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  • Contents

  • Introduction

  • Chapter 1. The Magic of Quantum Mechanics

    • 1.1 History of a revolution

    • 1.2 Postulates

    • 1.3 The Heisenberg uncertainty principle

    • 1.4 The Copenhagen interpretation

    • 1.5 How to disprove the Heisenberg principle? The Einstein-Podolsky-Rosen recipe

    • 1.6 Is the world real?

    • 1.7 The Bell inequality will decide

    • 1.8 Intriguing results of experiments with photons

    • 1.9 Teleportation

    • 1.10 Quantum computing

  • Chapter 2. The Schrödinger Equation

    • 2.1 Symmetry of the Hamiltonian and its consequences

    • 2.2 Schrödinger equation for stationary states

    • 2.3 The time-dependent Schrödinger equation

    • 2.4 Evolution after switching a perturbation

  • Chapter 3. Beyond the Schrödinger Equation

    • 3.1 A glimpse of classical relativity theory

    • 3.2 Reconciling relativity and quantum mechanics

    • 3.3 The Dirac equation

    • 3.4 The hydrogen-like atom in Dirac theory

    • 3.5 Larger systems

    • 3.6 Beyond the Dirac equation…

  • Chapter 4. Exact Solutions - Our Beacons

    • 4.1 Free particle

    • 4.2 Particle in a box

    • 4.3 Tunnelling effect

    • 4.4 The harmonic oscillator

    • 4.5 Morse oscillator

    • 4.6 Rigid rotator

    • 4.7 Hydrogen-like atom

    • 4.8 Harmonic helium atom (harmonium)

    • 4.9 What do all these solutions have in common?

    • 4.10 Beacons and pearls of physics

  • Chapter 5. Two Fundamental Approximate Methods

    • 5.1 Variational method

    • 5.2 Perturbational method

  • Chapter 6. Separation of Electronic and Nuclear Motions

    • 6.1 Separation of the centre-of-mass motion

    • 6.2 Exact (non-adiabatic) theory

    • 6.3 Adiabatic approximation

    • 6.4 Born-Oppenheimer approximation

    • 6.5 Oscillations of a rotating molecule

    • 6.6 Basic principles of electronic, vibrational and rotational spectroscopy

    • 6.7 Approximate separation of rotations and vibrations

    • 6.8 Polyatomic molecule

    • 6.9 Non-bound states

    • 6.10 Adiabatic, diabatic and non-adiabatic approaches

    • 6.11 Crossing of potential energy curves for diatomics

    • 6.12 Polyatomic molecules and conical intersection

    • 6.13 Beyond the adiabatic approximation…

  • Chapter 7. Motion of Nuclei

    • 7.1 Rovibrational spectra - an example of accurate calculations: atom - diatomic molecule

    • 7.2 Force fields (FF)

    • 7.3 Local Molecular Mechanics (MM)

    • 7.4 Global molecular mechanics

    • 7.5 Small amplitude harmonic motion - normal modes

    • 7.6 Molecular Dynamics (MD)

    • 7.7 Simulated annealing

    • 7.8 Langevin Dynamics

    • 7.9 Monte Carlo Dynamics

    • 7.10 Car-Parrinello dynamics

    • 7.11 Cellular automata

  • Chapter 8. Electronic Motion in the Mean Field: Atoms and Molecules

    • 8.1 Hartree-Fock method - a bird's eye view

    • 8.2 The Fock equation for optimal spinorbitals

    • 8.3 Total energy in the Hartree-Fock method

    • 8.4 Computational technique: atomic orbitals as building blocks of the molecular wave function

    • 8.5 Back to foundations…

    • Results of the hartree–fock method

    • 8.6 Mendeleev Periodic Table of Chemical Elements

    • 8.7 The nature of the chemical bond

    • 8.8 Excitation energy, ionization potential, and electron affinity (RHF approach)

    • 8.9 Localization of molecular orbitals within the RHF method

    • 8.10 A minimal model of a molecule

  • Chapter 9. Electronic Motion in the Mean Field: Periodic Systems

    • 9.1 Primitive lattice

    • 9.2 Wave vector

    • 9.3 Inverse lattice

    • 9.4 First Brillouin Zone (FBZ)

    • 9.5 Properties of the FBZ

    • 9.6 A few words on Bloch functions

    • 9.7 The infinite crystal as a limit of a cyclic system

    • 9.8 A triple role of the wave vector

    • 9.9 Band structure

    • 9.10 Solid state quantum chemistry

    • 9.11 The Hartree-Fock method for crystals

    • 9.12 Long-range interaction problem

    • 9.13 Back to the exchange term

    • 9.14 Choice of unit cell

  • Chapter 10. Correlation of the Electronic Motions

    • Variational methods using explicitly correlated wave function

    • 10.1 Correlation cusp condition

    • 10.2 The Hylleraas function

    • 10.3 The Hylleraas CI method

    • 10.4 The harmonic helium atom

    • 10.5 James-Coolidge and Kolos-Wolniewicz functions

    • 10.6 Method of exponentially correlated Gaussian functions

    • 10.7 Coulomb hole ("correlation hole")

