Ideas of Quantum Chemistry

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Front Matter
Compose your own book accordingto your needs
Ideas of Quantum Chemistry,
Volume 2: Interactions
Copyright
Dedication
Contents
Introduction (2)
	TREE
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1 Electronic Orbital Interactions in Periodic Systems
	1.1 Primitive lattice
	1.2 Wave vector
	1.3 Inverse lattice
	1.4 First Brillouin zone (FBZ)
	1.5 Properties of the FBZ
	1.6 A few words on Bloch functions
		1.6.1 Waves in 1D
		1.6.2 Waves in 2D
	1.7 Infinite crystal as a limit of a cyclic system
		1.7.1 Origin of the band structure
		1.7.2 Born-von Kármán condition in 1D
		1.7.3 k dependence of orbital energy
	1.8 A triple role of the wave vector
	1.9 Band structure
		1.9.1 Born-von Kármán boundary condition in 3D
		1.9.2 Crystal orbitals from Bloch functions (LCAO CO method)
		1.9.3 SCF LCAO CO equations
		1.9.4 Band width
		1.9.5 Fermi level and energy gap: insulators, metals, and semiconductors
	1.10 Solid state quantum chemistry
		1.10.1 Why do some bands go up?
		1.10.2 Why do some bands go down?
		1.10.3 Why do some bands stay constant?
		1.10.4 More complex behavior explainable - examples
	1.11 The Hartree-Fock method for crystals
		1.11.1 Secular equation
		1.11.2 Integration in the FBZ
		1.11.3 Fock matrix elements
		1.11.4 Iterative procedure (SCF LCAO CO)
		1.11.5 Total energy
	1.12 Long-range interaction problem
		1.12.1 Fock matrix corrections
		1.12.2 Total energy corrections
		1.12.3 Multipole expansion applied to the Fock matrix
		1.12.4 Multipole expansion applied to the total energy
	1.13 Back to the exchange term
	1.14 Choice of unit cell
		1.14.1 Field compensation method
		1.14.2 The symmetry of subsystem choice
2 Correlation and Anticorrelation of Electronic Motions
	Variational methods using explicitly correlated wave functions
	2.1 Correlation cusp condition
	2.2 The Hylleraas CI method
	2.3 Two-electron systems
		2.3.1 Harmonium - the harmonic helium atom
		2.3.2 High accuracy: the James-Coolidge and Kołos-Wolniewicz functions
		2.3.3 High accuracy: neutrino mass
	2.4 Exponentially correlated Gaussian functions
	2.5 Electron holes
		2.5.1 Coulomb hole (\"correlation hole\")
		2.5.2 Exchange hole (\"Fermi hole\")
	Variational methods with Slater determinants
	2.6 Static electron correlation
	2.7 Dynamic electron correlation
	2.8 Anticorrelation, or do electrons stick together in some states?
	2.9 Valence bond (VB) method
		2.9.1 Resonance theory - hydrogen molecule
		2.9.2 Resonance theory - polyatomic case
	2.10 Configuration interaction (CI) method
		2.10.1 Brillouin theorem
		2.10.2 Convergence of the CI expansion
		2.10.3 Example of H2O
		2.10.4 Which excitations are most important?
		2.10.5 Natural orbitals (NOs) - a way to shorter expansions
		2.10.6 Size inconsistency of the CI expansion
	2.11 Direct CI method
	2.12 Multireference CI method
	2.13 Multiconfigurational self-consistent field (MC SCF) method
		2.13.1 Classical MC SCF approach
		2.13.2 Unitary MC SCF method
		2.13.3 Complete active space (CAS SCF) method is size-consistent
	Nonvariational methods with Slater determinants
	2.14 Coupled cluster (CC) method
		2.14.1 Wave and cluster operators
		2.14.2 Relationship between CI and CC methods
		2.14.3 Solution of the CC equations
		2.14.4 Example: CC with double excitations
		2.14.5 Size consistency of the CC method
	2.15 Equation of motion method (EOM-CC)
		2.15.1 Similarity transformation
		2.15.2 Derivation of the EOM-CC equations
	2.16 Many-body perturbation theory (MBPT)
		2.16.1 Unperturbed Hamiltonian
		2.16.2 Perturbation theory - slightly different presentation
		2.16.3 MBPT machinery - part one: energy equation
		2.16.4 Reduced resolvent or the \"almost\" inverse of (E0( 0) -Ĥ( 0) )
		2.16.5 MBPT machinery - part two: wave function equation
		2.16.6 Brillouin-Wigner perturbation theory
		2.16.7 Rayleigh-Schrödinger perturbation theory
	2.17 Møller-Plesset version of Rayleigh-Schrödinger perturbation theory
		2.17.1 Expression for MP2 energy
		2.17.2 Is the MP2 method size-consistent?
		2.17.3 Convergence of the Møller-Plesset perturbation series
		2.17.4 Special status of double excitations
	Nonvariational methods using explicitly correlated wave functions
	2.18 Møller-Plesset R12 method (MP2-R12)
		2.18.1 Resolution of identity (RI) method or density fitting (DF)
		2.18.2 Other RI methods
3 Chasing the Correlation Dragon: Density Functional Theory (DFT)
