Ideas of quantum chemistry

Contents......Page 8
Introduction......Page 22
Chapter 1. The Magic of Quantum Mechanics......Page 36
1.1 History of a revolution......Page 39
1.2 Postulates......Page 50
1.3 The Heisenberg uncertainty principle......Page 69
1.4 The Copenhagen interpretation......Page 72
1.5 How to disprove the Heisenberg principle? The Einstein-Podolsky-Rosen recipe......Page 73
1.6 Is the world real?......Page 75
1.7 The Bell inequality will decide......Page 78
1.8 Intriguing results of experiments with photons......Page 81
1.9 Teleportation......Page 82
1.10 Quantum computing......Page 84
Chapter 2. The Schrödinger Equation......Page 90
2.1 Symmetry of the Hamiltonian and its consequences......Page 92
2.2 Schrödinger equation for stationary states......Page 105
2.3 The time-dependent Schrödinger equation......Page 111
2.4 Evolution after switching a perturbation......Page 114
Chapter 3. Beyond the Schrödinger Equation......Page 125
3.1 A glimpse of classical relativity theory......Page 128
3.2 Reconciling relativity and quantum mechanics......Page 144
3.3 The Dirac equation......Page 146
3.4 The hydrogen-like atom in Dirac theory......Page 158
3.5 Larger systems......Page 164
3.6 Beyond the Dirac equation…......Page 165
Chapter 4. Exact Solutions - Our Beacons......Page 177
4.1 Free particle......Page 179
4.2 Particle in a box......Page 180
4.3 Tunnelling effect......Page 188
4.4 The harmonic oscillator......Page 199
4.5 Morse oscillator......Page 204
4.6 Rigid rotator......Page 211
4.7 Hydrogen-like atom......Page 213
4.8 Harmonic helium atom (harmonium)......Page 219
4.9 What do all these solutions have in common?......Page 223
4.10 Beacons and pearls of physics......Page 224
Chapter 5. Two Fundamental Approximate Methods......Page 230
5.1 Variational method......Page 231
5.2 Perturbational method......Page 238
Chapter 6. Separation of Electronic and Nuclear Motions......Page 252
6.1 Separation of the centre-of-mass motion......Page 256
6.2 Exact (non-adiabatic) theory......Page 259
6.3 Adiabatic approximation......Page 262
6.5 Oscillations of a rotating molecule......Page 264
6.6 Basic principles of electronic, vibrational and rotational spectroscopy......Page 270
6.7 Approximate separation of rotations and vibrations......Page 273
6.8 Polyatomic molecule......Page 276
6.9 Non-bound states......Page 282
6.10 Adiabatic, diabatic and non-adiabatic approaches......Page 287
6.11 Crossing of potential energy curves for diatomics......Page 290
6.12 Polyatomic molecules and conical intersection......Page 295
6.13 Beyond the adiabatic approximation…......Page 303
Chapter 7. Motion of Nuclei......Page 310
7.1 Rovibrational spectra - an example of accurate calculations: atom - diatomic molecule......Page 313
7.2 Force fields (FF)......Page 319
7.3 Local Molecular Mechanics (MM)......Page 325
7.4 Global molecular mechanics......Page 327
7.5 Small amplitude harmonic motion - normal modes......Page 329
7.6 Molecular Dynamics (MD)......Page 339
7.7 Simulated annealing......Page 344
7.8 Langevin Dynamics......Page 345
7.9 Monte Carlo Dynamics......Page 346
7.10 Car-Parrinello dynamics......Page 349
7.11 Cellular automata......Page 352
Chapter 8. Electronic Motion in the Mean Field: Atoms and Molecules......Page 359
8.1 Hartree-Fock method - a bird\'s eye view......Page 364
8.2 The Fock equation for optimal spinorbitals......Page 369
8.3 Total energy in the Hartree-Fock method......Page 386
8.4 Computational technique: atomic orbitals as building blocks of the molecular wave function......Page 389
8.5 Back to foundations…......Page 404
8.6 Mendeleev Periodic Table of Chemical Elements......Page 414
8.7 The nature of the chemical bond......Page 418
8.8 Excitation energy, ionization potential, and electron affinity (RHF approach)......Page 424
8.9 Localization of molecular orbitals within the RHF method......Page 431
8.10 A minimal model of a molecule......Page 452
Chapter 9. Electronic Motion in the Mean Field: Periodic Systems......Page 463
9.1 Primitive lattice......Page 466
9.2 Wave vector......Page 468
9.3 Inverse lattice......Page 471
9.5 Properties of the FBZ......Page 473
9.6 A few words on Bloch functions......Page 474
9.7 The infinite crystal as a limit of a cyclic system......Page 480
9.8 A triple role of the wave vector......Page 483
9.9 Band structure......Page 484
9.10 Solid state quantum chemistry......Page 495
9.11 The Hartree-Fock method for crystals......Page 503
9.12 Long-range interaction problem......Page 510
9.13 Back to the exchange term......Page 520
9.14 Choice of unit cell......Page 523
Chapter 10. Correlation of the Electronic Motions......Page 533
Variational methods using explicitly correlated wave function......Page 537
10.1 Correlation cusp condition......Page 538
10.3 The Hylleraas CI method......Page 541
10.4 The harmonic helium atom......Page 542
10.5 James-Coolidge and Kolos-Wolniewicz functions......Page 543
10.7 Coulomb hole (\"correlation hole\")......Page 548
10.8 Exchange hole (\"Fermi hole\")......Page 551
10.9 Valence bond (VB) method......Page 555
10.10 Configuration interaction (CI) method......Page 560
10.12 Multireference CI method......Page 568
10.13 Multiconfigurational Self-Consistent Field method (MC SCF)......Page 570