    • 10.8 Exchange hole ("Fermi hole")

    • Variational methods with slater determinants

    • 10.9 Valence bond (VB) method

    • 10.10 Configuration interaction (CI) method

    • 10.11 Direct CI method

    • 10.12 Multireference CI method

    • 10.13 Multiconfigurational Self-Consistent Field method (MC SCF)

    • Non-variational methods with slater determinants

    • 10.14 Coupled cluster (CC) method

    • 10.15 Equation-of-motion method (EOM-CC)

    • 10.16 Many body perturbation theory (MBPT)

    • 10.17 Moller-Plesset version of Rayleigh-Schrödinger perturbation theory

  • Chapter 11. Electronic Motion: Density Functional Theory (DFT)

    • 11.1 Electronic density - the superstar

    • 11.2 Bader analysis

    • 11.3 Two important Hohenberg-Kohn theorems

    • 11.4 The Kohn-Sham equations

    • 11.5 What to take as the DFT exchange-correlation energy Exc?

    • 11.6 On the physical justification for the exchange correlation energy

    • 11.7 Reflections on the DFT success

  • Chapter 12. The Molecule in an Electric or Magnetic Field

    • 12.1 Hellmann-Feynman theorem

    • Electric phenomena

    • 12.2 The molecule immobilized in an electric field

    • 12.3 How to calculate the dipole moment

    • 12.4 How to calculate the dipole polarizability

    • 12.5 A molecule in an oscillating electric field

    • Magnetic phenomena

    • 12.6 Magnetic dipole moments of elementary particles

    • 12.7 Transitions between the nuclear spin quantum states - NMR technique

    • 12.8 Hamiltonian of the system in the electromagnetic field

    • 12.9 Effective NMR Hamiltonian

    • 12.10 The Ramsey theory of the NMR chemical shift

    • 12.11 The Ramsey theory of NMR spin-spin coupling constants

    • 12.12 Gauge invariant atomic orbitals (GIAO)

  • Chapter 13. Intermolecular Interactions

    • Theory of intermolecular interactions

    • 13.1 Interaction energy concept

    • 13.2 Binding energy

    • 13.3 Dissociation energy

    • 13.4 Dissociation barrier

    • 13.5 Supermolecular approach

    • 13.6 Perturbational approach

    • 13.7 Symmetry adapted perturbation theories (SAPT)

    • 13.8 Convergence problems

    • 13.9 Non-additivity of intermolecular interactions

    • Engineering of intermolecular interactions

    • 13.10 Noble gas interaction

    • 13.11 Van der Waals surface and radii

    • 13.12 Synthons and supramolecular chemistry

  • Chapter 14. Intermolecular Motion of Electrons and Nuclei: Chemical Reactions

    • 14.1 Hypersurface of the potential energy for nuclear motion

    • 14.2 Accurate solutions for the reaction hypersurface (three atoms)

    • 14.3 Intrinsic reaction coordinate (IRC) or statics

    • 14.4 Reaction path Hamiltonian method

    • 14.5 Acceptor-donor (AD) theory of chemical reactions

    • 14.6 Barrier for the electron-transfer reaction

  • Chapter 15. Information Processing - the Mission of Chemistry

    • 15.1 Complex systems

    • 15.2 Self-organizing complex systems

    • 15.3 Cooperative interactions

    • 15.4 Sensitivity analysis

    • 15.5 Combinatorial chemistry - molecular libraries

    • 15.6 Non-linearity

    • 15.7 Attractors

    • 15.8 Limit cycles

    • 15.9 Bifurcations and chaos

    • 15.10 Catastrophes

    • 15.11 Collective phenomena

    • 15.12 Chemical feedback - non-linear chemical dynamics

    • 15.13 Functions and their space-time organization

    • 15.14 The Measure of information

    • 15.15 The mission of chemistry

    • 15.16 Molecular computers based on synthon interactions

  • Appendices

    • A. A Reminder: Matrices and determinants

      • 1. Matrices

      • 2. Determinants

    • B. A few words on spaces, vectors and functions

      • 1. Vector space

      • 2. Euclidean space

      • 3. Unitary space

      • 4. Hilbert space

      • 5. Eigenvalue equation

    • C. Group theory in spectroscopy

      • 1. Group

      • 2. Representations

      • 3. Group theory and quantum mechanics

      • 4. Integrals important in spectroscopy

    • D. A two-state model

    • E. Dirac delta function

      • 1. Approximations to delta(x)

      • 2. Properties of delta(x)