	3.1 Electronic density - the superstar
	3.2 Electron density distributions - Bader analysis
		3.2.1 Overall shape of ρ
		3.2.2 Critical points
		3.2.3 Laplacian of the electronic density as a \"magnifying glass\"
	3.3 Two important Hohenberg-Kohn theorems
		3.3.1 Correlation dragon resides in electron density: equivalence of Ψ0 and ρ0
		3.3.2 A secret of the correlation dragon: the existence of energy functional minimized by ρ0
	3.4 The Kohn-Sham equations
		3.4.1 A Kohn-Sham system of noninteracting electrons
		3.4.2 Chasing the correlation dragon into an unknown part of the total energy
		3.4.3 Derivation of the Kohn-Sham equations
	3.5 Trying to guess the appearance of the correlation dragon
		3.5.1 Local density approximation (LDA)
		3.5.2 Nonlocal density approximation (NLDA)
		3.5.3 The approximate character of the DFT versus apparent rigor of ab initio computations
	3.6 On the physical justification for the exchange-correlation energy
		3.6.1 The electron pair distribution function
		3.6.2 Adiabatic connection: from what is known towards the target
		3.6.3 Exchange-correlation energy and the electron pair distribution function
		3.6.4 The correlation dragon hides in the exchange-correlation hole
		3.6.5 Electron holes in spin resolution
		3.6.6 The dragon\'s ultimate hide-out: the correlation hole!
		3.6.7 Physical grounds for the DFT functionals
	3.7 Visualization of electron pairs: electron localization function (ELF)
	3.8 The DFT excited states
	3.9 The hunted correlation dragon before our eyes
4 The Molecule Subject to Electric or Magnetic Fields
	4.1 Hellmann-Feynman theorem
	Electric phenomena
	4.2 The molecule immobilized in an electric field
		4.2.1 The electric field as a perturbation
		4.2.2 The homogeneous electric field
		4.2.3 The nonhomogeneous electric field: multipole polarizabilities and hyperpolarizabilities
	4.3 How to calculate the dipole moment
		4.3.1 Coordinate system dependence
		4.3.2 Hartree-Fock approximation
		4.3.3 Atomic and bond dipoles
		4.3.4 Within the zero-differential overlap approximation
	4.4 How to calculate the dipole polarizability
		4.4.1 Sum over states (SOS) method
		4.4.2 Finite field method
		4.4.3 What is going on at higher electric fields
	4.5 A molecule in an oscillating electric field
	Magnetic phenomena
	4.6 Magnetic dipole moments of elementary particles
		4.6.1 Electron
		4.6.2 Nucleus
		4.6.3 Dipole moment in the field
	4.7 NMR spectra - transitions between the nuclear quantum states
	4.8 Hamiltonian of the system in the electromagnetic field
		4.8.1 Choice of the vector and scalar potentials
		4.8.2 Refinement of the Hamiltonian
	4.9 Effective NMR Hamiltonian
		4.9.1 Signal averaging
		4.9.2 Empirical Hamiltonian
		4.9.3 Nuclear spin energy levels
	4.10 The Ramsey theory of the NMR chemical shift
		4.10.1 Shielding constants
		4.10.2 Diamagnetic and paramagnetic contributions
	4.11 The Ramsey theory of NMR spin-spin coupling constants
		4.11.1 Diamagnetic contribution
		4.11.2 Paramagnetic contribution
		4.11.3 Coupling constants
		4.11.4 The Fermi contact coupling mechanism
	4.12 Gauge-invariant atomic orbitals (GIAOs)
		4.12.1 London orbitals
		4.12.2 Integrals are invariant
5 Intermolecular Interactions
	Theory of intermolecular interactions
	5.1 Idea of the rigid interaction energy
	5.2 Idea of the internal relaxation
	5.3 Interacting subsystems
		5.3.1 Natural division
		5.3.2 What is most natural?
	5.4 Binding energy
	5.5 Dissociation energy
	5.6 Dissociation barrier
	5.7 Supermolecular approach
		5.7.1 Accuracy should be the same
		5.7.2 Basis set superposition error (BSSE)
		5.7.3 Good and bad news about the supermolecular method
	5.8 Perturbational approach
		5.8.1 Intermolecular distance - what does it mean?
		5.8.2 Polarization approximation (two molecules)
		5.8.3 Intermolecular interactions: physical interpretation
		5.8.4 Electrostatic energy in the multipole representation plus the penetration energy
		5.8.5 Induction energy in the multipole representation
		5.8.6 Dispersion energy in the multipole representation
		5.8.7 Resonance interaction - excimers
	5.9 Symmetry-adapted perturbation theory (SAPT)
		5.9.1 Polarization approximation is illegal
		5.9.2 Constructing a symmetry-adapted function
		5.9.3 The perturbation is always large in polarization approximation
		5.9.4 Iterative scheme of SAPT
		5.9.5 Symmetry forcing
		5.9.6 A link to the variational method - the Heitler-London interaction energy
