catalysis and zeolites......Page 411
9.13 Photophysics and photochemistry......Page 412
9.14 Biophysics and biochemistry......Page 415
10.2 Boys–Wannier, population, ELF, and Fukui electronic structure analyses......Page 419
10.3 Dipole moments, infrared and Raman spectroscopy......Page 422
10.4 Magnetism, NMR and EPR spectroscopy......Page 423
10.5 Electronic spectroscopy and redox properties......Page 424
10.6 X-ray di.raction and Compton scattering......Page 425
10.7 External electric .elds, scanning probe imaging, conductivity, and currents......Page 426
11 Outlook......Page 428
Bibliography......Page 431
Index......Page 562