      • 3. An application of the Dirac delta function

    • F. Translation vs momentum and rotation vs angular momentum

      • 1. The form of the U operator

      • 2. The Hamiltonian commutes with the total momentum operator

      • 3. The Hamiltonian, J2 and Jz do commute

      • 4. Rotation and translation operators do not commute

      • 5. Conclusion

    • G. Vector and scalar potentials

    • H. Optimal wave function for a hydrogen-like atom

    • I. Space- and body-fixed coordinate systems

    • J. Orthogonalization

      • 1. Schmidt orthogonalization

      • 2. Löwdin symmetric orthogonalization

    • K. Diagonalization of a matrix

    • L. Secular equation (h-epsilons)c=0

    • M. Slater-condon rules

    • N. Lagrange multipliers method

    • O. Penalty function method

    • P. Molecular integrals with gaussian type orbitals 1s

    • Q. Singlet and triplet states for two electrons

    • R. The hydrogen molecular ion in the simplest atomic basis set

    • S. Population analysis

    • T. The dipole moment of a lone electron pair

    • U. Second quantization

    • V. The hydrogen atom in the electric field - variational approach

    • W. NMR shielding and coupling constants - derivation

      • 1. Shielding constants

      • 2. Coupling constants

    • X. Multipole expansion

    • Y. Pauli deformation

    • Z. Acceptor-donor structure contributions in the mo configuration

  • Name Index

  • Subject Index

Nội dung

[...]... main ideas of quantum chemistry I have tried to stress this integral point of view, and this is why the book sometimes deviates from what is normally considered as quantum chemistry I sacrificed, not only in full consciousness, but also voluntarily quantum cleanness” in favour of exposing the inter-relationships of problems In this respect, any division between physics and chemistry, organic chemistry. .. courtesy of Professor Akira Tonomura, n Japan p 112 – with permission from National Physical Laboratory, courtesy of Dr R.C McGuiness, UK p 220 – courtesy of Professor J.D Roberts, California Institute of Technology, USA p 287 – reused from International Journal of Quantum Chemistry (1989), Symp 23, © 1989 John Wiley&Sons, Inc., reprinted with permission of John Wiley&Sons, Inc p 392 – courtesy of Mr... with all extent textbooks on quantum mechanics Therefore, one has to choose a set of important topics, those that represent a key to an understanding of the broad domains of knowledge To this end, it often pays to master a complex mathematical apparatus Such mastery often leads to a generalization or simplification of the internal structure of a theory Not all chapters are of equal importance At this... imagined students sitting in front of me In discussions with students I often saw their enthusiasm, their eyes showed me a glimpse of curiosity First of all, this book is an acknowledgement of my young friends, my students, and an expression of the joy of being with them Working with them formulated and influenced the way I decided to write this book When reading textbooks one often has the impression that... in space 8 At least in the time scale of a chemical experiment Instability of some nuclei is used in nuclear chemistry and radiation chemistry XXIII XXIV Introduction On the vast scale of attainable temperatures9 chemical structures may exist in the narrow temperature range of 0 K to thousands of K Above this range one has plasma, which represents a soup made of electrons and nuclei Nature, in its... “Answers” • For those interested in recent progress in quantum chemistry, we suggest sections “From the research front” in each chapter • For those interested in the future of quantum chemistry we propose the sections labelled, “Ad futurum” in each chapter, and the chapters designated by ( ) • For people interested in the “magical” aspects of quantum chemistry we suggest sections with the label ( ) – Is... traditional quantum chemistry This book is a direct result of my lectures at the Department of Chemistry, University of Warsaw, for students specializing in theoretical rather than experimental chemistry Are such students the target audience of this book? Yes, but not exclusively At the beginning I assumed that the reader would have completed a basic quantum chemistry course19 and, therefore, in the first version... atoms and molecules do exist, the surfaces of dielectrics and their existence may be described in detail by quantum mechanics using what is known as the wave function The axioms of quantum mechanics provide the rules for the derivation of this function and for the calculation of all the observable properties of atoms and molecules What is it all about History of a revolution ( ) p 4 Postulates ( ) p... creation of matter, we suggest p 134 and subsequent material – For those interested in tunnelling through barriers, please look at p 153 and subsequent material The target audience I hope that the TREE structure presented above will be useful for those with varying levels of knowledge in quantum chemistry as well as for those whose goals and interests differ from those of traditional quantum chemistry. .. areas of operation of particular branches of science Introduction Strong interactions produce the huge pressures that accompany the gravitational collapse of a star and lead to the formation of neutron stars, where the mass deficiency approaches 40% At smaller pressures, where individual nuclei may exist and undergo nuclear reactions (strong interactions4 ), the mass deficiency is of the order of 1% . class="bi x0 y0 w0 h0" alt="" IDEAS OF QUANTUM CHEMISTRY

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