		5.9.7 Summary: the main contributions to the interaction energy
	5.10 Convergence problems
		5.10.1 Padé approximants may improve convergence
	5.11 Nonadditivity of intermolecular interactions
		5.11.1 Interaction energy represents the nonadditivity of the total energy
		5.11.2 Many-body expansion of the rigid interaction energy
		5.11.3 What is additive, what is not?
		5.11.4 Additivity of the electrostatic interaction
		5.11.5 Exchange nonadditivity
		5.11.6 Induction nonadditivity
		5.11.7 Additivity of the second-order dispersion energy
		5.11.8 Nonadditivity of the third-order dispersion interaction
	Engineering of intermolecular interactions
	5.12 Idea of molecular surface
		5.12.1 van der Waals atomic radii
		5.12.2 A concept of molecular surface
		5.12.3 Confining molecular space - the nanovessels
		5.12.4 Molecular surface under high pressure
	5.13 Decisive forces
		5.13.1 Distinguished role of the valence repulsion and electrostatic interaction
		5.13.2 Hydrogen bond
		5.13.3 Coordination interaction
		5.13.4 Electrostatic character of molecular surface - the maps of the molecular potential
		5.13.5 Hydrophobic effect
	5.14 Construction principles
		5.14.1 Molecular recognition - synthons
		5.14.2 \"Key-lock,\" template-like, and \"hand-glove\" synthon interactions
		5.14.3 Convex and concave - the basics of strategy in the nanoscale
6 Chemical Reactions
	6.1 Hypersurface of the potential energy for nuclear motion
		6.1.1 Potential energy minima and saddle points
		6.1.2 Distinguished reaction coordinate (DRC)
		6.1.3 Steepest descent path (SDP)
		6.1.4 Higher-order saddles
		6.1.5 Our goal
	6.2 Chemical reaction dynamics (a pioneers\' approach)
	AB INITIO approach
	6.3 Accurate solutions (three atoms)
		6.3.1 Coordinate system and Hamiltonian
		6.3.2 Solution to the Schrödinger equation
		6.3.3 Berry phase
	Approximate methods
	6.4 Intrinsic reaction coordinate (IRC)
	6.5 Reaction path Hamiltonian method
		6.5.1 Energy close to IRC
		6.5.2 Vibrational adiabatic approximation
		6.5.3 Vibrational nonadiabatic model
		6.5.4 Application of the reaction path Hamiltonian method to the reaction H2 + OH -> H2O + H
	6.6 Acceptor-donor (AD) theory of chemical reactions
		6.6.1 A simple model of nucleophilic substitution - MO, AD, and VB formalisms
		6.6.2 MO picture -> AD picture
		6.6.3 Reaction stages
		6.6.4 Contributions of the structures as the reaction proceeds
		6.6.5 Nucleophilic attack - the model is more general: H- + ethylene -> ethylene + H-
		6.6.6 The model looks even more general: the electrophilic attack H+ + H2 -> H2 + H+
		6.6.7 The model works also for the nucleophilic attack on the polarized bond
	6.7 Symmetry-allowed and symmetry-forbidden reactions
		6.7.1 Woodward-Hoffmann symmetry rules
		6.7.2 AD formalism
		6.7.3 Electrocyclic reactions
		6.7.4 Cycloaddition reaction
		6.7.5 Barrier means a cost of opening the closed shells
	6.8 Barrier for the electron transfer reaction
		6.8.1 Diabatic and adiabatic potential
		6.8.2 Marcus theory
		6.8.3 Solvent-controlled electron transfer
7 Information Processing - The Mission of Chemistry
	7.1 Multilevel supramolecular structures (statics)
		7.1.1 Complex systems
		7.1.2 Self-organizing complex systems
		7.1.3 Cooperative interactions
		7.1.4 Combinatorial chemistry - molecular libraries
	7.2 Chemical feedback - a steering element (dynamics)
		7.2.1 A link to mathematics - attractors
		7.2.2 Bifurcations and chaos
		7.2.3 Brusselator without diffusion
		7.2.4 Brusselator with diffusion - dissipative structures
		7.2.5 Hypercycles
		7.2.6 From self-organization and complexity to information
	7.3 Information and informed matter
		7.3.1 Abstract theory of information
		7.3.2 Teaching molecules
		7.3.3 Dynamic information processing of chemical waves
		7.3.4 Molecules as computer processors
		7.3.5 The mission of chemistry
APPENDIX
A Dirac Notation for Integrals
APPENDIX
B Hartree-Fock (or Molecular Orbitals) Method
APPENDIX
C Second Quantization
APPENDIX
D Population Analysis
APPENDIX
E Pauli Deformation
APPENDIX
F Hydrogen Atom in Electric Field - Variational Approach
APPENDIX
G Multipole Expansion
APPENDIX
H NMR Shielding and Coupling Constants - Derivation
APPENDIX
I Acceptor-Donor Structure Contributions in the MO Configuration
Acronyms and Their Explanation
Author Index
Subject Index
Sources of Photographs and Figures
Tables
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