10.14 Coupled cluster (CC) method......Page 574
10.15 Equation-of-motion method (EOM-CC)......Page 583
10.16 Many body perturbation theory (MBPT)......Page 586
10.17 Moller-Plesset version of Rayleigh-Schrödinger perturbation theory......Page 593
Chapter 11. Electronic Motion: Density Functional Theory (DFT)......Page 602
11.1 Electronic density - the superstar......Page 604
11.2 Bader analysis......Page 606
11.3 Two important Hohenberg-Kohn theorems......Page 614
11.4 The Kohn-Sham equations......Page 619
11.5 What to take as the DFT exchange-correlation energy Exc?......Page 625
11.6 On the physical justification for the exchange correlation energy......Page 627
11.7 Reflections on the DFT success......Page 637
Chapter 12. The Molecule in an Electric or Magnetic Field......Page 650
12.1 Hellmann-Feynman theorem......Page 653
12.2 The molecule immobilized in an electric field......Page 655
12.3 How to calculate the dipole moment......Page 668
12.4 How to calculate the dipole polarizability......Page 670
12.5 A molecule in an oscillating electric field......Page 680
Magnetic phenomena......Page 682
12.6 Magnetic dipole moments of elementary particles......Page 683
12.7 Transitions between the nuclear spin quantum states - NMR technique......Page 687
12.8 Hamiltonian of the system in the electromagnetic field......Page 688
12.9 Effective NMR Hamiltonian......Page 693
12.10 The Ramsey theory of the NMR chemical shift......Page 701
12.11 The Ramsey theory of NMR spin-spin coupling constants......Page 703
12.12 Gauge invariant atomic orbitals (GIAO)......Page 708
Chapter 13. Intermolecular Interactions......Page 716
13.1 Interaction energy concept......Page 719
13.4 Dissociation barrier......Page 722
13.5 Supermolecular approach......Page 724
13.6 Perturbational approach......Page 727
13.7 Symmetry adapted perturbation theories (SAPT)......Page 745
13.8 Convergence problems......Page 756
13.9 Non-additivity of intermolecular interactions......Page 761
13.10 Noble gas interaction......Page 776
13.11 Van der Waals surface and radii......Page 777
13.12 Synthons and supramolecular chemistry......Page 779
Chapter 14. Intermolecular Motion of Electrons and Nuclei: Chemical Reactions......Page 797
14.1 Hypersurface of the potential energy for nuclear motion......Page 801
14.2 Accurate solutions for the reaction hypersurface (three atoms)......Page 810
14.3 Intrinsic reaction coordinate (IRC) or statics......Page 816
14.4 Reaction path Hamiltonian method......Page 818
14.5 Acceptor-donor (AD) theory of chemical reactions......Page 833
14.6 Barrier for the electron-transfer reaction......Page 863
Chapter 15. Information Processing - the Mission of Chemistry......Page 883
15.1 Complex systems......Page 887
15.2 Self-organizing complex systems......Page 888
15.3 Cooperative interactions......Page 889
15.5 Combinatorial chemistry - molecular libraries......Page 890
15.6 Non-linearity......Page 892
15.7 Attractors......Page 893
15.8 Limit cycles......Page 894
15.9 Bifurcations and chaos......Page 895
15.10 Catastrophes......Page 897
15.11 Collective phenomena......Page 898
15.12 Chemical feedback - non-linear chemical dynamics......Page 901
15.14 The Measure of information......Page 910
15.15 The mission of chemistry......Page 912
15.16 Molecular computers based on synthon interactions......Page 913
Appendices......Page 922
1. Matrices......Page 924
2. Determinants......Page 927
1. Vector space......Page 930
2. Euclidean space......Page 931
3. Unitary space......Page 932
4. Hilbert space......Page 933
5. Eigenvalue equation......Page 935
1. Group......Page 938
2. Representations......Page 948
3. Group theory and quantum mechanics......Page 959
4. Integrals important in spectroscopy......Page 964
D. A two-state model......Page 983
1. Approximations to delta(x)......Page 986
3. An application of the Dirac delta function......Page 988
1. The form of the U operator......Page 990
2. The Hamiltonian commutes with the total momentum operator......Page 992
3. The Hamiltonian, J2 and Jz do commute......Page 993
5. Conclusion......Page 995
G. Vector and scalar potentials......Page 997
H. Optimal wave function for a hydrogen-like atom......Page 1004
I. Space- and body-fixed coordinate systems......Page 1006
1. Schmidt orthogonalization......Page 1012
2. Löwdin symmetric orthogonalization......Page 1013
K. Diagonalization of a matrix......Page 1017
L. Secular equation (h-epsilons)c=0......Page 1019
M. Slater-condon rules......Page 1021
N. Lagrange multipliers method......Page 1032
O. Penalty function method......Page 1036
P. Molecular integrals with gaussian type orbitals 1s......Page 1039
Q. Singlet and triplet states for two electrons......Page 1041
R. The hydrogen molecular ion in the simplest atomic basis set......Page 1044
S. Population analysis......Page 1050
T. The dipole moment of a lone electron pair......Page 1055
U. Second quantization......Page 1058
V. The hydrogen atom in the electric field - variational approach......Page 1064
1. Shielding constants......Page 1067
2. Coupling constants......Page 1070
X. Multipole expansion......Page 1073
Y. Pauli deformation......Page 1085
Z. Acceptor-donor structure contributions in the mo configuration......Page 1093
Name Index......Page 1100
Subject Index......Page 1112